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DigitalMicrograph EELS Analysis User's Guide

1. 2 4 3 Additional tools for manipulating single or multiple spectra Right clicking your mouse with the cursor situated within a spectrum s image window opens menu containing a number of useful display and editing options as shown in Figure 2 2 Since multiple spectra can be displayed within a single image window a color coded legend provides the mechanism for specifying the current spectrum selected for adjustment see Figure 2 3 Right clicking on one of the titled legends reveals a menu containing additional items specific to the corresponding spectrum When initiated in this way the display command will be carried out in the majority of cases solely on the selected spectrum Hence spectrum specific display parameters may be adjusted within an image window containing multiple spectra enabling for example spectra with different intensity or energy ranges to be overlaid and rescaled with respect to each other for comparison The functions contained within the options list are as follows CUT Copy and PASTE these commands carry out the same functions as in other Windows applications and are described in detail the following section IMAGE DISPLAY initiates the IMAGE DispLay INFO dialog allowing display and acquisition properties to be viewed and edited SHOW LEGEND reveals the color coded legend bar within the image window HIDE LEGEND hides the legend list from the window display EELS Analysis User s Guide Rev 1 2 1
2. EELS Analysis User s Guide Rev 1 2 EELS Script Commands EELSFourierRatioDeconvolveWithGaussianModifier Summary Deconvolves plural scattering from a core loss spectrum using the Fourier ratio approach with a Gaussian function modifier Prototype image EELSFourierRatioDeconvolveWithGaussianModifier image src image src_low number ModifierFWHM number ZLPIndex Description This function performs the same routine as described above for EELSFourierRatioDeconvolveWithZLPModifier except that a Gaussian function is used instead of the zero loss peak as the modifier Hence an extra parameter ModiferFWHM is passed to the function which defines the width of the Gaussian modifier as a multiple of the full width half maximum of the extracted zero loss peak For further details please refer to EELSFourierRatioDeconvolveWithZLPModifier above EELSKramersKronigAnalysis Summary Perform Kramers Kronig analysis on a low loss single scattering distribution Prototypes void EELSKramersKronigAnalysis image src image I0 number E0 number BetaEff number RefIndex number FracTol number Maxlter image amp eps1 image amp eps2 image amp Srfelf image amp TNM void EELSKramersKronigAnalysis image src number I0 number E0 number BetaEff number RefIndex number FracTol number Maxlter image amp eps1 image amp eps2 image amp Srfelf number amp TNM void EELSKramersKronigAnalysis image src image 10 number E0 number BetaEff
3. GetDefaultPreferences This method is called when adding the model to the model list and ensures the Global Tags contain default parameter values to start with Performs a check to see if the tag s exist s if not writes the default values to prefs void GetDefaultPreferences object self taggroup prefs if Prefs TagGroupGetTagAsNumber fAttenuateEnergy string fAttenuateEnergy Prefs TagGroupSetTagAsNumber fAttenuateEnergy string fAttenuateEnergy Default SetPreferences Prefs is the zlp model tag group amp is passed into the function Contains all the preferences set by GetDefaultPreferences void SetPreferences object self taggroup prefs if Prefs TagGroupGetTagAsNumber fAttenuateEnergy string fAttenuateEnergy fAttenuateEnergy fAttenuateEnergy Default number debug 0 Set this to 1 for testing if debug 0 else These commands add the model to the zlp model manager object model alloc ExampleZLPModel GetZLPAlgorithmManager AddAlgorithm model These commands are useful for testing i e before adding the model to zlp manager object model alloc ExampleZLPModel image lowloss GetFrontImage image zeroloss lowloss ImageClone model ExtractZLP lowloss zeroloss EELS Analysis User s Guide Rev 1 2 Adding Custom Zero Loss Models showimage zeroloss Note that a degree of familiarity with the DigitalMicrograph script
4. To perform this command to splice a pair of spectrum images select the corresponding menu item with one of the datasets front most The routine will proceed as described above for the one dimensional spectrum case Observe that in addition to the suitability criteria described above for the single spectrum instance the two datasets must also be of the same spatial dimensionality Note also that the algorithm makes no consideration as to whether the two datasets are spatially registered hence any drift alignment required between the datasets should be performed prior to performing this command EELS Analysis User s Guide Rev 1 2 1 Sharpen Figure 3 8 The SHARPEN SPECTRUM PREFERENCES dialog w Sharpen Spectrum Preferences xj Specify a separate zero loss profile Extract the zero loss profile using the model below aloss model Use Extract Zero Loss setting Cancel OK 3 4 Sharpen The SHARPEN sub menu contains items for recovering some of the spectral detail lost to the broad tails of the zero loss peak Specifically the SHARPEN sub menu items perform the following 3 4 1 Preferences Selecting this item opens the SHARPEN SPECTRUM PREFERENCES dialog shown above in Figure 3 8 The SHARPEN SPECTRUM routine described below requires a reference zero loss profile as an input The method for finding the zero loss profile is specified in this dialog If the SPECIFY A SEPARATE ZERO LOSS PROFILE option is se
5. s This command allows you to confirm and make adjustments to the energy scale calibration of the selected spectrum An example of the energy calibration mode is shown in Figure 3 5 Before the CALIBRATE ENERGY SCALE command is selected an ROI should be placed on the spectrum to designate the reference points to be used in the calibration procedure As described in Section 2 4 above this may be done by placing the cursor with the pointer tool selected at the first reference point usually a feature of well defined energy loss such as the zero loss peak holding down the left mouse button and dragging the cursor to a second reference point before releasing This will create a rectangular marker outlined by a discontinuous colored box as indicated The low energy vertical boundary of this rectangle denotes the low energy reference channel and likewise the high energy vertical denotes the high energy reference channel Alternatively clicking once on the spectrum will place a single channel ROI at that point Depending on whether the region selected covers a single energy channel or a range of channels the energy scale calibration routine follows two different routes For the single channel case the procedure requests the energy corresponding to the selected channel and also the spectral dispersion in eV per channel Use this mode if you know the dispersion accurately and you have at least one feature of well defined energy loss When calibra
6. s title Alternatively the acquisition information is also contained within the spectrum s IMAGE DISPLAY INFO This information may be viewed and edited by selecting IMAGE DISPLAY under the OBJECTS menu or by clicking the right button of your mouse while the spectrum is selected and choosing the IMAGE DISPLAY option and then selecting TAGs in the presented dialog box Performing Calibrations The energy dispersions of your spectrometer or imaging filter will have been calibrated during installation For a detailed description of the calibration procedure for your hardware please refer to your spectrometer manual Spectra acquired using DigitalMicrograph will automatically have their energy scale 2 3 2 4 2 4 1 Acquiring Spectra calibrated with the pre measured dispersion of the spectrometer For post acquisition calibration of the energy loss scale based on known features of your spectrum use the CALIBRATE ENERGY SCALE item under the EELS menu In order to get the most accurate representation of the true EELS spectrum from your detection system it is necessary to characterize the response of your array Ensure that DARK COUNT AND GAIN detector correction is used for final spectrum acquisition which will ensure that corrections for both the dark count readout and the channel to channel or pixel to pixel variation in gain response are applied Additionally use the routine PREPARE GAIN REFERENCE found in the CA
7. Figure 3 28 The KRAMERS KRONIG ANALYSIS setup dialog tea Kramers Kronig Analysis x r cquisition amp sample details Beam energy keV 200 0 Collection semi angle mrad fi 2 0 Refractive index for visible light fi 000 0 Convergence semi angle mrad fod rDutput V Absolute specimen thickness Tl Effective number of electrons per unit vol Optical absorption co efficient I Surface loss intensity L 7 z Cancel OK A very brief overview of the technique is described as follows The observed energy loss spectrum is closely related to a quantity referred to as the energy loss function Im 1 e E via the relationship neglecting surface effects S E K in hl E E O where S E is the single scattering distribution K is a proportionality constant and J and are the effective collection and characteristic scattering angles respectively Hence after suitable corrections are applied and scaling using the proportionality constant which may be computed from an estimate of the specimen thickness incident beam energy and zero loss intensity the energy loss function can be retrieved from the low loss spectrum with no plural scattering The quantity Re 1 e E is related to the energy loss function via the Kramers Kronig transformation 2 Re 1 Pf Im PE E x 98 E E E where P indicates the Cauchy principal
8. Oj x ROI handle Region of interest ROI marker Navigating a spectrum The axes of a spectrum are used as navigation controls By clicking and dragging on an axis you can either zoom or translate that axis To translate an axis Click and drag on the part of the spectrum containing the scale for an axis Note that the entire spectrum is translated as you move the mouse Figure 2 2 2 4 Working with Spectra in DigitalMicrograph To zoom an axis Click and drag on the axis while holding down the CTRL key Note that the x and y axes zoom in slightly different ways The x axis zooms around whichever point you click on while the y axis zooms around zero To restore a spectrum to its unzoomed view Right click on the spectrum and select HOME from the pop up menu to restore a spectrum to its default unzoomed view Alternatively use the 5 key if you use the number pad on a PC make sure that NUM LOCK is turned on Turning auto scaling on and off By default a new spectrum window has auto scaling switched on This means that when the intensity increases or decreases the y axis automatically adjusts to scale to the new intensities At times it is useful to turn this feature off particularly when trying to focus a spectrum Zooming or translating an axis automatically turns off auto scaling for that axis Restoring a spectrum to its unzoomed view automatically turns auto scaling ba
9. The easiest way to draw an ROI on a spectrum is to simply click on a spectrum with the pointer tool If this does not produce an ROI on the spectrum make sure that the pointer tool in the STANDARD TOOLS floating window is selected To create a wide ROI Click and drag on an image to create an ROI that is wider than a single channel EELS Analysis User s Guide Rev 1 2 1 Figure 2 1 EELS Analysis User s Guide Rev 1 2 1 2 4 2 Working with Spectra in DigitalMicrograph To create multiple ROIs Hold the SHIFT key down while creating a new ROI to prevent any ROIs already on the image from being deleted To move an ROI Drag on the ROI s handle the dot near the top of the ROI Note that the calibrated width and position of the ROI are displayed when the ROI is dragged To delete an ROI Select it by clicking on its handle A selected handle looks like a solid square An unselected handle looks like a sign Hit the BACKSPACE or DELETE key to delete the selected ROI To create a background or signal designated ROI Hold down the CTRL key while creating a new ROI to generate a background fitting or signal integration designated ROI The order of ROI designation is background followed by signal followed by background again multiple background fitting regions are suitable for example when tying background models to a post edge region EELS spectrum with region of interest ROI marker D High Tc superconductor F
10. Thus it is especially important that you properly assess and enter this parameter into the EXPERIMENTAL CONDITIONS dialog before you acquire spectra for such analyses If no suitable parameters have been entered you will be prompted for these when initializing the quantification routine The EELS SI QUANTIFICATION OUTPUT OPTIONS dialog tra EELS SI Quantification Output Optic xj Dutput the following IV Extracted core loss signal Areal density V Relative composition Cancel OK EELS Analysis User s Guide Rev 1 2 1 Quantification Notes for Spectrum Imaging Users To perform quantification on an EELS spectrum image first set up the QUANTIFICATION LIST and signal extraction parameters as you would for the single spectrum case explained above on an exploration spectrum extracted from the spectrum image When doing this it is recommended that you move the exploration tool position to ensure signal extraction parameters are suitable for each edge at various spatial positions within the spectrum image Once satisfied with the specified parameters select the QUANTIFY button with the exploration spectrum front most When prompted specify the parent spectrum image for analysis You will then be presented with the EELS SI QUANTIFICATION OUTPUT OPTIONS dialog shown above in Figure 3 36 The dialog allows you to specify what quantities are computed and output The output options are explained as follows EXTRACTED C
11. is normalized using a proportionality constant computed via a form of the Kramers Kronig sum rule The sum rule also yields an estimate of the sample thickness t which is computed and stored for use in step 7 5 Compute Re 1 e E using the Kramers Kronig transform Re 1 e E is computed from the energy loss function using the Fourier based approach for Kramers Kronig analysis of Johnson see above description for details 6 Compute lt and amp The real and imaginary parts of the dielectric function are calculated from Im 1 e E and Re 1 e E using the expression described above 7 Compute and correct for surface contribution and iterate to convergence The surface loss function is computed from and amp using the relationship as described above This function is then scaled using the proportionality constant and estimated sample thickness adjusted for angular effects and then subtracted from the prepared input data Steps 4 7 are then iterated until the calculation converges or the maximum number of allowed iterations is reached 20 by default Convergence is reached when the fractional difference between successive computed proportionality constants is less than a pre set tolerance by default this value is set to 1 part in 10 000 8 Compute any additional quantities as specified Once convergence is successfully achieved any additional properties as specified in the KRAMERS KRONIG ANALYSIS dialog as desc
12. region is active with the model fit being updated in response to any appropriate changes e g moving or resizing the NLLS fit region or in the case of an exploration spectrum from a spectrum image changing the spectrum s data by moving the spectrum exploration tool In addition to the fitted Gaussian model the residual signal is also displayed see Figure 2 1 above EELS Analysis User s Guide Rev 1 2 1 3 41 Figure 3 26 3 42 3 12 3 3 12 4 NLLS Fitting Additional NLLS fitting regions can be added by repeating the procedure described please refer to the PREFERENCES section above for details regarding NLLS fitting multiple models The NLLS MopeL Fit PROPERTIES dialog t a NLLS Model Properties x ROI label Fit1 Gaussian Model Gaussian Amplitude J Constrain parameter value Value Center J Constrain parameter value I Constrain parameter value Value ey 13 4771 Cancel OK Constrain Model Parameters Select this menu item to constrain one or more of the selected NLLS model fit parameters to its current or specified value s To perform this operation ensure a single spectrum is front most with an active NLLS fit region selected and select this menu item This will open the NLLS MODEL PROPERTIES dialog shown above in Figure 3 26 This dialog contains information relating to the selected NLLS fit region The fit region label and model are displ
13. spectra Please refer to the specific descriptions under the appropriate menu item headings throughout this section for details An additional sub section titled Notes for Spectrum Imaging Users is also included where appropriate to outline any differences or additional information relating to the analysis of spectrum images For the sake of simplicity the term spectrum image will be used throughout this documentation to refer to both spectrum line traces spatially one dimensional and spectrum images spatially two dimensional alike As a general rule of thumb to apply an EELS menu command to a spectrum image simply perform the same procedure as described for the single spectrum case but with either the spectrum image or an exploration spectrum created from the spectrum image using the spectrum image exploration tool S front most Ifan exploration spectrum is front most then a dialog will be presented asking if you to specify if you mean to perform the operation on the exploration spectrum only or alternatively its parent spectrum image as shown in Figure 3 2 Select the latter option to perform the command on the spectrum image Some of the analyses require a pre step of setting up parameters on the exploration spectrum prior to commencement e g Quantification NLLS fitting For these analyses the menu item can only be selected with the exploration spectrum front most please refer to the specific details for menu item of intere
14. the corresponding output datasets will have identical dimensionality to the input dataset EELS Analysis User s Guide Rev 1 2 1 Figure 3 18 EELS Analysis User s Guide Rev 1 2 1 3 10 Remove Plural Scattering Remove Plural Scattering Use the items of this sub menu to remove plural scattering by deconvolution Two methods are provided the Fourier log and Fourier ratio techniques Please refer to Egerton Chapter 4 pp 245 256 and pp 262 269 for a detailed discussion of these techniques and of plural scattering deconvolution in general Although the input data needed for the two methods differ slightly in form see below the physical principles behind the deconvolution techniques and the experimental conditions under which the data must be acquired in order to ensure their validity are fundamentally the same Both techniques are based upon the premise that plural scattering gives rise to a redistribution of counts within the spectrum according to the probability distribution represented by the shape of the low loss part of the spectrum Since this is equivalent to a mathematical convolution operation deconvolution is used to counteract this redistribution The aforementioned premise is only valid if the following conditions are met during the data acquisition 1 The probed specimen area is of fairly uniform thickness and most importantly does not include any perforations or large voids that extend over a significant frac
15. using complex arithmetic multiplies by the reconvolution function and inverse Fourier transforms the result Finally the resultant spectrum is corrected for any residual horizontal offset introduced by the reconvolution function 7 Output result Finally the resultant deconvolved spectrum is displayed in a new image display Notes for Spectrum Imaging Users To perform Fourier ratio deconvolution on a spectrum image select the FOURIER RATIO menu item with either the core loss spectrum image or an associated exploration spectrum taken from the core loss spectrum image front most If an exploration spectrum is front most specify the parent spectrum image as the input dataset when prompted The routine will proceed as described above for the one dimensional spectrum case Observe that in addition to the suitability criteria described above for the one dimensional spectrum instance both core loss and the corresponding low loss datasets must be of the same spatial dimensionality Note also that the algorithm makes no consideration whether the two datasets are spatially registered hence any drift alignment required between the datasets should be performed prior to performing this routine The MLLS FITTING PREFERENCES dialog xi Use fit weights Set equalto 1 J Residual misfit signal IV Fit reduced chi squared values J Fit uncertainties Cereal o MLLS Fitting This sub menu contains commands for sett
16. 1 2 1 3 15 3 7 4 3 7 5 3 7 6 3 7 7 Numerical Filters greatly reducing the intensity in the slowly varying portions such as the smooth power law background The smoothed copy is obtained via channel averaging over an interval of specified width as for the SMoorTu filter The width in eV w of the averaging interval is set independently of the smoothing width under STRUCTURE HIGH Pass in the FILTER SETUP dialog First derivative This item calculates an approximate first derivative of the foreground spectrum and places the result in a new display leaving the original data unchanged The routine first smoothes the data over an interval w eV wide then it calculates the difference between values dE eV apart and places the result in the channel midway between two The parameters w and dE are set under the First LoG DERIVATIVE heading of the FILTER SETUP dialog Finally the spectrum is divided by w dE to yield an approximation of the first derivative with respect to energy Log derivative This item calculates an approximate logarithmic derivative of the foreground spectrum and places the result in a new display leaving the original data unchanged The routine performs the same procedure as FIRST DERIVATIVE but adds one final step dividing the result by the original spectrum Log log derivative This item calculates the approximate derivative of the foreground spectrum as plotted on a log log scale and places the result
17. 2 5 Working with Spectra in DigitalMicrograph SHOW SPECTRUM NAME displays the corresponding spectrum in the image window in addition to any spectra already present The displayed spectrum will have the same color as the corresponding legend tab HIDE SPECTRUM NAME conceals the corresponding spectrum from the image window When a spectrum is contained within an image window but is hidden the corresponding legend tab will not be colored HIDE OTHERS hides all spectra within the image window with the exception of the currently selected spectrum SHOW ALL displays all the spectra contained within the image window SEND BEHIND sends the corresponding spectrum to the back most plane of the image window BRING TO FRONT brings the corresponding spectrum to the front most plane of the image window ZOOM TO ROI rescales a spectrum with the region within the ROI zoomed to fill the entire spectrum window in both the x and the y directions This is particularly useful when working with spectra containing a zero loss peak It is a quick way of rescaling the spectrum to view the detail in the higher energy loss regions ZOOM VERTICALLY TO ROI performs a vertical rescaling of the spectrum with the intensity range falling within the ROI filling the image window but keeping the horizontal scaling unchanged Home DISPLAY returns the spectrum display to its default values ALIGN SLICE By provides a sub menu for aligning overlaid spectra w
18. LIST ready for quantification When you are unsure about the elemental constituents of your sample the easiest way to proceed is to select this However please be EELS Analysis User s Guide Rev 1 2 1 Figure 3 31 EELS Analysis User s Guide Rev 1 2 1 Quantification aware that EELS Analysis s edge detection algorithm cannot match an experienced human analyst s ability to discriminate weak edges and overlapping features Also note that the accuracy of the algorithm s identifications is strongly dependent on a properly calibrated energy loss scale The details of the edge detection and identification routine employed by EELS Analysis are surprisingly complicated and even a bit arcane for what on the surface might appear to be a relatively simple task A thorough discussion of the algorithm may be found in the following references M K Kundmann and O L Krivanek Automated processing of parallel detection EELS data Microsc Microanal and Microstruct 2 1991 245 M K Kundmann and O L Krivanek Automated quantitative analysis for parallel EELS Microbeam Analysis 1991 D G Howitt ed San Francisco Press 1991 263 The EELS EDGE AUTO IDENTIFICATION SETUP dialog for non EELS SI users fea EELS Edge Auto Identification Setup xi Detection Transform Parameters Transfom Log difference yi Diff delta eV o o a Structure fiter eV 30 0 ait Diff smooth eV 4 0 IV Apply powerlaw noise
19. NLLS FITTING PREFERENCES dialog 3 40 Fitting a single Gaussian to the Cr L white line using NLLS fitting 3 41 The NLLS MODEL FIT PROPERTIES dialog 3 42 The SI NLLS FITTING OUTPUT OPTIONS dialog 3 43 The KRAMERS KRONIG ANALYSIS setup dialog 3 45 The EELS QUANTIFICATION dialog the QUANTIFY tab 3 50 Identification of a core loss edge 3 52 The EELS EDGE AUTO IDENTIFICATION SETUP dialog for single spectra 3 53 The EELS EDGE AUTO IDENTIFICATION SETUP dialog EELS SI only 3 56 The SAVE QUANTIFICATION TEMPLATE dialog 3 60 The LOAD QUANTIFICATION TEMPLATES dialog 3 60 Post quantification results 3 61 The EELS SI QUANTIFICATION OUTPUT OPTIONS dialog 3 64 The EELS QUANTIFICATION dialog the EDGE SETUP tab 3 66 Specifying signal extraction parameters in the EDGE SETUP dialog 3 71 Background subtracted edge with calculated cross section 3 73 The EELS REPORT PREFERENCES dialog 3 74 Quantification results prepared using the REPORT menu items 3 74 EELS Analysis User s Guide Rev 1 2 1 1 Introduction Although EELS is a powerful technique it is generally recognized and is often a source of frustration that EELS requires careful account and consideration of a large number of details both in setting up the experiment and in performing the data analysis The goal with EL P Gatan s previous EELS analysis package was to off load as much as possible the concern for technical details from the microscopist a
20. eee 26 where c is the speed of light in a vacuum and other parameters are as defined elsewhere in this section Surface loss intensity Selecting this item outputs the surface loss intensity that is the computed surface loss contribution to the input data The routine used follows the fundamentals of the KRAKRO routine of Egerton see Appendix B3 pp 414 416 for details Specifically the routine performs the following 1 Check input The input data should be a low loss spectrum with the 0eV channel within the acquisition range In addition plural scattering should have been removed beforehand using the Fourier log deconvolution routine described above In the event that the specimen is thin enough to assume plural scattering is negligible then the zero loss intensity should be removed beforehand using the ZERO Loss REMOVAL routines Note that since the input data should no longer have the zero loss peak in place the routine has no means available for confirming the accuracy of the dispersion calibration Hence it is most important to ensure that the dispersion calibration is accurate in particular that zero loss channel is correctly positioned before performing this operation If there are any problems with the input data then a suitable alert is posted Finally the routine requires the zero loss integral as input this value is taken from the spectrum s image tags if present as it should be if the EELS ANALYSIS routines
21. enable identification of transitions from sub shells or alternatively select the SHELL radio button to display only the lowest energy and usually the most prominent transition for each shell It should be observed that while grouping by shell is selected the elemental markers overlaid on the spectrum identify all corresponding sub shell transitions within the visible recorded energy range If grouping by sub shell is selected then only the highlighted transition is marked Identification of a core loss edge ga A BN on holey carbon fra EELS Quantification shell transition Ey energy of the 168eV highlighted edge ta Identified core 7 185 ev loss edge Sowby e 3 ev ia 227ev I Label Clean _aito 0 R Hl Guantify Edge ID This button initiates the manual edge identification process When you mark an edge of interest by clicking on its threshold and then press on the identify selection button EELS Analysis looks up the marked threshold energy in its internal tabulation of the EELS Slide Rule data and makes a tentative identification An example of edge identification is shown in Figure 3 30 The result is presented in the EDGE List as the entry with the closest threshold energy shown highlighted subject to the selected shell and sub shell grouping Auto ID This button performs a fully automated edge detection and identification on your spectrum adding the identified edge s to the QUANTIFICATION
22. extract the zero loss peak is specified in the ZERO LOss MODEL pull down menu in the COMPUTE THICKNESS PREFERENCES dialog Selecting USE EXTRACT ZERO LOss SETTING implements the same zero loss model as determined in the REMOVE ZERO LOSS PREFERENCES dialog Once extracted the zero loss is summed to yield the zero loss counts Note that if the selected spectrum has previously had plural scattering removed by Fourier log deconvolution the zero loss integral will be taken automatically from the spectrum s image tags 2 Correct for spectrum truncation The loss part of the spectrum is extrapolated up to 2000 eV loss with a power law background The last 10 positive valued channels of the loss spectrum serve as input to the fit routine and the power law exponent r is constrained to be less than or equal to 1 3 Compute relative thickness t The thickness is computed as a multiple of the inelastic MFP using the log ratio method via the following see Egerton p 302 I 1 exp t t Aln 1 where J is the sum of zero loss peak counts Zis the sum of total spectrum counts zero loss peak plus extrapolated loss part and is the inelastic MFP If the plural scattering has been removed from the spectrum then an appropriately modified form of this relationship is applied 4 Output result The result is displayed as appropriate in units of inelastic mean free path see Figure 3 17 Further the thickness value and t
23. for each edge following Egerton s Equation 4 67 It should be noted that Equation 4 67 is true for spectra that have had plural scattering removed by example using a Fourier based technique as described earlier or from a very thin sample area If the spectrum contains significant plural scattering this should be removed prior to quantification Failing this applying identical signal integration windows to all the edges to be analyzed provides an approximate correction for plural scattering refer to Egerton for details In addition a further relative quantification is performed where the percentage composition relative to the total sum of the constituents analyzed is computed Note that the total sum of the constituents does not necessarily constitute the sum of the species present in the sample under analysis 6 Output the results The computed absolute and relative concentrations are logged to the RESULTS window along with all intermediate results and parameters of the computation as shown in Figure 3 35 A graphical output of the background subtracted edges and accompanying energy differential cross sections are also displayed in the spectrum s image display Please note the importance of the collection angle parameter for performing an absolute quantification or for relative quantification based on edges widely separated in energy In such cases the results will be a sensitive function of the collection angle parameter you provide
24. further reserves the right to revise this manual and to make changes to its contents at any time without obligation to notify any person or entity of such revisions or changes Copyright and Trademarks 2003 All rights reserved DigitalMicrograph is a registered trademark of Gatan Inc registered in the United States EELS Analysis User s Guide Rev 1 2 1 Support Contacting Gatan Technical Support Gatan Inc provides free technical support via voice Fax and electronic mail To reach Gatan technical support call or Fax the facility nearest you or contact by electronic mail e Gatan USA West Coast Tel 925 463 0200 Fax 925 463 0204 e Gatan USA East Coast Tel 724 776 5260 Fax 724 776 3360 e Gatan Germany Tel 089 352 374 Fax 089 359 1642 e Gatan UK Tel 01865 253630 Fax 01865 253639 e Gatan Japan Tel 0424 38 7230 Fax 0424 38 7228 e Gatan France Tel 33 0 1 30 59 59 29 Fax 33 0 1 30 59 59 39 e Gatan Singapore Tel 65 235 0995 Fax 65 235 8869 e Gatan Online http www gatan com Info gatan com help gatan com EELS Analysis User s Guide Rev 1 2 1 iii EELS Analysis User s Guide Rev 1 2 1 Table of Contents Preface i Support iii Table of Contents v List of Figures vii 1 Introduction 1 1 2 Performing EELS 2 1 2 1 Entering and Accessing Physical Setup Data 2 1 2 2 Performing Calibrations 2 1 2 3 Acquiring Spectra 2 2 2
25. identified simply by their threshold energies provided the energy loss axis has been accurately calibrated With tabulated edge data at hand such as the Gatan EELS Slide Rule or the EELS Atlas shipped with your spectrometer or imaging filter the energy threshold of an edge can usually be uniquely correlated with a particular element and electron shell the ionization of which gives rise to the observed feature The left hand side of the QUANTIFY tabbed dialog is dedicated to this purpose see Figure 3 29 allowing the user to identify edges to check or correct their identity and possibly to mark them for further quantitative analysis or alternatively enabling edges of elements suspected of being present to be specified for quantification Once successfully identified the edge may be added to the QUANTIFICATION LIsT on the right hand side of the QuANTIFY tab for quantitative EELS Analysis User s Guide Rev 1 2 1 Quantification analysis in the next stage of the edge analysis process Finally once the list of edges to be analyzed has been compiled and appropriate signal extraction parameters specified via the EDGE SETUP tab group described in the following section the group of buttons located in the bottom right of the QUANTIFICATION tab allow quantification to be initiated or for selected lists to be loaded or saved for rapid analysis of multiple spectra or for future analyses respectively The function of each control in the Q
26. image RefIndex number FracTol number Maxlter image amp eps1 image amp eps2 image amp Srfelf image amp TNM Description This function performs Kramers Kronig analysis on a low loss single scattering distribution to yield the energy dependence of the real and imaginary parts of the dielectric function eps and eps2 respectively It requires a calibrated low loss spectrum or spectrum image as the input source dataset src with plural scattering removed for example the output of the routine EELSFourierLogDeconvolveWithZLPModifier described above is ideal In addition the function must be passed values for the refractive index of the material for visible light RefIndex the primary electron beam energy 0 in keV the effective collection semi angle BetaEff in mrad and also the zero loss integral 70 The zero loss integral can be specified as a number for single spectrum analysis or alternatively as a line plot or 2D image of suitable dimensionality for analysis of spectrum line traces or spectrum images respectively the output of the EELSExtractZLPIntegral routine is suitable Note that for spectrum image analysis the parameter RefIndex can also be specified as an image This image must be of compatible spatial dimensionality to the input data set and should contain the appropriate values of the refractive index at corresponding pixels Two other values must be provided the Fractol parameter defines the fractional tolerance of
27. in a new display In regions dominated by the power law background the resultant value reflects the local power law exponent This is why the transform is sometimes referred to as an R plot The routine performs the same procedure as LOG DERIVATIVE but adds one final step multiplying the result by the energy loss Second derivative This item calculates an approximate second derivative of the foreground spectrum and places the result in a new image display The routine averages over an interval w eV wide and subtracts half the aver ages in two adjacent wings of width w as illustrated and set under the SECOND DERIVATIVE heading in the FILTER SETUP dialog Finally the spectrum is divided by the squared sum of w and w to yield an approximation of the second derivative with respect to energy EELS Analysis User s Guide Rev 1 2 1 Figure 3 15 EELS Analysis User s Guide Rev 1 2 1 Zero Loss Removal The ZERO Loss EXTRACTION PREFERENCES dialog xi Zero4oss model Reflected tail Btracted signal integral s J Mean zerodoss energy Sma o 3 8 Zero Loss Removal The ZERO Loss REMOVAL sub menu contains items for modeling and extracting the zero loss peak from low loss spectra The individual menu items are described as follows 3 8 1 Preferences Select this menu item to open the ZERO LOSS REMOVAL PREFERENCES dialog shown above in Figure 3 15 This dialog contains the preferences
28. is the most robust and gives the most reasonable fit for typical EELS edge data However if an edge is in the low loss regime below about 100 eV or if another edge precedes it closely then the simple power law model will likely fail It is often possible to tell by eye whether the model provides an accurate fit for example if the extrapolated background intersects the spectrum soon after the edge then most likely the background fit is inadequate and an alternative model could yield a better fit In the case of a low loss background a polynomial or log polynomial model function will sometimes yield better results For example see the following reference A R Wilson Detection and quantification of low energy low level electron energy loss edges Microsc Microanal and Microstruct 2 1991 269 Since the polynomial and log polynomial background models are far less robust and require an experienced eye it is recommended that the power law model be used first and foremost 3 5 2 Extrapolate Background Use this command to model and extrapolate the characteristic background under an edge Egerton pp 269 277 The background model applied is taken from the default setting as specified in the BACKGROUND MODEL DEFAULTS dialog as described above Once created it may be adjusted using the CHANGE CURRENT MODEL function described next in this section In general a power law model of the form AE is most commonly applied and it is
29. menu heading EELS Analysis User s Guide Rev 1 2 1 1 EELS Analysis User s Guide Rev 1 2 1 2 Performing EELS 2 1 2 2 EELS Analysis User s Guide Rev 1 2 Entering and Accessing Physical Setup Data Whenever doing EELS several experimental parameters should always be noted so that quantitative analyses can be carried out later With DigitalMicrograph such information can be stored directly with your spectra rather than being relegated to a separate notebook or easily lost sheets of paper Before acquiring spectra select EXPERIMENTAL CONDITIONS under the EELS menu and enter the relevant information in the dialog box For example in order to carry out quantitative analyses of EELS spectra accurate values for the incident beam energy as well as the convergence and collection angles are required Within this dialog entering the relevant information within the tabbed dialog field labeled GLOBAL will set the global values These values are automatically transferred to all subsequently acquired spectra making this information available to the analytical routines If conditions change from one spectra to the next or if you have forgotten to set the global values before acquisition the acquisition conditions for a single spectrum may set by selecting EXPERIMENTAL CONDITIONS with the desired spectrum s image window front most and entering the relevant information in the tabbed dialog field labeled with the spectrum
30. over the specified signal integration energy range to yield a partial cross section In addition EELS Analysis can output the energy differential cross section in real time to the spectrum s image display for visual comparison to the measured edge profile as shown in Figure 3 39 The routines used by EELS Analysis to calculate the energy differential cross sections are based on the routines used in Gatan s EL P software The computed cross section incorporates the essential physics needed to convert raw edge counts into a number that is proportional to the actual concentration of the associated atomic species Refer to the discussion of QUANTIFY above for specific details regarding the quantification procedure The cross section routine can perform the calculation based on either hydrogenic with or without white line corrections or Hartree Slater atomic wave functions as specified in the CROSS SECTION pop up menu Note that depending on element and edge type some or all of the cross section models may be unavailable The subsections that follow provide specific details concerning the two methods that may be chosen for cross section calculation Hydrogenic model The calculation of hydrogenic cross sections is based on Egerton s programs SIGMAK2 and SIGMAL2 see Egerton Appendix B pp 420 425 As a result the cross sections calculable by the hydrogenic branch of this routine are subject to the same constraints as SIGMAK2 and SIGMAL
31. part of the spectrum it is important to take account of them when performing the zero loss peak separation In the reflected tail model this is achieved by assuming the zero loss tails are relatively symmetric and uses a reflection of the left side tail to model the tail on the energy loss side Specifically it a replicates the spectrum from the first channel to a cutoff point at 1 5 FWQM full width at quarter maximum before the peak b reflects the replicated tail about the zero loss maximum c removes any mean background offset from the reflected tail measured from the region on the low energy loss side below 3 FWQM from the zero loss center using at most the first 5 of non zero channels in the spectrum and at least the first 3 non zero channels d vertically scales the reflected tail using the ratio of the sum of the overlapping 3 channels if possible scaling down to 1 channel with decreasing FWQM at the low loss cutoff and the high loss join point e attenuates the reflected tail at the first non positive channel and f replaces the high loss spectrum above the join point with the reflected tail to yield the zero loss peak g This zero loss model is subtracted from the original spectrum to yield the inelastic signal and all channels from the beginning of the spectrum range to the rightmost negative count residual in the inelastic signal within the zero loss extrapolation range are set to zero then finally i the inelastic signal is th
32. results The spectrum must meet the same requirements of the EXTRACT ZERO LOSS routine described above since accurate extraction of the zero loss intensity is required by the routines The spectrum must be corrected for detector background Residual detector background can be among the largest sources of error in a thickness calculation particularly for samples less than 1 MFP thick Hence ensure spectra are acquired with DARK SIGNAL AND GAIN correction selected ensuring both pixel to pixel variations and dark current are corrected The spectrum s zero loss peak must not be saturated i e the number of counts in the peak channel must be at least a few percent lower than the maximum per pixel readout of the detector Generally this can be achieved by acquiring with short integration time and weak incident beam intensity The zero loss peak must be modeled accurately for effective separation of the zero loss peak from the loss part of the spectrum The probed specimen area must be of uniform thickness it cannot contain holes or have wedge like thickness profile The low loss spectrum should be acquired up to and past a suitable energy at which the extrapolated power law used to correct for truncation of the spectrum may be assumed to be valid This energy will vary depending on the specimen composition and thickness but generally the power law relationship may be considered to be applicable at 200eV loss and beyond The collection a
33. saved and used as a template for analyzing spectra in future analysis sessions see below As with the EpGE List double clicking on any of the entries in this list will automatically zoom in the spectrum display on the appropriate edge energy on the spectrum if within the energy loss range and indicate the edge transition threshold energy with a labeled marker If a spectrum image is front most then the display will also automatically shift to the corresponding energy loss EELS SI only EELS Analysis User s Guide Rev 1 2 1 3 59 Quantification Figure 3 33 The SAVE QUANTIFICATION TEMPLATE dialog Save Quantification Template x Existing Quantification Template list 304 stainless steel 316 stainless steel Generic biological High Tc superconductor Semiconductor Save As Catalyst 83 Cancel a Save Compiled QUANTIFICATION Lists and their associated signal extraction parameters for the constituent edges can be saved for use in future analyses as a quantification template see LoAD below This feature provides a powerful and convenient way of analyzing successive spectra with similar compositions To save a compiled QUANTIFICATION LIST as a template press this button This will launch the SAVE QUANTIFICATION TEMPLATE shown in Figure 3 33 specify an appropriate name and press OK Note that all characteristics regarding the QUANTIFICATION LIsT will be saved including the specific edge extraction para
34. script functions and provide a summary a prototype and a description of each function Note that each function can be applied to single spectra spectrum line traces and also spectrum images alike spectrum imaging analysis functionality is available only if the spectrum imaging package is installed Please refer to the corresponding description for each function under the appropriate menu heading in Section 3 for more details on the algorithms used The second part of this section describes how to add you own custom zero loss removal algorithms to the zero loss model manager enabling these routines to be used for zero loss modeling throughout the EELS Analysis routines EELS Script Commands EELSComputePowerLawBackground Computes a power law background to a spectrum image EELSComputePowerLawBackground image src number starteV number endeV image EELSComputePowerLawBackground image src number starteV number endeV image amp redChi2 image amp A image amp r number amp meanEnergy This command computes a power law background of the type AE where A is a scaling constant E is energy loss and r is the background slope exponent for a specified spectrum or spectrum image The background is least squares fitted over the given fitting range specified in calibrated units The routine requires the calibrated source data set src as well as the background fitting start and end energies starteV and endeV The routine returns the
35. spectrum to yield the output zero loss peak Note for advanced users the Gaussian and zero loss intensity ratio fit range may be varied by opening EELS gt SETTINGS gt ZERO LOSS MODELS gt FIT PRE MEASURED ZERO LOSS in the GLOBAL INFO tags and entering an appropriate value in units of eV in the FIT START and FIT END fields as appropriate Additionally the post extrapolation clean up steps g i can be disabled by setting the PERFORM POST FIT CLEANING tag to FALSE 2 Gaussian fit The 2 Gaussian model uses least squares fitting to fit two Gaussian functions to the zero loss peak It is reasonably robust but is not well suited to zero loss peaks with long tails arising from high detector point spread function Specifically it a fits a single Gaussian model to the zero loss peak to accurately measure the zero loss center and half width half maximum HWHM then b attempts to fit two Gaussian models to the spectrum over a fitting region by default from 6 to 3 times the zero loss HWHM either side of the zero loss center To ensure a sensible fit one of the Gaussian models has its center position constrained to the zero loss center whilst the second has its width constrained to that of the zero loss peak c The sum of the Gaussian models is subtracted from the original spectrum to yield the inelastic signal All channels from the beginning of the spectrum range to the rightmost negative count residual in the inelastic signal within th
36. the 3 53 3 54 Quantification trade offs involved in optimizing them are fairly understandable However a few of them are largely heuristic in nature and are best optimized by trial and error The default settings stored within EELS Analysis provide a good starting point giving the best overall results on the spectra within the EELS Atlas which may be found in the DigitalMicrograph installation folder successfully detecting and identifying the majority of the edges within this data set The edge detection parameters fall into two main categories 1 Those that define the transform used to accentuate the spectrum edge signals and 2 Those that guide the analysis of the transformed spectrum These are labeled DETECTION TRANSFORM and FEATURE DETECTION respectively in the EDGE AUTO IDENTIFICATION SETUP dialog The DETECTION TRANSFORM parameters specify the following TRANSFORM TYPE use this pop up menu to choose the type of difference filter applied to the spectrum to improve the signal to background ratio The log difference filter is a good choice because it involves only a single derivative and because it tends to flatten the large dynamic range and strong power law decay of typical EELS core edge data Please refer to the following reference for more detailed discussion of the relative merits of the various difference filter types M K Kundmann and O L Krivanek Automated processing of parallel detection EELS d
37. the Gaussian amp Lorentzian model This model fits the sum of a Maxwell Boltzmann distribution described above and a Lorentzian function that models the extended zero loss tails This model is therefore suited to asymmetrical distributions recorded using a detector with high point spread function By default the start value of T is 800 K The fitting procedure is identical to that described for Gaussian amp Lorentzian above It should be noted that all the preset zero loss fitting routines find the zero loss peak initially by searching for the maximum intensity peak after applying a filter that emphasizes features as a function of their distance from the 0 eV channel as calibrated Hence the routines should successfully locate the zero loss peak even for very thick samples providing they are reasonably well calibrated the zero loss peak should be located to within approximately 10eV for spectra from thicker regions with larger error margins for spectra from thinner regions User defined models can be added to the zero loss model list by creating and installing a custom script written in the DigitalMicrograph script language details of which are given in Section 4 2 Note that any custom zero loss models will also appear in the zero loss model pull down list for other routines that require zero loss extraction for example the COMPUTE THICKNESS routine described below 3 21 3 22 3 8 3 3 9 Compute Thickness C
38. the list of dimensionally compatible spectra below A BN edges 1 Cancel Splice Spectrum Select this item with one of the spectra you wish to splice front most You will then be presented with a dialog requesting you to select from a list of dimensionally compatible spectra the spectrum to splice with see Figure 3 7 above The routine uses the spectrums calibrated energy scales to decide how to concatenate the displayed segments and as a result they must be properly calibrated for best results If the data must be rebinned to a common dispersion before splicing the software will ask the user for confirmation before proceeding The overlapping channels of each pair of neighboring spectra are used to normalize the lower energy segment to the higher energy segment The spliced result is then displayed in a new image window Note that you may see a distinct change in the signal to noise around the area where the two spectra are joined together If the exposure time of the lower energy loss spectrum is less than that of the higher energy loss spectrum a common situation due to the steep change in the background as a function of energy then the lower energy loss portion will have a lower signal to noise ratio near the overlap region The scaling will compensate for different exposure times but it cannot compensate for the lower signal to noise in the spectrum acquired with a shorter exposure time Notes for Spectrum Imaging Users
39. the parameters are altered the BACKGROUND and SIGNAL numerical fields described in this section are refreshed automatically with the new values It should be noted that in this mode the computed energy differential cross section falling within the defined signal integration window is also displayed in real time 2 Alternatively you may enter the specific BACKGROUND and SIGNAL window values directly in the OFFSET and WIDTH numerical fields provided The spectrum display will be automatically refreshed with the updated background fitting and signal integration windows along with the calculated background contribution and extracted edge profile see Figure 3 38 The definitions of the various combinations of background fitting and signal integration window offsets and widths are as follows BACKGROUND OFFSET enter the number of eV from the edge threshold at which the background fit interval for normal edge extraction analysis begins BACKGROUND WIDTH enter the width in eV of the background fit interval for normal edge extraction analysis SIGNAL OFFSET enter the number of eV from the edge threshold at which to begin computing the differential cross section and integrating counts for the elemental concentration computation SIGNAL WIDTH enter the width in eV of the count and cross section integration range for the elemental concentration computation The criterion for the optimal offset energy and width of the background fitt
40. the ratio of successively computed proportionality constants before convergence is reached a value of le 5 is a reasonable value with lower values specifying higher convergence accuracy and the parameter Max ter refers to the maximum number of iterations to perform before aborting 20 is a suitable value The arrays eps eps2 Srfelf EELS Analysis User s Guide Rev 1 2 4 7 Summary Prototype Description Summary Prototype Description Summary Prototype Description EELS Script Commands and TNM will be returned containing the real and imaginary parts of the dielectric function the surface energy loss function and the specimen thickness respectively Note that if the refractive index is specified as an image then the specimen thickness array must be initiated as an image also EELSSharpenSpectrum Sharpens a spectrum by deconvolution of the extended zero loss tails image EELSSharpenSpectrum image src image ZLP This function sharpens the input spectrum or spectrum image by applying an algorithm that deconvolves the extended zero loss peak tails associated with the detector point spread function please refer to Section 3 4 for more details on the algorithm used The function requires a calibrated spectrum or spectrum image as source dataset src In addition it also requires a calibrated zero loss profile ZLP acquired preferably but not necessarily at the same dispersion The output of the ExtractZLP routine pr
41. the spectrum corresponding to Slice 0 Note that to perform this procedure the front most image display must contain two or more visible spectra with at least two channels of overlap Any hidden spectrum slices will be excluded from the procedure In addition any change in vertical scaling is ignored hence allowing the user to manipulate the intensity scales of the individual spectra as an aid to manual alignment whilst preserving the counting statistics in the final summed spectrum To perform this operation do the following 1 Place the spectra to be summed into a single image display as shown in Figure 3 13 To achieve this cut and paste or right click drag the spectra into a single line plot image display e g the image display of one of the spectra of interest Please refer to Section 2 4 4 for more details on displaying multiple spectra in a single image display If the spectra are calibrated they will be automatically aligned with respect to their energy loss regardless of their dispersion 3 13 Numerical Filters 2 Manually align the spectra by shifting them horizontally To do this a Ifthe line plot s image display legend is not already visible right click on the image display and select SHow LEGEND b Right click on the appropriately colored legend corresponding to the spectrum slice you wish to align and select DETACHED in the HORIZONTAL CONSTRAINTS sub menu c Left click on the spectrum display to cr
42. to a spectrum image EELSMLLSFit image src object RefList object amp ValList object amp SigmaList image amp RedChiSqu number FitStarteV number FitEndeV number ComputeFitsFromData This function performs multiple linear least squares fitting of the specified reference spectra to the source spectrum or spectrum image over the specified fitting region The MLLS fit and fitting co efficients are returned The routine requires a calibrated spectrum or spectrum image as the source array src It EELS Analysis User s Guide Rev 1 2 4 2 EELS Analysis User s Guide Rev 1 2 Adding Custom Zero Loss Models also requires the calibrated reference spectra compiled as an object list RefList Below is an example of compiling a reference list RefList with two spectra ref and ref2 object ReflList alloc objectlist RefList AddObjectToList alloc ObjectListImageUtils init ref1 RefList AddObjectToList alloc ObjectListImageUtils init ref2 Hence by simply perform the above as many reference spectra can be added to the list as required a minimum of two must be specified You must also specify the calibrated fitting range limits FitStarteV and FitEndeV and whether you want to perform the MLLS fit using fit weighting computed from the source data ComputeFitsFromData 1 or if you wish to apply equal fit weighting ComputeFitsFromData 0 please refer to Section 3 11 fora discussion on the significance of this The routine retur
43. to truncation the routine next smoothly extrapolates both ends of the data to zero by means of a cosine bell function see Egerton p 251 for details The width of each cosine bell region is set at 40 of width of the spectrum 4 Prepare the zero loss peak The zero loss component z E is modeled using the procedure described in the EXTRACT ZERO LOSS routine previously in this section The integral of the extracted zero loss peak yields the zero loss integral which is used in the calculation if a Gaussian modifier is specified in the FOURIER DECONVOLUTION PREFERENCES dialog Additionally if a Gaussian modifier is to be used then the width of the zero loss peak is measured for use in calculating the Gaussian reconvolution function in the next step 5 Prepare the reconvolution function Because of the noise in any measured spectrum a simplistic deconvolution of the entire zero loss profile will cause the Fourier components of the noise to dominate those of the deconvolved spectrum resulting in a useless result This is avoided by use of a reconvolution function which represents and restores the system resolution to the deconvolution and hence acts as a noise limiting function The reconvolution function to be used is determined by the selection in the RECONVOLUTION METHOD pull down menu in the FOURIER DECONVOLUTION PREFERENCES dialog If ZERO LOSS MODIFIER is selected then the zero loss peak extracted in the previous step is use
44. used by the EXTRACT ZERO Loss command described below The current zero loss model is specified in the ZERO LOss MODEL pull down list This list contains all the preset zero loss models described in detail in the following sub section in addition to any user defined models Quantities output in addition to the extracted zero loss peak can be specified in the OUTPUT group of options at the bottom of the dialog Selecting the output INELASTIC CONTRIBUTION tick box results in the inelastic contribution being computed and displayed If the output EXTRACTED SIGNAL INTEGRAL S box is ticked then the routine will also output the zero loss and if specified as above inelastic signals integrated in energy loss Selecting output MEAN ZERO LOSS ENERGY results in the mean energy loss of the extracted zero loss peak being output this quantity is useful for example for removing any zero loss drift from a spectrum image acquisition see CORRECT ZERO LOSS CENTERING SI USERS ONLY below for details 3 8 2 Extract Zero Loss The EXTRACT ZERO Loss command extracts the zero loss peak from the front most spectrum and displays the peak in a new image window If specified in the REMOVE ZERO LOSS PREFERENCES dialog as described above the inelastic signal and or the zero loss and inelastic signal integrals are also output To initiate this routine select the EXTRACT ZERO LOss menu item with the image window containing the low loss spectrum of interest positi
45. values for the incident beam energy and the convergence collection angles are required When carrying out quantification if any required fields have been left blank you will be prompted to enter these before continuing A tabbed dialog field labeled GLOBAL is presented in the EXPERIMENTAL CONDITIONS dialog irrespective of whether an image display is selected when initiating this command see Figure 3 4 The data entered within this field are automatically copied to the IMAGE DISPLAY INFO tags of all subsequently acquired spectra In addition these settings are preserved from one DigitalMicrograph session to the next so that most need only be entered once Note that the IMAGE DispLay INFO data stored with any spectra already acquired are not changed when you enter information within the GLOBAL field To edit the data associated with a particular spectrum initiate the EXPERIMENTAL CONDITIONS dialog with the desired spectrum image window selected The dialog will now contain an additional tagged dialog field labeled with the title of your spectrum Values entered within this field will be particular to the corresponding spectrum Note if the spectrum was imported from EL P the experimental conditions stored by EL P will be read by EELS Analysis Calibrate Energy Scale Figure 3 5 Calibrating the spectrum energy scale s Energy calibration dialog Selected E High energy T E I e eae boundary 6 3 2 Calibrate Energy Scale
46. 2 In particular only K and some L edges can be computed The K edge calculation is a theoretical calculation from first principles requiring no empirical input Any K edge listed in the EpGE List dialog H K through to Ti K can be computed The L edge computation on the other hand requires input of a semi empirical parameter that Egerton tabulates within SIGMAL2 Since this data only extends through Zn the range of accessible L edges on the hydrogenic model is AIL through to Zn L When available the empirical white line contribution Egerton computes in SIGMAL2 can be included or left out at your discretion by selecting HYDROGENIC WITH WHITE LINES or HYDROGENIC respectively There are a few technical differences between EELS Analysis s calculation of hydrogenic cross sections and Egerton s SIGMAK2 and SIGMAL2 The numerical results however agree within a few percent in all cases One difference is that EELS Analysis takes account of finite convergence angle directly within the GOS integral rather than treating it as a separate correction as Egerton does in his CONCOR program The basis of this correction is the factor F defined by Egerton in equation 4 71 of his book However instead of multiplying the integrated cross section by a value of F valid only at the midpoint of the integration range as in Egerton s equ 4 72 the factor F is taken inside the energy integral and its value is recomputed at each energy loss for which do dE is
47. 2 1 EELS Analysis User s Guide Rev 1 2 1 Zero Loss Removal residual in the inelastic signal within the zero loss extrapolation range are set to zero Finally the inelastic signal is then subtracted from the original spectrum to yield the output zero loss peak Note for advanced users the fitting range to the left and right of the zero loss center can be adjusted by opening EELS gt SETTINGS gt ZERO LOSS MODELS gt GAUSSIAN amp LORENTZIAN in the GLOBAL INFO tags and entering an appropriate value in units of HWHM in the appropriate fields Additionally the post fitting clean up step c can be disabled by setting the PERFORM POST FIT CLEANING tag to false Gaussian amp Lorenzian This model uses least squares fitting to fit the sum of a single Gaussian and a Lorentzian function squared to the zero loss peak The squared Lorentzian has extended tails to suit detectors of high point spread but less so than the preceding model The fitting procedure is identical to that described above for the Gaussian amp Lorentzian model Maxwell Boltmann This model fits a Maxwell Boltzmann distribution of the form X eee E x E where J is intensity E is energy loss A a constant and T the emitter temperature in K The model produces an asymmetric distribution and is suitable for spectra acquired using a cold FEG source By default the start value of T is 800 K The fitting procedure is identical to that described above for
48. 2 mrad collection Angle 2 8 mrad Analysis Results Background removal parameters Elem Fitting range ev Model Red chi 2 B 167 0 183 0 power law 0 18 N 358 0 393 0 power law 0 06 Signal quantification parameters Elem Signal counts Edge Type Integration range eV Cross section barns Cross section model B 2 04e 005 523 K 188 0 213 0 2230 223 Hartree Slater N 3 02e 004 217 K 401 0 426 0 323 32 Hartree Slater Absolute quantification Elem Areal density Catoms nm 2 B 9 16e 011 9 2e 010 sum spec N 9 37e 011 9 4e 010 sum spec Relative quantification Elem Atomic ratio N Percent content B 0 98 0 139 49 45 6 1 N 1 00 0 000 50 55 6 2 H z 4 Label Selecting Label places a labeled marker at the threshold energy for each edge group listed in the QUANTIFICATION LIsT To clear the labels select either an edge in the EDGE or QUANTIFICATION lists or alternatively press the CLEAN button see below Clean This button performs the same function as the Clean Spectrum menu item in brief it removes all quantification related markers and sub images from the front most spectrum e g background model edge id markers Quantify This command initiates elemental analysis of the spectrum using the edges contained within the QUANTIFICATION LisT The edges within the QUANTIFY LIST are specified as described above Adjusting their individual signal extraction parameters is describ
49. 250 300 350 400 450 Energy Loss ev 3 4 2 Sharpen Spectrum The SHARPEN SPECTRUM item is a deconvolution routine for recovering some of the spectrum detail lost to the broad tails of the zero loss peak see for example Figure 3 9 and Figure 3 10 To initiate the routine select this item with the spectrum to sharpen front most The routine requires two inputs the spectrum to be sharpened and the zero loss peak to be used as a reference for the deconvolution The latter may be a specified zero loss peak for example measured through a hole in the sample or pre extracted from a low loss spectrum using for example the EXTRACT ZERO Loss command as described later in this section Alternatively it may be extracted from a specified low loss spectrum or from the spectrum to be sharpened itself if it contains a zero loss peak The source of the zero loss reference is determined by the EELS Analysis User s Guide Rev 1 2 1 Sharpen preference set in the SHARPEN SPECTRUM PREFERENCES dialog please refer to the PREFERENCES section above for more details After some preparation of the reference zero loss peak explained below the two inputs are Fourier transformed the spectrum Fourier transform is divided by the zero loss peak Fourier transform and the result is inverse Fourier transformed to yield a spectrum largely free of the effects of the strong zero loss peak tails Once the procedure is complete the sharpened result wi
50. 4 Working with Spectra in DigitalMicrograph 2 2 2 4 1 Regions of Interest ROIs 2 2 2 4 2 Navigating a spectrum 2 3 2 4 3 Additional tools for manipulating single or multiple spectra 2 5 2 4 4 Moving spectra among image displays and to other applications 2 7 2 5 Performing mathematical operations on spectra 2 8 2 6 Analyzing spectra 2 8 2 7 Obtaining printouts 2 8 3 The EELS menu 3 1 3 1 Experimental Conditions 3 5 3 2 Calibrate Energy Scale 3 2 3 3 Splice 3 3 3 3 1 Preferences 3 3 3 3 2 Splice Spectrum 3 4 EELS Analysis User s Guide Rev 1 2 1 vi 3 4 Sharpen 3 5 3 5 3 6 3 7 3 8 3 9 3 4 1 Preferences 3 5 3 4 2 Sharpen Spectrum 3 6 Background Model 3 9 3 5 1 Preferences 3 9 3 5 2 Extrapolate Background 3 9 3 5 3 Change Current Model 3 11 3 5 4 Extract Background Model 3 11 3 5 5 Extract Background Subtracted Signal 3 12 Sum Overlaid Spectra 3 13 Numerical Filters 3 14 3 7 1 Preferences 3 14 3 7 2 Smooth low pass 3 15 3 7 3 Structure high pass 3 15 3 7 4 First derivative 3 16 3 7 5 Log derivative 3 16 3 7 6 Log log derivative 3 16 3 7 7 Second derivative 3 16 Zero Loss Removal 3 17 3 8 1 Preferences 3 17 3 8 2 Extract Zero Loss 3 17 3 8 3 Correct Zero Loss Centering SI users only 3 22 Compute Thickness 3 22 3 9 1 Preferences 3 24 3 9 2 Log Ratio relative 3 24 3 9 3 Log Ratio absolute 3 25 3 9 4 Kramers Kronig Sum Rule 3 26 3 9 5 All Methods 3 28 3 10 Remov
51. Analysis User s Guide Rev 1 2 1 3 23 Figure 3 16 Figure 3 17 3 24 3 9 1 3 9 2 Compute Thickness The ComPUTE THICKNESS PREFERENCES dialog ry Compute Thickness Preferences xi Zero loss model Use Extract Zero Loss setting x Preferences The PREFERENCES sub menu item opens the COMPUTE THICKNESS PREFERENCES dialog shown above in Figure 3 16 The dialog contains items allowing the zero loss extraction model and output preferences to be set Please refer to the description of the individual commands below for details on the effect of the preferences set here Log ratio thickness calculation using the COMPUTE THICKNESS routine LIM ox DigitalMicrograph xj Q Relative sample thickness 0 230163 inelastic mean free paths log ratio relative LI ox l welcome to DigitalMicrograph 12 9 2002 4 52 49 PM Compute Thickness Log ratio relative 12 9 2002 4 59 20 PM Relative sample thickness 0 230163 inelastic mean free paths log ratio relative m Log Ratio relative The COMPUTE THICKNESS by LOG RATIO RELATIVE routine carries out the following steps EELS Analysis User s Guide Rev 1 2 1 Compute Thickness 1 Isolate zero loss counts The first step is to separate the loss portion of the spectrum from the counts of the zero loss peak The procedure for doing this is the same as described in the preceding section EXTRACT ZERO Loss The zero loss model used to
52. DigitalMicrograph EELS Analysis User s Guide Gatan Inc 5933 Coronado Lane Pleasanton CA 94588 Tel 925 463 0200 FAX 925 463 0204 July 2003 Revision 1 2 1 gatan Preface About this Guide This EELS Analysis User s Guide is written to provide procedure for the analysis of EELS spectra and spectrum images using the EELS Analysis and EELS SI Analysis packages within DigitalMicrograph This Guide assumes the user is familiar with image manipulation within DigitalMicrograph and only addresses those features specific to the EELS Analysis and EELS SI Analysis packages Preview of this Guide EELS Analysis User s Guide Rev 1 2 1 The EELS Analysis User s Guide includes the following chapters Chapter 1 Introduction summarizes the features of the EELS Analysis software Chapter 2 Performing EELS provides an overview to the EELS acquisition and analysis process using DigitalMicrograph Chapter 3 EELS Analysis provides detailed instruction and information regarding the items contained within the EELS menu Chapter 4 The EELS Analysis Script Interface provides details regarding the script interface provided by EELS Analysis Disclaimer Gatan Inc makes no express or implied representations or warranties with respect to the contents or use of this manual and specifically disclaims any implied warranties of merchantability or fitness for a particular purpose Gatan Inc
53. EFERENCES above for details on changing the global background defaults To apply any changes made press OK to revert to the original state press CANCEL 3 5 4 Extract Background Model Use this command to extract an active background model and display it in a new image window To initiate this routine select the menu item with a spectrum front most with an active background model in place The routine will duplicate the background model displaying it in a new image window Note that the extracted background model will be inactive and hence will not change in response to any alteration of the background fitting or modeling parameters on the source spectrum EELS Analysis User s Guide Rev 1 2 1 3 11 3 5 5 Background Model Notes for Spectrum Imaging Users To extract fit and extract the background model on a pixel by pixel basis from a spectrum image perform the ROI set up procedure as described above for the single spectrum case on an exploration spectrum taken from the spectrum image Select the EXTRACT BACKGROUND MODEL menu item and specify the parent spectrum image for analysis when prompted The background fit will then be applied on a pixel by pixel basis on the spectrum image using the fitting region and background model as specified for the exploration spectrum The background model dataset which will have the same dimensionality as the input data will be displayed in a new image window Note that log poly
54. I0 The zero loss integral can be specified as a number for single spectrum analysis or alternatively as a line plot or 2D image of suitable dimensionality for analysis of spectrum line traces or spectrum images respectively The output of the EELSExtractZLPIntegral routine provides a suitable input dataset Note that for spectrum image analysis the parameter RefIndex can also be specified as an image Again this image must be of compatible spatial dimensionality to the input data set and should contain the appropriate values of the refractive index at corresponding pixels The computed thickness is returned as an image containing a single pixel for single spectra or a line profile for spectrum line traces or as a 2D image for spectrum images EELSFourierLogDeconvolveWithZLPModifier Summary Deconvolves plural scattering from a low loss spectrum using the Fourier log approach with a zero loss peak modification function Prototypes image EELSFourierLogDeconvolveWithZLPModifier image src number ZLPIndex image EELSFourierLogDeconvolveWithZLPModifier image src image ZLP Description This function removes plural scattering from a low loss spectrum or spectrum image using the Fourier log deconvolution approach The function may be called using either the ZLPIndex number parameter to specify by index which EELS Analysis User s Guide Rev 1 2 4 5 Summary Prototypes Description Summary Prototype Description EELS Sc
55. L Cancel OK 3 12 5 Apply Model to Parent Spectrum Image Note that this menu item is only present on systems with the Spectrum Imaging optional package installed This menu item applies NLLS fitting on a pixel by pixel basis to the parent spectrum image associated to the front most exploration spectrum outputting the model fit properties as a line profile or map respectively To perform this operation an exploration spectrum created using the spectrum imaging exploration tool must be front most with one or more active NLLS fitting regions The associated parent spectrum image must also open On initiation the routine will first present you with the SI NLLS FITTING OUTPUT OPTIONS dialog as shown above in Figure 3 27 This dialog enables you to specify the properties that are output by the routine A description of each option in the dialog follows The FIT PARAMETERS group at the top of the dialog contains items relating to the fit computation that is the fitting parameters and measure of goodness of fit These properties have only one output value per spectrum hence the images output from options selected in this group of items will have the same spatial dimensionality as the input data i e a 3d spectrum image will result in a 2d map being output Output fit parameters Selecting this option will result in the individual NLLS model fit parameters amplitude center and width for a Gaussian model being output in a new image d
56. MERA menu on a regular basis following the procedure outlined in you spectrometer manual to ensure that an up to date gain reference is used for gain correction Acquiring Spectra Spectra are acquired within DigitalMicrograph using the AutoPEELS or AutoFilter software depending on your spectrometer type as supplied with your detector For a detailed description of how to acquire spectra using AutoPEELS or AutoFilter please refer to the dedicated documentation supplied these packages Working with Spectra in DigitalMicrograph Spectra within DigitalMicrograph may be viewed manipulated and labeled in a similar manner to any other line plot image display please refer to USING LINE PLOT IMAGE DISPLAYS in your DigitalMicrograph manual for a more general description of line plot image displays This section covers the tools within DigitalMicrograph for working with and manipulating your acquired spectra It should be noted that these tools are part of DigitalMicrograph itself not part of the EELS Analysis package Since some of the tools described are new to later releases of DigitalMicrograph it is worthwhile even for experienced users to review this section Regions of Interest ROIs A region of interest or ROI is used to indicate a location on a spectrum An example of a spectrum with an ROI is shown in Figure 2 1 Normally there is only one ROI on a spectrum at a time so each time you create a new ROI the other ROI s are deleted
57. ORE LOSS SIGNAL This option is always selected by default and outputs the extracted core loss signal for each edge specified in the QUANTIFICATION LIST as computed in step 1 described above The individual single edge output of this routine is identical to that of the CREATE BACKGROUND SUBTRACTED MAP item in the SI menu AREAL DENSITY Selecting the AREAL DENSITY option will output the absolute concentration map or line plot as computed in step 4 above of each specified edge in the QUANTIFICATION LIST RELATIVE COMPOSITION If the QUANTIFICATION LIST contains two or more edges selecting RELATIVE COMPOSITION outputs the computed elemental composition as a percentage of the total species analyzed This computation assumes that the edges analyzed sum to 100 composition over the field of view i e the QUANTIFICATION LIST contains all significant species present This computation is the same as the percentage composition output for the single spectrum case as described in the latter part of step 5 above Please note that this method of quantification may not be well suited to all quantifications since it can result in noise dominated image regions where the sum of the specified constituents is close to zero Once the output options are specified the quantification procedure is applied to the spectrum image as described above To abort the procedure at any point during the computation hit the Esc key Quantification of a spectrum line trac
58. OUTPUT OPTIONS group of items allows additional properties to be computed and output by the routine By default the KRAMERS KRONIG ANALYSIS routine outputs the real and imaginary parts of the dielectric function and as well as the surface energy loss function In addition the following properties can be specified for output Absolute sample thickness Selecting this option outputs the computed absolute thickness The thickness is calculated using the Kramers Kronig sum rule relation as described in EELS Analysis User s Guide Rev 1 2 1 Kramers Kronig Analysis COMPUTE THICKNESS above The result produced here differs slightly however in that the iterative computation takes account of the surface loss component Effective number of electrons per unit vol Select this option to output a calculation of the effective number of electrons per unit volume in units of e nm The effective number of electrons per unit volume can be computed from the imaginary part amp of the dielectric function using Egerton Chapter 4 p 262 2e LEMo Ney e 77 Sa E e E dE mie where amp is the permittivity of free space A the Planck constant e the electronic charge and my the electron rest mass Optical absorption co efficient Ticking this box results in the routine computing and outputting the optical absorption co efficient FE computed from the complex dielectric function using the relationship 1 1 u E Eal
59. UANTIFY tab dialog is as follows Edge List Since edge identification in EELS Analysis is primarily based on the energy of the edge threshold it is useful to have a tabulation of all EELS edges sorted by their threshold energies Such a facility is provided by the scrolling list in the upper left hand portion of the QUANTIFY tabbed dialog which contains a look up table containing the chemical symbol atomic number Z atomic shell index for the transition and the edge threshold energy respectively see Figure 3 29 Whenever EELS Analysis performs an identification of an edge it scrolls through the table then displays and highlights the element with the closet match in energy A marker labeled with the chemical symbol of the element is also displayed on the spectrum image display at the specified threshold energy Depending on whether grouping by shell or sub shell has been specified as described later in this section the sub shell transitions of the specified edge will also be marked as an aid to accurate identification Other possible candidate species with similar onset energies are shown above and below the most likely candidate If you are not satisfied with an identification proposed in the dialog you may select one of the alternate nearby candidates by clicking on it The marker in the spectrum image display window will move to mark the threshold energy of the newly selected edge assuming it is within the spectral energy range Use th
60. a spectrum with respect to another For example after manual alignment of an overlaid spectrum by means of relaxing the horizontal constraints see below selecting this option recalibrates the foreground spectrum using the displayed scale HORIZONTAL CONSTRAINTS is a sub menu facilitating adjustment of the horizontal constraints of the overlaid spectra ATTACHED is the default setting with the spectrum attached to the horizontal axis DETACHED removes this constraint allowing the selected spectrum to be moved freely with respect to the x axis To move the spectrum once DETACHED has been selected double left click on it and drag the mouse with the left button held down Holding down CTRL while performing this action allows the horizontal scaling to be adjusted about the point shown by the vertical marker BASELINE FIXED enables rescaling of the horizontal axis with channel 0 remaining fixed To adjust the spectrum once baseline fixed has been specified double click on the spectrum then drag the mouse with the left button held down and the CTRL key depressed Scale fixed performs the same operation as detached but keeping the horizontal scaling fixed throughout VERTICAL CONSTRAINTS this sub menu provides the same function as described above for HORIZONTAL CONSTRAINTS except in the sense of the y axis DRAW STYLE this sub menu contains options for defining the draw style of the selected spectrum Selecting DRAW FILL toggles the spectrum fi
61. al operations on spectra Mathematical operations are predominantly the domain of the Process menu For arbitrary mathematical manipulations of spectra use the SIMPLE MATH tool The FFT and INvERsE FFT items facilitate custom processing involving Fourier transforms Further spectral processing operations are found within the EELS menu item described in Chapter 3 Concatenation of spectrum segments acquired over different energy ranges is facilitated by SPLICE SPECTRA Various preprogrammed digital filters are also available under the NUMERICAL FILTERS hierarchical menu You can tailor these to your own needs via NUMERICAL FILTER SETUP Analyzing spectra All spectrum analysis commands specific to EELS are grouped under the EELS menu Use the items of this menu to extract sample specific information from EELS spectra Most of the items in this menu are self explanatory and most will automatically prompt you for any required information missing from the EXPERIMENTAL CONDITIONS dialog As their names imply these items help you COMPUTE THICKNESS of the probed area REMOVE PLURAL SCATTERING from the spectrum and perform QUANTIFICATION to establish the elemental composition of your sample and to determine the relative concentrations of the sample s constituents All of these routines have been designed to give you quick efficient access to such information requiring a minimum of input from you and returning results within a few seconds See t
62. an image This image must be of compatible spatial dimensionality to the input data set and containing the appropriate values of the refractive index at corresponding pixels The computed thickness is returned as an image containing a single pixel for single spectra or a line profile for spectrum line traces or a 2D image for spectrum images EELSComputeThicknessKKSumRuleSSD Summary Computes the absolute thickness from a low loss single scattering distribution using the Kramers Kronig sum rule Prototypes image EELSComputeThicknessK KSumRuleSSD image src number RefIndex number E0 number BetaEff number I0 image EELSComputeThicknessK KSumRuleSSD image src number RefIndex number E0 number BetaEff image 10 image EELSComputeThicknessKKSumRuleSSD image src image RefIndex number E0 number BetaEff image 10 Description This function computes the absolute specimen thickness from a low loss single scattering distribution using the Kramers Kronig sum rule It requires as input a calibrated low loss source dataset svc with the plural scattering removed The output of the EELSFourierLogDeconvolveWithZLPModifier routine described below provides a suitable input dataset for this routine In addition the function must be passed values for the refractive index of the material for visible light RefIndex the primary electron beam energy 0 in keV the effective collection semi angle BetaEff in mrad and also the zero loss integral
63. annel the routine will extract the zero loss profile from the spectrum image itself on a spectrum by spectrum basis If the spectrum image does not contain the 0 eV channel you will be requested to specify a low loss single spectrum that is suitable for the zero loss profile to be extracted from This profile will then be applied to each spectrum in the dataset Note that for this routine the output dataset has identical dimensionality to the input dataset The BACKGROUND MobDEL DEFAULTS dialog w Background Model Defaults Xf Fit Model Power Law x Degree 1 v Cancel OK EELS Analysis User s Guide Rev 1 2 1 Background Model 3 5 Background Model The BACKGROUND MODEL sub menu facilitates fitting extrapolation and subtraction of the characteristic energy loss background from your spectrum The sub menu items are described as follows 3 5 1 Preferences A number of models may be used to model the energy dependence of the characteristic background signal Selecting this sub menu item opens the BACKGROUND MODEL DEFAULTS dialog through which the default background model may be defined Figure 3 11 Supported models include power law polynomial or log polynomial functions If polynomial or log polynomial is selected the user may also specify the degree polynomial to be used The model specified in this dialog will be applied when creating all subsequent background models In general the power law background model
64. ata Microsc Microanal and Microstruct 2 1991 245 DIFF DELTA enter here the difference filter shift parameter in eV Please see the discussion of the derivative filters provided under NUMERICAL FILTERS described previously in this section for a detailed explanation of this parameter DIFF SMOOTH enter here the difference filter smoothing parameter in eV Again for details please see the discussion of the derivative filters provided under NUMERICAL FILTERS in the EELS menu STRUCTURE FILTER an additional filter which isolates spectrum structure and eliminates any residual background is applied to the spectrum after its initial derivative transform see above reference Enter the smoothing width in eV of the applied structure filter again please see NUMERICAL FILTERS described earlier in this chapter APPLY POWER LAW NOISE SUPPRESSION this applies a post transform correction to account for the increase in Poisson noise in the source spectrum which in turn is amplified in the transformed spectrum arising from decreasing spectral intensity at increased energy loss The transformed spectrum is multiplied the square root of a power law curve AE where A is an arbitrary constant and R is the noise suppression exponent as specified in the SUPPRESSION EXPONENT R field Since the correction accounts for the decrease in intensity with increasing energy loss the value for R should typically be approximately 2 3 increasing this
65. aw noise suppression Suppression exponent R 3 0 Feature Detection Parameters Low4oss cutoff eV 50 0 Max segment space g Discriminator sigma 2 0 Overlap jump ratio 20 rSl Post Transform Search Parameters Max spatial size pixels fe4 Edge energy spread eV 20 0 Nearest neighbor threshold 10 25 Max no of identifications fio Load Default Settings Notes for Spectrum Imaging Users To perform edge Auto ID on a spectrum image press the AUTO ID with the data set front most If an exploration spectrum taken from the spectrum image is front most then when prompted specify the parent spectrum image as the input dataset The routine will then proceed to search the SI dataset for ionization edges and post the results both to the RESULTS window and to the QUANTIFICATION List As described above for the single spectrum case the search algorithm preferences can be specified in the EDGE AUTO IDENTIFICATION SETUP dialog launched by selecting the z button situated next to the AuTO ID button in the QUANTIFICATION dialog Figure 3 32 The EELS SI version of this dialog contains individual setup preferences for different data acquisition modes single EELS spectrum EELS line scan EELS spectrum images and EFTEM spectrum image hence allowing you to specify search parameters optimized to the data type under analysis When initiating the routine the source data type is determined automatically from the image tags in
66. ayed at the top of the dialog followed by the fit parameters and their current values To constrain a particular parameter click on the appropriate CONSTRAIN PARAMETER VALUE check box The current fit parameter value will be displayed in the VALUE field leave this value unchanged to constrain the fit parameter to its current value or alternatively enter a different value Once complete select OK to close the dialog the fit model will be refreshed to reflect any changes made and any constrained fit parameters will remain unchanged for any subsequent model updates for example if the active fit window is moved Output Fit Values to Results Window This menu item simply outputs the NLLS fitting parameters for the front most spectrum to the RESULTS window For a Gaussian model three fit parameters are output per model peak center width and amplitude To initiate this routine select this sub menu item with the NLLS fitted spectrum of interest front most The fit parameters will be posted in the RESULTS window see Figure 3 25 EELS Analysis User s Guide Rev 1 2 1 Figure 3 27 EELS Analysis User s Guide Rev 1 2 1 NLLS Fitting The SI NLLS FITTING Output Options dialog za SI NLLS Fitting Output Options x r Fit Parameter Output WF es V Don t show constrained values I Reduced chi squared equal weights r Fit Model Output J Individual fit models J Sum of models IV Residual signal
67. ccurs during the first attempt then alert the user with an appropriate error message This would occur if for example hydrogenic cross sections are specified and an M edge is selected or if Hartree Slater cross sections are specified and the H S GOS TABLES folder could not be found in the DigitalMicrograph directory 3 Ifthe computation is successful output the result Output is provided in several forms If requested EELS Analysis outputs the background subtracted edge signals with their corresponding energy differential cross sections do dE to the spectrum s image display for visual comparison Additionally the integrated partial cross section with the ratio of EELS Analysis User s Guide Rev 1 2 1 3 69 3 70 Quantification the integrated partial cross section to the edge counts over the specified integration range is posted to the PRoGrREss floating window If the routine is called by the QUANTIFY routine described below the integrated partial cross section and a complete listing of the computation are logged to the RESULTS window In effect within the limitations of the theory used to compute the cross section do dE is a theoretical model of the edge shape The accuracy and consistency one can expect to achieve in the quantitative reduction of edge signals to elemental concentrations are reflected in the degree of correspondence between the measured edge shape and the theoretical differential cross section p
68. ck on again for both axes Display options revealed by right clicking on a spectrum B High Tc superconductor loj xj Paste Delete ImageDisplay Show Legend 500 550 600 650 700 750 3800 850 Show All o ROI Home Display Hints You can press and release the CTRL key without releasing the mouse to alternately zoom and then translate an axis When you click inside the axes of a spectrum a new ROI is created on the image and the old ones are removed but when you click outside the axis to navigate a spectrum all the ROIs are left intact The LINE PLOT Toots floating window can still be used to navigate spectra but it is generally faster to navigate spectra with the mechanisms described above EELS Analysis User s Guide Rev 1 2 1 Working with Spectra in DigitalMicrograph Figure 2 3 Detailed menu revealed by right clicking the color encoded legend i D High Tc superconductor oj x 60000 Spectrum E der 1 Cut Copy Paste Delete ImageDisplay Hide Legend Counts Hide Log deriv Hide Others Show All Send Behind Bring To Front Zoom To ROI Zoom Vertically To ROI Home Display 650 700 750 800 300 Align Slice By b Energy Loss eV Align Slice Horizontally By gt Calibration Align Slice Vertically By Uncalibrated Units Counts Integral Maximum Horizontal Constraints Baseline Vertical Constraints Draw Style Recalibrate Slice
69. constraining parameters 3 42 outputting results 3 42 preferences 3 40 ROI selection 3 41 to spectrum images 3 43 Numerical filters 3 14 P Plural scattering in thickness calculations 3 22 removal by deconvolution 3 28 Printing overview 2 8 Q Quantification of spectra 3 49 of spectrum images 3 64 procedure 3 63 Quantification List compiling 3 58 description 3 58 loading 3 60 saving 3 60 Quantify dialog 3 66 R Region of interest 2 2 Remove plural scattering 3 28 Fourier log 3 30 Fourier ratio 3 33 from spectrum images 3 32 3 35 preferences 3 29 Report generating 3 75 setting up 3 74 S Second derivative filter 3 16 Sharpen spectra 3 5 spectrum images 3 8 Signal integration window 3 71 Smooth filter 3 15 Spectra acquiring 2 2 analyzing 2 8 calibrating 3 2 cleaning 3 75 moving to other applications 2 7 multiple 2 5 navigating 2 3 printing 2 8 quantifying 3 49 sharpen 3 5 splicing 3 3 summing 3 13 working with 2 2 Spectrum image analysis 3 2 background modeling 3 12 background removal 3 12 calibration 3 3 Fourier log deconvolution 3 32 Fourier ratio deconvolution 3 35 MLLS fitting 3 39 NLLS fitting 3 44 quantification 3 64 sharpening 3 8 splicing 3 4 thickness computation 3 28 zero loss extraction 3 21 Splice spectra 3 3 spectrum images 3 4 T Thickness computation 3 22 all methods 3 27 Kramers Kronig sum rule 3 26 log rati
70. ctra provided might be inadequate for an accurate analysis If the COMPUTE FROM DATA fit weights option is selected via the MLLS FITTING PREFERENCES dialog see above then you will be asked to specify the location of the original source data that the fit spectrum may have originated from for example in the event of MLLS fitting to background extrapolated data Be sure to specify the original source data as acquired in this dialog to ensure a trustworthy x least squares fit parameter is computed In the event that the specified source data is not calibrated in intensity units of primary electrons e you will also be asked to provide confirm the conversion factor from detector counts to primary beam counts for the equipment used to record the data Please read the rest of this section below for more details The computation then proceeds and the optimum fit is output in a new image display If output RESIDUAL MISFIT SIGNAL is selected in the MLLS FITTING PREFERENCES dialog then the misfit residual that is the difference between the fit data and the computed optimum fit will also be displayed A detailed listing of all the fit parameters and their uncertainties by which the quality of the fit may be judged are displayed as appropriate If output FIT REDUCED CHI SQUARED VALUES SIGNAL is selected in the MLLS FITTING PREFERENCES dialog then the reduced x parameter will also be posted If in the above example the fit does not match the s
71. d as the reconvolution function The extracted zero loss peak is well suited as the reconvolution function since it representative of the system resolution However if the zero loss peak contains any asymmetries arising for example from spectrometer misalignment then these will be reintroduced into the deconvolution Alternatively if GAUSSIAN MODIFIER 1s specified then a Gaussian reconvolution function is used with a EELS Analysis User s Guide Rev 1 2 1 3 31 3 32 Remove Plural Scattering FWHM determined using the zero loss width in order to maintain a similar energy resolution as the original data as described in detail by Egerton p 266 As the Gaussian used has the same area as the zero loss integral the resultant spectrum s intensity scale is ensured to be representative of its source The width of the Gaussian function can be altered by changing the value in the GAUSSIAN MODIFIER WIDTH field in units of FWHM with values above unity generally suppress noise while having a smoothing effect on the data and values below unity having a sharpening effect Please note if the low loss spectrum has long tails then the use of a Gaussian reconvolution function will sharpen the spectrum in a similar manner to the SHARPEN SPECTRUM function described above Increase the GAUSSIAN MODIFIER WIDTH value if you wish to counter this effect 6 Perform Fourier transform manipulations The routine next Fourier transforms the modified foreg
72. d hence the user should check the selected settings are suitable via the EDGE SETUP tab and tailor them to their specific spectrum before proceeding with quantification If the selected edge to be added falls outside the energy loss range of the spectrum an alert will be posted informing the user that the operation could not be performed Note also that although sub shells may be identified within the spectrum shell groups only can be added to the QUANTIFICATION LIST e g an Lz edge added to the QUANTIFICATION LIST would be added as an L edge group with Z3 Lz and L contributions x Remove Clicking on this button will remove the highlighted edge from the QUANTIFICATION LIST Replace This will replace the highlighted edge in the QUANTIFICATION List with the highlighted edge in the EDGE List This is particularly useful for replacing any wrongly identified entries in the QUANTIFICATION LIsT after for example performing an edge AUTO ID 5 Clear This button resets the EELS Quantification dialog removing any elements entered in the Quantification List and removing any markers on the spectrum e g edge id markers background model Please note that it is not necessary to have an EELS data set front most to compile a QUANTIFICATION List If the front most image is not an EELS data set or if no images are open a list may be compiled containing any edge s irrespective of energy loss range The compiled list may then be
73. e program has picked out the significant unipolar segments in the difference spectrum it must decide which ones actually represent different edges and which are all part of the fine structure of a single edge The first criterion the routine uses is contiguity All significant lobes that are contiguous with each other are classified as being part of the same edge However sometimes noise and the specific details of the fine structure cause a few non significant segments to appear among the significant ones of an edge The purpose of the MAX SEGMENT SPACE parameter is to make the grouping of contiguous segments more robust With it you specify the maximum number of non significant segments that can intervene between significant ones while still classifying this entire range of the transformed spectrum as belonging to a single edge Increase this parameter if the feature detection routine frequently incorrectly claims to detect edges in among the fine structure of another edge Decrease it if the program tends to lump several successive edges into a single feature OVERLAP JUMP RATIO this is another very heuristic parameter Its purpose is to make the feature detection routine more robust in the face of overlapping edges In such a situation the significant unipolar segments of the two neighboring edges will be completely contiguous especially if the MAX SEGMENT SPACE parameter is nonzero However a common characteristic of edges is that the fine s
74. e spectrum image yields elemental line plots whilst quantification of a 3d spectrum image produces elemental maps Note that log polynomial backgrounds and polynomial background models of order greater than 1 are not supported for use with spectrum images EELS Analysis User s Guide Rev 1 2 1 3 65 Quantification Figure 3 37 3 66 The EELS QuaANnTIFICATION dialog the EDGE SETUP tab 10 xi Quantify Edge Setup Quantification List rBkgd and Signal Windows Offset Width Bkgd 21 0 fie eV Signal o o 25 0 eV Cross Section _ _ _ Background Model Hartree Slater Fit Model Power Law v I Chemical Shit 00 eV Degree fi z A BN on holey carbon 3 14 2 The Edge Setup tab The quantification of an EELS spectrum requires the input of a number of important parameters Some of them such as the beam energy convergence angle and collection angle are read directly from the experimental conditions stored with each spectrum Others such as the background fit and edge integration intervals or the type of cross section to use hydrogenic or Hartree Slater are at your discretion and must be specified separately The EDGE SETUP tabbed dialog is the mechanism by which you can provide EELS Analysis with this discretionary information for each edge to be quantified Selecting this tab reveals a dialog field as shown in Figure 3 37 containing parame
75. e Plural Scattering 3 29 3 10 1 Preferences 3 30 3 10 2 Fourier log 3 30 3 10 3 Fourier ratio 3 33 3 11 MLLS Fitting 3 35 3 11 1 Preferences 3 36 3 11 2 Perform Fitting 3 36 3 12 NLLS Fitting 3 39 EELS Analysis User s Guide Rev 1 2 1 EELS Analysis User s Guide Rev 1 2 1 3 12 1 Preferences 3 40 3 12 2 Fit Gaussian to ROI 3 41 3 12 3 Constrain Model Parameters 3 42 3 12 4 Output Fit Values to Results Window 3 42 3 12 5 Apply Model to Parent Spectrum Image 3 43 3 13 Kramers Kronig Analysis 3 44 3 14 Quantification 3 49 3 14 1 The Quantify tab 3 50 3 14 2 The Edge Setup tab 3 66 3 15 Report 3 75 3 15 1 Preferences 3 75 3 15 2 Generate Report 3 75 3 16 Clean Spectrum 3 75 The EELS Analysis Script Interface 4 1 4 1 EELS Script Commands 4 1 4 2 Adding Custom Zero Loss Models 4 9 Index I 1 viii EELS Analysis User s Guide Rev 1 2 1 Figure 2 1 Figure 2 2 Figure 2 3 Figure 3 1 Figure 3 2 Figure 3 3 Figure 3 4 Figure 3 5 Figure 3 6 Figure 3 7 Figure 3 8 Figure 3 9 Figure 3 10 Figure 3 11 Figure 3 12 Figure 3 13 Figure 3 14 Figure 3 15 Figure 3 16 Figure 3 17 EELS Analysis User s Guide Rev 1 2 1 List of Figures EELS spectrum with region of interest ROI marker 2 3 Display options revealed by right clicking on a spectrum 2 4 Detailed menu revealed by right clicking the color encoded legend 2 5 The EELS menu 3 1 Specifying the single spectrum or parent spectrum image datas
76. e affect both the Fourier log and Fourier ratio deconvolution routines The zero loss model to be used is specified in the ZERO Loss PEAK REMOVAL pull down list Selecting UsE EXTRACT ZERO LOSS SETTING designates the zero loss model to be as specified in the ZERO Loss REMOVAL preferences dialog please refer to the ZERO Loss REMOVAL section above for more details The RECONVOLUTION METHOD pull down list allows the reconvolution modifier described below to be specified as the extracted zero loss or alternatively as a Gaussian function If a Gaussian function is selected then the Gaussian modifier width can be specified as a multiple of the measured zero loss peak width in the GAUSSIAN MODIFIER WIDTH field Fourier log deconvolution of a low loss spectrum F Latex low loss E l x Deconvolved Oo al Low loss spectrum a as recorded a Low loss spectrum with plural scattering removed by Fourier log deconvolution counts x 1044 Fourier log Select this item to correct a spectrum for plural scattering by the Fourier log method see Egerton pp 245 254 262 264 In principle this method correctly removes plural scattering from all energy loss regions of the spectrum at the same time making it a very efficient procedure However for the practical reasons explained below Fourier log deconvolution is typically only applied to low loss spectra The FOURIER LOG routine requires only a single inpu
77. e effective atomic number of the material at corresponding pixels The computed thickness is returned as an image of identical spatial dimensionality as the src array but with no energy loss dimension hence this is an image containing a single pixel for single spectra or a line profile for spectrum line traces or a 2D image for spectrum images EELSComputeThicknessKKSumRule Computes the absolute thickness from a low loss spectrum using the Kramers Kronig sum rule applying a correction to account for plural scattering image EELSComputeThicknessKK SumRule image src number RefIndex number E0 number BetaEff number ZLPIndex image EELSComputeThicknessKKSumRule image src image RefIndex number E0 number BetaEff number ZLPIndex This function computes the absolute specimen thickness from a low loss spectrum or spectrum image with plural scattering still in place using the Kramers Kronig sum rule followed by an approximate correction to account for the effect of plural scattering In addition to the calibrated source low loss dataset src the function must be passed values for the refractive index of the EELS Analysis User s Guide Rev 1 2 EELS Script Commands material for visible light RefIndex the primary electron energy EO in keV the effective collection semi angle BetaEff in mrad and also the zero loss model index ZLPIndex Note that for spectrum image analysis the parameter RefIndex can also be specified as
78. e items allow you to specify whether signal extraction information cross section parameters and background removal information should be placed in the report also A typical example of a post quantification printout generated in this way is shown in Figure 3 41 3 15 2 Generate Report Selecting this item generates a report of the selected spectrum prepared in page format for printing and displaying the spectrum with title experimental conditions and any quantification results on a page Additional text output can be specified via the EELS REPORT PREFERENCES dialog described above The page attributes may be adjusted in the PAGE SETUP menu item located in the FILE menu The font attributes may be determined prior to or after preparation for printing by specifying the text options accordingly in the OBJECT menu 3 16 Clean Spectrum This menu item removes all quantification related markers and sub images from the front most spectrum e g background model edge id markers EELS Analysis User s Guide Rev 1 2 1 3 75 4 1 Summary Prototypes Description EELS Analysis User s Guide Rev 1 2 The EELS Analysis Script Interface The EELS Analysis software contains script commands for accessing the majority of the EELS analysis functionality via custom scripts Using these commands complex analysis procedures can be automated and integrated with for example custom acquisition routines The first part of section will list these
79. e refractive index for visible light of the material S E is the single scattering distribution 2 the collection semi angle and 6z is referred to as the characteristic scattering angle at an energy E If the spectrum has not had plural scattering removed then an approximate correction factor C is also applied to the value of to correct for plural scattering following the relationship given by EELS Analysis User s Guide Rev 1 2 1 3 27 3 28 3 9 5 Compute Thickness C 1 0 3 A 0 3In I Note that this correction becomes increasingly less valid with increasing specimen thickness and hence it is advised to remove plural scattering using Fourier log deconvolution beforehand Please refer to Egerton Chapter 5 pp 307 310 for a detailed discussion regarding the use of this technique for thickness determination 6 Output Result The result is output as appropriate in units of nm see Figure 3 17 Further the thickness value and the calculated zero loss and total spectrum intensity integrals are written to the spectrum s IMAGE DISPLAY INFO tags All Methods Selecting this menu item will compute the sample thickness using all three methods described above Please refer to the appropriate section above for a detailed account of each specific technique Notes for Spectrum Imaging Users To perform the above thickness computations on a spectrum image select the appropriate menu item with either the spectrum image
80. e scroll bar to scan through the look up table and view additional candidates in either direction along the energy loss scale Note double clicking on an entry in the EDGE List will automatically zoom the spectrum about the selected edge to aid visualization If a spectrum image is front most then the spectrum image s display will also automatically shift to the corresponding energy loss EELS SI only The order and content of the EDGE List may be selected using the radio buttons to the left of the look up table these items are described in the following two sub sections If you are satisfied that the highlighted element corresponds to a genuine core loss feature in your spectrum and you wish to add it to the QUANTIFY List for quantification do so by selecting the gt button at the center of the dialog described in greater detail later in this section Sort by These radio buttons allow the user to specify the EDGE List ordering options are by increasing energy loss atomic number Z or alphabetically by chemical symbol It should be noted that the content of the list remains unaffected by changing this option EELS Analysis User s Guide Rev 1 2 1 3 51 Figure 3 30 3 52 Quantification Group by This item allows grouping within the element list by shell or sub shell determining if sub shell transitions are listed in addition to the major transition for each shell Select the SUBSHELL radio button to display and hence
81. e zero loss extrapolation range are set to zero d Finally the inelastic signal is then subtracted from the original spectrum to yield the output zero loss peak Note for advanced users the Gaussian fit ranges to the left and right of the zero loss center can be adjusted by opening EELS gt SETTINGS gt ZERO LOSS MODELS gt 2 GAUSSIAN in the GLOBAL INFO tags and entering an appropriate value in units of HWHM in the appropriate fields Additionally the post fitting clean up step c can be disabled by setting the PERFORM POST FIT CLEANING tag to false Gaussian amp Lorentzian fit This model uses least squares fitting to fit the sum of a single Gaussian and a Lorentzian function to the zero loss peak The Lorentzian function has long tails and hence this model is suited to spectra recorded on detectors with high point spread Specifically it a fits a single Gaussian to the zero loss peak to accurately measure the zero loss center and half width half maximum HWHM then b attempts to fit a Gaussian and a Lorentzian model to the spectrum over a fitting region by default from 6 to 3 times the zero loss HWHM either side of the zero loss center An AMOEBA simplex algorithm is used to perform the least squares fitting c The sum of the Gaussian models is subtracted from the original spectrum to yield the inelastic signal All channels from the beginning of the spectrum range to the rightmost negative count EELS Analysis User s Guide Rev 1
82. eate a solid vertical marker Left click dragging on this marker will now allow you to offset the spectrum slice horizontally Holding down CTRL while performing this action will allow you to change the horizontal scaling Repeat for all of the spectrum slices you wish to align 3 Once the spectra are aligned to your satisfaction select the SUM OVERLAID SPECTRA menu item with the image display front most The summed spectrum will be displayed in a new image window Figure 3 14 The NUMERICAL FILTERS PREFERENCES dialog xi r Smooth Low pass _ r Structure High pass we 20 0 ev it w 60 0 Va rM First Log Derivative r Second Derivative dE 0 0 ev oft we roo ev oi w 200 ev ile w oo ev e m Load defaults for _Lowsesotition 3 _Highresolution 32 OK Cancel 3 7 Numerical Filters The NUMERICAL FILTERS hierarchical menu provides a variety of filtering routines primarily for noise and background reduction These filters may be carried out on single spectra spectrum line traces or EELS EFTEM spectrum images alike 3 7 1 Preferences The PREFERENCES item initiates a dialog for specifying the various filter parameters used in these operations see Figure 3 14 Numerical filtering is of interest for noise and background reduction and additionally for revealing 3 14 EELS Analysis User s Guide Rev 1 2 1 Numerical Fi
83. ed in the following section The list of edges to be quantified is passed to the analysis routine along with the spectrum acquisition details which quantifies each entry in the list in turn EELS Analysis User s Guide Rev 1 2 1 3 61 3 62 Quantification Each edge in the QUANTIFICATION LIST is reduced to a numerical value that reflects the projected concentration atoms nm of the element to which it corresponds Please note that the value returned represents the average concentration projected through thickness over the specimen area probed by the electrons that are allowed to enter the spectrometer aperture It then goes one step further and converts these two pieces of information along with the low loss spectrum integral when available to an estimate of the elemental concentration Finally a relative quantification is performed to represent each elemental concentration as a ratio to the element of highest concentration and also as a percentage of the total species quantified Once complete a visual representation of the analysis is displayed in the spectrums image display and a compositional summary is logged to the RESULTS window as shown in Figure 3 35 The physics behind the analysis performed by this routine is described fully in Egerton s book pp 277 283 The fundamental relationship is given by I Nlo where N is the areal concentration atoms nm of the atoms giving rise to the ionization edge k J i
84. en subtracted from the original spectrum to yield the output zero loss peak Note for advanced users the reflected tail cutoff point may be varied by opening EELS gt SETTINGS gt ZERO LOSS MODELS gt REFLECTED TAIL in the GLOBAL INFO tags and entering an appropriate value in units of FWQM in the REFLECTED TAIL cut off field Additionally the post extrapolation clean up EELS Analysis User s Guide Rev 1 2 1 Zero Loss Removal step g can be disabled by setting the PERFORM POST FIT CLEANING tag to FALSE Fitted log tail This simple model fits and extrapolates a logarithmic function to model the ve energy loss tail of the zero loss peak Since the model is relatively simple and as the fitting range may be user specified it is both robust and versatile On initiating the routine the user is requested via a dialog to specify the log model fitting range The fit range is measured in eV with respect to the zero loss peak maximum by default from 2eV to 4eV loss The dialog also contains checkboxes for specifying i to have the specified range remembered for future use and ii to suppress displaying the dialog in future computations The routine then proceeds as follows a the position of the zero loss peak maximum is measured b the fit range is replicated and a log transform is applied c a straight line is least squares fitted over the fit range note all non positive channels are ignored d using the fit coefficients the ve los
85. endeV number degree This routine performs the same function as described above for EELSComputePolynomialBackground but instead fitting a log polynomial function Please refer to EELSComputePolynomialBackground for details EELSSubtractPowerLawBackground Computes and subtracts a power law background from a spectrum image EELSSubtractPowerLawBackground image src number starteV number endeV This command performs the same function as described above for EELSComputePowerLawBackground but performs the extra step of subtracting the computed background from the source dataset to return the background subtracted signal Refer to EELSComputePowerLawBackground above for further details EELSSubtractPolynomialBackground Computes and subtracts an n degree polynomial background from a spectrum image EELSSubtractPolynomialBackground image src number starteV number endeV number degree This command performs the same function as described above for EELSComputePolynomialBackground but performs the extra step of subtracting the computed background from the source spectrum to return the background subtracted signal Refer to EELSComputePolynomialBackground above for further details EELS Analysis User s Guide Rev 1 2 Summary Prototype Description Summary Prototype Description Summary Prototype Description Summary Prototype Description Summary EELS Analysis User s Guide Rev 1 2 EELS Scrip
86. epositioned or resized by moving or resizing the ROI labeled BKGD as described above under EXTRAPOLATE BACKGROUND Spectrum Controls In addition to the QUANTIFICATION and the EDGE SETUP tab dialog fields described above the EELS QUANTIFICATION dialog also contains five buttons as described below EELS Analysis User s Guide Rev 1 2 1 3 73 Figure 3 40 Figure 3 41 3 74 Quantification the spectrum region of interest image window The EELS REPORT PREFERENCES dialog w EELS Report Preferences xj J Format for printing in new image window Always format for printing after quantification J Output signal extraction information T Output cross section parameters Tl Output background removal information Cancel OK ZERO Y refreshes the spectrum display with the zero intensity baseline at the bottom of the image window RESCALE Y initiates a vertical rescaling of the displayed portion of ZOOM TO ROI redisplays the spectrum zoomed in on the selected Home redisplays the whole spectrum auto scaled to fit within the Quantification results prepared using the REPORT menu items BN on holey carbon section 200 300 400 500 600 Energy Loss eV Experimental Conditions am Energy 200 kev Convergence Angle 2 mrad Collection Angle 2 8 mrad Composition Information Elem Atomic ratio C N Percent content Areal density Catoms
87. es i xj Number of defect channels to ignore at the edges of the spectra 4 Number of overlap channels used to calculate the splice scaling factor fi 0 Cancel OK Splice The items in the SPLICE sub menu allow you to piece together a single continuous spectrum from two segments acquired over different but overlapping energy loss ranges The individual sub menu items are described below Preferences To change the default preferences used when performing the SPLICE SPECTRUM procedure described below select the PREFERENCES menu item in the SPLICE sub menu to open the preferences dialog shown above in Figure 3 6 Via this dialog the user can specify the number of channels either end of the spectrum to discard and also the number of overlapping channels to consider in the calculation of the scaling factor Discarding the initial or final channels of a spectrum is useful for detectors that have a few channels of bad data at either end The purpose of changing the number of channels used in calculating the scaling factor is to ensure that the splicing procedure does not produce artifacts The default values for these parameters 4 for the number of channels to discard and 10 for the number of channels to consider in calculating the scaling factor work well in most cases Figure 3 7 3 4 3 3 2 Splice The SPLICE SPECTRUM dialog Spice Specta S Please select the spectrum to splice with BN low loss 1 from
88. es the smallest power of 2 that is at least 1 5 times the number of non zero channels in the selected spectrum Remove truncation discontinuities in the target spectrum To avoid artifact ringing due to truncation the routine next smoothly extrapolates the endpoints of the spectrum to be sharpened to zero using a cosine bell function Prepare deconvolution function Because of the noise in any measured spectrum a simplistic deconvolution of the entire zero loss profile will cause the Fourier components of the noise to dominate those of the deconvolved spectrum resulting in a useless result The important point is not to try to recover more than the inherent resolution of the spectrum which is reflected in the steepness of the central portion of the zero loss peak The method used here is to fit a Gaussian to the narrow central portion of the zero loss peak and to replace that portion of the peak with a 6 function of equal area The Gaussian portion is isolated by fitting a Gaussian to EELS Analysis User s Guide Rev 1 2 1 3 7 Figure 3 11 Sharpen the zero loss peak data over the range that is within 90 of the zero loss peak amplitude minimum of three channels The fit is subtracted negative residual values being set to zero The total count differential between this processed result and the original deconvolution function is placed in the single channel which previously contained the maximum of the zero loss peak This modif
89. et for analysis 3 3 Fourier log deconvolution of an EELS SI in progress 3 3 The EXPERIMENTAL CONDITIONS dialog 3 5 Calibrating the spectrum energy scale 3 2 The SPLICE PREFERENCES dialog 3 3 The SPLICE SPECTRUM dialog 3 4 The SHARPEN SPECTRUM PREFERENCES dialog 3 5 Low loss sharpening by deconvolution of the zero loss peak tails 3 6 Core loss sharpening by deconvolution of the zero loss peak tails 3 6 The BACKGROUND MODEL DEFAULTS dialog 3 8 Power law background modeling under a core loss edge 3 10 Example of the SUM OVERLAID SPECTRA command 3 13 The NUMERICAL FILTERS PREFERENCES dialog 3 14 The ZERO LOSS EXTRACTION PREFERENCES dialog 3 17 The COMPUTE THICKNESS PREFERENCES dialog 3 24 Log ratio thickness calculation using the COMPUTE THICKNESS routine 3 24 Figure 3 18 Figure 3 19 Figure 3 20 Figure 3 21 Figure 3 22 Figure 3 23 Figure 3 24 Figure 3 25 Figure 3 26 Figure 3 27 Figure 3 28 Figure 3 29 Figure 3 30 Figure 3 31 Figure 3 32 Figure 3 33 Figure 3 34 Figure 3 35 Figure 3 36 Figure 3 37 Figure 3 38 Figure 3 39 Figure 3 40 Figure 3 41 The FOURIER DECONVOLUTION PREFERENCES dialog 3 29 Fourier log deconvolution of a low loss spectrum 3 30 Selecting the appropriate low loss spectrum for Fourier ratio deconvolution 3 33 Fourier ratio deconvolution of a core loss edge 3 34 The MLLS FITTING PREFERENCES dialog 3 35 Specifying reference models spectra for MLLS fitting 3 37 The
90. evaluated It should also be remarked that the geometric portion of the convergence angle correction the factor B a is not included EELS Analysis User s Guide Rev 1 2 1 3 67 3 68 Quantification in the cross section calculation but is applied directly to the low loss spectrum when necessary For example computation of an actual elemental concentration requires the ratio of edge counts to total low loss spectrum counts In this case the geometric convergence correction is applied to the total spectrum counts before taking the ratio Another difference between EELS Analysis s hydrogenic calculation and that of SIGMAK2 and SIGMAL2 is in the interpolation and integration of do dE Whereas Egerton s programs primarily sample the differential cross section at equally spaced energy intervals usually 10eV and integrate it with the assumption of a power law dependence EELS Analysis s approach is to use exponentially varying sample intervals i e fine sampling 1 eV near the edge threshold coarse sampling gt 10eV well beyond it and cubic spline interpolation and integration This optimizes the time consuming evaluation and integration of the generalized oscillator strength GOS over momentum transfer and shortens the overall computation time for a given level of precision One last difference is that in SIGMAL2 Egerton switches from an L23 GOS to an L23 L GOS whenever the sampled energy coordinate is above the L edge th
91. f these two types of cross sections at the user interface level You must simply indicate your preferred calculation method in the EDGE SETUP dialog With one or two exceptions all differences between the routines lie in internal technical details that are largely transparent to you Whereas the hydrogenic GOS is evaluated via closed form analytic expressions encoded within EELS Analysis the Hartree Slater GOS is read from edge specific table files stored in the H S GOS Tables folder of your DigitalMicrograph directory Note that this means that you can replace the GOS data with more accurate EELS Analysis User s Guide Rev 1 2 1 Quantification tabulations which you may compute yourself or receive from another source The GOS files are in ASCII format so that they may be easily read and edited Apart from the different GOS data the Hartree Slater calculations also differ from the hydrogenic ones on a few technical points Instead of using Egerton s method convergence angle correction is included directly within the GOS integral over momentum transfer by means of the aperture cross correlation method developed by Kohl in the following reference H Kohl A simple procedure for evaluating effective scattering cross sections in STEM Ultramicroscopy 16 1985 265 Another difference is that Egerton s SIGMAL2 computes the L23 doublet as a single contribution while EELS Analysis s Hartree Slater routine computes each component of
92. fied selections EELS Analysis User s Guide Rev 1 2 1 3 49 Figure 3 29 3 50 Quantification for the spectrum under analysis It also contains tools for initiating the quantification process and for managing pre defined lists of edges and their signal extraction parameters for quantification referred to as quantification templates The second group EDGE SETUP gives complete control over the signal extraction parameters for each edge to be quantified The procedure is designed to allow the user to rapidly extract and summarize elemental composition information for single or multiple edges from loss spectra All intermediate calculations such as calculated background contributions and computed edge cross section profiles are displayed with automatic refresh so that you can check on what the program is doing and adjust parameters accordingly for optimal results The final quantification results are logged to the RESULTS window The EELS QuaANTIFICATION dialog the QUANTIFY tab fra EELS Quantification lonization threshold energy Atomic shell 3 14 1 The Quantify tab The first thing any EELS edge analysis program must do is establish which spectral features are edges of interest and which ionization transitions and therefore which elements they represent Because the onset of an edge occurs at a fairly fixed energy loss compared to the typical separations between edges EELS edges can in the main be
93. fitted background as an array of identical dimensionality and size as the source array Note also that if 4 1 4 2 Summary Prototype Description Summary Prototype Description Summary Prototype Description Summary Prototype Description EELS Script Commands the routine is called with the extra image parameters redChi2 A and r and the number parameter meanEnergy then these parameters will be returned containing the background fit reduced chi background scaling constant background slope exponent and mean background window energy value s accordingly EELSComputePolynomialBackground Computes an n degree polynomial background to a spectrum image EELSComputePolynomialBackground image src number starteV number endeV number degree This function calculates an n degree polynomial background where n 0 3 for a spectrum or spectrum image The background is least squares fitted over the specified fitting range The function requires the calibrated source data set src the background fitting start and end energy losses starteV and endeV specified in calibrated units and the polynomial degree degree The routine returns the computed background model as an array of identical dimensionality and size as the source array EELSComputeLogPolynomialBackground Computes an n degree log polynomial background to a spectrum image EELSComputeLogPolynomialBackground image src number starteV number
94. fo dialog If the output image is a spectrum image the energy range being displayed may not contain any information Use the SLICE floating palette opened by selecting SLICE in the FLOATING WINDOWS sub menu located in the WINDOws menu to change the displayed energy range to contain information Alternatively the spectrum image exploration tool can be used to explore the output dataset Please refer to the appropriate documentation for details on using these visualization tools The image may genuinely contain no information In this instance check the error text output in the progress floating palette If the algorithm is failing at each spectrum in the dataset then abort the process and i ensure EELS Analysis User s Guide Rev 1 2 1 Figure 3 4 EELS Analysis User s Guide Rev 1 2 1 3 1 the input data is appropriate for the analysis being performed and ii specify alternate algorithm preference settings if appropriate before proceeding The EXPERIMENTAL CONDITIONS dialog x B BN on holey carbon Global Beam energy keV 200 09 Convergence angle mrad 20 Collection angle mrad 28 Cancel OK Experimental Conditions This item initiates the EXPERIMENTAL CONDITIONS dialog Figure 3 4 Use this dialog to record the physical parameters of your particular acquisition setup It is not necessary that you supply values for all the fields However in order to carry out quantitative elemental analyses accurate
95. g the left hand mouse button reposition the background fitting region by dragging it to a new position Alternatively left clicking on the low energy or high energy boundaries and dragging allows the fitting region to be resized The arrow keys can be used to the same effect with the left and right keys moving the window left and right by single channel increments respectively and the up and down keys increasing and decreasing the width of the fitting region The modeled background contribution and background subtracted spectrum are recalculated and redisplayed as the model parameters are altered making it very convenient to interactively modify the background fit interval to get the best possible background fit To extract either the background model or subtracted edge and place it in its own image display use the EXTRACT BACKGROUND MODEL or SUBTRACT BACKGROUND commands respectively as described later in this section 3 5 3 Change Current Model This routine allows the attributes for an existing background model to be altered To initiate this function select the menu item with the appropriate spectrum front most A dialog similar to the BACKGROUND MODEL DEFAULTS dialog shown in Figure 3 11 will open allowing you to alter the model attributes while viewing the effect of any changes on the spectrum Note that changes initiated here will apply to the selected spectrum only and will have no effect on the global background model defaults see PR
96. hape of the unknown very well and x turns out to be considerably greater than 1 then something other than a simple mixture of the two oxide phases is indicated for your unknown If output FIT UNCERTAINTIES is selected then the fit uncertainty ois also output Note this 3 37 3 38 MLLS Fitting output is only available if the USE FIT WEIGHTS COMPUTED FROM DATA option is selected see below As mentioned above the USE FIT WEIGHTS pull down menu in the MLLS FITTING PREFERENCES dialog allows you to specify the type of weighting to use whenever a x least squares fit parameter is computed during MLLS fitting The weighting of data points has significant influence on the fit results and it completely determines the interpretability of the reduced y parameter as a measure of the goodness of fit For a detailed discussion of this topic and of multiple linear fitting in general please refer to the following P R Bevington Data Reduction and Error Analysis for the Physical Sciences McGraw Hill Book Company New York 1969 chs 5 10 W H Press B P Flannery S A Teukolsky and W T Vetterling Numerical Recipes The Art of Scientific Computing Cambridge University Press New York 1985 ch 14 When calculating a fit it is usually desirable to weight each data point inversely to its measurement uncertainty In other words points which have large error bars should not be given as much weight in determining the best fit as tho
97. hat this correction has been made Thus the quantification routine knows that Egerton s Equation 4 64 applies If deconvolution has not been applied Equation 4 65 is used instead to correct for the effects of plural scattering If there is no zero loss information available in your spectrum absolute quantification cannot be computed outright and EELS Analysis will output the result relative to the undetermined low loss integral Yet another form of the fundamental expression can be used when J is not available e g because the low loss part of the spectrum was not measured EELS Analysis User s Guide Rev 1 2 1 Quantification and provides a useful and reliable method of quantification even when Jp is available In this case elemental atomic ratios can be extracted from a spectrum following Egerton Equation 4 67 i Lal A o p B A N 7 1 B A O alB A where the subscripts a and b represent different elemental species j and k are shell indices and 2 and A represent the scattering capture semi angle angle and signal integration width respectively This approach offers the additional benefit of being largely insensitive to the effects of plural scattering provided similar signal integration windows are applied and can correct in part the inaccuracies in computing the inelastic cross sections involved if edges of similar type are used EELS Analysis utilizes this latter relationship also representing the concentration
98. have been used throughout In the unlikely event that this cannot be found then you will be prompted to specify this value explicitly EELS Analysis User s Guide Rev 1 2 1 3 47 3 48 Kramers Kronig Analysis 2 Prepare data The truncation at the high energy loss end of the data is extrapolated effectively to zero a high energy using an AE power law model Since Fourier transforms are used later in the routine the data is first copied to an array of a size determined the smallest power of 2 that will accommodate the data from 0eV up to the minimum specified extrapolation energy loss which is by default 500eV The power law scaling constant A and slope exponent r are measured using by default a fitting range of 5 the input array size Finally any low energy loss residual noise left over from the zero loss and or Fourier log deconvolution procedures is cleaned using a procedure that zeros all the channels from channel 0 up to and including the last non positive channel before a threshold energy loss SeV by default 3 Perform angular corrections Angular corrections are applied to the input data to yield an energy loss distribution that is proportional to the energy loss function Im 1 e E The angular correction accommodates the influences of the convergence and collection angles on the recorded spectrum 4 Compute the proportionality constant K and thickness estimate t The energy loss function Im 1 e E
99. hbors having only half weighting Appropriate corrections are made to account for image boundary effects Any spatial distribution maps that have a nearest neighbor ratio below the threshold EELS Analysis User s Guide Rev 1 2 1 3 57 3 58 Quantification value specified in the NEAREST NEIGHBOR THRESHOLD field in the EELS SI EDGE AUTO IDENTIFICATION SETUP dialog is treated as a misidentification and omitted from the next step 6 Identify and group edge identification clusters A one dimensional edge identification occurrence histogram is compiled from the edge list post nearest neighbor filtering The maximum occurrence energy is then searched for and all identifications from the original edge energy list within an energy spread dE as defined in the EDGE ENERGY SPREAD field of the EELS SI EDGE AUTO IDENTIFICATION SETUP dialog are used to compile an edge threshold distribution image The value dE represents the uncertainty in the edge energy identification process which can arise for example through chromatic effects edge chemical shift and general uncertainties in the auto id algorithm The threshold energy for the identification is taken as the mean energy loss for the image The procedure is then repeated searching for the next occurrence maximum until all identifications have been grouped 7 Truncate identifications to maximum number of identifications If the total number of edge identifications exceeds the maximum permi
100. he calculated zero loss and total spectrum intensity integrals are written to the spectrum s IMAGE DISPLAY INFO tags for later use by other routines If SHow CALCULATED COMPONENTS is selected in the COMPUTE THICKNESS PREFERENCES dialog then the extracted zero loss peak is also displayed in a new image display and the zero loss and total spectrum integrals are output as appropriate 3 9 3 Log Ratio absolute The COMPUTE THICKNESS by LOG RATIO ABSOLUTE routine carries out the same calculations as described for LOG RATIO RELATIVE above but goes one step further and converts the relative thickness value to an absolute value based on a calculation of the inelastic MFP derived from the effective atomic number of the material under investigation Specifically it carries out following steps EELS Analysis User s Guide Rev 1 2 1 3 25 3 26 3 9 4 Compute Thickness 1 Prompt the user for spectrum specific parameters The LoG RATIO ABSOLUTE routine requires some additional information regarding the spectrum in order to compute the inelastic mean free path 4 This is achieved using the parameterized approach as described by Malis et al as described in the following reference T Malis S C Cheng and R F Egerton EELS log ratio technique for specimen thickness measurement in theTEM J Electron Microscope Technique 8 1988 193 It should be noted that this method is valid only for high refractive index materials metal
101. he detailed descriptions of these items in Chapter 3 for limitations on their applicability Obtaining printouts You will find printing commands situated in the FILE menu Additionally the contents of the REPORT sub menu in the EELS menu provides the functionality to automatically format the spectrum within the image display for printing as a report together with the spectrum title and a text description of the experimental conditions and any signal extraction parameters specified This sub menu is explained in greater detail in Section 3 15 EELS Analysis User s Guide Rev 1 2 1 3 The EELS menu Figure 3 1 EELS Analysis User s Guide Rev 1 2 The EELS menu shown in Figure 3 1 contains the analysis routines you need to extract physical data about your specimen from its EELS spectrum Suitably acquired spectra will yield information such as relative specimen thickness and relative or absolute concentrations of chemical constituents In contrast to the generic mathematical tools provided by the Process menu the routines of the EELS menu are specifically tailored to act on EELS spectra Most of the routines are optimized for spectra obtained with Gatan EELS systems The following sections give brief descriptions of the techniques used in each of the analysis routines Further details may be found in the references listed in each section and in the book Electron Energy Loss Spectroscopy in the Electron Microscope 2 Edition Ple
102. he list of edges that EELS Analysis will attempt to quantify in the next call to the QUANTIFY routine described later in this section The QUANTIFICATION LIST may be compiled in a number of ways It can be compiled directly from by identifying an edge via the EDGE List and then adding it as described below In this way a list can be built up edge by edge until all suspected edges are included Alternatively the AUTo ID function described above can be used to automatically identify and add detected edges to EELS Analysis User s Guide Rev 1 2 1 Quantification the list Finally a previously compiled and saved quantification template can be loaded as described later in this section enabling multiple spectra with similar compositions to be analyzed rapidly using a common QUANTIFICATION LIST There are three buttons situated between the EDGE List and the QUANTIFICATION List that facilitate the addition and removal of edges to and from the QUANTIFICATION LIST gt Add Clicking on this button will add the edge selected in the EDGE LIST to the QUANTIFICATION List Edges added to the quantification list will automatically have appropriate default signal extraction parameters assigned to them which can be viewed and adjusted via the EDGE SETUP tab see Section 3 14 2 for further details Please note though that these default parameters do not take into account spectrum specific factors such as preceding edges or chemical shifts an
103. his value is usually measured and noted by the Gatan engineer at installation for photodiode array detectors it is usually in the range 20 30 and for CCD detectors it is more often in the range 1 3 The inverse of the estimated uncertainty is then incorporated as the weighting factor in any fit computation Please note that the Poisson uncertainty estimate in the spectral data points does not take account of apparent noise due to the detector channel to channel gain variation or to any fixed pattern in the dark count background Thus be prepared to see relatively large values of reduced x when performing fit analyses on EELS spectra that have not been corrected for these detector artifacts The simple Poisson estimate also does not consider true noise in the dark count background so even when detector corrected spectra are analyzed EELS Analysis User s Guide Rev 1 2 1 NLLS Fitting the y values may sometimes be somewhat larger than expected Note that if there are any non positive values in the specified spectral range the fit weights can no longer be computed from the data a warning will be posted and the fit weights method will revert to EQUAL TO 1 Equal to 1 If you prefer to weight each point of your data set equally then choose this option Please be aware however that with this option the magnitude of the reduced x value returned by any of the analysis routines no longer provides any meaningful measure of the quality
104. ied deconvolution function is then normalized to an integral of 1 and it is shifted with endpoint wraparound so that the function peak is in channel 0 These last two steps ensure that the deconvolved spectrum contains the same number of counts as the original and that there is no horizontal offset between them Perform Fourier transform manipulations The two inputs suitably prepared the routine next Fourier transforms them using a Fast Fourier Transform FFT algorithm It divides the spectrum transform by the deconvolution function transform using complex arithmetic and inverse Fourier transforms the result Output result Finally the resultant deconvolved spectrum is displayed in a new image display Notes for Spectrum Imaging Users To sharpen a spectrum image dataset select the SHARPEN SPECTRUM menu item with either the spectrum image or an associated exploration spectrum taken from the spectrum image front most If an exploration spectrum is front most specify the parent spectrum image as the input dataset when prompted If SPECIFY A SEPARATE ZERO LOSS PROFILE is selected in the SHARPEN SPECTRUM PREFERENCES dialog you will then be requested to specify a suitable single spectrum zero loss profile to be used in the sharpen algorithm If EXTRACT THE ZERO LOSS PROFILE USING THE MODEL BELOW is selected in the preferences dialog the routine will follow one of the following two routes If the spectrum image contains the 0 eV ch
105. ing region are discussed above in the EXTRAPOLATE BACKGROUND section When selecting a signal integration range for quantitative analysis it is best to choose an energy interval that either completely integrates through the near edge fine structure or starts somewhere beyond it Integrating over near edge structure can introduce a quantification error as the signal integral may be affected by changes in chemical state as well as elemental concentration On the other hand going too far past the edge threshold can lead to very large background extrapolation errors and also increases the chance of erroneously including counts from succeeding edges Typically an interval 50 100 eV in width and starting either at the edge threshold or 30 50 eV beyond it gives fairly consistent results In practice because of the leading edge tail which results from the substantial zero loss peak tails it is actually often beneficial to start the integration range 5 10 eV before the edge threshold to make sure all edge counts are included Note that the default integration interval provided does exactly that It starts 5 eV before the edge threshold and extends with the interval width being dependent on the edge threshold energy Caution must be EELS Analysis User s Guide Rev 1 2 1 Quantification taken to ensure the signal integration window does not overlap any other edges and is situated within an energy loss range where the calculated background contrib
106. ing language is both assumed and required for more details on the scripting language visit the Gatan web site for on line help http www gatan com software and or refer to the Scripting section in the DigitalMicrograph help section opened by hitting F1 from the DigitalMicrograph application For convenience it is recommended you test your algorithm thoroughly before adding it to the zero loss model manager since error messages essential for debugging purposes are suppressed by the menu driven routines To test your algorithm for debugging purposes set the debug parameter in the above script to 1 and execute the script as normal using ctrl return within DigitalMicrograph to apply it to the front most image Once satisfied that your routine is reliable set the debug value back to 0 and install the script as part of the scripting library To do this select the INSTALL SCRIPT item in the FILE menu with your custom script front most click on the LIBRARY tab and specify an appropriate library name for your routine this will be used to identify your script if removing it in the future Once installed restart DigitalMicrograph to reinitiate the zero loss model manager If successful your algorithm should be situated in the zero loss model pull down list of all appropriate EELS ANALYSIS PREFERENCES dialogs If you wish to remove your custom algorithm for example in the event of the model producing errors or for modification p
107. ing up and performing multiple linear least squares MLLS fitting Specifically the sub menu commands perform the following 3 35 3 36 3 11 1 3 11 2 MLLS Fitting Preferences Selecting this sub menu item will open the MLLS FITTING PREFERENCES dialog as shown above in Figure 3 22 The USE FIT WEIGHTS pull down menu allows you to specify whether the MLLS fit weights are set equal to 1 or computed from the source data The implications of the selection made here are explained in detail later in this sub section The output RESIDUAL MISFIT SIGNAL output FIT REDUCED CHI SQUARED VALUES and output FIT UNCERTAINTIES tick boxes allow you to specify if these quantities are output by the MLLS fitting routine Again these options are explained in greater detail below Perform Fitting This command performs a MLLS fit of any spectra and or models to a specified portion of the selected spectrum In more precise terms the program forms a model function consisting of a linear combination of the specified spectra and or models and then fits that model to the foreground spectrum by adjusting the coefficient of each linear term to minimize the square deviation between the model and the selected spectrum In effect this command is a general linear fitting facility that can be applied to the analysis of overlapping edges and superimposed fine structure For example suppose you have a specimen that you know to be a fine grained co
108. is User s Guide Rev 1 2 1 Figure 3 23 EELS Analysis User s Guide Rev 1 2 1 MLLS Fitting Specifying reference models spectra for MLLS fitting Multiple LLS Fit x Please select the reference models spectra to be used in MLLS fitting A Spectrum 0 GliceO C Silicon oxide reference Edge Ac Spectrum O Bkad puj B Si reference C Silicon oxide reference SliceO SSE D Silicon nitride reference C Silicon oxide reference Bkgd Cancel If the fit spectrum has one or more image slices you will first be asked to specify which slice you wish to perform MLL S fitting on Next you will be prompted to specify the spectra or models to be used in the fit see Figure 3 23 at least two valid and appropriate spectra must be specified for the procedure to commence You are then prompted to specify confirm the range over which you wish to perform the fit Please note that if you placed an ROI on the fit spectrum before executing this command to specify the fitting region then the values corresponding to the ROI range will be in the appropriate dialog fields If the reference spectra do not cover fully the specified range a suitable alert will be posted In the event that the reference spectra have dispersions different to the spectrum to be fitted to they will be interpolated to the same eV ch Ifthe interpolation factor is deemed to be too extreme then a warning will be posted to inform the user that the reference spe
109. isplay labeled appropriately for identification When the DON T SHOW CONSTRAINED VALUES option is selected constrained parameters are not output Please refer to the CONSTRAIN MODEL FIT PARAMETERS section above for more details regarding constraining model fit parameters Selecting this option is recommended since by their nature constrained parameters will contain no variation within the output data since each pixel will be set to the constrained value 3 43 3 44 3 13 Kramers Kronig Analysis Reduced chi squared equal weights Selecting this option outputs a goodness of fit image in the form of a reduced chi squared image The FIT MODELS group of items contains items for specifying the output of the computed models themselves or their by products Note that each output image will have the same dimensionality as the input dataset i e will have the same width height and dispersion size The output options in this group perform the following Individual Fit Models Selecting this option will output an individual computed model for each fitting region specified Sum of Models Selecting this option will result in the sum of all the individual fit models being output Note that this option is enabled only when 2 or more NLLS models are being fitted Residual Signal When selected the residual signal will be output that is the misfit between the input spectrum and the sum of all the individual fit model
110. ith respect to the image window s original spectrum By CALIBRATION aligns the spectra by the x and y axis calibrated units By UNCALIBRATED UNITS aligns the spectra by the channel number and uncalibrated counts ALIGN SLICE HORIZONTALLY By provides a sub menu for horizontally aligning overlaid spectra with respect to the image window s original spectrum The sub menu items are as for ALIGN SLICE By described above except the alignment is performed horizontally only ALIGN SLICE VERTICALLY By provides a sub menu for vertically aligning overlaid spectra with respect to the image window s original spectrum The first two sub menu items CALIBRATION and UNCALIBRATED UNITS are as for the ALIGN SLICE By item described above except the alignment is performed vertically only Selecting INTEGRAL performs a y axis alignment rescaling the overlaid spectrum to have equal integral area to the original spectrum The alignment may be performed over the full range of the image window or over a discrete region denoted by an ROI Selecting MAxImuM rescales the vertical scaling or region of as defined by an ROI to give equal maxima Choosing BASELINE aligns spectra with respect to their vertical baselines EELS Analysis User s Guide Rev 1 2 1 Working with Spectra in DigitalMicrograph RECALIBRATE SLICE performs an x axis recalibration on the selected spectrum using the current spectrum display calibration This command is useful for calibrating
111. ject spectrum i e have the same degree of spectral smoothing arising from the point spread function b the reference zero loss peak is rebinned to the same dispersion as the low loss spectrum if necessary c the zero loss center position of both the reference spectrum and the low loss spectrum are found by least squares fitting a Gaussian function to their zero loss peaks over a fitting region by default of 2 HWHM on the low energy loss side to 1 HWHM on the high energy loss side where HWHM is the half width half maximum of the zero loss peak d the reference zero loss peak is aligned with the low loss zero loss peak using sub channel interpolation e an intensity scaling factor is established by computing the intensity ratio over a fitting region by default from 1 75 to 3eV in loss measured with respect to the zero loss maximum and then f the spectrum is replicated up to the fitting mid point and is spliced with EELS Analysis User s Guide Rev 1 2 1 3 19 3 20 Zero Loss Removal the scaled aligned zero loss reference beyond this point up to the first ve channel or reference array end to give the elastic peak g The elastic peak is subtracted from the low loss spectrum to yield the inelastic signal h all channels from the beginning of the spectrum range to the rightmost negative count residual in the inelastic signal up to SeV loss by default are set to zero i the inelastic signal is then subtracted from the original
112. lected then the SHARPEN SPECTRUM routine will ask you to specify explicitly the zero loss profile to use from a list compiled from the dimensionally compatible open images In this instance the specified zero loss profile is assumed to not need extraction and hence a model does not need to be specified in the ZERO LOSS MODEL pull down list which will be inactive Alternatively if the EXTRACT THE ZERO LOSS PROFILE USING THE MODEL BELOW option is specified then the routine will follow one of two routes If the spectrum to be sharpened contains the 0 eV loss channel then it will attempt to automatically extract the zero loss reference from this spectrum If it does not the routine will prompt you to specify an appropriate low loss spectrum from which a zero loss peak can be extracted Whichever route is followed the zero loss peak will be extracted using the model specified in the ZERO LOSS MODEL pull down list For a more in depth description of the EELS ANALYSIS procedure zero loss removal please refer to EXTRACT ZERO Loss later in this section EELS Analysis User s Guide Rev 1 2 1 3 5 Figure 3 9 Figure 3 10 Sharpen Low loss sharpening by deconvolution of the zero loss peak tails K BN low loss E lol x Sharpened Counts lt 1043 20 10 o 10 20 30 40 50 60 70 80 Energy Loss ev Core loss sharpening by deconvolution of the zero loss peak tails G BN core loss 5 x Counts 1043 200
113. lectron counts This conversion factor should have been measured for your system at installation and will be initiated automatically when required Notes for Spectrum Imaging Users This version of EELS Analysis contains functionality for EELS analysis of spectrum image datasets enabling each of the items in the EELS menu to be applicable not only to single spectra but also to spectrum line traces and spectrum images This advance adds a new dimension of flexibility and potential to your EELS analysis capabilities allowing complex EELS processing and analyses to be applied to entire spectrum image datasets enabling results previously only measurable as a single value to be computed and visualized as a line plot or map This functionality referred to as EELS SI Analysis throughout this documentation requires the spectrum imaging package to be installed in your version of DigitalMicrograph The EELS SI Analysis routines use the same core algorithms as their single spectrum counterparts and are applied iteratively on a pixel be pixel basis Hence for these analyses the output datasets have the same spatial dimensionality as the input data Depending on the analysis performed the output may also have identical or similar energy loss dimensions as the input data or alternatively will have no dispersion information at all For example consider an analysis that yields another spectrum as output when applied to a single spectrum e g removal
114. ll appear in a new image display This routine checks the suitability of the inputs and takes specific measures to minimize noise amplification The exact procedures are as follows Check inputs The program first checks that the front image contains spectrum data If the spectrum contains a zero loss peak and if told to do so it then extracts the zero loss peak from the spectrum using the zero loss model specified in the SHARPEN SPECTRUM PREFERENCES dialog please refer to EXTRACT ZERO Loss later in this chapter for details Otherwise it uses the zero loss peak as specified by the user which must be an open and calibrated single spectrum containing the OeV channel within its range Finally it checks that the specified zero loss spectrum is in fact a symmetrical zero loss peak If not the routine posts a suitable warning Ensure identical dispersions Based on the dispersion of the spectrum to be sharpened the zero loss spectrum is interpolated to the same eV ch if required If the ratio of the dispersions exceeds a factor of two then a warning is posted to alert the user that the accuracy of the routine may be compromised Determine size of Fourier transform to be used Based on the range of non zero channels in each of the inputs the routine next establishes the number of channels needed for the Fourier transform computations In order to provide enough empty buffer channels to allow for smooth extrapolations the routine choos
115. lling DRAW LINE toggles the spectrum outline FILL COLOR allows the color of the spectrum filling to be defined LINE COLOR enables the color of the spectrum outline to be altered 2 4 4 Moving spectra among image displays and to other applications To move spectra among image displays within DigitalMicrograph use the CUT Copy and PASTE items from the Epit menu They work very much the same way as they do in other Windows applications placing copies of the selected data into a temporary storage area CUT Copy and copying its contents to the foreground image display PASTE If an ROI is placed on the spectrum then these functions will operate on the sub image as defined by the ROI bounds You can paste data into a new image display by pressing Ctrl Alt V simultaneously You may also use the EDIT menu commands to transfer data from the foreground spectrum to any application capable of handling this information for example to your favorite spreadsheet application If you wish to copy and paste the actual image representation within your spectrum s image window convert the spectrum to an RGB image by selecting CREATE IMAGE FROM DISPLAY in the OBJECT menu An RGB image representation will be displayed in a new image window which may then be transferred to other applications supporting this image type EELS Analysis User s Guide Rev 1 2 1 2 7 2 5 2 6 2 7 Performing mathematical operations on spectra Performing mathematic
116. loss and is dispersive in dimension 0 The empty zero loss array zlp is also passed to the function Place the extracted zero loss data into zlp as calibrated void ExtractZLP object self image lowloss image amp zlp A crude amp simple example method just attenuate the zero loss peak at the specified energy First initialise the zlp array zlp 0 Get the lowloss image size amp calibration information from the lowloss spectrum number e channels lowloss ImageGetDimensionSize 0 number scale lowloss ImageGetDimensionScale 0 number offset lowloss ImageGetDimensionOrigin 0 number attenuate_ch fAttenuateEnergy offset scale If the attenuation channel is within the spectrum bounds copy the zero loss data if e_channels gt attenuate_ch zlp 0 0 1 attenuate_ch lowloss 0 0 1 attenuate_ch If not throw an error else Throw Error Zero loss attenuation channel is out of the image bounds Below are preference tag handling functions enables preference default values for the zlp fitting parameters to be written to the Global tags using GetDefaultPreferences Each time the algorithm is then used it then takes the value if present from the Global Tags Hence the user can change these through the Global Info dialog box if desired NOTE not strictly neccessary can hard code the parameters in ExtractZLP and leave these functions empty for simplicity
117. lters features or variations that may normally be obscured by the accompanying electron energy loss signal First and second difference filters are particularly useful within this context Hence the main applications of the NUMERICAL FILTERS are 1 Background reduction to make edge signals easier to distinguish and 2 Transformation of previously acquired reference spectra such as those of the EELS atlas for comparison to newly acquired spectra All filter parameters are specified in eV the calibrated unit in the energy loss plane rather than in channels The actual number of channels of shift or averaging is thus a function of the spectrum eV channel The significance of each filter parameter and its precise interpretation for each filter routine is described fully under the appropriate subheading of this section Two buttons are also provided to allow the user to quickly set preset default filter values appropriate for the mode in which the spectral information was acquired The HIGH RESOLUTION button sets values suitable for analysis of spectral information acquired in spectroscopy mode as a spectrum spectrum line trace or spectrum image Alternatively the Low RESOLUTION button sets values suitable for lower spectral resolution information acquired for example as an EFTEM spectrum image The default values for these options may in turn be altered to suit preference selecting the 2 button situated next to the appropriate defaul
118. m via Fourier Log deconvolution the routine simply takes the counts in the modeled zero loss peak as required by Egerton s Equation 4 64 Otherwise it sums the counts up to an energy loss equal to the width of the integration range as required by Egerton s Equation 4 65 Finally if the convergence angle is greater than the collection angle the resultant low loss spectrum integral is multiplied by the geometric portion of the convergence angle correction factor f a If the low loss region of the spectrum is not available the computation proceeds but the result is computed relative to the undetermined low loss integral only EELS Analysis User s Guide Rev 1 2 1 3 63 Figure 3 36 3 64 Quantification 4 Compute the absolute concentration of the element corresponding to the selected edge The routine divides the edge signal obtained in step 1 by the cross section computed in step 2 If the low loss data was available the result is divided by the spectrum count integral determined in step 3 to yield an absolute projected concentration in atoms nm If not the absolute projected concentration is computed relative to the undetermined low loss integral 5 Compute relative concentrations using all the results from all the edges analyzed After steps 1 3 are repeated for each edge in the QUANTIFY LIST the individual results are ratioed to the most abundant species in the analysis thus yielding an atomic concentration ratio
119. mbination of two oxide phases each of which has a distinct oxygen K near edge fine structure that you have measured previously from a pure sample of each phase You find that from any area you are able to probe in your unknown the oxygen K edge structure always appears to be some mixture of that of the two pure forms But is it just a linear combination of the two pure forms as one might expect of a simple mixture or is an alteration of the electronic structure and or a third phase indicated One way to shed light on this question is to attempt a MLLS fit of the pure phase oxygen K edge profiles to that of the unknown In order to do so you must make sure that all three spectra 2 standards and unknown have been acquired under the same conditions and preferably with the same eV channel It also particularly important that the energy scales of the three spectra are accurately calibrated and aligned using the applied drift tube voltage i e no assumptions should be made about the oxygen K edge threshold position in each spectrum The oxygen K edges of the three spectra must then be isolated using the EXTRACT BACKGROUND SUBTRACTED SIGNAL command as described in the BACKGROUND MODEL section above Then invoke the PERFORM FIT command with the spectrum to fit to front most Please note that at least two other suitable spectra must be open to perform this command if not an appropriate alert will be posted and the process halted EELS Analys
120. meters for each edge in the list specified via the EDGE SETUP dialog tab see Section 3 14 2 Figure 3 34 The LOAD QUANTIFICATION TEMPLATES dialog Load Quantification Template xi Please choose a Quantification Template Delete 316 stainless steel Generic biological High Tc superconductor Semiconductor Cancel 5 Load This button initiates a dialog that allows saved quantification templates to be recalled and applied to the spectrum of interest Figure 3 34 The main part of the dialog consists of a list of quantification templates currently contained within the EELS Quantification Templates folder in your DigitalMicrograph directory To select the template of your choice simply click on it to highlight it Selecting OK will then load and apply the template to the current spectrum Note that any edges falling outside the energy range of the spectrum will be excluded an alert will be posted to inform you of this There is also a DELETE button to allow you to remove any unwanted templates just highlight the appropriate entry and press this button 3 60 EELS Analysis User s Guide Rev 1 2 1 Quantification Figure 3 35 Post quantification results A BN on holey carbon Cee escren Energy Loss eV 3 x welcome to DigitalMicrograph 16 05 2002 15 13 56 EELS Analysis of BN on holey carbon Beam Energy 200 kev convergence Angle
121. nd to hand that task over to a well designed computer program with a good deal of built in knowledge about the technique In this way you are free to concentrate more on the implications of your experimental results rather than on the details of acquiring them and the tedium of the data reduction The analysis routines built into DigitalMicrograph EELS Analysis follow wherever possible a similar or often identical approach to that adopted in EL P Accordingly many of the procedures described should be familiar to past users Continuing the underlying philosophy of EL P the EELS Analysis routines encapsulate many details in a few high level commands that lead you directly to the results for which you performed EELS in the first place In this user guide we attempt to describe the connection between DigitalMicrograph s EELS Analysis commands and real world EELS analysis Each section starts with a given generic task one might wish to perform in the course of EELS analysis and proceeds with a description of how that task can be performed with the specific facilities available within EELS Analysis Chapter 2 provides an overview outlining the general procedure for acquiring and analyzing spectra with DigitalMicrograph This is followed in Chapter 3 by a more thorough discussion of each command within the EELS menu i e precisely what it does when and how to use it its adjustable parameters and its basis in the literature described in order of
122. ngle must be large enough so that the plural scattering obeys Poisson statistics This is an implicit assumption of the log ratio calculation method Additionally the use of Fourier log deconvolution to obtain the single scattering distribution as input to the Kramers Kronig sum rule also relies on this please refer to the section regarding removal of plural scattering for more details Fortunately this condition is not overly restrictive due to a serendipitous property of the angular distributions of the plural scattering components as described in the following references 1 R F Egerton and S H Liou A remarkable property of the angular distribution of plural inelastic scattering with benign consequences for the deconvolution of electron energy loss spectra Proc of the 47th Ann EMSA Meeting 1989 380 2 R F Egerton and Z L Wang Plural scattering deconvolution of electron energy loss spectra recorded with an angle limiting aperture Ultramicroscopy 32 1990 137 According to the above works a collection semi angle of 5 10 mrad suffices to ensure Poisson statistics to within 10 accuracy for typical beam and edge energies In this case the effect of the finite acceptance aperture can be subsumed as collection angle dependence of the inelastic MFP The safest way to use the COMPUTE THICKNESS routines is for comparing the thickness of similar samples The actions of the individual sub menu items are described below EELS
123. nm 2 B 0 98 0 6 1 9 16240 139 49 45 16e 011 9 2e 010 sum spec N 1 00 0 000 50 55 6 2 9 37e 011 9 4e 010 sum spec Signal Extraction Elem Signal counts Integration range ev 8 2 04e 005 523 188 0 213 0 N 3 02e 004 217 401 0 426 0 Cross Section Parameters Elem Edge Type Cross section barns Cross section model B K 2230 22 Hartree S ater e N K 323 32 Hartree 5later Background Removal Elem Fitting range eV Mode Red chi 2 167 0 183 0 power aw N 358 0 393 0 power law 0 06 EELS Analysis User s Guide Rev 1 2 1 Report 3 15 Report The REPORT sub menu contains items to facilitate the preparation of spectra for output to a printing device It contains the following sub menu items 3 15 1 Preferences Selecting this sub menu item initiates the EELS REPORT PREFERENCES dialog which contains a number of tick boxes see Figure 3 40 Tick the FORMAT FOR PRINTING IN NEW IMAGE WINDOW tick box for a copy of the source spectrum to be generated and displayed suitable for printing in a new image window If this tick box is left blank the source spectrum will be displayed suitable for printing in it s original image display When ticked the second tick box ALWAYS FORMAT FOR PRINTING AFTER QUANTIFICATION will automatically prepare the spectrum and quantification results for printing after quantification of the spectrum has been performed The last thre
124. nomial backgrounds and polynomial background models of order greater than 1 are not supported for spectrum imaging use Extract Background Subtracted Signal Use this command to permanently subtract the active background model from the spectrum yielding the background extrapolated signal displayed in a new image window To initiate this routine a spectrum must be front most with an active background model present The routine duplicates the background subtracted core loss signal and displays it in a new image window Note that the extracted background subtracted signal will be inactive and hence will not change in response to any alteration of the background fitting or modeling parameters on the source spectrum Notes for Spectrum Imaging Users To perform background subtraction on a spectrum image perform the ROI set up procedure as described above for the single spectrum case on an exploration spectrum taken from the spectrum image Select the EXTRACT BACKGROUND SUBTRACTED SIGNAL menu item and specify the parent spectrum image for background subtraction The background subtraction will then be applied on a pixel by pixel basis on the spectrum image using the fitting region and background model specified on the exploration spectrum The background subtracted signal dataset which will have the same dimensionality as the input data will be displayed in a new image window This routine applied is identical to the Create Backg
125. ns the MLLS fitted data as an array of dimensionality identical to the input dataset over the specified fitting range The return arrays ValList SigmaList and RedChiSqu contain the individual fit coefficients the individual fit coefficient uncertainties and the overall reduced chi for the fit respectively ValList and SigmaList are object lists and contain an image for each reference spectrum specified hence for two spectra the two fit coefficient images can be retrieved using image vall ValList ObjectAt 0 GetImage image val2 ValList ObjectAt 1 GetImage and likewise for the fit uncertainties RedChiSqu is returned as a conventional image The dimensionality of the returned array images are determined by the dimensionality of the source dataset hence an image is returned containing a single pixel for single spectra a line profile for a spectrum line trace or a 2D image for a spectrum image Adding Custom Zero Loss Models As mentioned in Section 3 8 ZERO LOss REMOVAL custom zero loss models written in the DigitalMicrograph scripting language can be added to the EXTRACT ZERO LOss routine This is achieved by adding the custom routine to the zero loss model manager hence allowing your own zero loss removal procedure to be accessed from all commands in the EELS ANALYsIS menu that use zero loss removal via the appropriate zero loss model pull down menu in the PREFERENCES dialog An example algorithm which should be used as a
126. num Press New York 1996 by Egerton This is an excellent text which is considered widely as an essential reference book for anyone involved in EELS The EELS menu EELS a Se 7 Experimental Conditions Calibrate Energy Scale Splice gt Sharpen gt Background Model Sum Overlaid Spectra Numerical Filters gt Zero Loss b Compute Thickness Remove Plural Scattering gt MLLS Fitting b NLLS Fitting Kramers Kronig Analysis Quantification Report b Clean Spectrum 3 1 An important distinction between the analysis routines described in this chapter and the processing routines contained in the PROcEss menu is that analysis usually involves some level of data reduction In other words a small number of physical parameters are extracted from the spectrum data points usually by way of least squares fitting techniques The significance of the derived parameters is typically indicated by the inclusion of an estimated uncertainty or standard error in the derived result which is propagated from uncertainties in the original data points Many of the routines below perform this propagation of uncertainties and indicate them by means of a value following the extracted quantity The uncertainties in the measured EELS data points from which the error propagation proceeds are estimated assuming Poisson counting noise and a constant conversion factor from displayed detector counts to true primary beam e
127. o absolute 3 25 log ratio relative 3 24 of spectrum images 3 28 preferences 3 23 Z Zero loss custom models 3 21 default models 3 18 extraction 3 17 preferences 3 17 removal 3 17 removal from spectrum images 3 21 EELS Analysis User s Guide Rev 1
128. of each constituent element specified for quantification as a ratio to the element of highest concentration in effect as an atomic concentration ratio If only one element is specified then the ratio returned is unity Here is a synopsis of the procedures performed by QUANTIFY 1 Extract the edge counts from an edge entry in the QUANTIFY LIST After signal extraction is performed the intensity is integrated over the specified signal integration window to yield the partial edge count integral Please refer to Section 3 14 2 later in this chapter for information regarding how the background extrapolation and edge signal integration parameters are determined 2 Calculate the partial inelastic scattering cross section on the same edge and integration range Once the energy differential cross section has been calculated using the specified theoretical model it is integrated over the defined signal integration window for that edge to give the partial inelastic scattering cross section A specific account of the calculation of the cross sections used is described in the CROSS SECTION sub section below 3 Determine the total low loss spectrum counts The routine checks whether the low loss part of the spectrum is included in the spectrum If it is the routine proceeds to integrate the low loss counts for input into the expression for the elemental concentration as discussed above If plural scattering has been removed from the spectru
129. of plural scattering by Fourier deconvolution When such an analysis is applied to a spectrum image the output data will have the same dimensionality as the input dataset that is be a spectrum image e g a spectrum image with plural scattering removed Alternatively in the case where an analysis produces a single value result when applied to a single spectrum e g computing the relative thickness this analysis will produce an image with the same spatial dimensionality as the source line plot spectrum image but with no dispersion information e g output a thickness plot or thickness map Hence in this instance the output dataset will have one dimension less than the source data for example the output from a three dimensional spectrum image will be a two dimensional map It is useful to consider the dimensionality of the output dataset when choosing the optimal DigitalMicrograph tools for visualizing and exploring your results EELS Analysis User s Guide Rev 1 2 1 Figure 3 2 Figure 3 3 EELS Analysis User s Guide Rev 1 2 1 Specifying the single spectrum or parent spectrum image dataset for analysis ima EELS Fourier log Deconvolution The selected spectrum has a parent spectrum image Apply to the single spectrum 2 parent spectrum image Cancel OK The procedure and criteria for performing the EELS Analysis commands on spectrum images are on the whole identical to those described for single
130. of the fit Its value is still minimized by the fitting routine to achieve the best possible fit but this minimum now reflects the average square deviation of each fitted point from the corresponding measured value rather than having a value near in the case of a good fit Notes for Spectrum Imaging Users MLLS fitting is a very powerful tool for spectrum image analysis since it can be used to extract accurately the core loss signal from overlapping core loss edges in instances where conventional background subtracted mapping fails If correctly performed the fit co efficient maps are directly proportional to the integrated core loss signal Additionally it can be used to measure and hence map chemical phase concentrations by quantitatively matching the shape of a specific core loss edge to the best fit of a linear combination of suitably chosen reference models again if performed correctly the fit coefficient datasets can be interpreted as the relative contribution maps of each reference model To perform MLLS fitting on a spectrum image select the appropriate menu item with either the spectrum image or an associated exploration spectrum taken from the spectrum image front most If an exploration spectrum is front most specify the parent spectrum image as the input dataset when prompted Then proceed with the routine as described for the single spectrum case above Note that the reference models must still be single spectra Some of the o
131. oms molecules per cubic nm at each pixel corresponding to the source dataset The criteria for source data suitability are the same as described above i e the dataset should contain the 0eV loss channel and have the plural scattering removed prior to performing this analysis The dimensionalities of some of the output properties e g the real and imaginary parts of the dielectric function the surface loss component the effective number of electrons are identical to the input dataset Other properties e g absolute thickness will be output as maps or line plots of identical spatial dimensionality of the input data Note that the algorithm assumes that the 0eV channel is correctly calibrated for every spectrum contained in the spectrum image hence the spectral calibration should be checked to be accurate and any achromaticity within the dataset should be measured and removed beforehand using for example the CORRECT ZERO LOSS CENTERING routine described above 3 14 Quantification This item initiates the EELS QUANTIFICATION dialog which contains a number of edge identification and analysis tools enabling quantitative analysis of EELS edges to yield elemental concentrations It is split into two distinct sections that may be accessed by clicking on the appropriately labeled tags The first group of analysis commands labeled QUANTIFY contains tools for edge identification and pre quantification selection of individual edges or pre speci
132. oned front most The requirements of this routine are 1 The spectrum s energy scale must be calibrated 3 17 3 18 Zero Loss Removal 2 It must be a low loss spectrum i e it must include the zero loss peak 3 The zero loss peak must not be too close to the left edge of the detector i e its leading tail should not be truncated If the first requirement is not met the routine will post a suitable alert and you will need to calibrate the energy scale before proceeding further If the last requirement is not met the procedure will continue but bear in mind that truncation of the zero loss leading tail may be detrimental to the accuracy of the results produced The extracted zero loss peak is displayed in addition to the inelastic component if specified in a new image display and any supplementary information posted as appropriate The extracted zero loss peak serves as a convenient input for the SHARPEN RESOLUTION routine see Section 3 4 above The routine has a number of pre defined routines for extracting the zero loss peak In addition user defined custom models can be added for further flexibility as described later in this section The preset zero loss models are described below Reflected tail This model is fast robust and well suited to the majority of cases It is therefore recommended for general use Because the tails of the zero loss peak can contain a substantial number of counts relative to the loss
133. ont most If an exploration spectrum is front most specify the parent spectrum image as the input dataset when prompted Note that the outputted extracted zero loss and inelastic signal datasets have identical dimensionality as the input dataset If output EXTRACTED SIGNAL INTEGRAL S is specified in the ZERO LOSS REMOVAL PREFERENCES dialog then the output datasets will have the same spatial dimensionality as the input dataset but no spectral information hence these datasets will be output as either line plots from spectrum line traces or maps from 3d spectrum images Compute Thickness The COMPUTE THICKNESS sub menu contains items for computing the relative or absolute specimen thickness from a low loss spectrum The commands calculate the specimen thickness using one of three different methods log ratio relative log ratio absolute and the Kramers Kronig sum rule The result as implied by the selected spectrum is returned in relative units of the mean free path MFP for inelastic scattering or absolute units of nm depending on the computation method used See Egerton pp 302 312 for a detailed discussion of thickness measurement by EELS Please note that the thickness returned by these routines is influenced by a number of experimental parameters The following is a list of the most EELS Analysis User s Guide Rev 1 2 1 Compute Thickness important conditions that must be met in order to achieve consistent and accurate
134. or associated exploration spectrum taken from the spectrum image front most If an exploration spectrum is front most specify the parent spectrum image as the input dataset when prompted Note that when computing thickness by the LoG RATIO ABSOLUTE method the EFFECTIVE ATOMIC NUMBER field in the COMPUTE THICKNESS dialog will allow not only a mean value of the materials effective atomic number to be specified but in addition an image to be specified for instances where the refractive index varies over the acquisition region This image should be of the same spatial dimensionality as the source dataset and contain the appropriate effective atomic number at pixels corresponding to those of the source data Likewise the REFRACTIVE INDEX field displayed in the COMPUTE THICKNESS dialog when computing thickness using the KRAMERS KRONIG SUM RULE also allows an image to be specified instead of a mean value Again the image must be of compatible spatial dimensionality as the input dataset and it should containing the appropriate refractive index at each pixel corresponding to those of the source dataset The output thickness dataset s will have identical spatial dimensionality to the input dataset but no spectral dimension Hence the output will be either a thickness line plot for a spectrum line trace as input or a thickness map for a 3d spectrum image If SHow CALCULATED COMPONENTS is specified in the COMPUTE THICKNESS PREFERENCES dialog then
135. orrect Zero Loss Centering SI users only Select this item to correct the zero loss peak centering with respect to the calibrated zero loss center from a spectrum line trace or spectrum image using a pre measured zero loss position map This procedure is useful for example for removing any zero loss drift from arising from chromatic effects or microscope high tension instability To perform this procedure select this menu item with the spectrum image front most The routine will then prompt you to specify the corresponding zero loss drift map from a list of the open images that are dimensionally compatible The selected image should contain the calibrated deviation of the input data s zero loss peak position the mean zero loss energy output of the EXTRACT ZERO LOSS routine as described above is ideal for this purpose If the zero loss position map is calibrated in incompatible units then an appropriate error will be posted to inform you that the calibrated units will be ignored In this event a shift calculated from the deviation of the uncalibrated zero loss position value from the mean of the zero loss position map will be applied Once complete the corrected spectrum image will be displayed in a new image window Notes for Spectrum Imaging Users To perform zero loss extraction from a spectrum image select the EXTRACT ZERO LOSS menu item with either the spectrum image or associated exploration spectrum taken from the spectrum image fr
136. ovides an ideal ZLP array Note that in the case of spectrum imaging analysis the ZLP array can be either a single spectrum or alternatively a dimensionally compatible spectrum image array i e the same spatial dimensionality as the src array If the latter is specified then the core loss spectrum at a given pixel will be sharpened using the zero loss profile extracted at the corresponding pixel co ordinate EELSSpliceSpectrum Splices two overlapping spectra to produce a single continuous spectrum image EELSSpliceSpectrum image srcl image src2 number BadChannels number ChannelsToA verage This routine splices two overlapping spectra taking into account any changes in spectral intensity and dispersion to yield a single continuous spectrum Please refer to Section 3 3 for more details on the algorithm used The routine requires two calibrated source spectra or spectrum images src and src2 whose calibrated dispersions overlap If spectrum images are specified then they must be dimensionally compatible i e have the same spatial dimensionality In addition two other parameters must be specified BadChannels refers to the number of channels at the end of the spectra to ignore and GoodChannelsToAverage is the number of valid overlap channels to use to determine the splice scaling factor The spliced image is returned as an array that is dimensionally similar to the input arrays EELSMLLSFit MLLS fit multiple reference spectra
137. parameters before the routine proceeds In addition the Kramers Kronig sum rule requires the refractive index for visible light for the material under investigation This may be approximated to any high value for metals and most semi conductors a value of 1000 will suffice with a more accurate value required otherwise 3 Obtain the zero loss integral Zo The zero loss integral is required for this procedure This value is read automatically form the spectrum s tags in the case of spectra with plural scattering removed using the Fourier log deconvolution command described in the following section If the spectrum has not had plural scattering removed by deconvolution then the routine will subtract the zero loss peak and isolate the zero loss counts using the procedure described in step 2 for COMPUTE THICKNESS by LOG RATIO above In the event that the zero loss integral cannot be deduced via the appropriate route you will be prompted to specify this value explicitly 4 Correct for spectrum truncation The high energy tail of the spectrum is extrapolated using the procedure described in step 3 for COMPUTE THICKNESS by LOG RATIO described above 5 Compute absolute thickness t The Kramers Kronig sum rule approach to computing specimen thickness t utilizes the following relationship 40 FE j S E dE I l n 4 Elnd B 62 where ay is the Bohr radius F is a relativistic factor Ey the beam energy Jp the zero loss intensity n th
138. part of the integral should be taken to avoid singularities at E E Numerical evaluation of the Kramers Kronig transformation is computationally demanding Instead the transform can be evaluated more efficiently using the Fourier based procedure of Johnson a detailed description of which can be found in Egerton Chapter 4 pp 259 260 Finally once Re 1 E has been retrieved the real and imaginary parts of the dielectric function can be calculated from Im 1 e E and Re 1 e E via the relationship assuming that the beam is perpendicular to the sample surface which is clean and oxide free EELS Analysis User s Guide Rev 1 2 1 3 45 3 46 Kramers Kronig Analysis Rell E iIm 1 Z Re l e E Im 1 e E In practice the surface loss contribution should be taken into account This is added as a refinement to the above based on first estimates of and 2 The computed surface contribution is subtracted from the single scattering distribution a new proportionality constant computed and the procedure iterated until convergence is reached e E 6 E E Since the energy loss function is related to the single scattering distribution S E the Kramers Kronig analysis routine requires as input a low loss spectrum including information down to and below OeV loss with plural scattering removed beforehand using ideally the EELS Analysis FOURIER LOG deconvolution routine described abo
139. recommended that inexperienced users apply this model since it is found to yield the most satisfactory results in the majority of cases EELS Analysis User s Guide Rev 1 2 1 3 9 Figure 3 12 3 10 Background Model Power law background modeling under a core loss edge A NiO with Cu impurity 10 x z FAN Background E fitting region Bia Core loss edge with background removed B W T Extrapolated background model 650 700 750 800 850 300 350 1000 1050 1100 1150 1200 1250 1300 ev To extrapolate the background below a core loss edge first define the portion of the pre edge background to be modeled and extrapolated by selecting a rectangular ROI over the desired range To do this with the pointer tool selected hold the left mouse button drag the mouse until the region is defined and then release Typically a range starting 40 50 eV before the edge threshold and 25 eV in width serves well for this purpose A good account of how to choose the optimal background fitting region widths and positioning for a given edge may be found in the following references 1 Liu D R and Brown L M Influence of some practical factors on background extrapolation in EELS quantification J Microsc 147 1987 37 49 2 Joy D C and Maher D M The quantitation of electron energy loss spectra J Microsc 124 1981 37 48 Please note that the routine requires the spectrum energy scale to be ro
140. reshold Since the L threshold may lie between two sample points small errors can result from this approach EELS Analysis computes the Lz and L contributions completely independently from their respective thresholds so that no artifacts are introduced at the L threshold Hartree Slater model The Hartree Slater calculations are based on tabulations of the generalized oscillator strength GOS due to Peter Rez Please see the following references for details concerning the computation of these GOS values 1 R D Leapman P Rez and D F Meyers K L and M shell generalized oscillator strengths and ionization cross sections for fast electron collisions Journal of Chemical Physics 72 1980 1232 11 29 2 C C Ahn and P Rez Inner shell edge profiles in electron energy loss spectroscopy Ultramicroscopy 17 1985 105 The Hartree Slater cross sections overcome many of the limitations of the simpler hydrogenic cross sections Most importantly they permit the computation of L edges that are beyond the range of SIGMAL2 and they also provide most M and N edges as well as a few O edges encountered in practical EELS work In effect virtually all elements of the periodic table can be quantified via the Hartree Slater cross sections Since the primary difference between the hydrogenic and Hartree Slater cross section routines lies in the content and form of the GOS data there is virtually no difference in the access to and application o
141. ribed above are computed EELS Analysis User s Guide Rev 1 2 1 Quantification 9 Output the results All computed data are output to a new image display or to the results window as appropriate It should be noted that the approach implemented is accurate for isotropic materials only and assumes the collection aperture is on axis Notes for Spectrum Imaging Users To perform Kramers Kronig analysis on a spectrum image select the appropriate menu item with either the spectrum image or an associated exploration spectrum taken from the spectrum image front most If an exploration spectrum is front most specify the parent spectrum image as the input dataset when prompted Note that the REFRACTIVE INDEX field in the KRAMERS KRONIG ANALYSIS dialog will allow not only a mean value if the materials refractive index to be specified but in addition an image for instances where the refractive index varies over the acquisition region This image should be of the same spatial dimensionality as the source dataset and contain the appropriate refractive index at the pixels corresponding to those of the source data Likewise the ATOMS MOLECULES PER CUBIC NM field used for computing the effective number of electrons per atom molecule also allows an image to be specified instead of to a mean value Again the image must be of compatible spatial dimensionality as the input dataset and it should contain the appropriate areal density at
142. rier transform is divided by the low loss Fourier transform and the result is inverse Fourier transformed to yield the desired deconvolution To use the routine initiate the command with the appropriate core loss spectrum front most If the front most image display has multiple spectra displayed in it for example if it contains an active background fit window then you will be prompted to specify the spectrum slice that corresponds to the background subtracted edge you wish to perform the routine on Next you will be prompted to specify the corresponding low loss spectrum from a list of dimensionally compatible EELS Analysis User s Guide Rev 1 2 1 3 33 Figure 3 21 3 34 Remove Plural Scattering candidates Figure 3 20 The deconvolved result will be displayed in a new image display Figure 3 21 Fourier ratio deconvolution of a core loss edge A Extracted signal from BN edges 1 deconyolved i iol x Core loss spectrum with DESE e DE Av background subtracted E 4 overlaid for illustration Background extrapolated edge with plural scattering removed by Fourier ratio deconvolution The preparatory checks and modifications of the input spectra are similar to those applied to the input of the FouRIER LoG routine The only change in the entire procedure is in the Fourier transform manipulations of the input The exact procedures are as follows 1 Check inputs The checks applied to the low loss inpu
143. ript Commands zero loss model to use for zero loss extraction or alternatively by passing the function an image of compatible dimensionality containing the pre extracted zero loss peak the output of the EELSExtractZLP routine is suitable for this purpose In either case the calibrated low loss spectrum or spectrum image must be specified as the source dataset src The extracted or specified zero loss profile is used as the modifier or reconvolution function for the deconvolution please refer to Section 3 10 for details The deconvolved dataset is returned as an array of identical size and dimensionality to the source data EELSFourierLogDeconvolveWithGaussianModifier Deconvolves plural scattering from a low loss spectrum using the Fourier log approach with a Gaussian modification function image EELSFourierLogDeconvolve WithGaussianModifier image src number ModifierFWHM number ZLPIndex image EELSFourierLogDeconvolve WithGaussianModifier image src number ModifierFWHM image zlp This function performs the same routine as described above for EELSFourierLogDeconvolveWithZLPModifier except that a Gaussian function is used instead of the zero loss peak as the modifier Hence an extra parameter ModiferFWHM is passed to the function which defines the width of the Gaussian modifier as a multiple of the full width half maximum of the extracted or specified zero loss peak Please refer to EELSFourierLogDeconvolveWithZLPModifier abo
144. rmined by their fitting ROI positions and widths see below then in favorable circumstances this has minimal impact Alternatively selecting FIT MULTIPLE NLLS MODELS SEQUENTIALLY causes the Gaussian models to be fitted individually in an ordered sequential manner This is performed by first linear least squares fitting the Gaussian model of lowest index as denoted by the numbering in the fit ROI label to the data over its designated fit region Once fitted the computed fit model is subtracted from the dataset to yield the residual signal The model of next lowest index is then fitted over its designated fitting region to the residual signal and the process repeated until all the models have been fitted Hence the algorithm is called once for each fit model specified though for each iteration the algorithm only fits a single model and hence only has to optimize at most three fitting parameters Additionally since the models are fitted sequentially each Gaussian is only fitted over its own designated fitting region This approach is EELS Analysis User s Guide Rev 1 2 1 Figure 3 25 3 12 2 NLLS Fitting much more robust and time efficient for fitting multiple models in comparison to the simultaneous fitting approach described above However it does offer the disadvantage of being difficult to set up in order to obtain satisfactory results where peaks are closely overlapping since the optimal combination of the fitting parameter
145. rofile Please note that for notational convenience the integrated partial cross sections posted in the RESULTS and PROGRESS windows are converted to barns A barn is 10 m so the posted values must be multiplied by 10 to yield the cross section in m Please also note the uncertainty posted with each computed result Unfortunately the accuracy of theoretically calculated cross sections is questionable To at least take some account of this unknown error in the final quantitative results posted by EELS Analysis a blanket 10 uncertainty is assumed for all computed cross sections This uncertainty is propagated through any calculations which use computed cross sections To refine the error estimate for a particular case compare the hydrogenic and Hartree Slater results for identical inputs The difference between these represents the minimum uncertainty in these computed values Chemical Shift This feature allows a positive or negative energy offset to be added to the edge threshold energy to account for a shift in edge threshold energy resulting from chemical state effects Activate this feature for the selected edge by checking the tick box and entering the chemical shift value in the field provided A positive value results in an increase in the edge threshold energy by the specified amount and vice versa Any chemical shift applied is automatically applied to the background fitting and signal integration regions and additionally
146. round Subtracted SI command in the SI menu Note that log polynomial backgrounds and polynomial background models of order greater than 1 are not supported for spectrum imaging use EELS Analysis User s Guide Rev 1 2 1 Sum Overlaid Spectra Figure 3 13 3 6 EELS Analysis User s Guide Rev 1 2 1 Example of the Sum OVERLAID SPECTRA command A SK edge zioz ziaz n Sendo ee SUM OVERLAID SPECTRA Summed spectra 1850 1300 1950 2000 2050 2100 2150 ev 13900 2000 2100 ev Sum Overlaid Spectra Use this menu item to sum multiple overlaid spectra that are displayed in the same image display The spectra are summed as displayed and hence may be manually aligned beforehand with respect to their dispersion scales using the standard DigitalMicrograph tools for manipulating spectrum slices Please refer to Section 2 4 3 in particular the HORIZONTAL CONSTRAINS sub section for further details on manipulating spectrum slices This command is therefore useful for the addition of separately acquired spectra possibly with different dispersions and automatically takes into account any changes in horizontal offset or scaling that the user may have applied to yield a single spectrum displayed in a new image display The output spectrum is automatically cropped to the energy range common to the overlaid spectra If necessary the spectra are also rebinned to a common dispersion as determined by
147. round spectrum and computes the Fourier transform of the single loss component j v using Egerton p 248 iV g v inliv 2v where v denotes the Fourier frequency and j V z v and g v are the Fourier transforms of the spectrum replicated zero loss component and reconvolution function respectively The result is inverse Fourier transformed to yield the single scattering distribution 7 Output result Finally the zero loss integral is written to the IMAGE DISPLAY INFO tags for future reference e g for thickness computation and quantitative analysis of elemental concentrations and the computed single scattering distribution is displayed in a new image display The shape of the resultant distribution itself provides a consistency check on the extracted single scattering spectrum If there are obvious excesses or deficits of counts at multiples of the dominant plasmon excitation the largest peak after the zero loss peak then it is likely that either the probed area was not of uniform thickness or the collection angle was too small Again please refer to the works of Egerton et al listed in the COMPUTE THICKNESS section for more information Notes for Spectrum Imaging Users To perform Fourier log deconvolution on a spectrum image select the menu item with either the spectrum image or an associated exploration spectrum taken from the spectrum image front most If an exploration spectrum is front most specify the paren
148. rrespond to the zero loss model you wish to use The computed thickness is returned as an image of identical spatial dimensionality as the src array but with no energy loss dimension hence this is an image containing a single pixel for single spectra or a line profile for spectrum line traces or a 2D image for spectrum images EELSComputeThicknessLogRatioAbsolute Compute the absolute thickness using the log ratio method and an estimated value of the inelastic mean free path 2 from a low loss spectrum image EELSComputeThicknessLogRatioA bsolute image src number ZEff number E0 number BetaEff number ZLPIndex image EELSComputeThicknessLogRatioAbsolute image src image ZEff number E0 number BetaEff number ZLPIndex This function can be used to compute the absolute specimen thickness from a low loss spectrum or spectrum image using the log ratio approach and an estimated value of the inelastic mean free path In addition to the calibrated source dataset src the function must be passed values for the effective atomic number of the material ZEff the primary electron energy 0 in keV the effective collection semi angle BetaEff in mrad and also the zero loss model index ZLPIndex Note that for spectrum image analysis the parameter ZEff can also be specified as an image This image must be of compatible spatial dimensionality to the input data set i e the same spatial dimensionality containing the appropriate values of th
149. rule This procedure should be performed on a single scatter distribution where possible obtained by removing plural scattering using for example the Fourier log deconvolution method described in Section 3 10 2 if not an approximate correction is applied that is valid for a relative sample thickness of below 1 2 inelastic mean free paths see the description below for more details The procedure carries out the following steps EELS Analysis User s Guide Rev 1 2 1 Compute Thickness 1 Performs a check to see if plural scattering has been removed The Kramers Kronig sum rule requires the low loss single scattering distribution SSD as input that is the low loss spectrum with plural scattering removed The easiest way to provide this is by performing the Fourier log deconvolution routine described in the following section on the spectrum of interest beforehand and using the output as input to this routine If the spectrum does not have plural scattering removed then a warning is posted You may still proceed with the routine and in this event an approximate correction will be applied to account for the effects of plural scattering see step 4 but bear in mind that the accuracy of the procedure will be compromised 2 Prompt the user for spectrum specific parameters A number of experimental parameters regarding the spectrum s acquisition are required for this routine You will be prompted to confirm or specify the relevant
150. rum image using the specified zero loss model The function is called with a calibrated source low loss spectrum src and the zero loss model index ZL PIndex corresponding to the zero loss model you wish to use Please refer to EELSPostZeroLossModelInfoToResults below for information on viewing the available models and their corresponding indexes The extracted zero loss integral is returned as an image of identical spatial dimensionality as the svc dataset but with no energy loss dimension EELSPostZeroLossModellnfoToResults Posts a list of zero loss models and indexes to the Results window void EELSPostZeroLossModelInfoToResults void This function outputs a list of the current zero loss models available along with their corresponding model indexes to the Results window EELSComputeThicknessLogRatioRelative Compute the relative thickness from a low loss spectrum using the log ratio method 4 3 4 4 Prototype Description Summary Prototypes Description Summary Prototypes Description EELS Script Commands image EELSComputeThicknessLogRatioRelative image src number ZLPIndex This function can be used to compute the relative thickness in units of the inelastic mean free path for inelastic scattering 2 from a low loss spectrum or spectrum image using the log ratio approach When calling this function a calibrated source low loss spectrum src is required In addition set the parameter ZLPIndex to co
151. run as background processes allowing you to continue using DigitalMicrograph or other applications during lengthy computations though please bear in mind performing other computationally intensive tasks will lengthen the overall computation time Background processing offers the advantage of enabling you to view the output data as the computation proceeds to ensure that all is proceeding as expected Further you can batch process multiple analyses simultaneously though bear in mind that computation times and memory requirements will increase appropriately At completion of each computation the total number of errors if any is posted in a dialog as a percentage of the total number of spectra analyzed Depending on the default image display settings as specified in the Image DIsPLAY INFO dialog opened by selecting the IMAGE DisPLAY menu item in the OBJECT menu or the type of data under analysis the real time display may appear blank There can be several reasons for this At an early stage of the computation there may be insufficient information displayed to be included in the image survey contrast range In these circumstances wait sufficient time for the output data to reach a state of completion where the image survey contrast mechanism includes it in the displayed range the display will be automatically refreshed as the computation proceeds Alternatively set the image s SURVEY method to WHOLE IMAGE via the IMAGE DispLay In
152. s Once the output preferences are specified then the computation will proceed on a pixel by pixel basis performing the NLLS fitting using the fit regions and parameters as specified for the exploration spectrum Notes for Spectrum Imaging Users Please refer to Section 3 12 5 above Apply Fits to Parent Spectrum Image for details Kramers Kronig Analysis This menu item performs Kramers Kronig analysis on the front most spectrum Kramers Kronig analysis enables the energy dependence of the real and imaginary parts of the dielectric function of the specimen and amp respectively to be calculated from the low loss single scattering distribution The real and imaginary parts of the dielectric function provide a reasonably complete local description of the electronic and optical properties of the specimen enabling optical properties such as the absorption coefficient and the reflectivity to be calculated The imaginary part of the dielectric function may also be linked to the optical joint density of states for low momentum transfers allowing comparison with optical measurements Additionally physical properties such as the absolute specimen thickness and electronic properties such as the effective number of electrons can be computed For a detailed discussion of Kramers Kronig analysis and its applications please refer to Egerton Chapter 4 pp 256 262 EELS Analysis User s Guide Rev 1 2 1 Kramers Kronig Analysis
153. s most semiconductors and some insulators please refer to Egerton Chapter 5 pp 304 307 for details The routine will first prompt you to confirm or specify the experimental acquisition parameters necessary to perform this calculation In addition a property called the effective atomic number Zis required this value is dependent on the composition of the specimen and may be calculated using the following Lenz model relationship ae ot Ae eff YZ where f is the atomic fraction of each elemental species of atomic number Z For approximate calculations an estimate of the mean Z of the region under investigation can often suffice Once all necessary values are specified the routine computes the estimated inelastic mean free path 1 for the material under investigation please refer to Egerton Chapter 5 pp 304 307 for a detailed description of the relationships used in this approach 2 Compute Relative thickness 1 This is achieved following steps 1 3 as described above for LoG RATIO RELATIVE 3 Convert Relative thickness to Absolute thickness t The relative thickness value computed in the previous step is converted to absolute thickness by conversion using the inelastic MFP value computed in step 1 4 Output Result as described for LOG RATIO RELATIVE step 4 above Kramers Kronig Sum Rule The CoMPUTE THICKNESS by KRAMERS KRONIG SUM RULE routine computes the absolute sample thickness using the Kramers Kronig sum
154. s for all the Gaussian models collectively is not found only the individual best fits on an iterative basis It should be noted that irrelevant of the fitting method selected the initial width center and amplitude of the Gaussian models are determined by the fitting range width divided by 2 the maximum value channel and the maximum channel value within the specified fitting range respectively Additionally when fitting only a single Gaussian both of the approaches described above are equivalent Fitting a single Gaussian to the Cr L3 white line using NLLS fitting ira G Extracted signal from Cr 0440 0940e Residual Signal 15 x al NLLS fit 1 8 2003 2 47 52 PM Fit 1 Gaussian Model Gaussian Amplitude 40815 6 Center 578 156 eV FWHM 3 28654 eV Fit channel range 285 297 Reduced chi square equal weights 3 0977e 006 m Fit Gaussian to ROI Select this item to assign the selected region of interest ROI as a Gaussian NLLS fit When performing this ensure a single spectrum is front most with a range ROI selected and positioned over the desired fitting range For more details on creating selecting and manipulating ROPT s please refer to Section 2 4 1 above Once selected the ROI will be designated as an NLLS fitting region as indicated by its labeling and solid outline and a Gaussian model will be fitted and displayed as shown in Figure 2 1 above The NLLS fit
155. s tail is then modeled and extrapolated over the spectrum s energy loss range and then e the spectrum and logarithmic tail are replicated and spliced at the fitting mid point to yield the extracted zero loss peak e This zero loss model is then subtracted from the original spectrum to yield the inelastic signal and all channels from the beginning of the spectrum range to the rightmost negative count residual in the inelastic signal within the specified log fitting range are set to zero and then finally f the inelastic signal is then subtracted from the original spectrum to yield the output zero loss peak Note for advanced users The post extrapolation clean up steps e f can be disabled by opening EELS gt SETTINGS gt ZERO LOSS MODELS gt FITTED LOG TAIL in the GLOBAL INFO tags and setting the PERFORM POST FIT CLEANING tag to FALSE Additionally setting the DON T SHOW RANGE DIALOG tag to FALSE will re enable the fit range dialog if disabled Fit Pre Measured Zero loss This routine fits a user specified zero loss profile to the zero loss peak of the selected spectrum The algorithm is relatively simplistic being both robust and relatively quick The routine proceeds as follows a It first requests the user to specify the reference zero loss peak which should be a single spectrum containing the zero loss peak only and ideally acquired at the same dispersion in order to have contain same detector response characteristics as the ob
156. s the sum of all counts in that edge without background Iis the total integrated number of counts and o is the cross section for ionization of an electron in the associated shell As discussed by Egerton for real world spectra it is usually necessary to work with one of a variety of approximate forms of the above expression depending upon the nature of the data analyzed For example it is usually not possible to accurately integrate all counts in an edge due to the presence of succeeding edges and cumulative errors in the background extrapolation A finite integration range is therefore normally defined and the resultant partial count integral and corresponding partial cross section are substituted above see Egerton Equation 4 64 This modification is fine as long as plural scattering is negligible or has been removed from the spectrum Otherwise it is also necessary to modify the parameter J to so that it represents a partial spectrum count integral including the zero loss peak up to an energy equal to the width of the edge integration range thus correcting the effect of plural scattering to a first order Egerton Equation 4 65 In order to simplify your work EELS Analysis automatically chooses the correct form of the fundamental quantification expression based on what it knows about your spectrum For example when you perform Fourier Log deconvolution to remove plural scattering a flag is set and stored with your spectrum indicating t
157. se with small error bars Another benefit of this type of weighting based on measurement uncertainties is that the least squares fit parameter reduced x which comes out of such a calculation will have a value on the order of 1 if the model function describes the data reasonably well If the reduced y comes out significantly greater than 1 then a bad fit is indicated Sometimes however the measurement uncertainty cannot easily be established As long as there is no reason to believe that some points of the data set have significantly more or less significance than the others it is then best simply to weight each data point equally and to let the resulting value of the fit parameter provide some idea of the average uncertainty in each measured data point You may specify either of these two weighting options as described below Computed from Data If this option is selected the measurement uncertainty in each channel of an analyzed spectrum is estimated assuming Poisson counting statistics and a constant conversion factor from measured counts to true primary electron counts When you select this option each time you perform a command that computes a reduced y value a check will be performed on the source spectrum to ensure it is in units of primary electrons e In the event that the spectrum is not calibrated in this unit a dialog is posted asking you to provide confirm the conversion factor from detector counts to primary beam counts T
158. st later in this section for more details Fourier log deconvolution of an EELS SI in progress TaB EELSSI E V Fourier log deconvolution SS SS a B EELS SI fra D EELS SI deconvolyed 5 x HO0000Roo0n Method zero loss modifier Avot For the majority of analyses once the spectrum image analysis has been started the output results are displayed in their own image windows These image windows are updated in real time as the calculation proceeds In addition a palette containing a progress bar will be opened in the top right corner of the screen for each analysis process informing you of the state of progress of the computation see Figure 3 3 above For large spectrum image datasets computation times can be significant so please allow sufficient time for completion In the event of an algorithm failure happening at a pixel for example if the spectrum at that point is not suitable for the analysis in progress then an appropriate failure message will be posted to the progress palette informing you of the nature of the error and the pixel co ordinate This will not halt the analysis which will proceed to the next pixel until completion Note that at any time during the computation clicking the ABorT button positioned in the appropriate progress palette will halt the routine Alternatively closing all of the output windows associated with the computation will also halt the routine The analysis routines
159. suppression Suppression exponent R Bo Feature Detection Parameters Low oss cutoff eV 40 0 Max segment space g Discriminator sigma 4 0 Overlap jump ratio 3 0 Algorithm Overview The basic principle of the algorithm is to take a derivative of the spectrum to turn edges into pronounced bipolar features and to statistically analyze these bipolar peak intensities to determine which of them represent significant signals above the noise level For each detected feature the first peak within the derivative spectrum is taken to be the onset of the edge and the peak s energy loss coordinate is used to tentatively identify the edge by means of a look up table of all EELS edges sorted by threshold energies The algorithm has a number of adjustable parameters that affect its edge detection sensitivity as well as its rate of false identifications These parameters may be adjusted within the EDGE AUTO IDENTIFICATION SETUP dialog Figure 3 31 launched by selecting the R button situated next to the AUTO ID button in the QUANTIFICATION dialog See the description below for details on how to tailor them to optimize the performance of the automatic edge detection routine for your typical spectra The edge detection and identification algorithm has number of adjustable parameters that affect its edge detection sensitivity as well as its rate of false identifications Most of these parameters have clearly defined effects and
160. t a continuous spectrum extending from zero energy loss through to the edges of interest and having neither gaps nor regions of detector saturation particularly important at the zero loss peak It is this very factor that limits the range of use of the technique since practical considerations such as detector saturation and finite energy loss range constrain its use to the low loss regime To use this EELS Analysis User s Guide Rev 1 2 1 Remove Plural Scattering deconvolution routine simply display the desired spectrum as the front most image window and select FOURIER LOG in the REMOVE PLURAL SCATTERING sub menu The deconvolved result will then be displayed in a new image display window The input low loss spectrum is checked to ensure it is suitable The exact procedures are as follows 1 Check input The program checks that the low loss spectrum has a calibrated energy scale and in fact represents a reasonable low loss spectrum i e contains a zero loss peak If not the routine posts a suitable alert 2 Determine size of Fourier transform to be used The routine next establishes the number of channels needed for the Fourier transform computations In order to provide enough empty buffer channels to allow for smooth extrapolations the routine chooses the smallest power of 2 that is large enough to accommodate the spectrum and cosine bell extrapolation 3 Prepare input spectrum To avoid artifact ringing due
161. t Commands EELSSubtractLogPolynomialBackground Computes and subtracts an n degree log polynomial background from a spectrum image EELSSubtractLogPolynomialBackground image src number starteV number endeV number degree This command performs the same function as described above for EELSComputeLogPolynomialBackground but performs the extra step of subtracting the computed background from the source signal to return the background subtracted signal For further details please refer to EELSComputeLogPolynomoalBackground above EELSExtractZLP Extracts the zero loss profile from a low loss spectrum image EELSExtractZLP image src number ZLPIndex This function can be used to extract the zero loss peak from a low loss spectrum or spectrum image using the specified zero loss model Call the function with a calibrated source low loss spectrum as src and the zero loss model index ZL PIndex corresponding to the zero loss model you wish to apply Please refer to EELSPostZeroLossModelInfoToResults below for information on viewing the available models and their corresponding indexes The extracted zero loss profile is returned as an image of identical dimensionality and size to the source array EELSExtractZLPintegral Extracts the zero loss integral from a low loss spectrum image EELSExtractZLPIntegral image src number ZLPIndex This function can be used to obtain the zero loss peak integral from a low loss spectrum or spect
162. t are the same as those applied to the input of FouRIER LOG routine described above The core loss spectrum leading edge is checked for background removal if the background is still present or has been poorly subtracted a warning is posted 2 Determine size of Fourier transforms to be used The same criterion as in the FOURIER LoG procedure described above 3 Remove truncation discontinuities in the target spectra The same modifications as those applied to the low loss input to FOURIER LOG described above are applied to both input spectra Since wraparound is implicit to the Fourier transform algorithm it is important that the pre edge background of the core loss spectrum is removed prior to Fourier ratio deconvolution 4 Extract zero loss counts The zero loss component z E is modeled from the low loss spectrum and replicated for use in the next step as described above for Fourier log deconvolution EELS Analysis User s Guide Rev 1 2 1 Figure 3 22 EELS Analysis User s Guide Rev 1 2 1 3 11 MLLS Fitting 5 Prepare reconvolution function The reconvolution function is prepared following the same criterion as described above for Fourier log deconvolution 6 Perform Fourier transform manipulations With the two inputs prepared and ready the routine next Fourier transforms them using a Fast Fourier Transform FFT algorithm It divides the spectrum transform by the low loss deconvolution function transform
163. t setup button opens a dialog containing the relevant settings for modification For advanced users removing the NUMERICAL FILTERS tag group found in the GLOBAL INFO menu will restore the original as installed default values The effect of each filter is described below 3 7 2 Smooth low pass The smoothing filter averages out some of the noise in a spectrum and places the result in a new display leaving the original data unchanged It acts by replacing the value in each spectrum channel by the average number of counts per channel in an interval w eV wide and centered on the channel in question In the case of the specified energy interval corresponding to an even number of channels an extra channel is added and only half of the contribution of the two end channels considered mimicking the specified smoothing interval without introducing a resultant energy shift into the final spectrum spectrum image The width w of the averaging interval is set under SMooTH LOW PASS in the FILTER SETUP dialog For the smooth filter and all the following filters endpoints are handled by repeating the first and last values in the spectrum as required 3 7 3 Structure high pass The structure filter isolates most of the interesting features in a spectrum and places the result in a new display leaving the original data unchanged It acts by subtracting a heavily smoothed copy of a spectrum from itself thereby EELS Analysis User s Guide Rev
164. t spectrum image as the input dataset when prompted Note that the output dataset has identical dimensionality as the input dataset EELS Analysis User s Guide Rev 1 2 1 Remove Plural Scattering Figure 3 20 Selecting the appropriate low loss spectrum for Fourier ratio deconvolution F Extracted signal from BN edges 1 i loj x Fourier Ratio deconvolution xi Please select the Low Loss spectrum to be used as deconvolution function 3 10 3 Fourier ratio Select this item to correct the front most spectrum for plural scattering using the Fourier ratio method see Egerton pp 264 269 Typically this method is applied to core edge spectra from which the power law background has already been completely removed The easiest way to obtain such a spectrum is to run the EXTRAPOLATE BACKGROUND routine followed by EXTRACT BACKGROUND SUBTRACTED SIGNAL found in the BACKGROUND MODEL sub menu on the edge of interest refer to the BACKGROUND MODEL section for details The FourIER RATIO routine requires two inputs 1 The isolated edge spectrum and 2 The corresponding low loss spectrum acquired under the same experimental conditions Both inputs should be acquired at or interpolated to the same eV ch if not the routine will automatically interpolate the low loss spectrum to the same dispersion as the core loss spectrum but bear in mind that a loss of accuracy may result The two inputs are Fourier transformed the spectrum Fou
165. tected 2 Identify and exclude any vacuum regions from the search A filter is applied to identify and exclude any regions containing little or no significant signal from the computation e g holes in the sample The dataset is integrated in the spectral dimension to yield a summed intensity image All pixels of a value less than the summed intensity image mean minus No where N is by default 1 2 and cis the standard deviation of the summed intensity image are excluded from the auto identification routine 3 Perform edge search The edge auto id algorithm as described for the single spectrum case proceeds on a pixel by pixel basis generating an edge list of the same spatial dimensionality as the input dataset 4 Compile edge energies The edge energy list is compiled to order edge identifications in ascending energy loss yielding a spatial distribution map for each individual identified energy loss 5 Apply nearest neighbor filter The spatial distribution map at each identified energy loss is analyzed to give a nearest neighbor ratio For spectrum image datasets the nearest neighbor ratio is computed as the total sum of the number of nearest neighbors i e adjoining pixels maximum of 8 for each pixel in the image divided by the maximum possible value For EELS line scans the same is performed except that nearest neighbors maximum of 2 and next nearest neighbors maximum of 2 are considered with next nearest neig
166. template and modified to accommodate your own custom routine is listed below with comments where appropriate Example ZLP Model Template Copyright Gatan Inc December 2002 class ExampleZLPModel You can rename this class number fAttenuateEnergy Default Default value for the only parameter in the example number fAttenuateEnergy Actual value for the only parameter in the example string fAttenuateEnergy string Descriptor string for tag in Global Tags ExampleZLPModel 4 9 4 10 Adding Custom Zero Loss Models Constructor these variables are initialized when the object is created i e each time the model is used The variables initialised here are global to the class i e can be seen by each function Set any required default parameter values here ExampleZLPModel object self Must have the same name as the class fAttenuateEnergy_string fAttenuateEnergy_Default fAttenuateEnergy Zero loss attenuation energy eV 6 in ev fAttenuateEnergy Default Initialise to default GetAlgorithmName This function is called to get name of algorithm as displayed in the Preferences dilaogs string GetAlgorithmName object self string name Example model Set the name for your ZLP Model here return name ExtractZLP This is the actual zero loss removal function place your function here The lowloss spectrum is passed into the function as a 1D spectrum low
167. ters for the quantification of the edges contained within the QUANTIFICATION LIsT These items allow all the quantification parameters from background model and fitting range signal integration range through to inelastic scattering cross section model to be specified individually for each edge within the QUANTIFICATION List whilst viewing the changes interactively in the spectrum s image display The functions of the items contained within the EDGE SETUP tab are described below Quantification List The QUANTIFICATION LIST contains the edges specified for quantification Please refer to the identically titled item in the previous section for details regarding the compilation of this list Within the context of the EDGE SETUP tab this list allows the user to specify which edge s signal extraction details are posted in the appropriate fields within the dialog and also displayed graphically in the spectrum s image display Hence to view and adjust the signal extraction setup for a particular edge select it in the QUANTIFICATION LIsT and then adjust the appropriate parameters Note that double clicking on an entry will zoom onto the appropriate edge in the spectrum s image display as an aid to visualization EELS Analysis User s Guide Rev 1 2 1 Quantification Cross Section During quantification of core loss edges EELS Analysis calculates the energy differential cross section do dE for the edge in question and integrates it
168. the doublet separately The L component is computed from its own threshold using the L GOS data multiplied by a factor of 2 4 to account for the relative occupancy of the L2 shell as compared to that of the L shell A similar approach with suitably modified relative occupancy factors is used for other doublets e g M23 Mas Nas etc Finally white line contributions are not currently included in EELS Analysis s Hartree Slater routine Calculation of cross sections As mentioned above the cross section is calculated both during quantification and also in real time for visual inspection during parameter determination for edge extraction What the routine actually does in a given case depends on your specified preference in the CROSS SECTION pop up menu and on the availability of the desired edge cross section within the wave function model you have chosen Given the edge threshold of interest specified signal integration range and the spectrum acquisition parameters the cross section calculation proceeds as follows 1 First try to compute the cross section via the preferred method indicated in the CROss SECTION pop up menu If the user has specified hydrogenic cross sections the routine checks that the selected edge is either a K edge or an L edge within the range of SIGMAL2 If Hartree Slater cross sections are preferred the routine checks that GOS data for the selected edge is available in the H S GOS TABLES folder 2 Ifan error o
169. the event of any ambiguity the user is prompted to specify the data acquisition mode EELS Analysis User s Guide Rev 1 2 1 Quantification All the set up profiles contain the parameters used to transform and identify core loss edges for single spectra as described above However because of the large amount of spectra present in a typical spectrum image the list of identified edges compiled by performing automated edge identification on a pixel by pixel basis is quite extensive and unordered requiring further interpretation to be useful Hence the line scan and spectrum image profiles contain an additional set of search parameters that are used in the post search processing of the data The procedure below is followed therefore for SI edge auto identification 1 Spatially rebin the dataset To reduce the size of the dataset to be searched and hence reduce the overall computation time the dataset is repeatedly rebinned spatially by a factor of two until all spatial dimensions are less than the maximum allowed dimension size specified in the MAX SPATIAL SIZE PIXELS field in the EELS SI EDGE AUTO IDENTIFICATION SETUP dialog This process has the additional benefit of improving the quality of the spectra analyzed by summing over multiple pixels The value of the maximum spatial size parameter should be low enough to facilitate rapid computation but should not be so low that small features are under sampled and hence are not de
170. ting multiple models to a single dataset The implications of each fitting approach are described below If FIT MULTIPLE NLLS MODELS SIMULTANEOUSLY is selected the fitting algorithm will attempt to find the optimal linear combination through least squares fitting for all the specified fit models simultaneously Hence in this mode the fitting algorithm is passed all the Gaussian models as input and the algorithm performs a single computation to best fit the models within the specified fitting regions This approach offers the advantage of giving the fitting algorithm the maximum freedom when determining the optimal fit parameters Hence if a feature of interest is for example comprised of two overlapping Gaussian like peaks then attempting to fit two Gaussian models in this fitting mode will most likely yield the most appropriate result This approach does however have its drawbacks The dimensionality of the problem the algorithm is attempting to solve increases sharply with additional models and hence computation time quickly increases whilst the algorithm s robustness quickly decreases Additionally since the Gaussian models are being fitted simultaneously there is no mechanism within the algorithm used for specifying the fit regions as being individual Therefore the result achieved is the best fit for all the models fitted over all the fitting regions specified However since the models are initiated with start parameters that are dete
171. ting the energy scale in this mode be sure to take into consideration any binning applied when specifying the dispersion the energy scale scale is defined in units of spectrometer dispersion x binning If more than one channel is highlighted by the rectangular marker the user is requested to specify the energy loss corresponding to the low energy boundary and in addition that corresponding to the high energy boundary The dispersion is then calculated based on the 3 2 EELS Analysis User s Guide Rev 1 2 1 Figure 3 6 EELS Analysis User s Guide Rev 1 2 1 3 3 3 3 1 Splice low and high marker energies and their separating interval This mode is more suitable when the dispersion is not accurately known and two distinct features of known origin are present within the spectrum e g the zero loss peak and a sharp core loss feature of known energy loss Notes for Spectrum Imaging Users To recalibrate a spectrum image select this menu item with an active exploration spectrum selected from the spectrum image front most The ENERGY LOSS CALIBRATION dialog shown above in Figure 3 5 will have an additional check box positioned at the bottom of the dialog titled APPLY To PARENT SPECTRUM IMAGE This is selected by default When this check box is selected any recalibration applied to the exploration spectrum will also be automatically applied to the parent spectrum image The SPLICE PREFERENCES dialog w Splice Preferenc
172. tion of the sample thickness 2 The composition of the probed specimen area does not vary appreciably in the lateral dimensions In particular the probe should not straddle several precipitates of markedly different composition particularly if each extends throughout the entire sample thickness 3 The collection angle of the experiment must be large enough to ensure that the scattering obeys Poisson statistics As mentioned under the discussion of the COMPUTE THICKNESS routine previously in this section this is not an overly restrictive condition Again please see the references given in that section Since both methods rely on information about the shape of the low loss part of the spectrum a requirement common to both of the deconvolution routines is a measurement of the low loss part of the spectrum This measurement must meet the same criteria as a potential input to the COMPUTE THICKNESS routine Please refer to the description of that item above for details The FOuRIER DECONVOLUTION PREFERENCES dialog wa Fourier Deconvolution Preferences x Zero loss peak removal Use Extract Zero Loss setting Reconvolution method zero loss modifier Gaussian modifier width 1 zlp width ji 0 Cancel OK 3 29 Figure 3 19 3 30 3 10 1 3 10 2 Remove Plural Scattering Preferences This menu item launches the FOURIER DECONVOLUTION PREFERENCES dialog shown above in Figure 3 18 Preferences specified her
173. to the calculated differential cross section Select this feature if you suspect the edge you are trying to identify has altered threshold energy as a result of chemical shift EELS Analysis User s Guide Rev 1 2 1 Quantification Figure 3 38 Specifying signal extraction parameters in the EDGE SETUP dialog T A BN on holey carbon Emx Signal Background o integration fitting window Computed energy differential cross section Calculated background contribution Core loss edge without background Edge under analysis Numerical values of background fit and Bkgd 210 fiso e signal integration Signal o0 250 eV window positions Section Model Hartree Slater rBackground Fit Model Power Law gt Selected background model I Chemical Shit 00 eV Energy differential cross section model Background and Signal Windows The widths and offsets of the background fitting and signal integration windows may be defined by two different methods EELS Analysis User s Guide Rev 1 2 1 3 71 3 72 Quantification 1 These parameters may be defined interactively by clicking the cursor on the corresponding rectangular markers overlaid on the spectrum display and labeled BKGD and SIGNAL respectively Their positioning and width can then be adjusted as described for EXTRAPOLATE BACKGROUND described previously in this chapter As
174. tructure starts with a relatively large amplitude near the edge threshold but decays rapidly thereafter This characteristic can be utilized to help detect the onset of an edge that overlaps a previous one If there is a sudden jump in the segment intensity somewhere in the middle of a contiguous grouping this jump might signal the presence of another edge The OVERLAP JUMP RATIO parameter tells the algorithm by what factor the intensity must jump before it is to be interpreted as a new edge threshold Increase this parameter if the routine too frequently claims to find non existent edges in among the fine structure of EELS Analysis User s Guide Rev 1 2 1 3 55 Figure 3 32 3 56 Quantification strong edges Decrease it if the program fails to resolve overlapping edges that you can clearly distinguish by visual inspection Load default settings the default edge auto identification settings for EELS spectra may be restored by clicking on this EELS button see Figure 3 31 As already mentioned these defaults have been optimized using a number of reference spectra and represent a good starting point The EELS EDGE AUTO IDENTIFICATION SETUP dialog EELS SI only jaa EELS Edge Auto Identification Setup x EELS EELS Line Scan EELS SI EFTEM SI Detection Transform Parameters Transform Log difference yi Diff delta eV 0 0 ab Structure filter eV 20 0 at Diff smooth eV 4 0 IV Apply powerl
175. tted value N specified in the MAX NO OF IDENTIFICATIONS field of the EELS SI EDGE AUTO IDENTIFICATION SETUP dialog then the list is ordered primarily according to each identified energies recomputed nearest neighbor ratio and if necessary secondly by their total number of occurrences in instances where the nearest neighbor value is equal The N most likely candidates are then returned 8 Output the results The identified edges are added to the exploration spectrum s QUANTIFICATION List for further analysis and also output to the RESULTS window Hence it can be seen that the optimal search parameters are heavily dependent on the acquisition mode of the source data set for example an EFTEM SI will typically be acquired with far coarser spectral resolution than an EELS SI hence requiring different transform and detection parameters to best pronounce the core loss features For this reason each parameter set s default values are acquisition mode specific and have been optimized using a number of reference datasets As with the single spectrum case selecting LOAD DEFAULT SETTINGS will restore the parameter set defaults to the selected profile Quantification List As the name suggests the QUANTIFICATION LIST specifies the core loss edges to be quantified This list is situated at the top right of the QUANTIFY tab and also at the top left of the EDGE SETUP tab described later in this section and allows you to compile and view t
176. ughly correct to give reliable results It is particularly important to confine your selection to spectrum ranges that exhibit true power law behavior in order to get a good fit when using the power law model for example This means that intervals which contain residual structure from preceding or overlapping edges or which include pre edge structure of the leading tail of the edge in question should be avoided Once you have highlighted the background fit interval select EXTRAPOLATE BACKGROUND Note that as an alternative to the above you can also create a background fit region by simply holding down the CTRL key and left click dragging over the background fit region on the spectrum In either instance the routine then does the following 1 Fit the background function to the selected background data over the specified fit region EELS Analysis User s Guide Rev 1 2 1 Background Model 2 Extrapolate the background fit to the last channel of the spectrum to obtain a full background model 3 Subtract the background model from the original spectrum 4 Display both the background model and the background subtracted spectrum within the original spectrum s image display Note that this routine will not alter the original spectrum in any way Additionally the selected background fitting region which may be described as active can be altered post modeling To do this place the cursor within the ROI labeled BKGD and holdin
177. urposes simple remove by selecting the script by reference to the library name specified on installing in the REMOVE PLUGIN dialog opened by selecting REMOVE SCRIPT in the FILE menu EELS Analysis User s Guide Rev 1 2 4 11 Index EELS Analysis User s Guide Rev 1 A Acquiring spectra 2 2 B Background change current model 3 11 defining fit region 3 9 extraction 3 11 extrapolation 3 9 integration window 3 71 preferences 3 9 removal 3 9 subtraction 3 12 Background Removal 3 9 Cc Calibration energy scale 3 2 of spectrum images 3 3 overview 2 1 Chemical shifts in quantification 3 70 Cross sections calculating 3 69 Hartree Slater 3 68 hydrogenic 3 67 overview 3 66 specifying model 3 66 D Deconvolution Fourier log 3 30 Fourier ratio 3 33 or spectrum images 3 32 3 35 E Edge identification 3 51 Experimental conditions 3 5 F First derivative filter 3 15 Fourier log deconvolution 3 30 Fourier ratio deconvolution 3 33 H High pass filter 3 15 Identify dialog 3 50 Inelastic mean free path 3 22 K Kramers Kronig analysis 3 44 analysis of spectrum images 3 49 sum rule 3 26 L Log derivative filter 3 16 Log log derivative filter 3 16 M Mathematical operations 2 8 MLLS Fitting 3 35 fit weights 3 38 EELS Analysis User s Guide Rev 1 M contd performing 3 36 preferences 3 36 to spectrum images 3 39 N NLLS Fitting 3 39
178. ution may be considered to be reliable A more rigorous procedure for determining the optimum signal integration range is given in the following reference Kothleitner G and Hofer F Optimization of the signal the noise ratio in EFTEM elemental maps with regard to different ionization edge types Micron 29 1998 349 357 Figure 3 39 Background subtracted edge with calculated cross section E B Edge with Hartree Slater cross section kc gO Background Counts Hartree Slater energy differential cross section 180 200 220 240 260 280 300 320 Energy Loss ev Background This box contains parameters regarding the background model used during quantification The Fir MODEL pop up menu allows the background model to be specified refer to Section 3 5 above for a full description of the models available If a polynomial or log polynomial model is selected the DEGREE field is activated where the degree of polynomial can be specified The displayed background contribution is calculated using the specified background model and background fitting region both of which may be adjusted interactively This ability to adjust the background fitting parameters and instantly visualize the change in calculated background allows for easy optimization of the background fitting parameters and enables suitable adjustments to be made to avoid overlap for edges in close proximity The background fitting region may be r
179. utput datasets the MLLS fit and the fit residual will be output as a spectrum image of similar dimensionality to the input data with the dispersion dimension truncated to the specified MLLS fitting energy range Other values such as the fit co efficients and reduced chi squared will be output as line plots or maps for input spectrum image line traces or 3d spectrum images respectively 3 12 NLLS Fitting The routines in the non linear least squares NLLS fitting sub menu facilitate the fitting of single or multiple Gaussian models to spectra enabling the characterization of spectral features in terms of the individual Gaussian fit parameters i e peak center amplitude and width This can be of use in EELS for example for the characterization of white line peaks e g the L 3 peaks in transition metals since the intensity ratio and relative positions of these features can reveal information relating to the occupation of the local density of states Use of the individual NLLS sub menu items are described as follows EELS Analysis User s Guide Rev 1 2 1 3 39 Figure 3 24 3 40 NLLS Fitting The NLLS FITTING PREFERENCES dialog x Ta NLLS Fitting Preferent Fit multiple NLLS models simultaneously sequentially Cancel OK 3 12 1 Preferences Selecting this sub menu item opens the NLLS FITTING PREFERENCES dialog shown above in Figure 3 24 The selection in this dialog determines the method used for fit
180. value suppresses high energy signals and vice versa This EELS Analysis User s Guide Rev 1 2 1 Quantification correction is recommended particularly for noisy data that covers a large energy loss range e g for EELS spectrum images The effects of the FEATURE DETECTION parameters are as follows Low Loss CUTOFF enter here the energy loss in eV below which the routine should not look for significant features This parameter prevents the algorithm from mistakenly trying to identify plasmon features as core edges DISCRIMINATOR after difference filtering the spectrum the area under each unipolar segment in the resultant bipolar curve is plotted on a histogram Significant edges will contribute bipolar lobes of high intensity to the filtered spectrum thus these features will appear in the tails of the histogram The DISCRIMINATOR parameter tells the algorithm where to cut the histogram to separate significant features from noise Its value is specified in sigma units where sigma is the robust standard deviation of the histogram For example the default value 4 specifies that any segment with an intensity of more than 4 sigma units from the mean usually 0 represents a significant edge signal Increase this parameter if the routine identifies too many noise peaks as edges decrease it if it misses edges you can clearly detect by visual inspection MAX SEGMENT SPACE this parameter is one of the more heuristic ones Once th
181. ve Hence to initiate the routine select the menu item with a low loss spectrum with plural scattering removed by deconvolution front most If the spectrum is deemed thin enough that plural scattering is negligible the inelastic component output using the EXTRACT ZERO LOSS command can be used as input The routine will first prompt you to specify necessary experimental and sample specific details in addition to which properties you would like to compute via the KRAMERS KRONIG ANALYSIS dialog shown in Figure 3 28 above The various dialog items and options are described below The ACQUISITION amp SAMPLE DETAILS group of items contains information regarding the material sample under investigation and the experimental parameters used to acquire the spectrum Specifically Beam energy convergence semi angle and collection semi angle These parameters are as described in the EXPERIMENTAL CONDITIONS section above Confirm these values are accurate and if not correct them Refractive index for visible light The refractive index is used when computing the absolute thickness of the specimen via the Kramers Kronig sum rule This is used computing the proportionality constant necessary for normalizing the energy loss function Since the refractive index n affects the computed thickness via a 1 n term this value can be approximated to a high value e g 1000 for any high refractive index material e g metals most semi conductors The
182. ve for further details EELSFourierRatioDeconvolveWithZLPModifier Deconvolves plural scattering from a core loss spectrum using the Fourier ratio approach using the zero loss peak as the modifier function image EELSFourierRatioDeconvolveWithZLPModifier image src image src_low number ZLPIndex This function removes plural scattering from a core loss spectrum or spectrum image using the Fourier ratio deconvolution approach The function requires a calibrated core loss spectrum or spectrum image to be specified as the source dataset svc Note that the leading background must be removed form this dataset prior to use the output of EELSSubtractPowerLawBackground provides a suitable input dataset for this routine The corresponding calibrated low loss spectrum or spectrum image must be specified as the input array src_low This dataset must contain the zero loss peak be spatially registered with the core loss data and must also be of compatible dimensionality i e identical spatial dimensionality and dispersive in the same dimension but not necessarily acquired at the same dispersion The zero loss model index for zero loss removal must also be specified as the parameter ZLPIndex The extracted zero loss profile is used as the modifier or reconvolution function for the deconvolution please refer to Section 3 10 for details The deconvolved dataset is output as an array of identical size and dimensionality as the input core loss array

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