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SIMNRA User's Guide

1. Description Thickness of layer number lay 101 atoms cm Parameters lay Number of the layer with 1 lt lay lt NumberOfLayers NumberOfElements Get Property NumberOfElements lay Integer Integer Description Number of different elements in layer number lay Number0fElements is readonly Parameters lay Number of the layer with 1 lt lay lt NumberOfLayers NumberOfLayers Get Property NumberOfLayers Integer 129 Description Total number of layers in the target NumberOfLayers is readonly SubstrateRoughness Get Set Property SubstrateRoughness Double Description FWHM of the substrate roughness deg Target HasSubstrateRoughness must be true otherwise SubstrateRoughness has no effect Related Properties and Methods Target HasSubstrateRougness 128 A 5 2 Methods AddElement Function AddElement lay Integer Boolean Description Adds an element to layer number lay The element has no name and zero concentration After adding the elements properties have to be set with ElementName and ElementConcentration Attention Do not use AddElement to add new elements to the target See ElementName for details Parameters lay Number of the layer with 1 lt lay lt NumberOfLayers Return Value Returns true if the element was added successfully Related Properties and Methods Target AddLayer 131 Target ElementConcentration 127 Target ElementName 127 130 AddLayer Function
2. Description If DeleteSpectrumOnCalculate is true the current simulated spectrum is deleted before a new spectrum is calculated If false the current simulated spectrum is conserved and the new spectrum is added to the current one Default is true Example Spectrum for scattering angle 160 Setup Theta 160 App CalculateSpectrum gt Spectrum for scattering angle 170 is now added to the previous spectrum App DeleteSpectrumOnCalculate false Setup Theta 170 App CalculateSpectrum Related Properties and Methods App CalculateSpectrum 114 Last Message Get Property LastMessage WideString 112 Description Text of the last error message or warning LastMessage is retained until a new error or warning is issued or it is read with LastMessage LastMessage is readonly See section A 9 for more details about error handling Related Properties and Methods App ShowMessages 113 Show Messages Get Set Property ShowMessages Boolean Default Value false Description Specifies if error messages are shown or suppressed If ShowMessages is true program execution is stopped if an error is encountered and a message box with an error description or warning is shown Program execution is resumed after pressing the OK button If ShowMessages is false the message box is suppressed and program execution continues The routine which produced the error like App Open or App CalculateSpectrum returns an error f
3. ParticlesSr Get Set Property ParticlesSr Double Description Number of incident particles times solid angle sr Theta Get Set Property Theta Double Description Scattering angle 0 deg Related Properties and Methods Setup Alpha 120 Setup Beta 120 A A Simnra Calc The Simnra Calc object represents the parameters of the calculation 122 A 4 1 Properties AutoStepwidthIn Get Set Property AutoStepwidthIn Boolean Description Specifies if automatic step width control for incident ions is used Related Properties and Methods Calc AutoStepwidthOut 123 AutoStepwidthOut Get Set Property AutoStepwidth0ut Boolean Description Specifies if automatic step width control for outgoing ions is used Related Properties and Methods Calc AutoStepwidthIn 123 dEin Get Set Property dEin Double Description Stepwidth incident ions keV Related Properties and Methods Calc dEout 124 dEout Get Set Property dEout Double 123 Description Stepwidth outgoing ions keV Related Properties and Methods Calc dEin 123 DualScattering Get Set Property DualScattering Description Specifies if dual scattering is calculated ElementSpectra Get Set Property ElementSpectra Description Boolean Boolean Specifies if individual spectra for each element in the target are calculated Related Properties and Methods Calc IsotopeSpectra 125 EMin Get
4. ch De 155 700 6000 11BPA0 R33 Symons 1963 B He po C 90 2050 4000 11B3HEP0 90 R33 McIntyre 1996 BC He po C 135 2050 4000 11B3HEP0_135 R33 McIntyre 1996 B He po C 90 3000 5400 11BTPO R33 Holmgren 1959 B He p1 2 3 C 90 3000 5400 11BTP123 R33 Holmgren 1959 B He Do C 90 3000 5400 11BTDO R33 Holmgren 1959 C D p C 135 520 2950 12CDP_1 R33 Jarjis 1979 TOD CH 165 800 1950 12CDP_2 R33 Kashy 1960 C He po N 90 2100 2300 12CTP0 R33 Tong 1990 2C PHe p1 N 90 2100 2400 12CTP1 R33 Tong 1990 2C He p2 N 90 2100 2400 12CTP2 R33 Tong 1990 TC He po N 159 4 1800 5400 12CTP0_1 R33 Kuan 1964 C He pi N 159 4 1800 5400 12CTP1_1 R33 Kuan 1964 SSC E 159 4 1800 5400 12CTP2_1 R33 Kuan 1964 C He a0 159 4 1800 5400 12CTA0 R33 Kuan 1964 BCO p So 135 600 2950 13CDP R33 Marion 1956 N D a0 C 150 600 1400 14NDA0_1 R33 Amsel 1969 TAN D a1 7C 150 600 1400 14NDA1_1 R33 Amsel 1969 N D po N 150 500 1900 14NDP0_1 R33 Simpson 1984 N D pi 2 N 150 600 1400 14NDP12 R33 Amsel 1969 TAN D p3 N 150 800 1400 14NDP3 R33 Amsel 1969 PND pas oN 150 600 1400 14NDP45 R33 Amsel 1969 PN D ps PN 150 600 1400 14NDP45 R33 Amsel 1969 AN He po OG 90 2100 4000 14N3HEP0_90 R33 McIntyre 1996 MN He po O 135 2100 4000 14N3HEP0_135 R33 McIntyre 1996 PNCHepr de 90 2100 4000 14N3HEP12_90 R33 McIntyre 1996 7N He pi2 135 2100 4000 14N3HEP12_135 R33 McIntyre 1996 NC Dep SE 90 2100 4000 14N3HEP34_90 R33 McIntyre 1996 N FHe p3
5. dE 4 3 Emin i Eqs 4 2 and 4 3 can be put together into a 2 dimensional integral which is computed by SIMNRA by means of a 2 dimensional Gauss Legendre integration The accuracy of the integration is about 1074 The area Q of the brick in fig 4 1 is calculated by SIMNRA by using the cross section at the mean energy E in the brick do Ax NAQ E Q qa ees 4 4 NAR is the number of incident particles times the solid angle of the detector and do dQ E is the differential cross section evaluated at the mean energy E The heights of the front and back side of the brick are adjusted to give the correct area when integrated SIMNRA interpolates the brick linearly as shown in fig 4 1 This is however only valid if the cross section does not vary strongly and the brick is sufficiently thin If the cross section has structures such as sharp resonances the stepwidth of the incoming particles must be sufficiently smaller than the width of the resonance 53 4 2 Atomic data The masses of the elements and all isotopes used by SIMNRA have been taken from the rec ommended values of the 1995 update to the atomic mass evaluation 14 The abundances of the isotopes have been taken from the recommended values of isotopic abundances in 15 Isotopic masses and abundances are stored in the file ATOMDATA DAT This file contains also the data of some isotopes which do not occur naturally but may be created in nuclear reactions and ar
6. to export spectra of individual elements or isotopes to a file e Copy Page Copies the visible graphics to the clipboard in enhanced metafile for mat You can paste the graphics into any word processing program such as Microsoft Word 3 4 Setup menu 3 4 1 Setup Experiment In the Setup Experiment menu the global parameters of the backscattering experi ment are defined Incident ion Selects the incident ions For incident protons H D T He or 4He ions the ions are selected by clicking the appropriate radio button For incident heavy ions select Other and enter the ions name in Other ion Element for example Si Cl I Lowercase and uppercase letters in the ions name are treated similar you can enter silicon as Si si SI or sI The ions mass is selected from the drop down box Energy Energy of the incident ions in keV Geometry Geometry of the experiment Incident angle a exit angle O and scattering angle 0 a and O are measured towards the surface normal see fig 3 2 All angles in degrees Note 1 0 lt a lt 90 Note 2 0 lt 8 lt 180 If 90 lt 6 lt 180 then transmission through the target is calculated Detector geometry Click the button to enter the detailed geometry of the detector beam diameter detector diaphragm width distance sample detector and shapes of incident beam and detector diaphragm This is only necessary if geometrical straggling due to the finite wid
7. 40 aw J 20 hae 4 0 1 1 S Es PA eee ci Depth 10 atoms cm Figure 4 7 Contributions of electronic energy loss straggling geometrical straggling and detec tor resolution to the total energy straggling at the sample surface for 2 6 MeV He incident on Co 99D0 01 Beam diameter 0 5 mm aperture width 0 5 mm distance sample detector aperture 100 mm detector resolution 15 keV FWHM Top RBS geometry with 0 165 a 0 8 15 for He backscattered from C Bottom ERDA geometry with 0 30 a 75 6 75 for the deuterium recoils TT Figure 4 8 Examples of ion trajectories with one two and three scattering events 4 8 Multiple and plural scattering 4 8 1 Overview SIMNRA uses straight lines as trajectories for the ingoing and outgoing particles with one single scattering event connecting the trajectories of the particles see fig 4 8 left This is only an approximation to physical reality because the particles on the ingoing and outgoing path suffer many small angle deflections with small scattering angles this has been called multiple scattering and additionally may perform more than one scattering event with large scattering angle see fig 4 8 middle and right before they are scattered towards the detector This has been called plural scattering Multiple scattering has been recently reviewed by Szilagy et al 31 Multiple scatter ing results in an angular spread of the particles and therefore in
8. a u o 370 375 380 385 390 Energy keV Figure 4 12 Angular and energy distributions in a depth of 1 09 x 1018 atoms cm for 500 keV incident He in Au at normal incidence The angle of trajectory is measured towards the surface normal Solid line TRIM SP calculation Dashed line SIMNRA 84 E E AE 2 After scattering the particles have the energies E K 0 E El KE E K 0 E with K the kinematic factor The FWHM of the energy spread contribution on the ingoing path AE could be obtained from AEn E El 4 67 However generally EY and E are not symmetric with respect to Es and AE obtained from eq 4 67 will neither describe the width of the high energetic part of the distribution nor the width of the low energetic part correctly Therefore SIMNRA uses AEn 2 E E 4 68 with E the higher energy This describes at least the higher energetic part of the distri bution correctly The energy spread contribution on the outgoing path is obtained in the following way a particle starting with some exit angle p in the depth x may be deflected on its outgoing trajectory by multiple scattering in such a way that it has the correct angle O at the target surface to reach the detector see Fig 4 13 bottom These particles have the energy Ela and E at the target surface and scattering angles 6 and 0 Again Elu and 6 are not independent As in the case of the energy spread cont
9. atoms cm TRIM SP o E o Z S gt S Distribution function a u 0 00 30 40 50 60 70 80 90 Angle of trajectory deg 0 10 Distribution function a u o o 0 00 e 200 350 400 450 500 Energy keV Figure 4 9 Angular and energy distributions in a depth of 1 6 x 10 atoms cm for 500 keV incident He in Au incident angle a 60 The angle of trajectory is measured towards the surface normal Solid line TRIM SP calculation Dashed line SIMNRA 81 500 keV He in Au a 60 Depth 3 25x10 atoms cm TRIM SP 0 04 SIMNRA 0 02 Distribution function a u Lu At 80 90 0 00 H Seil 30 40 0 03 0 02 0 01 Distribution function a u 0 00 300 350 400 450 500 Energy keV Figure 4 10 Same as Fig 4 9 but for a depth of 3 25 x 10 atoms cm 82 500 keV He in Au a 60 0 04 Depth 6 47x10 atoms cm TRIM SP 0 02 Distribution function a u 0 00 etl ais 30 40 50 60 70 80 90 Angle of trajectory deg 0 015 0 010 4 0 005 Distribution function a u 0 000 300 350 400 450 500 Energy keV Figure 4 11 Same as Fig 4 9 but for a depth of 6 47 x 10 atoms cm 83 500 keV He in Au a 0 Depth 1 09x10 atoms cm gt bo 0 2 0 1 Distribution function a u 2 o hb oO N o Lu oO Distribution function
10. 1 MeV amu This may result in the appearance of kinks in the spectrum Nuclear stopping for incident hydrogen deuterium and tritium ions is negligible for incident energies above about 10 keV amu 1 and is neglected by SIMNRA Se 61 Helium If Andersen Ziegler stopping is selected then for incident He and He ions the electronic stopping power data by Ziegler 2 are used for all elements The electronic stopping power Se in eV 101 atoms cm for incident He ions with energy E in keV is given by 5 g a Tia Ge with Stow Ai E 4 28 and As de Suen E h 4 Ae 4 29 A As are fitting coefficients and tabulated in 2 They are stored in the file STOPHE DAT Equations 4 27 4 29 are valid for 1 keV lt E lt 10 MeV He stopping at higher energies above 10 MeV is not implemented in the program The stopping power of He is identical to the stopping power of He at the same velocity 2 The stopping power of He with energy E is obtained by taking the stopping power value at the energy E He 4 3 E He The stopping power for He is valid in the energy range 10 keV lt E lt 7 5 MeV Nuclear stopping for incident helium ions is calculated with the Krypton Carbon Kr C potential 26 The nuclear stopping Sn in eV 10 atoms cm for He ions with incident energy E in keV is given by 8 462 Z1 Zo M SS Ss 1 3 4 30 M M zi 2 S Sa Sn is the reduced nuclear stopping and Z1 M are th
11. 165 1800 4700 C6LiLiC R33 Mayer 2001 TOR 150 2500 7000 19F6LILiF R33 Pastuovi 1998 27 A 140 4000 8000 Nurmela 6Li A1 140 R33 Nurmela 1999 7Al 170 4000 8000 Nurmela 6Li Al_170 R33 Nurmela 1999 Si 140 4500 7750 Nurmela 6Li Si_140 R33 Nurmela 1999 Si 170 4500 7750 Nurmela 6Li Si 170 R33 Nurmela 1999 Ti 140 5000 11000 Nurmela 6Li Ti_140 R33 Nurmela 1999 Ti 170 5000 11000 Nurmela 6Li Ti_170 R33 Nurmela 1999 C 165 2900 5400 C7LiLiC R33 Mayer 2001 180 170 2750 6250 1607LiLiO R33 Rauhala 1988 27 A 140 4000 7900 Nurmela 7Li Al_140 R33 Nurmela 1999 27Al 170 3460 7960 27A17LiLiA1 R33 R is nen 1993 Si 140 4500 7800 Nurmela 7Li Si_140 R33 Nurmela 1999 Si 170 4450 7710 Si7LiLiSi R33 R is nen 1993 Ti 140 5250 11000 Nurmela 7Li Ti_140 R33 Nurmela 1999 Ti 170 4950 11460 Ti7LiLiTi R33 R is nen 1993 28 Table 3 4 Non Rutherford ERDA cross sections 29 0 Lab Energy keV File Reference H He H He 20 2000 3000 1HTP1X1 R33 Terwagne 1996 H He H He 30 1900 3000 THTPIX2 R33 Terwagne 1996 H a H a 30 2500 4500 1HAP4HE30 R33 Bogdanovi Radovi 2001 H a H a 40 2500 4500 1HAP4HE40 R33 Bogdanovi Radovi 2001 H a H a 45 2500 4500 1HAP4HE45 R33 Bogdanovi Radovi 2001 H a H a 50 2500 4500 1HAP4HE50 R33 Bogdanovi Radovi 2001 H a H a 55 2500 4500 1HAP4HE55 R33 Bogdanovi
12. 91 Distribution Gamma Figure 4 18 Comparison of Gaussian distribution functions centered at 1 dashed lines and Gamma distribution functions solid lines with mean value d 1 and different standard deviations E the thickness variation is much smaller than the mean film thickness o d 0 1 only the low energy edge of the film is affected by the roughness and gets broader With increasing roughness the broadening of the low energy edge increases until at o d 0 6 the high energy edge begins to decrease The energy Eu at which the low energy edge has decreased to its half height remains fairly constant until large roughness amplitudes of the order o d 0 6 i e until the high energy edge begins to decrease For sufficiently thick films i e if the film is completely resolved this energy is therefore a rather robust measure of the mean film thickness even for large roughnesses as long as the high energy edge is not affected The energy spectrum of 1 5 MeV He backscattered from a rough Ni film deposited on polycrystalline carbon is shown in Fig 4 20 The measured spectrum is well reproduced in the simulation by a mean Ni layer thickness of 2 17 x 1018 Ni atoms cm 238 nm and a roughness with standard deviation o 2 12 x 10 Ni atoms cm 23 nm solid line The experimental data are not well reproduced by the spectrum of a smooth Ni layer dashed line The roughness of the Ni film was determined from line scans with
13. Data Deletes all simulated data from the plot Zooming into the plot To zoom into the plot click with the left mouse button into the upper left corner of the range you want to zoom in Keep the mouse button down and tear a rectangle to the lower right corner of the zooming range Panning Click with the right mouse button into the plot keep the mouse button down and move the mouse Zooming out Click with the left mouse button into the plot Keep the mouse button down and move the mouse towards the upper left corner Or use Plot Unzoon 37 3 10 Options menu e Create Reaction List SIMNRA uses a file named CRSEC LST in the cross sections directory to know which cross section data are available Create Reaction List will create this file You have to recreate the reaction list if you add or delete cross section data files see section 3 14 Note In some cases files are not readable by SIMNRA due to format errors These files will be ignored The program displays a list of all ignored files e Preferences Allows to set global program preferences These preferences are stored permanently The Print tab White background for print If checked then the grey background of the graph is changed to white in the printout Show Print What dialog If checked then a dialog asking what to print experimental conditions graph is displayed If unchecked this dialog is omit ted and everything is printed The Spectrum Data t
14. EnergylossInLayer Function EnergylossInLayer Z1 Integer M1 Double E Double TargetID Integer lay Integer Double Description Energy loss of an ion Z1 in a target or foil layer The layer is tra versed perpendicularly incident angle o and exit angle are ignored The stopping power model is selected with Calc ZBStopping p 126 and Calc HighEnergyStopping p 125 and may be additionally modi fied by a correction factor to the stopping power see Section 3 5 The accuracy of the energy loss calculation is influenced by the settings of Calc AutoStepwidthOut p 123 and Calc dE0ut p 124 Parameters Z1 Nuclear charge of the ion M1 Mass of the ion amu 141 E Incident energy keV TargetID Selects target or foil lay Number of the target or foil layer Return Value Returns the energy loss in the layer keV Related Properties and Methods TargetID 141 Stopping StoppingInLayer 143 StoppingInElement Function StoppingInElement Z1 Integer M1 Double E Double Z2 Integer Double Description Stopping power of an ion Z1 in element Z2 The stopping power model is selected with Calc ZBStopping p 126 and Calc HighEnergyStopping p 125 Parameters Z1 Nuclear charge of the ion M1 Mass of the ion amu E Incident energy keV Z2 Nuclear charge of the target element Return Value Returns the stopping power in element Z2 keV 10 atoms cm 142 Related Properties an
15. Hechtl and J Roth J Nucl Mater 265 1999 22 96 R Amirikas D N Jamieson and S P Dooley Nucl Instr Meth B77 1993 110 101 107 J Vorona J W Olness W Haeberli and H W Lewis Phys Rev 116 1959 1563 107 M Wielunski M Mayer R Behrisch J Roth and B M U Scherzer Nucl Instr Meth B122 1997 113 109 J E E Baglin A J Kellog M A Crockett and A H Shih Nucl Instr Meth B64 1992 469 109 F Besenbacher I Stensgaard and D Vase Nucl Instr Meth B15 1986 459 109 156
16. Institut fiir Plasmaphysik You agree that any copies of SIMNRA will contain the same proprietary notices which appear on and in the software You are not alowed to distribute any modified versions of SIMNRA 4 Warranty SIMNRA is provided AS IS AND WITH ALL FAULTS The author and the Max Planck Institut fiir Plasmaphysik make no warranties with respect to the program and the program data The author and the Max Planck Institut ftir Plasmaphysik do not warrant that the program or any of its data is error free The author and the Max Planck Institut fiir Plasmaphysik disclaim all warranties with respect to the software or its data either express or implied including but not limited to implied warranties of merchentability fitness for a particular purpose and nonfringement of third party rights No liability is assumed for damages direct or consequential which may result from the use of this software Contents 1 Overview 1 2 Installation 3 21 Syster ENEE ue do cr Ra ee EI AEN e ee d A A 22 o 2 ag ows SE Be ee a ee ee be e Er Ae Ba 3 23 Uninstalling SIMN RA ec c eo D e oe Pa ee ea ee A ee RS 3 3 Using SIMNRA 5 Ol Basie STOPS s oreg ao eH BAe ee aha ow eee EI Be Ee ca Bl SS 5 Ge Pile mem e ek i a BO ee a Bee EO 6 Bis BANE TORU oie ee cy Pon oe kek eR ee A RN 9 Oe EEN 2 do e ee Be ee ee ee bee peeing Eo 10 3 4 1 Setup Experiment o 10 3 4 2 Detector geometry 13 34 3 Setup Calculation lt se 2 662654 sra SG eee es 14
17. a spread of path lengths Due to the path length differences we get an energy spread of the particles in a given depth Plural scattering with 2 3 4 scattering events is responsible for the background behind the low energy edge of high Z elements on top of low Z elements and the steeper increase of the spectra towards low energies than calculated with single scattering 45 46 47 48 49 SIMNRA is able to calculate dual scattering i e all particle trajectories with two scattering events 4 8 2 Multiple small angle scattering Angular and lateral spread due to multiple collisions with small deflection angles was treated analytically and numerically by Sigmund et al 50 51 for realistic screened interaction potentials of the Thomas Fermi and Lenz Jensen type However their theory is only valid for 1 Single elemental targets 2 The stopping of ions is neglected Due to these two assumptions the original Sigmund theory is only of limited practical use But as will be shown below the Sigmund theory can be extended to multi elemental targets with stopping The Sigmund theory is valid for small angle deflections with each deflection lt 20 78 The Sigmund theory is formulated with the reduced variables 7 and which are defined by 7 20 d 4 63 T is the reduced thickness a is the Lindhard Scharff screening radius and d the real target thickness in atoms Jem is defined by d D 4 64 with 8 a a A 4
18. any user defined format A dynamic link library dll has to be supplied by the user which reads the data and passes them to SIMNRA See Section 3 13 for more details Write Spectrum Data This menu item exports the experimental and simulated data as columns into an ASCII file You can import this file easily into any plot program such as Excel Origin or Mathematica The file format is as follows The first line is a comment line which contains infor mation about the contents of the different columns The first column is the channel number the second column contains the experimental data This column is set to zero if experimental data are not available the third column contains the simulated data This column is set to zero if simulated data are not available If the Element spectra option in Setup Calculation is checked then the next columns will contain the simulated spectra for each element in the target The columns are sep arated with blanks RUMP Read RBS File This menu item allows to read a binary RBS file pro duced by RUMP containing experimental parameters Type of incident particles incident energy scattering geometry etc and spectral data Note 1 RUMP stores the description of the sample and the absorber foil in sample description files LCM You can read sample description files with RUMP Read Sample Description File Note 2 The RBS file may contain only one experimental spectrum Compression l
19. broadening due to the characteristics of the stopping power curve and for larger energy losses the beam width gets larger than in Bohr s theory When the mean beam energy has decreased below the energy of the stopping power maximum the beam width becomes skewed As can be seen from fig 4 3 the deviation of the Chu correction from Bohr s theory is largest for high Z and low energies Fig 4 5 shows the beam width FWHM of 1 MeV 4He penetrating through gold The deviation from Bohr s theory is large The stopping power maximum is at about 960 keV For low energy losses the beam width increases due to the statistical broadening because the nonstochastic skewing which occurs for beam energies below the stopping power maximum is small and the stochastic broadening wins For larger energy losses however the beam width gets skewed Fig 4 6 shows the measured RBS spectrum for 1 0 MeV He ions incident on a gold layer with a thickness of about 100 nm and a scattering angle of 165 compared with simu lations using Bohr straggling and Chu straggling As can be seen at the low energy edge of the layer the Bohr straggling is broader than the experimental data The Chu straggling 70 2 5 MeV He in Si S10 20 Straggling keV FWHM Depth 1 o atoms cm Figure 4 4 Beam width FWHM of 2 5 MeV He ions penetrating through silicon The solid line is the beam width calculated by SIMNRA using eq 4 51 the dashed line is the predi
20. cross section file format April 2002 By I C Vickridge Groupe de Physique des Solides UMR 7588 du CNRS Tour 23 Universits de Paris 7 et 6 2 Place Jussieu 75251 Paris B 1 Introduction In September 1991 in response to the workshop on cross sections for Ion Beam Analysis IBA held in Namur July 1991 Nuclear Instruments and Methods B66 1992 a simple ascii format was proposed to facilitate transfer and collation of nuclear reaction cross section data for Ion Beam Analysis IBA and especially for Nuclear Reaction Analysis NRA Although intended only as a discussion document the ascii format referred to as the R33 DSIR Report 33 format has become a de facto standard In the decade since this first proposal there have been spectacular advances in computing power and in software usability however the simplicity and cross platform compatibility of the ascii character set has ensured that the need for an ascii format remains Nuclear reaction cross section data for Nuclear Reaction analysis has been collected and archived on the Sigmabase websites google Sigmabase for about the last 7 years This data has largely been entered in the R33 format although there is a series of elastic cross sections that are expressed as the ratio to the corresponding Rutherford cross sections that have been entered in a format referred to as RTR ratio to Rutherford During this time the R33 format has been modified and added to firstly to take into
21. distribution is asymmetric with a steep increase at the high energy side and a tail towards lower energies which is also not reproduced by SIMNRA The half width of the energy distribution is somewhat underestimated by SIMNRA However it should be noted that the influence of multiple scattering for normal incidence is small The half width of the multiple scattering energy distribution shown in Fig 4 12 is about 3 keV which is considerably smaller than energy loss straggling about 8 8 keV FWHM and the energy resolution of the detector Therefore the deviations at normal incidence between SIMNRA and physical reality are hardly ever visible To calculate the energy spread due to multiple scattering the energy spread contribu tions on the ingoing and outgoing paths have to be considered The energy spread contribution on the ingoing path is obtained in the following way Particles without angular spread have a mean energy E and incident angle o in a given depth x see Fig 4 13 top Particles with angular spread to one side have incident angle a A 2 with A the FWHM of the angular spread and energy Hl E AE 2 with AE the FWHM of the energy spread see Fig 4 13 top The scattering angle with fixed exit angle 3 for these particles is 6 Note that E and 0 are not independent The same applies for particles with angular spread to the other side These particles have the energy 80 500 keV He in Au a 60 Depth 1 6x10
22. format is described in full detail by I C Vickridge in the file R33Help htm which should be present in your SIMNRA installation directory and in Appendix B SIMNRA reads the updated R33 file format of April 2002 but is also able to read older R33 files which conform to the original specification from the year 1991 An example for a valid file in the R33 format is shown in fig 3 7 Each line must end with lt CR gt lt LF gt Carriage Return and Line Feed SIMNRA uses not only the data points but also a part of the information supplied in the file header The following lines are used by SIMNRA and must be present in the file Though the lines may be arranged in any order it is recommended to arrange them in the same order as shown in Fig 3 7 Any other entries than the ones listed below are ignored by SIMNRA but may be necessary to form a valid R33 file See Appendix B or the file R33Help htm for details e A line containing the string Source The rest of the line has to contain a reference or other source for the data and will appear as description in the reaction menu e A line containing the string Reaction SIMNRA will interpret the nuclear reaction string written in that line In the example of fig 3 7 160 d a0 14N to find out which particles are involved in the nuclear reaction The masses of the particles are ignored e A line containing the string Masses SIMNRA will read the masses of the particles from thi
23. in one layer must be equal to 1 0 999 lt gt c lt 1 001 If the sum of concentrations is not equal to 1 the word concentration is written in red colour if the sum of concentrations is equal to 1 the word concentration is written in black colour You can use the small buttons to set the concentration of the element to 1 minus the sum of concentrations of all other elements c 1 gt 45 j Isotopes These buttons can be used to change the concentrations of isotopes of that element in the actual layer You will need this only if this element does not have the natural composition of isotopes You can create for example a layer of enriched 1 C on top of 2C or the like The sum of concentrations of all isotopes of one element must be equal to 1 Note The Isotopes check box in the Setup Calculation menu must be checked to manipulate individual isotopes Correction factor s for stopping power SIMNRA uses Bragg s rule to cal culate the stopping power of a layer see Section 4 6 3 for more details However it has been shown experimentally that for several compounds like hydrocarbons or oxides deviations from Bragg s rule occur To account for deviations from Braggg s rule a correction factor f can be used and the program will use the stopping power S E as function of energy E S E Sg SBragg E 3 2 19 SBragg E is the stopping power according to Bragg s rule Note that the factor f is energy independ
24. likely to hit a segment which is perpendicular to the incident trajectory than an inclined segment and obviously it is impossible to hit a segment which is tilted parallel to the incident beam It is important to note that a profiler or a scanning tunneling microscope STM which samples the surface at a constant step width parallel to the surface measures the distribution p y rather than p y Large tilt angles are under represented and tilt angles of 90 cannot be measured at all RBS NRA and ERDA spectra of a smooth film on a rough substrate are approximated by a superposition of M spectra with different local incident angles amp where a la y 4 74 and local exit angles 6 The choice of is discussed below M can be adjusted by the Number of angular stepsinthe Setup Calculation menu see section 3 4 3 The weight of each sub spectrum is determined according to the distribution function p y For each sub spectrum the substrate is treated to be smooth i e a spectrum for a smooth layer but with angles and 3 is calculated Incident angles amp gt 90 are excluded This represents a line segment which cannot be hit by the incident beam As in the case of a rough film on a smooth substrate surface correlation effects like shadowing of one line segment by another and multiple surface crossings are neglected By using a simple 2 dimensional model one can choose analogue to Eq 4 74 as local exit angle B PB 18 4 7
25. multiple scattering of 500 keV incident He penetrating gold at an angle a 60 at different depths The model used by SIMNRA is compared to TRIM SP calculations TRIM SP is a Monte Carlo code which calculates realistic trajectories for each incident particle taking all collisions with target atoms into account 52 53 1000 incident particles were used for Figs 4 9 4 11 The stopping power data from 2 were used in both calculations In Fig 4 9 the incident beam has reached a depth of 1 6 x 10 atoms cm and has lost about 35 keV due to electronic energy loss The Gaussian angular and energy dis tributions which are used by SIMNRA underestimate the wings of both distributions however the central part of the distributions is sufficiently well reproduced In Figs 4 10 and 4 11 the incident beam has reached depths of 3 25 x 10 atoms cm and 6 47 x 10 atoms cm respectively The electronic energy losses are about 70 keV and 135 keV respectively The angular and energy spread due to multiple scattering get broader and the approximation with a Gaussian shape now is better fulfilled As already mentioned the approximations used by the program are not fulfilled for normal incidence Figure 4 12 shows the angular and energy distributions of 500 keV incident He in Au in a depth of 1 09 x 1018 atoms cm comparing TRIM SP calculations and SIMNRA The angular distribution has a minimum at 0 which is not reproduced by SIMNRA The energy
26. no easy recipe for the best choice of a fixed stepwidth Usually the best compromise between speed and accuracy is automatic stepwidth control Cutoff Energy All particles are calculated until their energy has decreased below the cut off energy You may speed up the calculation if you increase the cut off energy The lowest possible value for the cut off energy is 10 keV Isotopes If checked backscattering from all isotopes of all elements in the target is calculated Especially for heavy elements with many isotopes this will slow down the calculation significantly If unchecked the program will use only the mean masses of the elements Default is checked Important Non Rutherford cross sections and nuclear reactions are only available if Isotopes is checked Straggling If checked electronic energy loss straggling and geometrical straggling if selected see section 3 4 2 is taken into account Default is checked Multiple Scattering If checked straggling due to multiple small angle scattering will be calculated Default is unchecked Dual Scattering Most particles are scattered into the detector with only one scattering event with large scattering angle However some particles may suffer more than one scattering event with large scattering angle before they reach the detector see fig 3 4 This is called plural scattering and results for example in the low background behind the low energy edge of high Z layers on top of low Z ele
27. reaction string in the same order as the mass entries The Zs could also be deduced directly from the reaction string but see the comment in the Masses entry O Natural lt string r string r gt Note This entry caters for elastic cross sections measured from targets that contain a mixture of isotopes from which the elastically particles are not resolved It consists of a list of isotopes and atom proportions or the value natural case insensitive which means that a target of naturally occurring isotopic composition has been used Isotopes are specified as for the reaction string without shorthand notation Example Target 12C 23 0 18C 26 0 If the proportions do not sum to 100 then it is assumed that they are relative amounts In the example given 23 49 of the atoms are 12C and 26 49 are 13C If the Composition entry exists and has a legal value then the values in the masses entry should correspond to the appropriate weighted sum indicated in the composition keyword For example if the target for an elastic cross section is natural silicon then the mass given should be 28 086 the weighted sum of stable Si isotopes in natural abundance R 0 0 lt r r r r r gt Note A list of up to five Q values expressed in keV separated by legal separators As explained in the Reaction entry some cross sections are for multiple particle groups for example when the groups are not resolved experimentall
28. real particle energy but a somewhat smaller energy This has been called pulse height defect The pulse height defect is due to 1 The energy and particle dependent energy loss in the top electrode and the dead layer of the semiconductor detector 9 10 11 2 Only the electronic energy loss in the active detector region is measured while nuclear energy loss is not detected 9 The nuclear energy loss is energy and particle dependent 3 Heavy ions produce a high density of electron hole pairs The electron hole pairs may recombine before separation by the electric field in the detector This has been called plasma effect 9 The plasma effect is energy and particle dependent The energy dependence of the pulse height defect results in a nonlinearity of the energy calibration The energy loss in the top electrode and the dead layer can be accounted in the following way e You can create a foil consisting of two layers in front of the detector Layer 2 is composed of the material of the top electrode usually Au and has the thickness of the electrode usually the thickness is supplied by the manufacturer of the detector Layer 1 is composed of silicon in the case of a silicon detector and has the thickness of the dead layer the dead layer is the insensitive region near the electrode The dead layer thickness can be obtained only experimentally by tilting the detector For swift ions protons and He this should be sufficient to achiev
29. section 3 3 for details 2 Via ASCII file With File Write Spectrum Data the experimental and simu lated data are exported as columns into an ASCII file You can import this file into any plot program such as Excel Origin or Mathematica See section 3 2 for details 3 12 2 RUMP SIMNRA can read and write sample description files LCM and read RBS files RBS used by the RUMP program Sample description files contain the composition of the sample and the absorber foil These files can be read and written by File RUMP Read Sample Description File and File RUMP Write Sample Description File RUMP stores experimental parameters Type of incident particles incident energy scat tering geometry etc and spectral data in binary files with extension RBS These files can be read by File RUMP Read RBS File SIMNRA can not write RBS files Sample Description Files SIMNRA supports only a subset of the RUMP sample description commands The sup ported command are listed in Table 3 6 All other commands will be neglected Note that especially the RUMP commands Equation Species and Fuzz are not supported If your sample description file contains these commands they will be neglected and a warning will be shown RBS Files SIMNRA can read RUMP s RBS file format version 1 1 from 8 94 with the following limitations 1 Data compression level 3 zero compressed is not implemented Levels 0 2 uncom pressed real uncompressed in
30. smooth W layer 3 6 um on a smooth C substrate including plural scattering Dashed line Calculated spectrum for a rough W layer 3 5 um o 0 30 wm on a rough substrate FWHM 20 Solid line As dashed line but including plural scattering 102 e Experimental Smooth layer 400 Rough layer o 0 3 um Rough layer o 0 6 um 300 200 Counts o e Experimental Substrate roughness 10 400 Substrate roughness 20 Substrate roughness 30 300 200 400 600 800 Channel Figure 4 27 Same experimental data as in Fig 4 26 compared to simulation calculations with different roughness parameters Top Calculations for a rough carbon substrate FWHM 20 and different W layer roughnesses characterized by a Gamma distribution with standard deviation o Bottom Calculations for a rough W layer o 0 3 um and different substrate roughnesses char acterized by a Lorentz distribution of tilt angles with different FWHM s Mean W layer thickness 3 5 wm plural scattering included 103 Chapter 5 Examples This chapter gives several examples for the abilities of SIMNRA All backscattering spectra were measured at the IPP Garching at a scattering angle 0 165 The solid angle of the detector was 1 08 x 107 sr A standard surface barrier detector with a nominal energy resolution of 15 keV FWHM was used 5 1 RBS Rutherford cross sections Fig 5 1 shows the measured and simulated spectra for 1 0 MeV He in
31. the local surface normal Such a rough surface is described by a distribution of local tilt angles p y The concept of a local tilt angle was already used by Kiistner et al for the calculation of the sputtering yield of rough surfaces by ion bombardment in the energy range 100 eV to several keV 68 In Kiistner s work the rough surface was treated as a fully 3 dimensional object which was necessary due to the 3 dimensional nature of the collision cascades created by keV ions In MeV ion beam analysis the trajectories of the incident and emerging ions can be approximated with good accuracy by straight lines and we have to consider only the intersection of the plane which is formed by the directions of the incident and emerging ions and the target surface see Fig 4 22 This is only a 2 dimensional line profile as the one shown in Fig 4 17b The tilt angle distribution is given by p y This distribution describes the frequency of occurence of a line segment inclined by y A rough surface without preferential orientation has a mean tilt angle 90 P eee 4 72 The probability distribution p y of hitting a surface tilted by p by an incident ion is given by Del ply cos a p 4 73 with the incident angle a of the ion is measured towards the surface normal of a non inclined surface The factor cos a p is due to the projection of the line segment into the 96 plane perpendicular to the incident ion trajectory It is more
32. this may be accommodated in the Comment field O C lt String gt O C lt String gt Note The address of the person or institution responsible for creating the R33 file Up to nine lines of address information may be included This can include telephone numbers emails and so on R 0 lt n gt Note The serial number will be a number providing a unique link back to the Exfor dataset from which the R33 file was generated The default value of zero means that this number has not been assigned R lt String gt Note the reaction string is written in a standard format that can be parsed without too much difficulty It conforms to the usual notation of target nucleus incident ion light product product nucleus Nuclei are specified by their chemical symbol preceded by A e g 2881 or 6Li The mass number is required Some common light species may also be represented by shorthand notation with lower case being required n neutron p proton d deuterium t triton a alpha particle h 3He L 2X 1AY g gamma The light product may correspond to a particular energy level of the product nucleus This is signalled by a postfix on the light product For example 16O d p1 170 is the d p reaction which leaves the residual 17 oxygen in the 1st excited state Some cross sections may be sums of several particle groups cor responding to different excited states of the compound or product nucleus Usually such a cross se
33. unchecked the program will use the medium energy formula which is valid only in the range 10 keV amu 1 MeV amu also at higher energies E gt 1 MeV amu The difference between the two formulas usually is small This switch is necessary because the two stopping power formulas do not fit smoothly together at 1 MeV amu The stopping power jumps at 1 MeV amu resulting in artificial kinks and steps in the simulated spectra This problem is overcome if High energy stopping is unchecked however this will result in less accurate stopping powers for energies gt 1 MeV amu A better solution is to use the Ziegler Biersack stopping powers where this problem does not occur This switch does not have any influence on the calculation of the stopping power of helium ions and is disabled For helium ions always the medium energy formula is used which is valid for all energies below 10 MeV The default is checked e Number of thickness steps Used for the calculation of layer roughness A rough 16 Figure 3 4 Examples of ion trajectories with one two and three scattering events layer is approximated by the superposition of N spectra with different layer thick nesses where N is the number of thickness steps If N is small the superposed spectrum may contain steps Larger values of N result in smoother spectra but slow down the calculation considerably Default is N 10 Note One rough layer requires the calculation of N spectra two rough layers o
34. 000 1 100000 Helium He He 0 25 2500 1 100000 Heavy ions 1 100000 1 100000 Table 3 1 Energy ranges in which the different stopping power formulas are valid High energy electronic stopping formula for energies gt 2 5 MeV amu from 1 not implemented 18 3 5 Target menu 3 5 1 Target Target In this menu the target is created A target consists of layers Each layer consists of different elements and has some thickness The composition of a layer does not change throughout his thickness To simulate a concentration profile you have to use multiple layers The layer number 1 is at the surface of the target the layer number 2 is below layer 1 and so on see fig 3 5 Thickness Thickness of the layer in 10 atoms cm The conversion factor from ug cm or um to atoms cm can be determined with Calculate Density for pure elements Number of Elements Number of different elements in this layer The maximum number of different elements in a layer is 20 Element Name of the element for example Si W Au Lowercase and uppercase letters in elements names are treated similar you can enter silicon as Si si SI or sl XX means that this element is unknown The special symbols D for deuterium T for tritium and A for tHe can be used Concentration Atomic concentration of the element in the actual layer The con centration c must be 0 0 lt c lt 1 0 The sum of the concentrations of all elements
35. 11BPPB_1 R33 Symons 1963 B p p B 161 4 1100 3800 11BPPB R33 Segel 1965 C p p C 150 1000 3500 12CPPC_1 R33 Amirikas 1993 C p p C 165 1000 3500 12CPPC R33 Amirikas 1993 C p p C 170 300 700 PC_LI93A RTR Liu 1993 C p p C 170 700 2800 PC_LI93B RTR Liu 1993 C p p C 170 300 3000 PC_LI93C RTR Liu 1993 C p p C 170 700 2500 PC_RAS5A RTR Rauhala 1985 C p p C 170 996 3498 PC_AM93A RTR Amirikas 1993 C p p C 170 1000 3500 12CPPC_2 R33 Amirikas 1993 2C pp C 179 2 4000 6600 12CPP179 R33 Tosaki 2000 2C pp PC 168 2 400 4500 PC_JA53A RTR Jackson 1953 TEN p p N 150 800 1900 PN_TA56A RTR Tautfest 1956 PN pp N 152 1035 1075 PN_HA57A RTR Hagedorn 1957 TN p p N 152 1450 1625 PN HA57B RTR Hagedorn 1957 14N p p N 152 650 1800 PN_HA57E RTR Hagedorn 1957 MN p p N 155 2 1850 3000 PN_LA67A RTR Lambert 1967 N p p N 158 7 1735 1760 PN_HA57C RTR Hagedorn 1957 TEN p p N 158 7 1785 1815 PN_HA57D RTR Hagedorn 1957 MN p p N 159 5 600 4000 PN_BA59A RTR Bashkin 1959 N p p 7N 165 1850 3000 PN_LA67B RTR Lambert 1967 14N p p N 167 2 3600 4100 PN_OL58A RTR Olness 1958 MN p p N 170 1450 2300 PN_RA85A RTR Rauhala 1985 O p p O 149 5 2450 2850 PO_GO65A RTR Gomes 1965 O p p O 170 1000 3580 PO_AM93A RTR Amirikas 1993 O pp O 170 700 4000 160PPO R33 Gurbich 1997 TF p p F 150 2000 5000 PF_BO93A RTR Bogdanovic 1993 TF p p F 160 500 1300 PF_DE56A RTR Dearnaly 1956 TF p p F 160 1300 2064 PF_DE56B RTR Dearnaly 1956 T
36. 18 look as follows dE T Le e 4 1 ES 4 19 E d de db da a o E sd dE d de de a y ae an ES SE E e le 4 21 With e d and e evaluated at Ep 1 2 1 2 E Ey Aze Az er gan e e e 2e 4 22 See ref 12 for a discussion of the accuracy of the above equations d and e are calculated by SIMNRA by numerical differentiation of the stopping power data The stepwidths Ax for the incoming and outgoing particles can be adjusted in the Setup Calculation menu The stepwidth of the incoming particle should be kept small in the range of 10 keV due to the cross section calculation see section 4 1 The stepwidth for outgoing particles can be chosen much larger due to the accuracy of eq 4 22 Typical values for the stepwidth of outgoing particles are around 200 keV 60 4 6 Stopping power data SIMNRA offers the possibility to use two different sets of electronic stopping power data for the stopping of swift and heavy ions in all elements The well known electronic stopping power data by Andersen and Ziegler 1 2 or the electronic stopping power data by Ziegler Biersack and Littmark 3 Generally the Ziegler Biersack data are more accurate and are also used by the SRIM 97 formerly TRIM program in calculations of stopping powers and ranges The difference between the two data sets is typically lt 5 but may be larger in some cases especially for ions other than H or He See 22 23 24 for a discussion of the ac
37. 3 44 45 46 47 48 49 J Liu Z Zheng and W K Chu Nucl Instr Meth B118 1996 24 61 J F Ziegler Nucl Instr Meth B136 138 1998 141 61 H Paul A Schinner and P Sigmund Nucl Instr Meth B164 165 2000 212 61 H Paul http www exphys uni linz ac at stopping 61 J F Ziegler Stopping Cross Sections for Energetic Ions in all Elements vol 5 of The Stopping and Ranges of Ions in Matter Pergamon Press New York 1980 62 J F Ziegler and J M Manoyan Nucl Instr Meth B35 1988 215 63 63 63 64 64 65 66 66 60 86 W H Bragg and R Kleeman Philos Mag 10 1905 318 65 D Boutard W M ller and B M U Scherzer Phys Rev B38 5 1988 2988 66 D I Thwaites Nucl Instr Meth B27 1987 293 66 E Szil gy F P szti and G Amsel Nucl Instr Meth B100 1995 103 67 68 70 70 75 78 79 79 85 85 E Szil gy Nucl Instr Meth B161 163 2000 37 67 M A Kumakhov and F F Komarov Energy Loss and Ion Ranges in Solids Gordon and Breach Science Publishers New York London Paris 1981 68 68 J R Bird and J S Williams Eds Jon Beams for Materials Analysis Academic Press Sydney New York Tokyo 1989 68 68 68 J Tirira Y Serruys and P Trocellier Forward Recoil Spectrometry Plenum Press New York London 1996 68 P V Vavilov Soviet Physics J E T P 5 1957 749 68 68 N Bohr Mat Fys Medd Dan Vid Selsk 18 8 1948 68 69 J W Mayer and E Rimini
38. 3 16 2 OLE automation summary This section describes OLE 2 0 automation support in SIMNRA SIMNRA is an OLE automation server which allows other applications to control SIMNRA This is useful for batch processing of a large number of spectra and the like A short overview of the OLE objects and methods is given below for a complete description of the parameters associated with OLE automation methods see appendix A Some sample programs can be found in section A 10 Objects SIMNRA exports the following OLE automation objects Simnra App The application itself Simnra Setup Experimental setup Simnra Calc Parameters for calculation Simnra Target Target with layers and elements Simnra Fit Fit parameters Simnra Spectrum Experimental and simulated spectra Plot properties Simnra Stopping Stopping powers energy loss and straggling in elements and layers Properties and methods SIMNRA exports the following OLE automation properties and methods grouped by object 47 Simnra App Active Specifies whether SIMNRA is active and has focus BringToFront Brings SIMNRA to the front above all other applications CalculateSpectrum Calculates a simulated spectrum CopySpectrumData Copies experimental and simulated spectra in ASCII format to the Windows clipboard DeleteSpectrumOnCalculate Specifies whether the current simulated spectrum is deleted if a new calculation is performe
39. 30 2000 180DA_1 R33 Amsel 1964 165 830 2000 180DA_2 R33 Amsel 1964 165 830 2000 180DA_3 R33 Amsel 1964 165 830 2000 180DA_4 R33 Amsel 1964 90 700 1900 19FPA_1 R33 Dieumegard 1980 150 700 2000 19FPA_2 R33 Dieumegard 1980 150 700 1900 19FDA0_1 R33 Maurel 1981 150 1000 1900 19FDA1_1 R33 Maurel 1981 150 1000 2700 32SDP R33 Healy 1998 150 1000 2700 325DP1 R33 Healy 1998 150 1000 2700 32SDP2 R33 Healy 1998 150 1000 2700 325DP3 R33 Healy 1998 150 1000 2700 325DP456 R33 Healy 1998 150 1000 2700 325DP7 R33 Healy 1998 32 3 7 Calculate menu In the Calculate menu all commands for calculating spectra scattering kinematics stop ping powers and data fitting are located Additionally some helpful tools density conver sions particles sr can be found here e Calculate Spectrum Calculates the simulated spectrum e Fit Spectrum Data fitting to experimental data See section 3 7 1 for details Kinematics Calculation of scattering kinematics Allows the calculation of the energies of backscattered particles recoils and nuclear reaction products e Stopping Calculation of stopping powers for any projectile in any target element and of energy loss in the different layers e Cross Section Calculation of Rutherford cross sections for backscattering and recoils e Density Density conversions for elements only Mass density to atomic den sity and conversion from atoms cm to g cm and nm e Partic
40. 3a variant is detailed here for completeness All R33a files are legal R33 files but R33a files have the fol lowing additional conditions 1 The Version entry is required and must be the first entry after the Comment 2 Only elastic cross sections can be in valid R33a files 3 Nvalues must either not be present so that Data and EndData entries are used or have a value of less than or equal to zero R CUnknown lt String gt Note A concise bibliographic source preferable or another indication of where the data has come from avoid if possible This field should contain the most authoritative original source for the data This will usually be the original publi cation or thesis reference In some cases data has been input by experimenters before or without publication In this case this entry should contain something like Measured and input by D Withrington It should be kept small an upper limit of 256 characters is suggested but not required It would be expected that further details pertaining to Mrs Withrington would be found in the Comment R Cunknown lt String gt 150 Address1 Address9 Serial Number Reaction Masses Note The name of person or institution responsible for creating the R33 file For R33 files automatically created from Exfor files this would be IAEA or NNDC or International Nuclear Data Network or whatever No provision is made here for including update histories however
41. 4 O 135 2100 4000 14N3HEP34_135 R33 McIntyre 1996 ANCHe p1 2 0 90 1600 2800 14NTP1X1 R33 Terwagne 1994 N He pi2 O 135 1600 2800 14NTP1X2 R33 Terwagne 1994 ANCHe p3 O 90 1600 2800 14NTP3X1 R33 Terwagne 1994 ANCHe p3 O 135 1600 2800 14NTP3X2 R33 Terwagne 1994 ANCHe pa O 90 1600 2800 14NTP4X1 R33 Terwagne 1994 ANCHe pa O 135 1600 2800 14NTP4X2 R33 Terwagne 1994 ANCHe ps O 90 1600 2800 14NTP5X1 R33 Terwagne 1994 N He ps O 135 1600 2800 14NTP5X2 R33 Terwagne 1994 ANCHe p7 O 90 1600 2800 14NTP7X1 R33 Terwagne 1994 ANCHe p7 O 135 1600 2800 14NTP7X2 R33 Terwagne 1994 MN He ap N 90 1600 2800 14NTAOX1 R33 Terwagne 1994 BN He a0 EN 135 1600 2800 14NTA0X2 R33 Terwagne 1994 BN a po O 135 4000 5000 14NAP1 R33 Giorginis 1995 BN p a YC 140 900 2860 15NPA R33 Hagedorn 1957 MN D a 3C 90 400 1600 15NDA90 R33 Vickridge 1996 BN D a C 135 400 2000 15NDA135 R33 Vickridge 1996 31 0 Lab Energy keV File Reference 150 400 2000 15NDA150 R33 Vickridge 1996 150 800 1300 15NDA_1 R33 Sawicki 1985 135 800 2000 160DA_2 R33 Amsel 1964 145 760 950 160DA_1 R33 Turos 1973 165 800 2000 160DA_3 R33 Amsel 1964 135 20 3000 160DP0_1 R33 Jarjis 1979 135 500 3000 160DP1 2 R33 Jarjis 1979 155 400 1100 16ODP1_1 R33 Amsel 1967 90 1600 2600 16OTA R33 Abel 155 1500 1800 180PA 2 R33 Alkemada 165 500 1000 180PA 1 R33 Amsel 1967 165 8
42. 5 This relation was used by SIMNRA 4 70 4 90 But it turned out that this 2 dimensional model is oversimplified and results in unrealistic spectra if a rough surfaces is bombarded at non normal incident angles a 0 We have to take the 3 dimensional nature of a rough surface into account which consists of inclined and rotated surface areas instead of just line segments as in the 2 dimensional case Each surface area can be described by a local tilt angle y and a rotation angle 4 Many different combinations y 4 result in identical local incident angles o but always with a different local exit angle For each amp we have a distribution of s instead of just one as in the 2 dimensional case 2 as function of amp and a control parameter 4 can be obtained as follows see Fig 4 23 Rotate the xy plane around the vector by an angle 4 This rotation can be described by a rotation matrix Ma 4 The normal vector of the rotated plane is n Y Ma w Z where 7 is the normal vector of the non rotated plane which is identical to the z axis The exit angle 3 is given by the scalar product of 4 and B with cos Dia WI where 3 is the vector which describes the exit beam For the exact solution of the 3 dimensional problem it would be necessary to take many different for each into account which increases the computing time considerably Therefore we replace the function 1 by its mean value s ww Been 4 76 where w 4 is a
43. 5 R33 Bogdanovi Radovi 2002 26 ile Reference Energy keV Fi S _ E 17 eD See 12CAA12C60 R33 Bogdanovi Radovic a gt 2100 4800 12CAA12C135 R33 Bogdanovi E Je RE 150 2100 4800 12CAA12C150 R33 Bogdanovi Radovi 2 acla E i AC_BA65A RTR Barnes 1965 ee oe an am AC_KE68A RTR Kerr 1968 l 650 4 a or say S 4700 AN_KA58A RTR Kashy 1958 nS E Feng 1994 HN le 165 2000 6200 AN R r Era S Set e IE Keser Foster 1993 N a a N 167 7090 9070 E a Na 167 8650 9000 AN_FO93C RT 2000 4000 AN_HE58A RTR Herring 1958 CS N 1057 1600 2600 AN_SM61A RTR Smothich 1961 e TE GC 2400 3800 AN SM61B RTR Smothich 1961 le 800 4800 AN_SM61C RTR Smothich 1961 coe S i 00 5600 AN SM61D RTR Smothich 1961 AO 1657 1500 5606 AN SMG61E RTR Smothich 1961 a W s i Sc AN_SMGIF RTR Smothich 1961 cos eS heen AN MO72A RTR Mo 1972 ACA 1585 vu a AO_HUG7A RTR Hunt 1967 TO a a O 158 6 6000 x EE a 165 2050 9000 AO_FE94A RT g me ett 9200 9900 AO_CA85A RTR Caskey 1985 oe E 9600 10500 AO_CA85B RTR Caskey 1985 PS KR AO_CA85C RTR Caskey 1985 a a ain AO CAS5D RTR Caskey 1985 o 1 le AO_CA85E RTR Caskey 1985 El ae Wd EA AO CAS5F RTR Caskey 1985 oe a Lea AO_CA85H RTR Caskey 1985 TO a a O 165 12500 13500 GE aa 1
44. 6 000 4 000 14 000 Zeds 1 8 2 7 Qvalue 3110 00 0 00 0 00 0 00 0 00 Theta 145 00 Sigfactors 1 00 0 00 Enfactors 1 00 0 00 0 00 0 00 Units mb Data 761 0 0 0 2 92E 0000 0 0 770 0 0 0 3 65E 0000 0 0 775 0 0 0 3 99E 0000 0 0 780 0 0 0 4 41E 0000 0 0 785 0 0 0 4 55E 0000 0 0 EndData Figure 3 7 Example for a cross section data file in the R33 file format 44 In some cases for example if the file contains elastic scattering data the cross section values are not for a specific isotope but for natural isotopic composition In this case the mean target mass should be used If the cross section values are for natural isotopic target composition rather than for a specific isotope a line containing the string Composition Natural has to be present In this case the given cross section is used for all isotopes This line has to be omitted if the cross section is for a specific isotope Other compositions than Natural must not be used A line containing the string QValue The Q value is the energy released in the nuclear reaction in keV Q 0 0 for elastic scattering Up to 5 different Q values are allowed for example for multiple particle groups which are not resolved SIMNRA will use the mean value of all non zero Q values A line containing the string Theta Theta should be given in degrees The value of theta is not used by SIMNRA but this line must be present and contain a value Optio
45. 65 a 22 ue is the reduced angle due to multiple scattering the real angle and y the scaling factor which connects the real and reduced angles E is the ion energy a the screening radius as above Z and Zu the nuclear charges of the incident ions and the target atoms respectively and e the electron charge The angular distribution due to multiple scattering can be described by a universal distribution function f 7 which is valid for all ion target combinations and energies fs describes the absolute angular deviations from the original direction spatial distribution The angular distribution due to multiple scattering is non Gaussian For lt A 2 with A the full width at half maximum FWHM of the angular distribution the distribution function can be approximated by a Gaussian see Fig 5 of ref 50 A Gaussian will however underestimate the wings of the distribution for gt A 2 For large target thicknesses the angular distribution becomes more and more Gaussian Szilagyi et al 31 have proposed a method how to extend the original Sigmund theory to multi elemental targets with stopping A multi elemental target is divided into shallow sublayers consisting of only one element The thickness of these sublayers is sufficiently small to allow a mean energy approximation with E Ey 2 E is the mean energy in the sublayer and E and Er the energies at the entrance and exit of the sublayer The
46. 9 SS os Zi S E RTR John 1969 l 12500 3 i m gt Geck AO_CH93A RTR Cheng 1993 AS o rs AO_LE90A RTR Leavitt 1990 i 1770 500 HICE Powers 1964 180 a O 160 2400 3500 oe power e F e F 165 1500 5000 ee RR E z aa w x a tr Cseh 1984 PE a a F 170 2300 3700 3 a 170 1500 4000 AF_CS84C RTR se et 0 3200 ANEGO54A RTR Goldberg 1954 Ne a a Ne 167 3 240 E Ge 3200 4000 ANEGO54B RTR o g A ara 2400 4000 ANEGO54C RTR Goldberg 1954 A i 2000 6000 ANACH9IA RTR Cheng 1991 GE 2000 9000 AMGCH93A RTR Cheng 1993 q an Si 3150 3900 AMGCS82A RTR Cseh 1982 lee Ma ae 4200 4900 AMGCS82B RTR Cseh 1982 i a 0 0 Me be 150 3900 AMGKA52A RTR Kaufmann 1952 elas ae t i AMGIK79A RTR Ikossi 1979 A m 16 6080 6140 AMGIK79B RTR Ikossi 1979 Melero Ms ASICH93A RTR Cheng 1993 Si a a Si 170 2000 6000 27 0 Lab Energy keV File Reference Si a a 170 6000 9000 ASICH93B RTR Cheng 1993 BSi a a 165 2400 4000 ASILE72A RTR Leung 1972 BSi a 0 165 4000 5000 ASILE72B RTR Leung 1972 BSi a a 165 5100 6000 ASILE72C RTR Leung 1972 BSi a a 165 2400 5000 ASILE72D RTR Leung 1972 AL 170 2000 9000 AALCH93A RTR Cheng 1993 Cl a a 165 2000 9000 ACLCH93A RTR Cheng 1993 Ar a a 170 1800 5200 AARLE86A RTR Leavitt 1986 2K a a 175 5 6000 8000 AK_FR82A RTR Frekers 1982 Ca a a 166 2200 8800 ACAHU90A RTR Hubbard 1990 MCa a a 145 5000 9000 ACASE87A RTR Sellschop 1987 C
47. AddLayer Boolean Description Adds a new layer The layer is the last layer in the stack has zero thickness and contains no elements After adding a layer at least one element has to be added with AddElement and layer properties like thickness roughness etc have to be set Parameters None Return Value Returns true if the layer was added successfully Related Properties and Methods Target AddElement 130 Target InsertLayer 132 DeleteElement Function DeleteEFlement lay el Integer Boolean Description Deletes element number el in layer number lay Parameters lay Number of the layer with 1 lt lay lt NumberOfLayers el Number of the element with 1 lt el lt Number0fElements lay Return Value Returns true if the element was deleted successfully Related Properties and Methods 131 Target DeleteLayer 132 DeleteLayer Function DeleteLayer lay Integer Boolean Description Deletes layer number lay Parameters lay Number of the layer to delete with 1 lt lay lt NumberOfLayers Return Value Returns true if the layer was deleted successfully Related Properties and Methods Target DeleteElement 131 Insert Layer Function InsertLayer lay Integer Boolean Description Inserts a new layer in front of layer number lay The layer has zero thickness and contains no elements After inserting a layer at least one element has to be added with AddElement and layer
48. E S BS de 10 E cua J Ki es 5 we incident ions pat lt A a x UN Lor ka 5 SECH 4 5 LO m e feo bp JH 4 E A lt 0 1000 900 800 700 Residual energy keV backscattered ions at surface Energy spread keV FWHM 0 1 1000 900 800 700 Residual energy keV Figure 4 14 Calculated energy spread contributions on the ingoing and outgoing paths to the total energy spread due to multiple scattering 1000 keV He in Au a 60 B 60 6 60 IBM geometry Top angular spread bottom energy spread Solid lines SIMNRA dashed lines DEPTH code 87 Figure 4 15 Geometry used for the calculation of dual scattering scattering see Fig 4 8 The contribution of trajectories with more than two large angle deflections is neglected Plural large angle and multiple small angle scattering may be combined in the calculations SIMNRA performs the calculation of dual scattering in the following way During each step of the incident ion particles are scattered into the whole sphere of 47 We introduce the polar system with the polar angles 4 see fig 4 15 After the first scattering event the scattered particles have the direction ap o The scattering angle 01 of the first scattering event is given by cos 01 sina sin y sin cos a cos Y SIMNRA uses the Rutherford cross section for the calculation of the number of scattered particles in the first scattering event The new angle a of the parti
49. Ein Stepwidth incident ions keV dEout Stepwidth outgoing ions keV DualScattering Specifies if dual scattering is calculated ElementSpectra Specifies if individual spectra for each element in the target are calculated EMin Cutoff energy keV HighEnergyStopping Selects high energy stopping Andersen Ziegler only Isotopes Specifies if isotopes are taken into account IsotopeSpectra Specifies if individual spectra for each isotope in the target are calculated MultipleScattering Specifies if multiple scattering is calculated Number OfAngle Variations Number of angle steps in the calculation of rough substrates Number OfD Variations Number of thickness steps in the calculation of rough lay ers Straggling Specifies if energy loss and geometrical straggling are taken into ac count ZBStopping Selects Ziegler Biersack or Andersen Ziegler stopping 49 Simnra Target AddElement Adds an element to a layer AddLayer Adds a layer to the target DeleteElement Deletes an element from a layer DeleteLayer Deletes a layer from the target ElementConcentration Concentration of an element in a layer ElementName Name of an element in a layer HasLayer Roughness Specifies if a layer is rough HasSubstrateRoughness Specifies if the substrate is rough InsertLayer Inserts a layer LayerRoughness FWHM of the roughness of a layer 101 at
50. F p p F 160 500 1300 PF_DE56C RTR Dearnaly 1956 TF p p F 160 1300 1550 PF_DE56D RTR Dearnaly 1956 TF p p PF 165 850 1010 PF_KN89A RTR Knox 1989 E pp F 165 1000 1875 PF_KN89B RTR Knox 1989 TF p p F 165 1350 1550 PF_KN89C RTR Knox 1989 25 0 Lab Energy keV File Reference TF p p F 158 7 600 1800 PF_WE55A RTR Webb 1955 F p p PF 158 7 1300 1500 PF_WE55B RTR Webb 1955 Ne p p Ne 166 CM 1500 2800 PNELA71A RTR Lambert 1971 WNa p p Na 156 5 550 1450 PNABA56A RTR Bauman 1956 Me p p Mg 164 400 4000 PMGMO51A RTR Mooring 1951 2Mg p p Mg 164 792 856 PMGMO51E RTR Mooring 1951 2Mg p Mg 164 1466 1501 PMGMO51F RTR Mooring 1951 Me p p Mg 164 1642 1671 PMGMO51G RTR Mooring 1951 Mg p p Mg 164 1991 2026 PMGMO51H RTR Mooring 1951 Mg p p Mg 164 2393 2431 PMGMO51I RTR Mooring 1951 Me p p Mg 170 700 2540 PMGRA88A RTR Rauhala 1988 27AXp p Al 170 1000 2450 PALRAS9A RTR Rauhala 1989 BSi p p PSi 167 2 1300 4000 PSIVO59A RTR Vorona 1959 Si p p Si 170 1000 3580 PSIAM93A RTR Amirikas 1993 Si p p Si 170 1470 2200 PSIRAS5A RTR Rauhala 1985 31P p p P 165 1000 2000 PP_CO63A RTR Cohen Ganouna 1963 2S pp 8 167 4 1300 4000 PS_OL58A RTR Olness 1958 S p p S 170 1500 2690 PS_RA88A RTR Rauhala 1988 Cl p p Cl 150 2000 5000 PCLBO93A RTR B
51. IPA R33 Maurel Be p a Li Total 30 700 OBEPA R33 Sierk 1973 Be p D Be Total 30 700 9BEPD R33 Sierk 1973 Be p D Be 135 780 3000 9BEPD_1 R33 Weber 1956 Bei D De 165 1400 1500 9BEPD_2 R33 Mayer 2001 Be D ao Li 165 500 1900 9BEDAO R33 Biggerstaff 1962 Be D a1 Li 165 500 1600 9BEDA1 R33 Biggerstaff 1962 BeHe po B 90 1800 5100 9BETP0_1 R33 Wolicki Be He p1 B 90 1800 5100 9BETP1_1 R33 Wolicki Be He po B 150 1800 5100 9BETP0_2 R33 Wolicki Be He p1 B 150 1800 5100 9BETP1_2 R33 Wolicki TB p ao Be 50 1800 10800 10BPA0_1 R33 Jenkin 1964 B p a1 Be 50 2350 10100 10BPA1_1 R33 Jenkin 1964 TB p ao Be 90 1800 9500 10BPA0_2 R33 Jenkin 1964 TB p a1 Be 90 2650 7100 10BPA1_2 R33 Jenkin 1964 B D ao Be 156 980 1800 10BDA0 R33 Purser 1963 TB D ai Be 156 980 1800 10BDA1 R33 Purser 1963 B He po C 90 2050 4000 10B3HEP0 90 R33 McIntyre 1996 BC He p YC 90 2050 4000 10B3HEP1_90 R33 McIntyre 1996 B He po C 135 2050 4000 10B3HEP0_135 R33 McIntyre 1996 BF He pi YC 135 2050 4000 10B3HEP1_135 R33 McIntyre 1996 B He po C 90 1300 5000 10BTP0 R33 Schiffer 1956 30 0 Lab Energy keV File Reference se om 90 1300 5000 10BTP1 R33 Schiffer 1956 B a po A 135 4000 5000 10BAP0 R33 Giorginis 1995 TB a p KE 135 4000 5000 10BAP1 R33 Giorginis 1995
52. IS PART OF SIMNRA USE OF SIMNRA PROVIDED WITH THIS AGREEMENT CONSTITUTES YOUR ACCEPTANCE OF THESE TERMS IF YOU DO NOT AGREE TO THE TERMS OF THIS AGREE MENT PROMPTLY REMOVE SIMNRA TOGETHER WITH ALL COPIES FROM YOUR COMPUTER THE CROSS SECTION DATA FILES IN R33 AND RTR FILE FORMAT R33 AND RTR FILES STORED IN THE CRSEC SUBDIREC TORY ARE EXCLUDED FROM THIS AGREEMENT THESE FILES HAVE BEEN TAKEN FROM SIGMABASE AND ARE SUBJECT TO THE TERMS LISTED IN http ibaserver physics isu edu sigmabase newuser html THE FILES SCOEF 95A and SCOEF 95B STORED IN THE STOP DIRECTORY ARE EXCLUDED FROM THIS AGREEMENT THESE FILES HAVE BEEN TAKEN FROM THE SRIM 97 CODE AND ARE SUBJECT TO THE TERMS LISTED IN THE SRIM MANUAL WHICH MAY BE OBTAINED FROM www research ibm com ionbeams PRODUCT LICENSE AGREEMENT 1 You have the right to use SIMNRA freely for thirty 30 days for the purpose of evaluation After thirty days you must either buy SIMNRA or remove it from your computer and stop using it 2 You may upload SIMNRA to any electronic bulletin board or demonstrate the soft ware and its capabilities If you copy or upload SIMNRA you must copy or upload it together with all files including this license You may not reproduce or distribute SIMNRA for resale or other commercial purposes including bundling with any prod uct that is offered for sale 3 Copyright SIMNRA is protected by international copyright law The owner of the copyright is the Max Planck
53. Jon Handbook for Material Analysis Academic Press New York San Francisco London 1977 68 69 69 69 70 70 73 M G Payne Phys Rev 185 2 1969 611 68 C Tschal r Nucl Instr Meth 61 1968 141 68 C Tschal r Nucl Instr Meth 64 1968 237 68 W K Chu Phys Rev 13 1976 2057 69 69 O Schmelmer G Dollinger C M Frey A Bergmaier and S Karsch Nucl Instr Meth B145 1998 261 73 73 D Dieumegard D Dubreuil and G Amsel Nucl Instr Meth 166 1979 431 75 75 A Weber H Mommsen W Sarter and A Weller Nucl Instr Meth 198 1982 527 78 A Weber and H Mommsen Nucl Instr Meth 204 1983 559 78 E Steinbauer P Bauer and J P Biersack Nucl Instr Meth B 45 1990 171 78 104 P Bauer E Steinbauer and J P Biersack Nucl Instr Meth B79 1993 443 78 104 W Eckstein and M Mayer Nucl Instr Meth B153 1999 337 78 104 155 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 P Sigmund and K B Winterbon Nucl Instr Meth 119 1974 541 78 79 A D Marwick and P Sigmund Nucl Instr Meth 126 1975 317 78 J P Biersack and W Eckstein Appl Phys A34 1984 73 80 W Eckstein Computer Simulation of Ion Solid Interactions vol 10 of Materials Science Springer Berlin Heidelberg New York 1991 80 R D Edge and U Bill Nucl Instr Meth 168 1980 157 90 A R Knudson Nucl Instr Me
54. LE automation reference 111 AT Dala TYPES ios ERT A er Ge a er o at A 111 A2 Sirs APP 22465440464 a a aa aa 111 AZA Properties s s uu sr sa NEE e ee eS 111 A29 Methods 254 024 NI ENEE EEN AN Ne a ed 113 AS o A A be ae ee Pha a RG DEE eee es 120 A Properties A E ek BP PE i we Se Ee me ee 120 Ad DUONG 2 6 2s ee ea a RE eRe ORD ERS Cee EY 122 d Eent A ee Soa Ge E Ge ee wR Eee eA de ee 123 AD SIMA geb e eee RATE DEES AEM ERASED 127 SST Properties 2 2 bbe be be ee ir E ERA EEE Ew a 127 SAS Methods e oona a 644 0446 be ebb ee eR et ee eRe ws 130 AG upper Fit e eo cee caaea ee eR eA A eS 133 AGI Properties 0 4 4 4454 bs ae a e ees a a 133 A 6 2 Methode 137 Bul SUNS DECIS oe ea Pe Pa ee a be ee te ee NN 137 Acid mpat parameter socs e c Gk EN E a ee Re e Ee 2 137 d Eet A sce E we bo DO Ge E ur Fs ee 3 138 Actes tee s fae He Be ee BR EA oe a ce A A 139 ALS Simnra StOppme lt lt osas Ge be waa eee he EE 141 A 8 1 Input parameter e 141 A 8 2 Methode 141 A 9 Error handling 144 A 10 Programming examples 145 B The R33 cross section file format 148 Bil Introduction sa eos hea Ge raed Ge ae a ae A a 148 B 2 The new R33 Format definition a aoo 149 KSE Syntax of an R3 Entry oda badaa a Net a Ae e 149 Bee Listo legal entries ea a ace SR dae ras NEE er A aa er a 150 iii Chapter 1 Overview This report describes the use of the program SIMNRA and the physical concepts imple mented therein SIMNRA is a Mic
55. Lindhard theory now can be applied to each sublayer The individual angular spread contributions of two sublayer are added according to Ad A A0 4 66 where A and Ab are the half widths in each sublayer and the exponent y depends on the reduced thickness 7 is already the projected angle instead of the spatial angle The functions A 7 and v 7 can be found in 31 To obtain the energy distribution after penetrating a sublayer with trajectory angle o towards the surface normal SIMNRA calculates the energies of particles penetrating the sublayer with trajectory angles o A 2 Additionally SIMNRA makes the following approximations 1 The angular and energy distributions are approximated by Gaussian functions This approximation will underestimate the wings of the multiple scattering distributions 79 2 It is always assumed that the energy distribution is symmetric i e that the energy of a particle penetrating the sublayer with angle a A 2 is Ey AE 2 and the energy of a particle with angle a A 2 is Ey AE 2 Left right symmetry where Ep is the energy of a particle penetrating the sublayer with angle a and AE the FWHM of the energy distribution This approximation is obviously not true for normal incidence and not well fulfilled for very oblique incidence In these cases the real energy distributions are asymmetric with respect to Ep Figs 4 9 4 11 show the angular and energy spreads due to
56. Object Simnra Fit Wait 1000 ms May be necessary for the server to start WScript Sleep 1000 Open a NRA file Result App Open c temp test nra Fit thickness and composition of layer number 2 Fit LayerNr 2 Fit LayerThickness True Fit LayerComposition True One fit region from channel 100 to 200 Fit NumberOfRegions 1 Fit RegionMinChannel 1 100 Fit RegionMaxChannel 1 200 Perform the fit Result App FitSpectrum 146 Sample program in Visual Basic Script showing how to add layers and elements Create the application object Set App CreateObject Simnra App Create the target object Set Target CreateObject Simnra Target Wait 1000 ms May be necessary for the server to start WScript Sleep 1000 Open a NRA file Result App Open c temp test nra Add an empty layer Will be the last layer Target AddLayer lay Target NumberOfLayers Set the layer thickness to 1000 x 101 atoms cm Target LayerThickness lay 1000 Add one element Will be the last element Target AddElement lay el Target NumberOfElements lay Set the element properties Attention Au already has to be present in an already existing layer Target ElementName lay el Au Target ElementConcentration lay el 1 0 Calculate the spectrum Result App CalculateSpectrum 147 Appendix B The R33 cross section file format The R33
57. Radovi 2001 H a H a 60 2500 4500 1HAP4HE60 R33 Bogdanovi Radovi 2001 H a H a 10 600 4800 HHEHHE10_KIM R33 Kim 1999 H a H a 15 600 4800 HHEHHE15_KIM R33 Kim 1999 H a H a 20 600 4800 HHEHHE20_KIM R33 Kim 1999 H a H a 25 600 4800 HHEHHE25_KIM R33 Kim 1999 H a H a 30 600 4800 HHEHHE30_KIM R33 Kim 1999 H a H a 35 600 4800 HHEHHE35_KIM R33 Kim 1999 H a H a 40 600 4800 HHEHHE40_KIM R33 Kim 1999 H a H a 10 1000 2500 ERD10H R33 Quillet 1994 H a H a 20 1000 2500 ERD20H R33 Quillet 1994 H a H a 30 1000 2500 ERD30H R33 Quillet 1994 H a H a 20 1000 3000 HHEHHE20 R33 Baglin 1992 H a H a 25 1000 3000 HHEHHE25 R33 Baglin 1992 H a H a 30 1000 3000 HHEHHE30 R33 Baglin 1992 H a H a 35 1000 3000 HHEHHE35 R33 Baglin 1992 H a H a 30 900 3000 CRSDA DAT No 125 Baglin 1992 H a H a 30 2000 7000 CRSDA DAT No 3 D a D a 10 1000 2500 ERD10D R33 Quillet 1994 D a D a 20 1000 2500 ERD20D R33 Quillet 1994 D a D a 30 1000 2500 ERD30D R33 Quillet 1994 D a D a 20 1000 3000 DHEDHE20 R33 Kellock 1993 D a D a 25 1000 3000 DHEDHE25 R33 Kellock 1993 D a D a 30 1000 3000 DHEDHE30 R33 Kellock 1993 D a D a 35 1000 3000 DHEDHE35 R33 Kellock 1993 D a D a 40 1000 3000 DHEDHE40 R33 Kellock 1993 D a D a 30 2200 3000 CRSDA DAT No 4 D a D a 30 1000 2070 CRSDA DAT No 130 Besenbacher 1986 D a D a 30 2070 2180 CRSDA DAT No 131 Besenbacher 1986 D a D a 30 2180 2800 CRSDA DAT No 132 Besenbacher 1986 Table 3 5 Nuclear reactions
58. SIMNRA and SRIM SRIM uses linear interpolation for some input data resulting in stop ping powers with a noncontinuous derivative SIMNRA uses spline interpolation instead of linear interpolation resulting in stopping powers with continuous second derivative The stopping powers calculated by SIMNRA are therefore more smooth than the original stopping powers calculated by SRIM the differences are typically below 1 4 6 3 Stopping in compounds SIMNRA uses Bragg s rule 28 for the determination of the stopping power in compounds Bragg s rule is a simple linear additivity rule of the stopping contributions of the different compound elements assuming that the interaction of an incident ion with a target atom is independent of the surrounding target atoms For a compound consisting of different 3For low energetic hydrogen ions E lt 10 keV there are differences because SIMNRA neglects nuclear stopping of hydrogen 65 elements with atomic concentrations c 3 cz 1 the total stopping power S is given by D 5 Ci Si 4 46 S is the stopping power of each element Bragg s rule assumes that the interaction between the ion and the atom is independent of the environment The chemical and physical state of the medium is however observed to have an effect on the energy loss The deviations from Bragg s rule predictions are most pronounced around the stopping power maximum and for solid compounds such as oxides nitrides and hydro
59. Set Property EMin Double Description Cutoff energy keV HighEnergyStopping Get Set Property HighEnergyStopping 124 Boolean Description Selects if high energy stopping power data are used or not This switch is only used together with the stopping power data by Andersen Ziegler and has no influence if Ziegler Biersack stopping is selected See section 3 4 3 for more details Related Properties and Methods Calc ZBStopping 126 Isotopes Get Set Property Isotopes Boolean Description Specifies if isotopes are taken into account IsotopeSpectra Get Set Property IsotopeSpectra Boolean Description Specifies if individual spectra for each isotope in the target are calculated Related Properties and Methods Calc ElementSpectra 124 MultipleScattering Get Set Property MultipleScattering Boolean Description Specifies if multiple scattering is calculated NumberOfAngleVariations 125 Get Set Property NumberOfAngleVariations Integer Description Number of angle steps in the calculation of rough substrates Related Properties and Methods Calc NumberOfDVariations 126 NumberOfD Variations Get Set Property Number0fDVariations Integer Description Number of thickness steps in the calculation of rough layers Related Properties and Methods Calc NumberOfAngleVariations 126 Straggling Get Set Property Straggling Boolean Description Specifies if energy loss and g
60. So Target Ment aos e A Ge ap ee ee Be a a ee a ee a 19 Boyd SEA III 19 3 5 2 Layer and substrate roughness 20 eo Target Polla coma ee p R OR Ra A 22 3 0 Reactions DEMI A AR eR HRA Se SAREE AA 23 a Galeulate MEDU o c a on ewe bee kw ee ee a he ee ed 33 Sek Fit SPCC go Ss eee ee eh ee Ree ee Es 33 38 TOS MEL 2 4 26 646642486 ns ea Cee ba A dhe eu 36 381 Data Reader 52545654682 Dee eee EER ARES A 36 38 2 Integrate Spectrum s c c so 5455855 8 eee Ea ae Re 36 Oe Plo MENU canes ook Mh a a ee A ao ae 37 B40 Options menw a aa AO a EE eG ee SN a A a a A 38 Old ene WCW 6 as eek he ek ee ee RA 39 3 12 Data exchange with other programs ecs e kene To ee eee 40 3 12 1 Graphics programs Excel Origin 40 A koe eg ee EE ea eS 40 3 123 IBA data furnace 644 82 58 E bE Ree a A 41 3 13 Importing spectrum data in any format 42 3 14 Adding new cross section data 43 314 1 The Ras file format sas ee ee EE EE E e 3 15 Energy calibration issues s o cc sc so ag toru rota 3 15 1 Detector nonlinearity gt s s ssa soaa saap aua ede aa aa 3 15 2 Energy calibration for different ion species e 3 10 Programming support e ee Be ee ee ee de eee SB 3 16 1 Command line parameters 2 2 00 000002 eee 3 16 2 OLE automation summary 2 500200 4 Physics Gl OVervieW sic 6644 eR a we ee Ee Ee E A2 AOE UAT i 4 kok a A hie ah wom Ba ew A we RA AR er Een wg 43 peatiering kinemati
61. T decimal commas are accepted Any format that can be read in a Borland Pascal readin r statement is acceptable B 2 2 List of legal entries Comment Version Source Name R CNone lt String gt Note An unlimited number of ascii characters including single CR LF sequences but terminating by a double CR LF sequence There is no requirement to embed CR LF sequences within the Comment however it is recommended to place CR LF sequences at convenient places at least every 80 characters so that if the file is printed the comment field is printed on successive lines that are not longer than 80 characters The double CR LF sequence that signals the end of the comment is simply a blank line It is not felt necessary to specify an upper limit to the size of the comment however it is expected that a useful comment would not be longer than a few tens of lines or a few thousand characters Note that Unix systems place only a LF character to signal an end of line This is illegal for R33 files There are freeware and shareware utilities that can add the necessary CR characters if R33 files are generated under Uniz O R33 lt String gt Note Allowed values are case insensitive R33 and R33a This entry can be used to signal that the file conforms to the special subset of R33 files pro posed by M O Thompson for elastic scattering cross sections for use in RUMP Sigmabase files will always be DSIR R33 but the R3
62. V and for the D He p a reaction for incident energies below about 1 8 MeV Note 2 Use the data files that came with SIMNRA Some of the original data files at SigmaBase contain small format errors such as additional blank lines which confuse the program Note 3 Non Rutherford cross sections and nuclear reactions are only available if Isotopes in the Setup Calculation menu is checked 24 Table 3 3 Non Rutherford backscattering cross sections 0 Lab Energy keV File Reference D p p D 151 1800 3000 PH_LA76A RTR Langley 1976 T p p T 163 2 2500 3500 PH_LA76B RTR Langley 1976 3He p p He 159 2 2000 3000 PHELA76A RTR Langley 1976 He p p He 161 4 1500 3700 PHELA76B RTR Langley 1976 He p p He 165 1500 3000 CRSDA DAT No 5 Li p p Li 164 1200 3100 PLIBA51A RTR Bashkin 1951 TLi p p Li 156 7 373 1398 PLIWA53A RTR Warters 1953 TLi p p Li 164 1700 3500 PLIBA51B RTR Bashkin 1951 Li p p Li 165 1300 2800 PLIMA56A RTR Malmberg 1956 Be p p Be 142 4 1600 3000 PBEMO56A RTR Mozer 1956 Be p p Be 158 7 200 1700 PBEMO56B RTR Mozer 1956 Be p p Be 170 5 2400 2700 PBELE94A RTR Leavitt 1994 1B p p B 154 1000 3000 PB OV62A RTR Overley 1962 HB p p B 150 500 2000 PB_TA56A RTR Trautfest 1956 TB p p B 155 2200 3300
63. a profiler The roughness distribution i e the deviation of the actual surface from the leveled one was approximately Gaussian For small values of o d a Gaussian and a Gamma distribution cannot be distinguished see Fig 4 18 The carbon substrate was already rough with a standard deviation og 18 2 nm The roughness of the Ni film on the substrate was oc Ni 26 5 nm This roughness is made up by the roughness of the carbon substrate plus the roughness of the Ni film own By assuming the two roughnesses to be independent i e 92 Counts a u 1000 1200 1 400 1 600 1800 Energy keV Figure 4 19 Calculated energy spectra for 2 MeV He backscattered from a smooth and rough gold layers with mean thickness d 1x10 8 Au atoms cm and different roughnesses with standard deviation The film thickness distributions are shown in Fig 4 18 Incident angle a 0 scattering angle 165 E 2 marks the energy at which the low energy edge has decreased to its half height 93 e Experiment Simulation Smooth Simulation Rough Counts 200 400 600 Channel Figure 4 20 1 5 MeV He backscattered at 165 from a rough Ni film with a mean thickness of 2 17 x 1018 Ni atoms cm on carbon substrate Dots Experimental data Dashed line Simulation assuming a smooth Ni layer Solid line Simulation assuming a rough Ni layer with roughness o 2 12 x 10 Ni atoms cm oyni 0 n the roughness of the Ni film alone is ab
64. ab Determines which menu entries are visible in the File Read Spectrum Data menu The Saving tab Create BACKUP NRA when saving If checked the old NRA file is saved to a file named BACKUP NRA each time File Save or File Save As is used In the case of erraneous overwriting of a file you can recover the old data from this file In each directory only one BACKUP NRA can exist 38 3 11 Help menu e User s Guide Opens the User s Guide in PDF format using Adobe Acrobat or Adobe Acrobat Reader Note 1 Adobe Acrobat or Acrobar Reader are not part of SIMNRA Adobe Acrobat Reader can be obtained freely from the Adobe web site at www adobe com while Adobe Acrobat is a commercial product Note 2 Context sensitive help is only available with Adobe Acrobat but not with Adobe Acrobat Reader The Reader always starts with the first page of the User s Guide which is due to some limitations of the Reader SIMNRA first tries to invoke Acrobat and if this fails Acrobat Reader e About Shows the version number of the program e Register Registration of the program 39 3 12 Data exchange with other programs 3 12 1 Graphics programs Excel Origin SIMNRA allows to exchange data with graphics programs by two different methods 1 Via the clipboard With Edit Copy Data the experimental and simulated spectra are copied in ASCII format to the windows clipboard They can be pasted into any spreadsheet program See
65. aboratory frame in degrees English is the preferred language Special note on data entry order The original R33 specification called for data to be listed as x y xerrror yerror however the R33 files originally generated for the Sigmabase contained data entries in the order x xerror y yerror The original specification was intended to allow for files containing no error information to be smaller since the two final entries could simply be omitted However given that the Sigmabase data fits easily on a single floppy without compression the file size arguments are not compelling and insisting on following the original specification will involve disrupting several existing readers as well as introducing confusion through the existence of two families of R33 files since copies of the erroneous files will probably lie around for years in different places So the new specification legalises the previous erroneous usage B 2 1 Syntax of an R33 Entry The syntax for the list of legal keywords and the associated data is Keyword Mx O R Default lt data type gt 149 Note Additional notes and guidelines concerning use of the entry Data type may be string an arbitrary series of ascii characters n integer a series of ascii characters without decimal point representing a signed integer number r real a series of ascii characters that represent a signed real number Format is fairly flexible but only decimal points and NO
66. account angular distributions which were not catered for in the first proposal and more recently to cater for elastic cross sections expressed as the ratio to Rutherford which it is useful to have for some elastic scattering programs It is thus timely to formally update the R33 format There exists also the large nuclear cross section data collections of the Nuclear Data Network the OECD NEA Nuclear data section the IAEA Nuclear data section and the Brookhaven National Laboratory National Nuclear Data Centre amongst others The R33 format is proposed to become a legal computational format for the Nuclear Data Network Nuclear Data Needs in Ion Beam Analysis I C Vickridge In Long Term Needs for Nuclear Data Development Report 148 INDC NDS 428 August 2001 International Atomic Energy Agency Vienna It is thus also necessary to provide an updated formal definition of the R33 format in order to provide the necessary specification for adoption of R33 as an accepted computational format Guiding considerations In defining the updated R33 format I have required that previous valid R33 files should also conform to the updated format This is so that R33 reading programs that conform to the updated specification will be able to read the existing R33 files provid ing backward compatibility There is also some redundancy in the format This is partly from intellectual laziness but also provides some checking of internal consistency to w
67. all be read Count Output parameter Pointer to a 32 bit signed integer value which indicates how many channels were actually read Data Input parameter Pointer to an array of 32 bit signed integer values which will take the spectrum data The array starts at channel 0 and has a maximum of 8192 channels The return value of ReadData is a 32 bit signed integer It must be 0 if the file was read successfully Any other return value indicates an error condition The calling convention of ReadData must be stdcall in Borland Delphi or WINAPT in Microsoft C A small code example in Pascal can be found in UserDLL sample dpr A more detailed example is given in UserDLL sample1 dpr 5The code examples are in Pascal Borland Delphi 4 42 3 14 Adding new cross section data To add new cross section data you have to perform the following steps 1 Create a cross section data file in the R33 file format The easiest way to do this is by using the R33Manager Alternatively you can use any text editor The file format is described below 2 Copy this file into the directory where all other cross section data files are subdi rectory CRSEC of your SIMNRA installation 3 Recreate the reaction list by clicking Options Create Reaction List Note If your file is ignored SIMNRA was not able to read or understand the file Carefully read the section about the R33 file format and try again 3 14 1 The R33 file format The R33 file
68. ameters a1 an we have to increase a and optimise a2 ay until Ay 1 As can be seen in fig 3 6 the error bar Aa becomes nonrealistic small if only a is fitted This is a consequence of the assumption that all nonfitted parameters are accurate To obtain realistic error bars all parameters should be fitted in one step A quantitative measure for the goodness of fit of the assumed model can be obtained from the value of y See 8 Chapter 14 1 or any good textbook about statistics for more information 35 3 8 Tools menu In the Tools menu several tools for spectrum evaluation are located You can find 1 a data reader to read out the contents of a specific channel 2 a tool for integrating spectra These tools appear as floating windows and are updated automatically if the spectrum is recalculated or if a new spectrum is loaded from disk 3 8 1 Data Reader The data reader is displayed as a small black crosshair with white legend in the plot The data reader control window displays the channel the energy of this channel and the number of counts in the channel The data reader is moved by entering the channel number or by using the spin up spin down buttons in the control window The data reader is updated automatically if a spectrum is recalculated or if a new spectrum is loaded from disk 3 8 2 Integrate Spectrum The Integrate Spectrum tool allows to integrate a specific spectrum The integral of a spectrum is the sum of a
69. and 4 34 is calculated using the universal screening length ay which is x 1 202 Z923 instead of the Firsov screening length ap iiz Ee which is used in eq 4 32 The difference between eq 4 31 and 4 33 is only some percent The nuclear stopping component for heavy ions may be large and cannot be neglected 4 6 2 Ziegler Biersack stopping Hydrogen If Ziegler Biersack stopping is selected SIMNRA uses the electronic stopping power data by Ziegler Biersack and Littmark 3 for the stopping of incident protons deuterons and tritons in all elements The electronic stopping power Se in eV 10 atoms cm for an incident hydrogen ion with energy mass E in keV amu is given by oe 4 35 with Stow CEP 04E 4 36 and Cs Cr Sig 502 In E di CsE 4 37 C Cg are fitting coefficients and partly tabulated in 27 They are stored in the file SCOEF 95A for all elements Equations 4 35 4 37 are valid in the energy range 63 10 keV amu lt E lt 10 MeV amu For energies in the range 10 100 MeV amu the electronic stopping power Se is given by Se C9 Ciot Cur Ce 4 38 x with x In E E Cy C12 are fitting coefficients and tabulated in the file SCOEF 95B For energies below 10 keV amu the electronic stopping power Se is given by ENY S E S 10 5 4 39 where Se 10 is the stopping power at 10 keV amu and y 0 45 for Z2 gt 6 and y 0 35 for Za lt 6 Nuclear stopping for incident hydrogen deuterium
70. and tritium ions is negligible for incident energies above about 10 keV amu 1 and is neglected by SIMNRA Helium If Ziegler Biersack stopping is selected then for incident He and He ions the electronic stopping power data by Ziegler Biersack and Littmark 3 are used for all elements The electronic stopping of He ions in elements Se is derived from the stopping power of protons for the same velocity S by using 3 27 Se Sp Lon Zuel 4 40 ZHe is the helium charge and zap can be obtained from the simple polynomial fit 5 Vie 1 exp gt cr 4 41 i 0 with E in keV amu The coefficients C are tabulated in 27 Nuclear stopping for incident helium ions is calculated with the universal ZBL potential 3 The nuclear stopping S in eV 10 atoms cm for He ions with incident energy E in keV is given by 8 462 Z Z2 M Wh Ma 03 29 Sn is the reduced nuclear stopping and Z1 M are the nuclear charge and mass of the helium ion and Z2 M are the nuclear charge and mass of the target element The reduced nuclear stopping Sn has the simple form Sn Sn 4 42 In 1 1 1383e e 4 43 Sn e 4 0 01321 021226 0 19593 05 Ss for e lt 30 and ne a 4 44 Sn ER 64 for e gt 30 e is the reduced energy and is given by WW 32 53 M2 E Zy Zz Mi Ma 278 Z3 4 45 Nuclear stopping is only important at incident energies E lt 100 keV at higher energies nuclear stopping
71. ata immediately follow the Data entry one point per line as for the Nvalues option and the file terminates with the end of the file or with the optional EndData entry Nvalues is maintained for backward compatibility but in practice most routines will simply read and count the number of lines read until the end of the file or an EndData entry is reached so this is the preferred option The use of the Enddata entry simply allows a check that all of the data values are contained in the file and have been read Data entries must be arranged in order of increas ing energy or angle Duplicate energy or angle values are not allowed the cross section must be single valued 153 Bibliography 10 11 12 13 14 15 16 17 18 19 20 21 H H Andersen and J F Ziegler Hydrogen Stopping Powers and Ranges in All Elements vol 3 of The Stopping and Ranges of Ions in Matter Pergamon Press New York 1977 16 18 61 61 61 61 61 64 J F Ziegler Helium Stopping Powers and Ranges in All Elements vol 4 of The Stopping and Ranges of Ions in Matter Pergamon Press New York 1977 16 61 62 62 62 80 J F Ziegler J P Biersack and U Littmark The Stopping and Range of Ions in Solids vol 1 of The Stopping and Ranges of Ions in Matter Pergamon Press New York 1985 16 16 61 63 63 63 63 63 63 64 64 64 65 65 65 J F Ziegler private communication 1997 16 J R Tesmer and M Nastasi Eds Handboo
72. ated spectra SIMNRA can use two different sets of elec tronic stopping power data for the stopping of swift and heavy ions in all elements The well known electronic stopping power data by Andersen and Ziegler 1 2 3 or the electronic stopping power data by Ziegler Biersack and Littmark 3 The Ziegler Biersack data are also used by Ziegler s SRIM formerly TRIM program in calculations of stopping powers and ranges The difference between these two data sets is typically lt 5 but may be larger in some cases According to Ziegler 4 the Ziegler Biersack data are more accurate and reliable than the Andersen Ziegler data The use of the Ziegler Biersack data is recommended and the program default The energy ranges in which the different stopping power formulas are valid are listed in table 3 1 Note If the stopping power data by Andersen Ziegler are used for incident hydrogen isotopes or heavy ions near 1 MeV amu artificial steps or kinks may appear in the simulated spectra This is due to a jump of the stopping power at 1 MeV amu See the description of the High energy stopping switch for a work around This problem does not appear if the Ziegler Biersack data are used e High energy stopping This switch is only available if Andersen Ziegler electronic stopping power data are used If checked the program will use the correct high energy stopping formula by Andersen and Ziegler for incident protons and heavy ions for E gt 1 MeV amu If
73. ation of nuclear reactions kinematics we use the quantities listed in table 4 1 We define the following quantities M M3 Ei Aua Mi M2 M3 Ma Er Ai AM Ei Al Mi M2 Mz Ma Er ta 1 BA Mi M2 Mz Ma M Er 55 Mass Energy Incident ion Mi Ei Target nucleus Mo 0 Light product M3 Ez Heavy product Ma Es Energy released in reaction Q Total energy Er F Q E3 E4 Table 4 1 Quantities used for the calculation of nuclear reactions kinematics The target nucleus is initially at rest For exotherm reactions Q gt 0 for endotherm reactions Q lt 0 MoM M dee E 2Ma E Mi M gt Mz Ma M Er The energy E3 of the light product created in the nuclear reaction is then given in the laboratory system by An a A E3 Er Aj3 cos0 3 sin d 4 8 13 0 is the emission angle of the light product in the laboratory system For 413 lt A24 only the plus sign in eq 4 8 applies If Aus gt 424 then eq 4 8 has two solutions and the maximum possible emission angle a of the light product is A 1 2 Oman arcsin 2 4 9 Ais The energy E4 of the heavy product created in the nuclear reaction is given in the laboratory system by A3 1 272 E ErAza cos O E sin d 4 10 Aja is the emission angle of the heavy product in the laboratory system For A14 lt Ax3 only the plus sign in eq 4 10 applies If 414 gt Aas then eq 4 10 has two s
74. becomes negligible Heavy ions The electronic stopping power of heavy ions in all elements is derived from the stopping power of protons using Brandt Kitagawa theory 3 27 The formalism is described in detail in ref 3 a short overview is given in 27 Fermi velocities of all target elements are stored in the file SCOEF 95A a small correction to the Fermi velocity in the file SCOEF 95B The ion s screening length A as a function of fractional charge is stored in the file SCOEF 95B Nuclear stopping for incident heavy ions is calculated with the universal ZBL potential from ref 3 The formalism is the same as for He ions see eq 4 42 4 45 For Zi and M the ions nuclear charge and mass respectively have to be used The nuclear stopping component for heavy ions may be large and cannot be neglected Differences between SIMNRA and SRIM 97 The program SRIM formerly TRIM by J Ziegler is the standard program for stopping power and range calculations If Ziegler Biersack stopping is selected SIMNRA uses the same stopping power routines and input data as SRIM 97 for elemental targets The routines for stopping power calculations have been taken from the SRIM source code the input data have been taken from the SRIM distribution For incident hydrogen and helium ions SIMNRA therefore uses exactly the same electronic and nuclear stopping powers as the SRIM program For incident heavy ions however there are small differences between
75. carbons The deviations from Bragg s rule predictions may be of the order of 10 20 27 29 For compounds with heavier atoms such as Fe203 NbC NbN Ta205 WOs Au alloys etc deviations from Bragg s rule disappear deviation lt 2 27 30 Ziegler and Manoyan 27 have developed the cores and bonds CAB model which assumes the electronic energy loss to have two contributions The effect of the cores and the effect of the bonds such as C H and C C The CAB model allows better predictions for the stopping in compounds however the bond structure has to be known Currently the CAB model or any other model which allows better predictions for the stopping in compounds is not implemented in SIMNRA However a correction factor f may be used for each ion species and each layer see Section 3 5 for details If a factor f is defined for a layer then the program will use the stopping power S E with E the ion energy S E SBragg E 4 47 SBragg E is the stopping power according to Bragg s rule Note that the factor f is energy independent 66 4 7 Straggling 4 7 1 Overview When a beam of charged particles penetrates matter the slowing down is accompanied by a spread in the beam energy This phenomenon is called straggling It is due to statistical fluctuations of the energy transfer in the collision processes Energy loss straggling has different contributions 1 Electronic energy loss straggling due to stat
76. ce SIMNRA makes full use of the graphics capacities of Windows This manual is organised in the following way e System requirements and the installation of the program are described in chapter 2 e The use of the program is described in chapter 3 A quick overview about the steps necessary to calculate a spectrum is given in chapter 3 1 More details are found in the rest of chapter 3 e The physical concepts implemented in the program are described in detail in chap ter 4 e Some examples for the abilities of the program are shown in chapter 5 Chapter 2 Installation 2 1 System requirements e SIMNRA requires Windows 95 98 NT 2000 or XP e Super VGA resolution of 800 x 600 pixels or higher is recommended e SIMNRA requires about 5 MB free hard disk space e The User s Guide and help system require Adobe Acrobat or Acrobat Reader See section 3 11 for more details e Reading spectrum data in Canberra s CAM file format requires the Genie 2000 soft ware package See section 3 2 for more details 2 2 Installation The installation of SIMNRA on Windows NT or Windows 2000 systems requires admin istrator privileges SIMNRA is distributed with a setup program To install SIMNRA simply run the setup program and follow the instructions After running the setup pro gram you should have obtained the files listed in table 2 1 To register run SIMNRA click About Register and enter your registration num ber in the appropriate f
77. cident ions on a gold layer with a thickness of about 100 nm on top of silicon The simulated spectrum fits the measured data very well The low background between the Si edge and the low energy Au edge is due to plural scattering this means the backscattered particles have suffered more than one scattering event with large scattering angle 47 48 49 which was not simulated for this example The deviation between experiment and simulation at low energies in the Si spectrum is due to the same reason Fig 5 2 compares simulated spectra with single and dual scattering for 500 keV He ions incident on a 100 nm gold layer on top of silicon with experimental data At this low energy plural scattering is important With the inclusion of dual scattering the ex perimental results are much better approximated Dual scattering gives the background between the low energy edge of Au and the Si edge and the steeper increase of the gold spectrum is better described The results with dual scattering are slightly lower than the experimental results This is due to trajectories with more than two scattering events which are not calculated 104 Energy keV 200 400 600 800 1000 es experimental 6000 simulated 4000 Counts 2000 100 200 300 400 500 600 700 800 Channel Figure 5 1 1000 keV He incident on Au on top of silicon 6 165 105 Energy keV 100 200 300 400 slats 14000 e Experimental Dual scattering 12000 Singl
78. cles after the first scattering is a 180 y The scattering angle 02 of the second scattering event is given by cos 02 sin 3 sin Y sing cos 8 cos y SIMNRA subdivides the whole sphere of 47 into 10 y intervals and 12 intervals resulting in 120 solid angle intervals SIMNRA considers only trajectories with scattering angles 01 02 gt 20 for dual scattering Trajectories with smaller scattering angles are very similar to single scattering trajectories For each solid angle interval a full backscattering spectrum with the starting depth of the particles equal to the depth of the incident ions and the new incident angle a and the new scattering angle 02 is calculated 88 Energy keV 100 200 300 400 500 e Experimental Dual scattering Single scattering Channel Figure 4 16 500 keV He ions incident on 100 nm Au on top of Si scattering angle 165 Circles experimental data points dashed line simulation with one scattering event solid line simulation with two scattering events Fig 4 16 compares the simulated spectra with single and dual scattering for 500 keV 4He ions incident on a 100 nm gold layer on top of silicon with experimental data With the inclusion of dual scattering the experimental results are much better approximated Dual scattering gives the background between the low energy edge of Au and the Si edge and the steeper increase of the gold spectrum is better described The results w
79. composed of the same elements in different concentrations The total amount of each element is the sum of this element in all layers 3 5 2 Layer and substrate roughness In this menu the roughnesses of the current layer and of the substrate are defined e Has thickness distribution Check if the current layer is rough i e if the layer thickness is not uniform but varies from point to point A rough layer is described by a distribution of layer thicknesses The distribution is divided into N steps The step number N can be adjusted by the Number of thickness steps in the Setup Calculation menu see section 3 4 3 20 Incident beam Target 40Ae7 Figure 3 5 Layer structure of target and foil For the target layer 1 is at the surface the layer with the highest number is the deepest layer Backscattered particles first penetrate the foil layer with the highest number the foil layer 1 is in front of the detector 21 Filename Material Common name INCON600 LAY Inconel 600 INCON625 LAY Inconel 625 SS14301 LAY Stainless steel 1 4301 AISI 304 US 14541 LAY Stainless steel 1 4541 V2A SS14571 LAY Stainless steel 1 4571 V4A SS316 LAY Stainless steel 316 US MYLAR LAY Polyethylenterephthalat Mylar Hostaphan Table 3 2 Predefined materials for stopper foils stored in the LAYERS directory e FWHM of thickness distribution SIMNRA assumes a Gamma distribution of layer thickn
80. cross sections Total means that the data file contains total cross section data 0 Lab Energy keV File Reference D d p T Tota 5 5000 2DDP R33 Bosch 1992 D d t p Tota 5 5000 2DDT R33 Bosch 1992 D d He n Tota 1 5000 2DD3HE R33 Bosch 1992 D t He n Tota 1 1370 2DTA_3 R33 Bosch 1992 D He a p Tota 380 1000 CRSDA DAT No 1 D He a p Tota 700 2000 CRSDA DAT No 111 D He a p Tota 300 2000 CRSDA DAT No 129 D He a p Tota 100 2500 2DTA_1 R33 M ller 1980 D He a p Tota 10 2240 2DTA_2 R33 Bosch 1992 D He p a Tota 380 1000 CRSDA DAT No 28 D He p a Tota 210 2150 2DTP_1 R33 M ller 1980 D He p a Tota 280 2400 2DTP_2 R33 Bonner 1952 D He p a Tota 100 2500 2DTP_3 R33 M ller 1980 D He pl Tota 10 2240 2DTP_4 R33 Bosch 1992 T d He n Tota 1 910 3TDA R33 Bosch 1992 GERS Ip Tota 250 660 CRSDA DAT No 2 3He d a p Tota 10 1500 3HEDA_1 R33 Bosch 1992 He D p a Tota 250 660 CRSDA DAT No 46 3He D p a Tota 190 1600 3HEDP_1 R33 Bonner 1952 He d p a Tota 10 1500 3HEDP_2 R33 Bosch 1992 Li p He He 60 650 2900 6LIP3HE R33 Marion 1956 Li p a He 60 650 2900 6LIPA R33 Marion 1956 Li D a He 150 400 1900 6LIDA_1 R33 Maurel 1981 SLi He po Be 165 900 5100 6LITPO R33 Schiffer 1956 SL i He p Be 165 900 5100 6LITP1 R33 Schiffer 1956 Li p a He 150 500 1500 7L
81. cs isu edu sigmabase which is maintained by I Vickridge See the file http ibaserver physics isu edu sigmabase newuser html for more information about SigmaBase The stopping power data and subroutines for Ziegler Biersack stopping have been taken from Ziegler s SRIM 97 program but were translated from BASIC to PASCAL The routines for reading RUMP s RBS file format were obtained from Peter Revesz Cor nell University USA They were translated from C to PASCAL The graphics subsystem for SIMNRA versions prior to 4 5 was developed by Achim von Keudell Max Planck Institut fiir Plasmaphysik Garching Germany Valuable input and many bug reports were obtained from Joachim Roth and Hans Maier Max Planck Institut fiir Plasmaphysik Garching Germany J rg R hrich and Swen Lindner Hahn Meitner Institut Berlin Germany Giinther Dollinger Technische Uni versit t M nchen Germany and Peter Revesz Cornell University USA Many additional cross section data were obtained from Iva Bogdanovi Radovi Rudjer Boskovi Institute Zagreb Croatia B Diaz Herrera Max Planck Institut fiir Plasma physik Garching Germany and LN Kim Max Planck Institut f r Plasmaphysik Garching Germany SIMNRA was developed at the Max Planck Institut f r Plasmaphysik Garching Ger many The R33 file format and the R33Manager were developed by Ian Vickridge Universit Paris France The text of Appendix was written by I Vic
82. ction of Bohr s theory The vertical lines denote the mean depth at which the beam has lost 10 20 and 50 of its initial energy Max denotes the depth at which the mean energy of the beam has decreased to the energy of the stopping power maximum 71 1 0 MeV He in Au Straggling keV FWHM 0 2 4 6 8 10 Depth 1 o atoms cm Figure 4 5 Beam width FWHM of 1 0 MeV He ions penetrating through gold The solid line is the beam width calculated by SIMNRA using eq 4 51 the dashed line is the prediction of Bohr s theory The vertical lines denote the mean depth at which the beam has lost 20 50 and 90 of its initial energy Max denotes the depth at which the mean energy of the beam has decreased to the energy of the stopping power maximum 72 fits the measured curve relatively well except of the multiple scattering contribution The straggling of outgoing particles is calculated with eq 4 51 as well Outgoing particles always start with an energy distribution with variance Sech which is given by Tiat K oi 4 54 with K the kinematic factor and oF the variance of the energy distribution of the incident beam 4 7 3 Nuclear energy loss straggling Fluctuations in the number of nuclear collisions lead to nuclear energy loss straggling which can be described by Bohr s theory of nuclear straggling The variance 0 in Bohr s approximation is given by Mi 2 Az 10 atoms cm 4 55 For light ions s
83. ction would be used when the particle groups are not resolved by the detection method employed In this case the postfix lists the states concerned separated by plus signs E g 14N d p5 6 15N Some elastic cross sections cor respond to targets having several isotopes In this case it is necessary to use the composition keyword R 1 1 1 0 lt r r r r gt 151 Zeds Composition Qvalue Distribution Theta Energy Note Four mass values in amu corresponding to the four nuclei specified in the reaction string separated by legal separators The order is m1 m2 m3 m4 for a reaction in which m1 m2 gt m3 m4 The specification of which of the two initial and final masses are m1 and m8 respectively is given by the reaction string in which we always have m2 m1 m8 m4 so that m1 corresponds to the projectile and m3 to the light product At present there is no intention to cater for the few cases in which there are three or more products for example 11B p a 2a In principle the masses could be deduced directly from the reaction string however in the interests of simplicity it seems worthwhile adding them to the R33 file to avoid having to write a reaction string parser in R33 readers In the special case where the composition keyword is used the values there override any contained in the Masses entry R 1 1 1 1 lt n n n n gt Note Four integers representing the atomic number of the four nuclei specified in the
84. curacy of stopping powers An up to date compilation of stopping power data can be found in 25 The routines and input data for Ziegler Biersack stopping have been taken from the SRIM 97 source code and were translated from BASIC to PASCAL 4 6 1 Andersen Ziegler stopping Hydrogen If Andersen Ziegler stopping is selected SIMNRA uses the electronic stopping power data by Andersen and Ziegler 1 for the stopping of incident protons deuterons and tritons in all elements The electronic stopping power Se in eV 10 atoms cm for an incident hydrogen ion with energy mass E in keV amu is given by 1 1 1 4 23 Se SLow SHigh with SLow Ag SE 4 24 and A a 3 4 A gt 2 As are fitting coefficients and tabulated in 1 They are stored in the file STOPH DAT Equations 4 23 4 25 are valid for 10 keV lt E lt 1 MeV For energies in the range 1 MeV 100 MeV the electronic stopping power Se is given by 2 4 gt ee p Lien In ei 4 26 Ag Axa are tabulated in 1 8 v c with v the ion velocity and c the speed of light Equa tion 4 26 is used only if the switch High energy stopping in the Setup Calculation menu is checked If unchecked the program will use Equations 4 23 4 25 at all energies The program default is checked The difference between eq 4 23 and eq 4 26 is small in most cases The main problem using eq 4 26 is that the first and second derivatives of eq 4 23 and eq 4 26 do not fit smoothly together at
85. d FitSpectrum Fits a spectrum Hide Hides SIMNRA LastMessage Text of the last error message or warning Maximize Maximizes SIMNRA to fill the whole screen Minimize Minimizes SIMNRA to the Windows task bar Open Opens a NRA file ReadSpectrumData Imports experimental data in different data formats Restore Restores the minimized application to its normal size SaveAs Saves a NRA file Show Shows SIMNRA if it was hidden ShowMessages Specifies if error messages are shown WriteSpectrumData Writes all spectra experimental simulated in ASCII format to a file Simnra Setup Alpha Incident angle deg Beamspread Energy spread of incident beam keV FWHM Beta Exit angle deg CalibrationLinear Linear calibration term B for energy calibration see eq 3 1 keV channel Calibration Offset Calibration offset A for energy calibration see eq 3 1 keV 48 CalibrationQuadratic Quadratic calibration term C for energy calibration see eq 3 1 keV channel DetectorResolution Detector resolution keV FWHM Energy Energy of incident ions keV ParticlesSr Number of incident particles times solid angle sr Theta Scattering angle deg Simnra Calc AutoStepwidthIn Specifies if automatic step width control for incident ions is used AutoStepwidthOut Specifies if automatic step width control for outgoing ions is used d
86. d Methods Calc ZBStopping 126 Calc HighEnergyStopping 125 StoppingInLayer Function StoppingInLayer Z1 Integer M1 Double E Double TargetID Integer lay Integer Double Description Stopping power of an ion Z1 in a target or foil layer The stopping power model is selected with Calc ZBStopping p 126 and Calc HighEnergyStopping p 125 and may be additionally modified by a correction factor to the stopping power see Section 3 5 Parameters Z1 Nuclear charge of the ion M1 Mass of the ion amu E Incident energy keV TargetID Selects target or foil lay Number of the target or foil layer Return Value Returns the stopping power in the layer keV 10 atoms cm Related Properties and Methods TargetID 141 Stopping EnergyLossInLayer 141 StragglingInLayer 143 Function StragglingInLayer Z1 Integer M1 Double E Double TargetID Integer lay Integer Double Description Energy loss straggling of an ion Z1 in a target or foil layer The layer is traversed perpendicularly incident angle a and exit angle are ignored See Stopping EnergylossInLayer for a listing of all switches which influence the straggling calculation Parameters Z1 Nuclear charge of the ion M1 Mass of the ion amu E Incident energy keV TargetID Selects target or foil lay Number of the target or foil layer Return Value Returns the full width at half maximum FWHM of the energy loss straggling in the laye
87. demm Se SIMNRA User s Guide Matej Mayer Max Planck Institut fiir Plasmaphysik Boltzmannstr 2 D 85748 Garching Germany email Matej MayerQipp mpg de Tel 49 89 32991639 Fax 49 89 32992279 www rzg mpg de mam This manual describes SIMNRA version 5 0 Max Planck Institut fiir Plasmaphysik 1997 2002 Additional publications about SIMNRA You can use the first as general reference for the program e M Mayer SIMNRA User s Guide Report IPP 9 113 Max Planck Institut fiir Plasmaphysik Garching Germany 1997 e M Mayer SIMNRA a Simulation Program for the Analysis of NRA RBS and ERDA Proceedings of the 15th International Conference on the Application of Ac celerators in Research and Industry J L Duggan and I L Morgan eds American Institute of Physics Conference Proceedings 475 p 541 1999 e W Eckstein and M Mayer Rutherford Backscattering from layered Structures be yond the Single Scattering Model Nucl Instr Meth B153 1999 337 e M Mayer Jon Beam Analysis of Rough Thin Films In print at Nucl Instr Meth B SIMNRA IS NOT FREE IT IS A SHAREWARE PROGRAM AND COSTS BETWEEN 200 300 US YOU CAN USE SIMNRA FOR A TRIAL PERIOD OF THIRTY 30 DAYS WITHOUT FEE IF YOU WANT TO USE SIMNRA AFTER THIS PERIOD YOU HAVE TO PAY THE REGISTRATION FEE AND YOU HAVE TO REGISTER THE PROGRAM The pricing is as follows 200 US for a single researcher 250 US for a university research laboratory 300 US for an in
88. dent angle a Calculated backscattering spectra for incident He ions backscattered from a gold layer with thickness 1 x 1018 atoms cm at a scattering angle of 165 are shown in Fig 4 25 for a smooth and rough substrates The rough substrates are described by a Lorentz distribution of tilt angles with different FWHM w On a rough substrate the low energy edge gets a tail which increases with increasing roughness This tail extends to energies close to zero With increasing roughness the Au peak also gets broader and the energy Fj 2 at which the low energy edge has decreased to its half height is no good measure for the film thickness It depends on the roughness of the substrate The high energy edge and the plateau are only slightly affected by substrate roughness and decrease only little at large roughnesses due to shadowing The backscattered particles do not reach the detector any more because the exit angle 8 points inside the layer For w the local tilt angles are equipartitioned and the corresponding spectrum represents the case of maximum roughness A measured spectrum for 2 5 MeV protons backscattered from a tungsten layer on top 98 200 200 0 500 1000 1500 201 X position um Y position um Experimental Gauss x cos 400 Lorentz x cos E e 300 Wm O D Q 200 E gt 100 60 40 20 0 20 40 60 Tilt angle 7 Figure 4 24 Top Line profile of a carbon fibre composite CFC surface Bottom Histo
89. distributions this is incorrect and results in an overestimation of the total straggling This error is negligible for light ions Ht He but may play a role for heavy ions 73 Energy keV 700 750 800 850 900 950 1000 Experimental 6000 4000 Counts 2000 O E 500 i DO 700 d Channel Energy keV s 740 750 760 770 780 790 800 6000 4000 2000 580 600 0 a 540 560 Channel Figure 4 6 Measured and simulated spectra using Bohr and Chu straggling of 1 0 MeV He ions incident on 100 nm Au on Si scattering angle 165 Bottom Magnification of the low energy gold edge 74 4 7 5 Geometrical straggling The finite size of the incident beam and the width of the detector aperture result in a spread AS of the exit angle 8 for outgoing particles This angular spread leads to differerent energies of the particles at the target surface due to 1 a spread A of the scattering angle 0 and therefore a spread of the transfered energy in the scattering process 2 different path lengths of the outgoing particles in the material These two contributions to geometrical straggling are not independent of each other and have to be considered simultaneously The spread Af of the exit angle O is given by 44 31 AB E e 4 57 Lp Lp cosa where d is the diameter of the incident beam w is the width of the detector aperture and Lp is the distance between the sample and the detector aperture
90. dustry research laboratory Registered users of any previous version of SIMNRA can upgrade their registration for a reduced fee 100 US registered users of any previous version of SIMNRA Please pay the registration fee to Max Planck Institut f r Plasmaphysik Account 5804058488 Bank Hypobank M nchen Bank Routing Code 70020001 Please indicate on the remitance that the money is intended for SIMNRA To register the program and get a registration number either send an email a letter by surface mail or send a fax to Dr Matej Mayer The address can be found on the title page of this manual You will receive your registration number within a few days Run the program and click HELP REGISTER to enter the registration number Most cross section data files included with SIMNRA have been taken from SigmaBase http ibaserver physics isu edu sigmabase These cross section data files are not in cluded in the shareware fee but are freely available from SigmaBase See the file ibaserver physics isu edu sigmabase newuser html for more information about SigmaBase The stopping power data files SCOEF 95A and SCOEF 95B have been taken from the SRIM 97 distribution These files are not included in the shareware fee but are freely available for scientific purposes SIMNRA was developed at the Max Planck Institut f r Plasmaphysik Garching Ger many NOTICE TO USERS CAREFULLY READ THE FOLLOWING LEGAL AGREE MENT THIS LICENSE AGREEMENT
91. e a linear energy cali bration But the nuclear energy loss and the plasma effect which are both important for heavy ions are not taken into account by this procedure An easier way to account for detector nonlinearities is to use a non linear energy calibration with a quadratic correction term of the form E keV A B x channel C x channel See section 3 4 1 for details 3 15 2 Energy calibration for different ion species As already shown in Section 3 15 1 the pulse height defect depends on the particle species This requires an individual energy calibration for each ion species if different ion species are detected as is the case in NRA and ERDA measurements with incident heavy ions SIMNRA offers the possibility to use an individual nonlinear energy calibration for each detected species see Section 3 4 1 for details 46 3 16 Programming support 3 16 1 Command line parameters regserver Registers the OLE automation server in the Windows Registry This is done automatically by SIMNRA so there should be rarely if ever the necessity to use this parameter unregserver Unregisters the OLE automation server from the Windows Registry This can be done before uninstalling SIMNRA Additionally SIMNRA accepts one optional command line parameter which is the name with full path of a NRA file This file is opened upon startup Use double quotes if the file name contains blanks Example simnra c ltest nra
92. e for ERDA Set all numbers to zero if geometrical straggling shall be neglected This is the program default See fig 3 3 for details e Diameter of incident beam Diameter of the incident beam in mm Please note that the size of the beam spot on the sample surface is d cosa e Shape of incident beam Circular or rectangular beams may be selected A ho mogeneous current distribution of the incident beam is assumed e Diameter of detector aperture Diameter of the detector aperture in mm e Shape of detector aperture Circular or rectangular apertures may be selected Use rectangular also for long narrow slits e Distance sample detector aperture Distance between the sample surface and the detector aperture in mm Note If Straggling in the Setup Calculation menu is unchecked then geometrical straggling and electronic energy loss straggling are neglected 13 3 4 3 Setup Calculation In the Setup Calculation menu the calculation parameters can be altered This affects the accuracy of the calculation but also the time necessary to calculate a simulated spectrum e Stepwidth incident ions Stepwidth of the incident ions used in the calculation See chapter 4 for details Automatic or Fixed can be selected If Automatic is selected the program will choose the stepwidth automatically This is usually the best choice for obtaining high accuracy and small computing times Automatic is the program default The automatically d
93. e necessary for kinematic calculations 54 4 3 Scattering kinematics 4 3 1 Elastic scattering Energy of backscattered projectiles The energy Ej of a backscattered projectile with incident energy Ey and mass M after scattering is given in the laboratory system by 2 M M2 ue E En sin 4 1 o7 A F fe 2 sin d 4 5 0 is the scattering angle and M3 the mass of the target nucleus initially at rest For M lt M only the plus sign in eq 4 5 applies If Mi gt M then eq 4 5 has two solutions and the maximum possible scattering angle Omax is given by Oman arcsin EA 4 6 The second solution for M gt Ma is obtained because different impact parameters d result in the same scattering angle 0 Consider for example the scattering angle 9 0 This angle is obtained for a head on collision with d 0 but also for very large impact parameters d oo SIMNRA version 3 50 and higher uses both solutions of eq 4 5 if kinematically pos sible Earlier versions of SIMNRA used eq 4 5 only with the plus sign the solution with the minus sign was neglected Energy of recoils The energy Ez of a recoil is given in the laboratory system by 4M M DM OTM Mp os 0 4 7 Eo is the energy of the incident projectile M the mass of the projectile Mz the mass of the target nucleus initially at rest and 0 the recoil angle with 0 lt 0 lt 90 4 3 2 Nuclear reactions For the calcul
94. e nuclear charge and mass of the helium ion and Z2 M are the nuclear charge and mass of the target element The reduced nuclear stopping Sn has the simple form In 1 e e 0 10718 0 37544 4 31 Sn 0 5 e is the reduced energy and is given by 32 53 Ma E e 2 4 32 1 2 2122 M Mo 230 z3 Nuclear stopping is only important at incident energies lt 100 keV at higher energies nuclear stopping becomes negligible 62 Heavy ions The electronic stopping power of heavy ions in all elements is derived from the stopping power of protons using Brandt Kitagawa theory 3 27 The formalism is described in detail in ref 3 a short overview is given in 27 The screening length A eq 3 29 of ref 3 is multiplied by an empirical correction factor which has been digitised from fig 3 25 of ref 3 The correction factor for all elements is stored in the file LCORRHI DAT Note that the switch High energy stopping in the Setup Calculation menu has influence on the calculation of the stopping power for heavy ions with incident energies above 1 MeV amu Nuclear stopping for incident heavy ions is calculated with the universal potential from ref 3 The reduced nuclear stopping s with the universal potential is given by In 1 1 1383 e 4 33 n 9 fe 0 01321 21226 0 19593 05 ee for e lt 30 For e gt 30 sn is given by l Se n e 4 34 2 The reduced energy e in eqs 4 33
95. e scattering 10000 2 8000 Leg 3 amp 6000 4000 2000 0 ES 200 300 Channel Figure 5 2 500 keV He ions incident on 100 nm Au on top of Si scattering angle 165 Circles experimental data points dashed line simulation with one scattering event solid line simulation with two scattering events 106 Energy keV 400 600 800 1000 1200 1400 14000 e experimental simulated 12000 10000 8000 Counts 6000 4000 2000 100 200 300 400 500 600 Channel Figure 5 3 2000 keV protons on carbon HOPG a 5 6 165 5 2 RBS Non Rutherford cross sections Fig 5 3 shows the measured and simulated spectra for 2 0 MeV protons incident on highly oriented pyrolytic graphite HOPG To avoid channelling the incident angle a was 5 The cross section is non Rutherford and the cross section data of Amirikas et al 69 were used for the simulation The pronounced peak in the spectrum is due to the resonance in the 2C p p C cross section at 1732 keV The measured and simulated spectra agree very well Fig 5 4 shows the measured and simulated spectra for 2 0 MeV protons incident on silicon To avoid channelling the incident angle o was 5 The cross section is non Rutherford and the cross section data of Vorona et al 70 were used for the simulation As in the case of carbon the measured and simulated spectra agree very well The struc tures in the simulated spectrum between channel 500 and 700 are due
96. e the correct cross sections The above formulas may be useful to estimate if the cross section is still Rutherford or not For non Rutherford cross sections SIMNRA uses experimentally determined differen tial cross sections taken from SigmaBase The use of non Rutherford cross sections is described in full detail in section 3 6 SIMNRA uses linear interpolation between the given data points 59 4 5 Evaluation of energy loss The energy E of a particle in the depth x is given by the integral equation E x Ep d Fee aly 4 16 0 da Here we assume that the particle starts with initial energy Ep at the surface x 0 dE dx E x x is the energy and depth dependent stopping power In principle eq 4 16 can be evaluated directly but this consumes a lot of computing time For evaluation of the energy loss SIMNRA uses the algorithm of Doolittle instead developed for RUMP 12 The beam loses energy according to the differential equation dE 748 4 17 where this is the defining equation for el ET the energy dependent stopping cross section x is the pathlength into the material measured in areal density 10 atoms cm e de dE is the first and e d e dE the second derivative of e If incoming or outgoing particles with incident energy Eo traverse a layer of material with thickness Az then the particles energy Ej after the layer can be expanded into a Taylor series dE ptt E The terms in eq 4
97. ectra with different layer thicknesses d N can be adjusted by the Number of thickness steps in the Setup Calculation menu see section 3 4 3 Typically about N 20 sub spectra are necessary to obtain a smooth superposition though N has to be increased to about N 50 for broad distributions with o gt d The weight mu Of each sub spectrum is determined according to the thickness distribution function For each sub spectrum the layer is treated to be smooth with thickness d Correlation effects such as incidence through a hump and emergence through a valley or multiple surface crossings are neglected This is only correct for backscattering at a scattering angle of exactly 180 and for transmission geometries However for scattering angles in the range 150 180 and non grazing incidence and emergence angles as are used in many RBS and NRA setups correlation effects still play only a minor role and can be neglected without severe loss of accuracy But it should be kept in mind that the used approximation gets invalid for grazing incidence or exit angles as is the case in ERDA in these cases correlation effects may be dominant and can change the shape of the spectra considerably The effect of layer roughness on the shape of RBS spectra is shown in Fig 4 19 for incident He ions backscattered from a gold layer at a scattering angle of 165 The film thickness distributions are described by the Gamma distributions shown in Fig 4 18 If
98. ed at the same time Related Properties and Methods Fit LayerNr 134 Fit LayerThickness 134 LayerNr Get Set Property LayerNr Integer Default Value 1 Description Specifies the number of the target layer which thickness or composition is fitted Only one layer can be fitted at the same time Fit LayerComposition and or Fit LayerThickness must be true otherwise layerNr has no effect Related Properties and Methods Fit LayerComposition 134 Fit LayerThickness 134 Layer Thickness Get Set Property LayerThickness Boolean Default Value false 134 Description Specifies if the thickness of a target layer is fitted The number of the layer is specified by the LayerNr property The thickness of layer number LayerNr is fitted if LayerThickness is true Only one layer can be fitted at the same time Related Properties and Methods Fit LayerNr 134 Fit LayerComposition 134 MaxlIterations Get Set Property MaxIterations Integer Default Value 20 Description Maximum number of fit iterations Fitting will be performed until the desired accuracy is obtained or the maximum number of iterations is reached Related Properties and Methods Fit Accuracy 133 NumberOfRegions Get Set Property NumberOfRegions Integer Default Value 1 Description Number of different regions where x is calculated see section 3 7 1 At least one region must exist and the regions should not overlap The lo
99. eed out errors B 2 The new R33 Format definition An R33 data file contains one cross section either as a function of laboratory incident energy or as a function of laboratory detection angle The file is made up of entries and the data section Each entry consists of a legal keyword followed by a colon followed by a space followed by data in Ascii format The keyword may be in any mixture of upper and lower case characters Legal separators for numerical data are space comma colon and semi colon characters Decimal points are represented only by full stops and not by commas as can be the case in some European countries The legal ascii character set for the purposes of R33 files is ascii 0 to ascii FF Apart from the Comment entry and the optional Version entry entries may be in any order Each entry ends with a carriage return line feed sequence Some entries are optional O most are required R and some are mutually exclusive Mx where all entries for which the value of x is the same are mutually exclusive See below for special conditions that apply to the keywords Comment Nvalues and Data and EndData Default values are suggested for R33 reading routines so that if an optional entry is omitted or if a required entry is unreadable or missing illegally the value of the corresponding variable in the reader is well defined All energies are expressed for the laboratory frame in keV and all angles in the l
100. elated Properties and Methods App Minimize 116 App Show 119 115 Maximize Procedure Maximize Description Maximizes SIMNRA to fill the whole screen SIMNRA must be visible i e not minimized or hidden otherwise Maximize has no effect Parameters None Return Value None Related Properties and Methods App Minimize 116 Minimize Procedure Minimize Description Minimizes SIMNRA to the Windows task bar Parameters None Return Value None Related Properties and Methods App Maximize 116 App Restore 118 App Active 111 App BringToFront 113 116 Open Function Open FileName WideString Boolean Description Opens a NRA file Parameters FileName The name of the NRA file including path Return Value Returns true if the file was opened successfully Related Properties and Methods App SaveAs 118 ReadSpectrumData Function ReadSpectrumData FileName WideString Format Integer Boolean Description Imports experimental data in different formats Parameters FileName The name of the spectrum data file including path Format Format of the spectrum data file Allowed values for Format are 1 Data in ASCII file format 2 Data in Canberra s CAM file format 4 Data in RUMP s RBS file format 5 Data in user defined format Requires a used supplied dll See section 3 13 for more details Return Value Returns true if the file was imported successfully Related Prope
101. ent An individual factor f for each ion species and each layer may be defined If no factor f is given the program uses f 1 i e uses Bragg s rule e Layer and substrate roughness Click the button if the current layer or the sub strate is rough See section 3 5 2 for details To manipulate layers use the buttons in the Layer manipulation box Additionally layers can be copied and pasted from the clipboard and layers can be saved and read from file Add Adds a layer The added layer will be the last layer The maximum number of different layers is 100 e Ins Inserts a layer in front of the current layer The maximum number of different layers is 100 e Del Deletes the current layer e Prev Go to the previous layer e Next Go to the next layer A layer can be copied to the clipboard with Edit Copy Layer or by pressing Ctrl C A layer can be pasted from the clipboard with Edit Paste Layer or by pressing Ctrl V A layer can be saved to file with File Save Layer A layer can be read from file with File Read Layer Attention If a layer is pasted from the clipboard or read from file the current layer is overwritten The whole target or foil with all layers can be saved to file with File Save Target A target or foil can be read from file with File Read Target Show Target summary displays the total amounts in atoms cm of all elements in the target This is mainly useful if the target consists of plural layers
102. eometrical straggling are taken into account ZBStopping Get Set Property ZBStopping Boolean Description Selects Ziegler Biersack or Andersen Ziegler stopping If ZBStopping is true Ziegler Biersack stopping is used while Andersen Ziegler is selected if ZBStopping is set to false See section 3 4 3 for more details about stopping power data Related Properties and Methods 126 Calc HighEnergyStopping 125 Ah Simnra Target The Simnra Target object represents the target with all layers and elements A 5 1 Properties ElementConcentration Get Set Property ElementConcentration lay el Integer Double Description Concentration of element number el in layer number lay The sum of con centrations of all elements in a layer must be equal to 1 This is not checked by SIMNRA If ElementConcentration is changed it is the responsibility of the programmer to assure that the sum of the concentrations is equal to 1 Parameters lay Number of the layer with 1 lt lay lt NumberOfLayers el Number of the element with 1 lt el lt NumberOfElements lay ElementName Get Set Property ElementName lay el Integer WideString Description Name of element number el in layer number lay Returns XX if the element is unknown Attention Do not use ElementName to add new elements to the target The element should already be present in at least one layer If you add new elements they will have undefined cross
103. ered from gold at different energies The dependence of the correction factor FAndersen from the scattering angle for He scattered from gold is shown in fig 4 2 for different He energies Dashed lines are the angular independent correction factor by L Ecuyer For large scattering angles the correc tion factors by L Ecuyer and Andersen are near to unity and similar however for small scattering angles the correction by Andersen becomes large and the angle independent L Ecuyer correction underestimates the deviations from the Rutherford cross section The Rutherford cross section for recoils is given in the laboratory system by Z1Z2 Mi Mz 2M2E keV cos 6 oERD mb sr 2 0731 x 107 4 15 0 is the recoil angle in the lab system SIMNRA applies the correction to the Rutherford cross section from eq 4 14 also for the recoil cross section 4 4 2 Non Rutherford cross sections At high energies the cross sections deviate from Rutherford due to the influence of the nuclear force A useful formula above which energy Ey deviations from Rutherford can be expected was given by Bozoian 19 20 21 Mi M2 Za Enr MeV At 10 for Z 1 58 M M Z1Z ENR MeV ae SC for Z1 gt 1 En is the energy at which the deviation from the Rutherford cross section gets gt 4 SIMNRA does not check if the cross sections at a given energy are Ruther ford or not It is in the responsibility of the user to choos
104. es the non statistic broadening or skewing of the energy distribution when penetrating a layer in the following way 31 Assume two particles with energies Ei and E AE AE E Eo ER centered around a mean energy Eg The energy difference Ej Ez of the two particles is AE After penetrating a layer the particles have the energies Ej and E centered around a mean energy Eq The energy difference AE behind the layer is given by E An 0 age fag 4 48 Eo Ei with the stopping power e dE dx er is the stopping power at the exit of the layer and e the stopping power at the entrance of the layer If f gt which is the case for all energies 68 above the stopping power maximum the energy difference increases and the distribution function is broadened If ef lt e the energy difference decreases and the distribution function gets skewed The shape of the distribution remains unchanged a Gaussian distribution remains gaussian but the width of the Gaussian is changed according to eq 4 481 To the non statistic broadening we have to add the statistical effects When the in cident beam with initial energy Ep and initial beam width 0 0 is the variance of the energy distribution the full width at half maximum FWHM is 2 V2In2o 2 355 0 penetrates a layer of matter with thickness Ax then the beam width o after penetrating the layer is given by a al o 4 51 2 ef and er are the stopping powers of t
105. escription Incident angle a deg Related Properties and Methods Setup Beta 120 Setup Theta 122 Beamspread Get Set Property Beamspread Double Description Energy spread of incident beam keV FWHM Related Properties and Methods Setup Energy 122 Beta Get Set Property Beta Double Description Exit angle 8 deg Related Properties and Methods Setup Alpha 120 Setup Theta 122 120 CalibrationLinear Get Set Property CalibrationLinear Double Description Linear calibration term B for energy calibration see eq 3 1 keV channel Related Properties and Methods Setup CalibrationOffset 121 Setup CalibrationQuadratic 121 CalibrationOffset Get Set Property CalibrationOffset Double Description Calibration offset A for energy calibration see eq 3 1 keV Related Properties and Methods Setup CalibrationLinear 121 Setup CalibrationQuadratic 121 CalibrationQuadratic Get Set Property CalibrationQuadratic Double Description Quadratic calibration term C for energy calibration see eq 3 1 keV channel Related Properties and Methods Setup CalibrationLinear 121 Setup CalibrationOffset 121 DetectorResolution Get Set Property DetectorResolution Double 121 Description Detector resolution keV FWHM Energy Get Set Property Energy Double Description Energy of incident ions keV Related Properties and Methods Setup Beamspread 120
106. escription Number of channels in the experimental or simulated spectrum NumberOfChannel1s is readonly Related Properties and Methods spID 137 A 7 3 Methods Data 139 Function Data spID chan Integer Double Description Value of experimental or simulated data in channel chan Parameters spID Selects the experimental or simulated spectrum chan Channel number with 0 lt chan lt NumberOfChannels Return Value Returns the value in channel chan Related Properties and Methods spID 137 Integrate Function Integrate spID lowChannel upChannel Integer Double Description Sum of counts of the experimental or simulated spectrum in the range from lowChannel to upChannel Parameters spID Selects the experimental or simulated spectrum lowChannel Lower channel with O lt lowChannel lt NumberOfChannels upChannel Upper channel with O lt upChannel lt NumberOfChannels Return Value Returns the sum of counts 140 Related Properties and Methods spID 137 A 8 Simnra Stopping The Simnra Stopping object allows to calculate stopping powers energy losses and energy loss straggling in elements target and foil layers A 8 1 Input parameter The methods of Simnra Stopping require the input parameter TargetID which specifies if a layer is in the target or foil The possible values for TargetID are TargetID 1 Target 2 Foil Other values are not allowed A 8 2 Methods
107. esses see section 4 9 for details with the layer thickness as mean value The width and shape of the distribution is determined by the full width at half maximum FWHM with FWHM 2 35482 o 3 3 where is the standard deviation FWHM in 1015 atoms cm e Has substrate roughness Check if the layers are on top of a rough substrate A rough substrate is described by a distribution of incident and exit angles and has no other influence Only one substrate can exist for all layers i e the substrate param eters are identical for all layers Substrate roughness is not available for foils The distribution of incident and exit angles is divided into M steps The step number M can be adjusted by the Number of angular steps in the Setup Calculation menu see section 3 4 3 FWHM of substrate roughness SIMNRA assumes a Lorentz distribution of angles Enter the full width at half maximum FWHM of the angle distribution in deg 3 5 3 Target Foil In this menu a foil in front of the detector can be created Like the target a foil can consist of multiple layers with different compositions See the previous section for details If the foil consists of multiple layers then backscattered particles first will penetrate layer n then layer n 1 etc layer 1 is directly in front of the detector see fig 3 5 The default is no foil in front of the detector Some common materials used as stopper foils are already stored in the LAYERS di
108. etermined stepwidth is kept always below the resolution of the experiment Because the resolution in larger depths degrades due to energy loss straggling the program uses a small stepwidth near the surface and a larger stepwidth in larger depths Fixed stepwidth The program uses a fixed stepwidth for the calculation If Fixed is selected the default for the stepwidth is 10 keV For incident heavy ions with energies in the range of several ten MeV this stepwidth can be increased to several 100 keV The stepwidth used for incident ions affects the time T necessary to perform a calculation strongly T depends on the stepwidth of the incoming ion AF roughly as T x 1 AE Decreasing the stepwidth by a factor of two will roughly double the computing time Note 1 The stepwidth of the incident ions is an important parameter for the accu racy of a simulation If the stepwidth of the incident ion is too high especially if the exit angle is close to 90 or the detector resolution is below 10 keV unwanted oscil lations or steps in the simulated spectra may occur This is due to rounding errors in the routine which calculates the contents of each channel If these oscillations occur you have to decrease the stepwidth of the incident ions If automatic stepwidth control is selected these problems should never occur The program always selects a stepwidth which is small enough Note 2 If the backscattering cross section contains narrow resonances the s
109. evel 3 zero compression is not implemented See section 3 12 for more details RUMP Read Sample Description File This menu item allows to read a sam ple description file produced by RUMP or the IBA data furnace NDF The default file extension of sample description files is LCM Note 1 RUMP stores the description of the sample and the absorber foil in sample description files LCM The experimental parameters Type of incident particles incident energy scattering geometry etc and spectral data are stored in files with extension RBS You can read RBS files with RUMP Read RBS File Note 2 SIMNRA supports only a subset of the RUMP sample description com mands Especially the RUMP commands Equation Species and Fuzz are not supported If your sample description file contains these commands they will be neglected and a warning will be shown See section 3 12 for more details This line may contain any comment lt CR gt lt LF gt This line may contain any comment as well lt CR gt lt LF gt Channel Counts lt CR gt lt LF gt 1 1000 lt CR gt lt LF gt 2 1000 0 lt CR gt lt LF gt 3 1 0E3 lt CR gt lt LF gt 4 1 0E3 lt CR gt lt LF gt lt EOF gt Figure 3 1 Example for a valid data file which can be imported with File Read Data ASCII The first three lines will be ignored by the program The channel number must be an integer number counts may be integer or floating point numbers e RUMP Write Sample Descri
110. f N spectra three rough layers of N spectra etc Number of angular steps Used for the calculation of substrate roughness A rough substrate is approximated by the superposition of M spectra with different incident and exit angles where M is the number of angular steps If M is small the superposed spectrum may contain steps Larger values of M result in smoother spectra but slow down the calculation considerably Default is M 20 Note Substrate roughness requires the calculation of M spectra one rough layers combined with substrate roughness of N x M spectra where N is the Number of thickness steps two rough layers combined with substrate roughness of N x M spectra etc Element Spectra If checked individual spectra for each element in the target are calculated and plotted If unchecked only the total spectrum is calculated and plotted Default is unchecked Isotope Spectra If checked individual spectra for each isotope in the target are calculated and plotted Default is unchecked Note The number of individual spectra is limited to 20 If the target contains many isotopes not all will be displayed Logfile If checked a file named SIMNRA LOG is created This file contains additional information about each step of the calculation The logfile is intended for debugging the program Default is unchecked 17 Incident ion Andersen Ziegler Ziegler Biersack keV amu keV amu Hydrogen H D T 1 100
111. g contributions at the sample surface for 2 6 MeV He incident on Co 99D0 01 as a function of depth for typical RBS and ERDA geometries An energy independent detector resolution of 15 keV FWHM is used For RBS geometry the contribution of geometrical straggling is small compared to energy loss straggling and the resolution of the detector and may be neglected without penalty For the ERDA geometry however geometrical straggling cannot be neglected Note that geometrical straggling first decreases until it reaches zero and then increases again This is due to the minus sign in eq 4 62 If the exit angle P decreases the outgoing path is closer to the surface normal then the scattering angle 6 increases The backscattered or recoiled particles start with a smaller energy However the path length in the material is smaller due to the exit angle which is closer to normal resulting in a smaller energy loss Near the surface the path lenght differences are small and geometrical straggling is governed by the kinematic spread With increasing depth the two effects compensate each other more and more until in large depths the path length differences become dominant and geometrical straggling increases 76 100 Energy loss straggling 80 Geometrical straggling Detector resolution 60 4 S 40 s 2 S 220p ee ee gt Pic deeg lee AE AE E AAA AER eet AE A V E a 0 K po E 80 S o A 5 E S j vi 60 E of PS E a iz
112. gram of the local tilt angle distribution of the CFC surface Solid line Experimental data Dashed line Lorentz distribution times cosine of the tilt angle Dotted line Gaussian distribution times cosine of the tilt angle 99 Counts a u 1000 1 200 1400 1600 1800 Energy keV Figure 4 25 Calculated energy spectra for 2 MeV He backscattered from a gold layer with thickness 1 x 1018 Au atoms cm on a rough substrate with different roughnesses The roughness is described by a Lorentz distribution of tilt angles with FWHM w w is an equipartition of tilt angles Incident angle a 0 scattering angle 165 100 of a rough carbon substrate is shown in Fig 4 26 The non Rutherford elastic scattering data from 69 were used for the C p p C cross section The substrate is the same CFC material which surface is shown in Fig 4 24 The mean W layer thickness was about 3 5 um while the standard deviation of the substrate roughness was about 8 2 um i e the substrate roughness was considerably larger than the thickness of the W layer The dotted line in Fig 4 26 is the calculated spectrum for a smooth W layer on a smooth carbon substrate Plural scattering in the W layer was included in dual scattering approximation see section 4 8 3 Plural scattering results for example in the small background visible between the carbon and tungsten signals in channels 500 650 This spectrum has only minor resemblance with the experimental cur
113. gy For F M values in the range 100 1000 keV amu the 7 SIMNRA versions before 3 30 used the equation AE 1 E As AE 4 49 d instead of eq 4 48 Equation 4 49 is obtained by a taylor expansion of ef around e considering only the linear term P Ef acide 4 50 where de dE is the derivative of the stopping power and Az the layer thickness e Az is the energy loss in the layer By putting the above equation into eq 4 48 we obtain eq 4 49 The difference between eq 4 48 and the previously used eq 4 49 is only 1 2 because of the relatively small stepwidths used by SIMNRA 69 E M ke V amu 5000 3000 2000 1500 H E M Z Figure 4 3 The Chu straggling correction for several values of E M as a function of the nuclear charge of the target Z Dots are original data from Chu 38 solid lines are extrapolated data taken from 31 data have been taken from ref 38 data for lower and higher F M values are based on an extrapolation performed in ref 31 Tabulated values for H are stored in the file CHU_CORR DAT For not tabulated values SIMNRA uses linear interpolation Fig 4 4 compares the beam width FWHM of 2 5 MeV He ions in silicon calculated by SIMNRA using eq 4 51 with Bohr s theory For small energy losses the beam width calculated by SIMNRA is slightly smaller than predicted by Bohr s theory due to the Chu correction However this is counterbalanced by the nonstochastic
114. hannel of data is rounded from real to integer This may result in differences of 0 5 channels between RUMP and SIMNRA if a non integer starting channel is used 3 12 3 IBA data furnace The IBA data furnace NDF was developed at the University of Surrey and is avail able from http www ee surrey ac uk Research SCRIBA ndf This program converts energy spectra to depth profiles The depth profiles are stored in RUMP s sample des crition format LCM You can read these files with the command File Read RUMP see section 3 12 2 41 3 13 Importing spectrum data in any format SIMNRA can read experimental spectrum data in several formats including ASCII see section 3 2 But many laboratories have their own spectrum data file formats SIMNRA offers the possibility to import any type of experimental data by supplying a dynamic link library DLL which reads the data and passes them to SIMNRA This DLL must be supplied by the user and is called if File Read Spectrum Data User is clicked This section describes the details of this DLL The DLL name must be user dl11 It must be located in the SIMNRA UserD11 subdi rectory otherwise SIMNRA will not find it The DLL must export a function ReadData exact spelling defined as follows Function ReadData FileName PChar Var Count Integer Data Pointer Integer stdcall Filename Input parameter Null terminated string with the full name including path to the file which sh
115. he material at the entrance and exit of the layer and o is the energy loss straggling in the layer The first term in eq 4 51 describes the non statistical broadening of the beam according to eq 4 48 due to the energy dependence of the stopping power the second term adds the statistical effects The electronic energy loss straggling is calculated by applying Chu s theory 42 38 0 H E Mi Z2 0 Rone 4 52 Tohr 18 the electronic energy loss straggling in Bohr approximation and is given by 37 38 Thonr ke V 0 26 Z Za Az 101 atoms cm 4 53 Bohr s theory of electronic energy loss straggling is valid in the limit of high ion velocities In this case the electronic energy loss straggling is almost independent of the ion energy For lower ion energies the Bohr straggling is multiplied by the Chu correction factor H E M Z2 which depends only on E M and the nuclear charge of the target atoms Zo H takes into account the deviations from Bohr straggling caused by the electron binding in the target atoms Chu 42 38 has calculated H by using the Hartree Fock Slater charge distribution This calculation gives straggling values which are considerably lower than those given by Bohr s theory The correction factor H as used by SIMNRA is shown in fig 4 3 The Z oscillations are clearly visible The Chu correction is mainly necessary for high Z and low energies For high energies H approaches 1 and becomes independent of Z2 and ener
116. he plural scattering background are the reason for this small discrepancy Additionally it should be kept in mind that the used model of inclined line segments see Fig 4 17 b is only an approximation to physical reality and the real surface has an additional fine structure The influence of the different roughnesses on the shape of the RBS spectrum is shown in more detail in Fig 4 27 The experimental data black dots and the solid line in the top and bottom figures are the same as in Fig 4 26 The substrate roughness is kept constant in Fig 4 27 top and the roughness of the W layer is varied from smooth to 0 6 ym The roughness of the W layer influences mainly the low energy edge of the W peak best fit is obtained for oe 0 3 ym The bottom part shows the influence of the carbon substrate roughness for constant W layer roughness Substrate roughness influences mainly the low energy tail below the W peak while the low energy edge of the W peak is less affected by substrate roughness Best fit is obtained for about 20 FWHM Due to the different effects of the two roughnesses on the shape of RBS spectra the two roughnesses can be easily distinguished 101 e Experimental Smooth plural scattering 400 Rough plural scattering 400 600 800 Channel Figure 4 26 2 5 MeV protons backscattered from 3 5 ym W on a rough carbon substrate scattering angle 165 Dots Experimental data Dotted line Calculated spectrum for a
117. ield 2 3 Uninstalling SIMNRA SIMNRA is shipped with an automatic uninstall program Refer to your Microsoft Win dows documentation on how to uninstall programs Directory Files SIMNRA EXE executable program README TXT Readme file CHANGES TXT Describes the changes since version 3 0 LICENSE TXT Product license agreement MANUAL PDF This manual ATOM ATOMDATA DAT atomic data STOP STOPH DAT electronic stopping power data Andersen Ziegler STOPHE DAT LCORRHI DAT SCOEF 95A electronic stopping power data Ziegler Biersack SCOEF 95B CHU_CORR DAT Chu correction data to Bohr straggling CRSEC CRSDA DAT cross section data R33 RTR DLL DLL dynamic link libraries used by SIMNRA SAMPLES NRA examples LAYERS LAY predefined materials mylar stainless steel DEFAULT SETUP NRA default experimental setup USERDLL SAMPLE DPR Code examples in Pascal for user supplied dynamic link libraries see Section 3 13 Table 2 1 Directory structure and files used by SIMNRA Chapter 3 Using SIMNRA 3 1 Basic steps This section gives a quick overview about the basic steps necessary to calculate a backscat tering spectrum Three steps must be performed before a backscattering spectrum can be calculated In a first step the experimental situation incident ions geometry has to be defined then the target must be created and in a third step the cross sections used for the calcula
118. in New Zealand at http pixe gns cri nz 23 The chosen cross sections for each type of scattering event must be unambiguous You can choose for example Rutherford cross section for backscattering in the energy range from 0 000 0 999 MeV some non Rutherford cross section for backscattering in the energy range from 1 000 1 999 MeV and a different cross section for backscattering in the energy range from 2 000 3 000 MeV You cannot choose however Rutherford cross section for backscattering in the range 0 000 2 000 MeV and another cross section for backscattering in the energy range from 1 000 2 000 MeV In this case the program does not know which cross section it should use in the range from 1 000 2 000 MeV and you will get the error message Energy overlap in cross sections All available cross section data are listed in tables 3 3 3 4 and 3 5 If you want to add new cross section data files see section 3 14 Note 1 Some files contain total cross section data o E In these cases the differen tiell cross section do dQ is obtained by SIMNRA for all kinematically allowed angles by assuming angular independence of the cross section in the center of mass system do 1 LG E 0 qn o E 3 4 This cross section is then transformed from the center of mass to the laboratory system The assumption of angular independence in the center of mass system is well fulfilled for the He D p a reaction for incident energies below about 1 2 Me
119. is In this case the units entry should specify rr for ratio to Rutherford Nevertheless it is recommended that elastic cross sections be stored as cross sections just like the inelastic scattering cross sections i e in mb sr The value tot indicates that the cross section is integrated over all angles and is expressed as a function of energy Thus if tot is used as a unit then the distribution must be energy and the value of theta has no meaning Nevertheless it is suggested that a valid real number be given for theta so that reading routines don t have to cater for non numerical values for theta such as Theta irrelevant O 1 0 0 0 0 0 0 0 lt r r r r gt Note Scale conversion factors and associated errors common to all the energy or angle data See original R83 publication in Appendix 1 for discussion M2 R 0 lt n gt M2 R O Note two methods are allowed for representing the data The first corresponds to the original R33 specification The data immediately following the Nvalues entry consists of the cross section data one point per line and each point represented by four values X dX Y dY energy or angle energy or angle random error sigma sigma random error The data ends after Nvalues lines of data Alternatively and recommended the data may be bracketed by Data and End data entries An entry of Nvalues 0 is equivalent to a Data entry The d
120. is calculated Up to 10 different regions may be used At least one region must be specified The regions should not overlap From To Lower and upper channel of each fit region Max Iterations Maximum number of Simplex iterations Fitting will be per formed until the desired accuracy is obtained or the maximum number of iterations is reached Fit Accuracy Desired accuracy of the fit The fit has converged if the relative change of all fitted parameters and of y is below Fit Accuracy The relative change of a parameter A is AA A where AA is the difference between the best vertex the vertex with the lowest x and the worst vertex the vertex with the highest 7 Calculate Fit Error If checked an error estimate for all fitted parameters is computed See below for details This is a time consuming process and may require more computing time than the fit itself Default is unchecked Fit error An error bar for fitted parameters can be obtained under the following assumptions 1 The physics model i e stopping powers cross sections etc is assumed to be accu rate with zero error Obviously in reality this is not the case and errors introduced by inaccurately known stopping powers or cross sections may largely exceed the com puted errors SIMNRA does not know whether a stopping power or cross section is accurate or not you should know that All nonfitted parameters are assumed to be accurate with zero error Again usua
121. is described by a distribution function p d with the film thickness d measured perpendicular to the substrate see Fig 4 17 a and d gt 0 In the literature usually a Gaussian distribution centered at d with variance 0 and cut off at zero is used for p d 64 65 However a more natural choice of a distribution function with only positive values d gt 0 is the Gamma distribution which is also fully described by its mean value d and standard deviation o The Gamma distribution is defined by pe p d Ta 8 d gt 0 4 71 90 a ion beam b ion beam Figure 4 17 Schematic representation of a rough film on a smooth substrate a and of a smooth film on a rough substrate b with a d o and 6 d 0 T a is the Gamma function The Gamma distribution is shown in Fig 4 18 for d 1 and different standard deviations The corresponding Gaussian distributions centered at 1 and identical are shown for comparison If o lt d i e if the width of the distribution is small compared to its mean value Gaussian and Gamma distributions are nearly identical see the curves for 0 1 in Fig 4 18 With increasing o the two distributions get more and more different see the curves for o 0 3 and 0 7 in Fig 4 18 For o d the Gamma distribution decreases exponentially with p d e 4 and for o gt d an integrable singularity develops at d 0 A RBS NRA or ERDA spectrum of a rough film is approximated by a superposition of N sp
122. istical fluctuations in the transfer of energy to electrons Nuclear energy loss straggling due to statistical fluctuations in the nuclear energy loss Geometrical straggling due to finite detector solid angle and finite beam spot size resulting in a distribution of scattering angles and different pathlengths for outgoing particles Straggling due to multiple small angle scattering resulting in angular and energy spread on the ingoing and outgoing paths Straggling due to surface and interlayer roughness and thickness inhomogeneities of absorber foils An additional contribution to the energy broadening visible in experimental spectra is the energy resolution of the detector The different straggling contributions excluding roughness have been reviewed by Szil gy et al 31 32 and can be included in SIMNRA calculations The details are described in the following sections 67 4 7 2 Electronic energy loss straggling There are four main theories describing electronic energy loss straggling 33 34 35 each applicable in a different regime of energy loss With AF the mean energy loss of the beam and E the energy of the incident beam we can distinguish AE E lt 10 Vavilov s Theory 36 34 For thin layers and small energy losses The energy distribution is non Gaussian and asymmetrical This energy range is not described properly by SIMNRA 10 20 Bohr s Theory 37 38 As the number of collisions beco
123. ith dual scattering are slightly lower than the experimental results This is due to trajectories with more than two scattering events which are not calculated 89 4 9 Surface roughness The quantitative application of ion beam analysis methods is usually restricted to later ally homogeneous and smooth films The experimentalist is often confronted with rough surfaces The effects of rough surfaces of thick targets on RBS were investigated in some detail by Edge and Bill 54 Knudson 55 Bird et al 56 and Hobbs et al 57 W est and Bochsler 58 and Yesil et al 59 60 attacked the problem by means of a Monte Carlo computer simulation taking into account correlation effects of the surface roughness and multiple surface crossings of the incident and emerging ions It turned out that effects of rough surfaces of thick targets occur only for grazing angles of the incident or emerging ions This is especially the case in ERDA on thick rough targets as was shown by Yesil et al 59 60 and Kitamura et al 61 Hydrogen depth profiling on rough surfaces by ERDA was studied experimentally by Behrisch et al 62 Astonishingly the effects of rough thin films were studied much more scarcely For RBS rough films on a smooth substrate were investigated by Shorin and Sosnin 63 and Metzner et al 64 65 Shorin and Sosnin 63 used a Monte Carlo computer simula tion The Monte Carlo approach suffers from long computing times of the order
124. k of Modern Ion Beam Materials Analysis Mate rials Research Society Pittsburgh Pennsylvania 1995 23 23 57 57 J A Nelder and R Mead Computer Journal 7 1965 308 33 M S Caceci and W P Cacheris Byte 5 1984 340 33 WH Press B P Flannery S A Teukolsky and W T Vetterling Numerical Recipes Cam bridge University Press Cambridge New York 1988 33 34 35 35 L Cliche S C Gujrathi and L A Hamel Nucl Instr Meth B45 1990 270 46 46 46 W Hosler and R Darji Nucl Instr Meth B85 1994 602 46 E Steinbauer P Bauer M Geretschl ger G Bortels J P Biersack and P Burger Nucl Instr Meth B 85 1994 642 46 R Doolittle Nucl Instr Meth B9 1985 344 52 60 60 90 R Doolittle Nucl Instr Meth B15 1986 227 52 90 G Audi and A H Wapstra Nuclear Physics A595 1995 409 54 P De Bievre and P D P Tylor Int J Mass Spectrom Ion Phys 123 1993 149 54 J L Ecuyer J A Davies and N Matsunami Nucl Instr Meth 160 1979 337 57 57 M Hautala and M Luomaj rvi Rad Effects 45 1980 159 57 H H Andersen F Besenbacher P Loftager and W Moller Phys Rev A21 6 1980 1891 57 57 M Bozoian K M Hubbard and M Nastasi Nucl Instr Meth B51 1990 311 58 M Bozoian Nucl Instr Meth B58 1991 127 58 M Bozoian Nucl Instr Meth B82 1993 602 58 154 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 4
125. kridge and has been taken from the file R33Help htm 110 Appendix A OLE automation reference This section describes OLE automation support in SIMNRA in full detail A short overview of the OLE objects and methods can be found in section 3 16 2 some sample programs are shown in section A 10 The properties and methods are grouped by object A 1 Data types SIMNRA is written in Borland Delphi and uses only automation compatible data types The data types used by Delphi the corresponding types in Microsoft s Interface Definition Language IDL and the corresponding types used in Variants are summarized below Delphi type IDL type Variant type Description Boolean VARIANT_BOOL VT_BOOL True 1 False 0 Double double VT_R8 8 byte real Integer long VTI 4 byte signed integer WideString BSTR VT_BSTR binary string A 2 Simnra App The Simnra App object represents the application itself A 2 1 Properties Active Get Property Active Boolean Description 111 Specifies whether SIMNRA is active and has focus Active is True while SIMNRA is active and False if it is not SIMNRA is active if it has focus and becomes inactive when a window from a different application is about to become activated Active is readonly Related Properties and Methods App BringToFront 113 App Minimize 116 App Restore 118 DeleteSpectrumOnCalculate Get Set Property DeleteSpectrumOnCalculate Boolean Default Value true
126. lag The text of the error message can be retrieved with LastMessage See section A 9 for more details about error handling Related Properties and Methods App LastMessage 113 A 2 2 Methods BringToFront Procedure BringToFront Description Brings SIMNRA to the front above all other applications 113 Parameters None Return Value None Related Properties and Methods App Active 111 App Minimize 116 App Restore 118 CalculateSpectrum Function CalculateSpectrum Boolean Description Calculates a simulated spectrum Parameters None Return Value Returns true if the calculation succeeded Related Properties and Methods App DeleteSpectrumOnCalculate 112 CopySpectrumData Procedure CopySpectrumData Description Copies experimental and simulated spectra in ASCII format to the Windows clipboard See Edit Copy Data in section 3 3 for a description of the format Parameters None 114 Return Value None Related Properties and Methods App WriteSpectrumData 119 FitSpectrum Function FitSpectrum Boolean Description Fits a spectrum You have to adjust the fit parameters in the Simnra Fit 133 object first before the fit can be performed with FitSpectrun Parameters None Return Value Returns true if the fit succeeded Hide Procedure Hide Description Hides SIMNRA The program is still running but not visible Parameters None Return Value None R
127. lculation of straggling in section 4 7 SIMNRA calculates the energy of backscattered particles from the front and the backside of the sublayer and the energy of these particles when reaching the detector after passing to the target surface and traversing a foil in front of the detector see fig 4 1 The contribution of each isotope in each sublayer will be referred to as a brick To account for energy straggling and the finite energy resolution of the detector the brick shown in fig 4 1 is convoluted with a Gaussian function f 0 with width 2_ 2 2 0 O Strageling Out T Detector 4 1 SCH aggling Out is the variance of the energy distribution of the outgoing particles due to energy loss straggling and on tte 5 the energy resolution of the detector The final contribution to the energy spectrum of each isotope in each sublayer is given 1A backscattered particle may be a recoil or a product in a nuclear reaction as well 52 Counts energy Energy Figure 4 1 Notation used for a single brick by S E SE f E 02 B dEl 4 2 Here So E is the energy spectrum before convolution and S E the spectrum after the convolution Note that the width of the Gaussian changes throughout the brick due to different straggling contributions The Number of counts N in each channel is given by integrating S E over the channel width from the minimum to the maximum energy of each channel Emaz i gt j we n S E
128. les sr Calculation of particles sr from the collected charge and detector solid angle 3 7 1 Fit Spectrum Data fitting to backscattering spectra is a nontrivial task In data fitting the quadratic deviation of the simulated from the measured data points 2 v Neap Z Nein 3 5 i is minimized by varying the input parameters of the calculation Nezp i is the number of counts in channel 7 of the measured spectrum Nsim i the number of counts in channel 7 of the simulated spectrum and o the statistical error of each data point Fast fitting algorithms such as the Levenberg Marquardt algorithm tend to be un stable and require the knowledge of the derivatives of x SIMNRA uses the Simplex algorithm for fitting 6 7 8 The Simplex algorithm is very stable and converges nearly always However the convergence is not very fast The Simplex algorithm always uses n 1 points called vertices in the parameter space for fitting where n is the number of free parameters You can fit 1 Energy calibration energy channel and offset only quadratic term is not changed 4SIMNRA uses 0 Nezp for Nesp gt 4 oi 2 for Nesp lt 4 due to Poisson statistics 33 2 3 4 Particles sr Thickness of a layer Composition of a layer independently or all at once Check which parameters should be varied Only one layer at a time can be fitted Number of fit regions Number of different regions where x
129. ll counts between a lower and an upper channel including the boundary channels The integration boundaries are displayed as small black vertical lines in the plot The boundaries are moved by entering the channel numbers or by using the spin up spin down buttons in the control window The integral is updated automatically if a spectrum is recalculated or if a new spectrum is loaded from disk 36 3 9 Plot menu This section describes all plot related commands including all commands which are not accessible via menus Autoscaling H checked the plot will be scaled automatically to minimum and maximum if experimental data are imported or a new calculation is performed If unchecked the axis scales remain fixed Rescale x Axis Scales the x axis to minimum and maximum of all visible spectra Rescale y Axis Scales the y axis to minimum and maximum of all visible spectra Unzoom Undo all zoom operations x Axis Scale the x axis manually by entering the axis minimum and maximum set logarithmic x axis Same as a double click with the left mouse button on the X axis y Axis Scale the y axis manually by entering the axis minimum and maximum set logarithmic y axis Same as a double click with the left mouse button on the y axis Legend Allows to alter the text of the legend Same as a double click with the left mouse button on the legend Delete Experimental Data Deletes the experimental data from the plot Delete Simulated
130. lly this will be not the case but SIMNRA is not able to quantify these errors It does not know how accurately you determined your energy calibration or performed the ion current measurement The error bar Aa of a fitted parameter a is determined by the shape of the x surface near the minimum A flat minimum of x allows a larger variation of a and will result in larger errors of a On a confidence level of 68 3 the usual 1 interval the error of a is obtained by varying a until x has increased by 1 8 Ax as X laa Kon 1 3 6 34 Figure 3 6 Ax 1 contour near the x minimum black dot for two fit parameters a and az Aa and Aaz are the fit errors for a and az if fitted simultaneously Aa the error for ou if only ay is fitted N n 18 the minimised x with an optimised parameter amin and the error Aa of a is Aa aa 1 Ga If we have more than one Dt parameter things get more complicated 8 As an example we consider the case of two fit parameters a and a The Ax 1 contour now is an ellipse fig 3 6 due to correlations between a and az and for more than two fit parameters a multi dimensional ellipsoid To find the confidence intervals for a and az we have to do the following Increase a by some amount black arrows in fig 3 6 Now find a new minimum of x by optimising az a remains unchanged dotted line in fig 3 6 Increase a and optimise as again and so on until Ay 1 For n fit par
131. ments The deviations at low energies between simulated and measured spectra are also mainly due to plural scattering SIMNRA can calculate all trajectories with two scattering events IfDual Scattering is unchecked then only one scattering event is calculated This is the default If Dual Scattering is checked additionally trajectories with two scattering events will be calculated Warning The calculation of dual scattering is a very time consuming process If Dual Scattering is checked this will slow down the calculation of a spectrum by a factor of about 200 increasing the computing time from several seconds to at least several minutes Note 1 Dual scattering should be used only if all cross sections are Rutherford For the calculation of dual scattering the cross sections for all possible scattering 15 angles between 0 and 180 must be known This is only the case for Rutherford cross sections Note 2 SIMNRA calculates dual scattering only for incident ions and not for recoils or reaction products of nuclear reactions Additional scattering in a foil in front of the detector if any is neglected Note 3 If Dual Scattering is checked then Straggling must be checked too SIMNRA will check Straggling automatically if Dual Scattering is checked As long as Dual Scattering is checked Straggling cannot be unchecked Stopping power data The selection of stopping power data has a large influence on the shape of the simul
132. mes large the distribution of particle energies becomes Gaussian 20 50 Symon s Theory 33 This theory includes non statistical broaden ing caused by the change in stopping power over the particle energy distribution If the mean energy of the beam is higher than the energy of the stopping power maximum then particles with a lower energy have a higher stopping power and particles with higher energy have a smaller stopping power This results in a nonstatistical broadening of the energy distribution The width of the particles energy distri bution in Symon s theory is significantly higher than predicted by Bohr s theory The distribution of particle energies is still Gaussian 50 90 Payne s and Tschal rs Theory 39 40 41 When the energy losses become very large and the mean energy of the beam decreases below the energy of the stopping power maximum the particle energy distribution again become skewed because now particles with lower energy have a lower stopping power than particles with higher energy The distribution is about Gaussian SIMNRA always assumes that the particles energy distribution is Gaussian This is only an approximation for thin layers In this case the energy distribution is described by the Vavilov distribution 36 34 However the straggling contribution of thin layers to the total energy broadening is much smaller than the contribution of the finite energy resolution of the detector SIMNRA calculat
133. n the number of counts must be given Double The two columns are separated by an arbitrary number of blanks or tabs Each line must end with lt CR gt lt LF gt The data file may contain up to 8192 channels An example for a valid data file is given in fig 3 1 Read Spectrum Data Canberra Allows the import of spectral data stored in Canberra s CAM file format SIMNRA uses Canberra s Genie 2000 software package for reading CAM files The Genie 2000 package is not part of SIMNRA and must be obtained separately from Canberra Industries This package must be installed correctly before you can read CAM files The dynamic link libraries sad dll etc must be in the search path and the virtual data manager VDM must be installed SIMNRA has been tested with Genie 2000 versions 1 3 and 1 4 Note SIMNRA reads only spectral data stored in CAM files Any other information which may be stored in the CAM file like energy calibration etc is ignored lt CR gt means Carriage Return 13 decimal lt LF gt means Line Feed 10 decimal Read Spectrum Data IPP Reads experimental data stored in the data file for mat used at the IPP Garching Germany This data file format will not be described here Read Spectrum Data ISI Reads experimental data stored in the data file format used at ISI J lich Germany This data file format will not be described here Read Spectrum Data User Allows to read experimental data stored in
134. nally a line containing the string Units may be present Valid values are mb for differential cross sections tot for total cross sections and rr for ratio to Rutherford Differential cross sections have to be in mbarn sr and total cross sections in mbarn If the Units line is omitted SIMNRA will assume mb i e differential cross sections The value tot indicates that the cross section is integrated over all angles Thus if tot is used the value of theta has no meaning Nevertheless a valid real number has to be given for theta A line containing either the string Nvalues or Data The value of Nvalues is ignored SIMNRA assumes that the data will start after this line The data are organised in 4 columns The first column is the energy in keV the second column is the energy error in keV ignored by SIMNRA the third column is the cross section in the laboratory frame and the fourth column is the cross section error ignored by SIMNRA The cross section units have to be mbarn sr for differential cross sections and mbarn for total cross sections SIMNRA expects the data to be arranged in order of ascending energy Scale conversion factors EnFactors and SigFactors must not be used as they are ignored by SIMNRA 45 3 15 Energy calibration issues 3 15 1 Detector nonlinearity A semiconductor detector which is used in most ion beam experiments does not measure the
135. nd saving files and data printing spectra and terminating the program are located New This menu item resets the program to its starting values All calculated spectra target foil and setup definitions are deleted Open This menu item reads a saved calculation from disk Save This menu item saves all current parameters target and foil definitions ex perimental and simulated data to disk The data are saved as an ASCII file The default file extension is NRA Depending on the settings in Options Preferences Saving see section 3 10 the old NRA file can be saved to a file named BACKUP NRA In the case of erraneous overwriting of a file you can recover the old data from this file Save as Like Save but you will be prompted for the name of the file Read Spectrum Data This menu item allows the import of experimental data The availability of menu items depends on the settings in Options Preferences Read Spectrum Data ASCII Allows the import of experimental data in ASCII format The data file format must be as follows The file may contain an arbitrary number of comment lines at the beginning of the file A comment line is a line that contains any non numeric character These lines will be ignored The first line that contains only numeric characters will be treated as the first line of data Each data line must consist of two columns In the first column the channel number must be given Integer in the second colum
136. of Inconel a stainless steel with high nickel content 94 300 250 200 150 Counts 100 50 200 400 600 Channel Figure 4 21 2 MeV He backscattered at 165 from a rough oxidised aluminum film on carbon The film was used as long term sample in the tokamak JET and was strongly eroded by plasma impact Additionally some Ni was deposited from the plasma Dots Experimental data Solid line Simulation with a mean film thickness of 1 11 x 101 atoms cm and roughness o 1 06 x 10 8 atoms cm Film composition 68 Al 30 O 2 Ni 95 l dit Ny hu SU Hh ii iW y A Q N y RY z S THLE CEES d Zz ime ST IZ V E been ee S LT IN GTR SE SEEN EE EE ELIT E SF LIED TRA ZL SEL Figure 4 22 Schematic representation of a rough surface In Direction of the incident beam Out Direction of the outgoing beam Light gray Plane spanned by the incident and outgoing beams Intersection Intersection of this plane with the rough surface 4 9 2 Smooth film on a rough substrate A film with homogeneous thickness d on a rough substrate is shown schematically in Fig 4 17b The substrate is considered to be rough if its roughness amplitude is much larger than the thickness d of the film We assume a rough substrate to consist of inclined line segments with local inclination angle y and the film thickness d is measured parallel to
137. of hours 60 rendering these codes impractical for evaluation of experimental spectra More over the Shorin Sosnin code treats only RBS with Rutherford cross sections neglecting non Rutherford scattering NRA and ERDA The theoretical approach of Metzner et al 64 65 allows to extract the thickness distribution of rough films from a measured spec trum However this approach is only valid for RBS with Rutherford cross sections a scattering angle of exactly 180 and constant stopping power thus severely limiting the practical applicability of this work The computer code RUMP 12 13 allows to fuzz the interface between two layers by roughening the top layer However this is intended only for small roughness amplitudes and the roughness distribution function is not documented Moreover all work done so far treats only the case of a rough film on a smooth sub strate But in practice also the case of a film deposited on a rough substrate Fig 4 17 b is sometimes encountered This section describes the algorithms used for the description of rough surfaces and compares results of code calculations with experimental data The limitations of the used approximations are discussed 4 9 1 Rough film on a smooth substrate A rough film on a smooth substrate is shown schematically in Fig 4 17 a The substrate can be considered to be smooth if its roughness is much smaller than the mean thickness d of the film The film thickness distribution
138. ogdanovic 1993 Ar p p Ar 159 5 1800 3600 PARBK61A RTR Barnhard 1961 Ar p p Ar 166 CM 1000 2000 PARCOG3A RTR Cohen Ganouna 1963 Ar p p PAr 166 CM 1825 1950 PARCO63B RTR Cohen Ganouna 1963 Ar p p Ar 155 1750 2750 PARFR58A RTR Frier 1958 Ca pp Ca 160 1800 3000 PCAWI74A RTR_ Wilson 1974 BT pp Ti 160 1800 2150 PTIPR72A RTR Prochnow 1972 Ti p p Ti 160 2150 2500 PTIPR72B RTR Prochnow 1972 BTi p p Ti 160 2500 2800 PTIPR72C RTR Prochnow 1972 T pp Ti 160 2900 3040 PTIPR72D RTR Prochnow 1972 Ti p p Ti 170 1000 2600 PTIRA89A RTR Rauhala 1989 TZ He He C 159 4 1800 5400 12CTTC R33 Kuan 1964 SLi a a Li 112 2500 4500 ALIBO72A RTR Bohlen 1972 Li a a Li 121 2500 4500 ALIBO72B RTR Bohlen 1972 Be a a Be 136 6000 20000 ABETAG5A RTR Taylor 1965 Be a a Be 157 5 1500 6000 ABEGO73A RTR Goss 1973 Be a a Be 170 5 575 4200 ABELE94A RTR Leavitt 1994 Bla B 170 5 975 3275 AB_MC92A RTR McIntyre 1992 TB a o B 150 8 2000 4000 AB_RA72A RTR Ramirez 1972 B a a B 160 5 4000 8000 AB_OT72A RTR Ott 1972 B a a B 170 5 980 3300 AB MC92B RTR McIntyre 1992 Cla a C 149 4000 12000 AC_MS72A RTR Marvin 1972 C a a C 165 1810 9050 AC_FE94A RTR Feng 1994 Cla a C 167 4000 7500 AC_BI54A RTR Bittner 1954 Cla a C 170 5000 9000 AC_CH94A RTR Cheng 1994 C a a C 170 5 1560 5000 AC_LE89A RTR Leavitt 1989 2C a a C 30 2000 4800 12CAA12C30 R33 Bogdanovi Radovi 2002 2C a a C 45 2000 4800 12CAA12C4
139. oil layer keV 10 atoms en EnergylossInLayer Energy loss in a target or foil layer keV StragglingInLayer FWHM of energy loss straggling in a target or foil layer keV ol Chapter 4 Physics 4 1 Overview During the last decade several programs for the simulation of backscattering spectra have been developed The most common program is Doolittle s RUMP 12 13 However RUMP uses several approximations to save computing time The increase in computer power during the last years has made it possible to drop several of the approximations used by RUMP SIMNRA offers more freedom in the use of non Rutherford cross sections and nuclear reactions treats several topics such as straggling and convolution more precise and adds new possibilities such as dual scattering This section describes the physics involved in the simulation of a backscattering spectrum as performed by SIMNRA The target is subdivided into shallow sublayers Each simulated spectrum is made up of the superimposed contributions from each isotope of each sublayer of the sample target The thickness of each sublayer is chosen in such a way that the energy loss in each sublayer is about the stepwidth of the incoming particles When the incident particles penetrate a sublayer they loose energy due to electronic and nuclear energy loss and the beam energy is spread due to straggling The calculation of the energy loss is described in detail in section 4 5 and the ca
140. olutions and the maximum possible emission angle dh of the heavy product is E 1 2 maz arcsin 4 11 SIMNRA uses eqs 4 8 and 4 10 only with the plus sign The second solution is neglected 56 4 4 Cross section data 4 4 1 Rutherford cross sections The Rutherford cross section for backscattering is given in the laboratory system by 4 12 2 E 3 Mi sin ol Mo COS d 6 Or mb sr 5 1837436 x 10 E keV 1 3 Mp sin 9 M2 M sin 6 0 is the scattering angle Z and Af are the nuclear charge and the mass of the projectile respectively and Z2 and M are the nuclear charge and the mass of the target atom respectively op is the differential cross section in the laboratory system Experimental measurements indicate that actual cross sections deviate from Rutherford at both high and low energies for all projectile target pairs The low energy departures are caused by partial screening of the nuclear charges by the electron shells surrounding both nuclei 16 17 18 5 This screening is taken into account by a correction factor F o FoR For 0 gt 90 the correction factor by L Ecuyer et al 16 is widely used 0 049 Z1 Z4 4 13 Ecm SS FL Ecuyer ie Ecm is the energy in the center of mass system in keV Tabulated values of FL Ecuyer can be found for example in 5 The correction for backscattering angles 0 gt 90 at typical energies used in ion beam analysis usuall
141. oms cm LayerThickness Thickness of a layer 10 atoms cm Number OfElements Number of different elements in a layer Number OfLayers Total number of layers in the target SubstrateRoughness FWHM of the substrate roughness deg Simnra Fit Accuracy Desired accuracy of the fit Chi2 Quadratic deviation x between the simulated and measured data points EnergyCalibration Specifies if the energy calibration is fitted LayerComposition Specifies if the composition of a layer is fitted LayerNr Specifies which layer is fitted Layer Thickness Specifies if the thickness of a layer is fitted Maxlterations Maximum number of fit iterations Number OfRegions Number of different fit regions ParticlesSr Specifies if the number of incident particles times solid angle is fitted RegionMarChannel Upper channels of fit regions RegionMinChannel Lower channels of fit regions 50 Simnra Spectrum AutoScale Specifies if the plot is scaled automatically BottomAxzisMaz Bottom axis maximum BottomAxisMin Bottom axis minimum LeftAxisMazx Left axis maximum LeftAxisMin Left axis minimum Data Data in a specific channel Integrate Integrates a spectrum Number OfChannels Number of channels in a spectrum Simnra Stopping StoppingInElement Stopping power in an element keV 10 atoms en StoppingInLayer Stopping power in a target or f
142. out 19 3 nm in good agreement with the result from He backscattering of 23 nm The energy spectrum of 2 0 MeV He backscattered from a rough oxidised aluminum film on polycrystalline carbon is shown in Fig 4 21 The carbon substrate was well polished and had a mean roughness lt 25 nm 67 The film was exposed for about 8 months as erosion monitor at the vessel wall of the nuclear fusion tokamak experiment JET 66 67 the wall temperature was about 300 C The initial Al layer thickness was 3 16 x 101 atoms cm 525 nm but decreased due to sputtering by bombardment with energetic hydrogen atoms from the nuclear fusion plasma to 7 5 x 1017 Al atoms cm At the same time the Al film was oxidised and some nickel which was initially eroded at an erosion dominated area of the JET vessel wall was redeposited on the Al film and incorporated The observed spectrum with the tails at the low energy sides of the O Al and Ni peaks cannot be reproduced by assuming a smooth layer But it is fairly well reproduced by a rough layer with a mean film thickness of 1 11 x 101 atoms cm roughness o 1 06 x 101 atoms cm and composition 68 Al 30 O 2 Ni solid line in Fig 4 21 The shape of the film thickness distribution is close to the curve with o 1 in Fig 4 18 This example shows clearly that non Gaussian distributions of layer thicknesses are observed in practice and can be described by a Gamma distribution The JET vessel walls consist
143. properties like thickness roughness etc have to be set Parameters lay Number of the layer with 1 lt lay lt NumberOfLayers Return Value Returns true if the layer was inserted successfully Related Properties and Methods 132 Target AddLayer 131 AG Simnra Fit The Simnra Fit object represents the fit parameters i e what to fit number of fit re gions maximum number of iterations etc You have to adjust the fit parameters in the Simnra Fit object first before the fit can be performed with the App FitSpectrum 115 method A 6 1 Properties Accuracy Get Set Property Accuracy Double Default Value 0 01 Description Desired accuracy of the fit see section 3 7 1 Fitting will be performed until the desired accuracy is obtained or the maximum number of iterations is reached Related Properties and Methods Fit MaxIterations 135 EnergyCalibration Get Set Property EnergyCalibration Boolean Default Value false Description Specifies if the energy calibration offset and linear term is fitted The energy calibration is fitted if EnergyCalibration is true 133 LayerComposition Get Set Property LayerComposition Boolean Default Value false Description Specifies if the composition of a target layer is fitted The number of the layer is specified by the LayerNr property The composition of layer number LayerNr is fitted if LayerComposition is true Only one layer can be fitt
144. ption File This menu item allows to store the structure of the target and the absorber foil in a sample description file in RUMP format The default file extension is LCM These files can be read by RUMP or the IBA data furnace NDF Note SIMNRA allows to define a correction factor for the stopping power of each layer for each ion species The correction factors are not stored in the sample de scription file e Print This menu item will print all parameters of the calculation and plot the experimental and simulated curves See also the print preferences on the Options Preferences tab Note 1 SIMNRA is not intended to produce high quality graphics If you want to obtain these you should use a graphics program such as Excel or Origin You can exchange data between SIMNRA and any graphics program by file with File Write Data and via the clipboard with Edit Copy Data e Exit Terminates the program 3 3 Edit menu e Copy Data Copies experimental and simulated data in ASCII format to the clip board They can be pasted into any spreadsheet program The format of the data in the clipboard is as follows The data are organised in three columns The first column contains the channel number the second column contains the experimental data and the third column contains the simulated data The columns are separated with tabs Spectra of individual elements or isotopes are not copied to the clipboard Use File Write Spectrum Data
145. r keV Related Properties and Methods TargetID 141 Stopping EnergylossInLayer 141 A 9 Error handling If SIMNRA is run as stand alone application i e not as OLE server it reports errors by showing message boxes with error messages or warnings and program execution is stopped until the OK button of the message box is pressed by the user This behaviour is reasonable for an interactive application but it is not wishful for an OLE server The server is controlled by another application or script and the display of a message box to a script is useless Therefore if SIMNRA is running as server it handles errors in a different 144 way Message boxes are suppressed and program execution continues even if an error is encountered The error is reported by an error flag as return value of the routine which produced it The text of the last error message can be retrieved with App LastMessage This behaviour can be changed by setting App ShowMessages true In this case error messages will be shown as message boxes and program execution is stopped until the OK button of the box is pressed SIMNRA is able to detect if it is running as stand alone application or as server and App ShowMessages is set to false automatically if invoked as server The following code in Visual Basic Script shows the use of the error handling routines Create the application object Set App CreateObject Simnra App Wait 1000 ms May be necessa
146. rec tory The materials and files are listed in table 3 2 These files can be imported in the Target menu with File Read layer 2Strictly speaking the Gamma distribution has only a standard deviation while the full width at half maximum FWHM is undefined However the Gamma distribution resembles a Gaussian distribution in many cases which justifies the use of the FWHM Internally SIMNRA uses only the standard deviation a which is derived from the FWHM through eq 3 3 22 3 6 Reactions menu In the Reactions menu the cross sections used for the calculation of the simulated spec trum are chosen Rutherford cross sections for backscattering of projectiles and creation of recoils are available for all ion target combinations if kinematically possible For heavy projectiles backscattered from light target nuclei two different solutions may be kinemat ically possible see eq 4 5 in section 4 3 The solution with the minus sign appears as Rutherford cross section low energy solution in the Reactions menu Additionally SIMNRA can handle non Rutherford cross sections for backscattering and recoil production and can use nuclear reactions cross sections SIMNRA is able to read three different file formats with cross section data 1 The file CRSDA DAT This file was developed in the years 1985 1995 at the IPP Garching and contains fitting coefficients to various cross section data A documen tation is not available and no guarantee i
147. ri bution of the incident beam with a full width at half maximum which can be entered in the Energy spread of incident beam field If this field is set to 0 0 SIMNRA assumes a monoenergetic incident beam The File menu allows to save experimental setups to disk and read experimental setups from disk All information contained in the Setup Experiment form the Detector 11 geometry form all energy calibrations and all detector resolutions are saved The NRA data file format is used for saving e Save as Default The current experimental setup is stored as startup default for SIMNRA in the file DEFAULTA SETUP NRA e Save Setup as Save the current experimental setup to file e Read Setup Reads an experimental setup from file Note You can read any NRA file with Read Setup Only the setup information will be read any other information such as target composition experimental spectra etc which may be present in the NRA file will be ignored 12 detector incident beam ES A gt detector aperture Figure 3 3 Detector geometry d is the diameter of the incident beam w the width of the detector aperture and Lp the distance between sample and the detector aperture Incident angle o and exit angle 6 3 4 2 Detector geometry In this menu the detailed geometry of the detector is entered This is only necessary if geometrical straggling is calculated Usually geometrical straggling is small for RBS but may be considerabl
148. ribution on the ingoing path SIMNRA uses as FWHM of the energy spread on the outgoing path A bag AE out 2 Eut Eout 4 69 with E the higher energy As in the case of the energy spread contribution on the ingoing path this describes the higher energetic part of the distribution correctly The energy spread contributions on the ingoing path AE in and on the outgoing path AF out are independent and can be added quadratically 31 If an absorber foil is used the multiple scattering induced energy spread in the foil is AF The final result for the FWHM of the total energy spread due to multiple small angle scattering A ue is therefore AEjys AEjn AE u AE Foi 4 70 out Fig 4 14 shows the contributions A Eu and A Eau for 1 MeV He in Au as a function of the residual He energy For comparison the results calculated by the DEPTH code 31 are included The agreement between the result of the two programs is good 4 8 3 Plural large angle scattering Plural large angle scattering cannot be treated analytically SIMNRA approximates plural scattering effects by calculating all particle trajectories with two scattering events dual 85 Path in Figure 4 13 Contributions of multiple scattering on the ingoing and outgoing paths 86 1000 keV He in Au a 60 0 60 B 60 20 r T T T E SIMNRA gt i Depth Es bs backscattered ions 4 z 15 at surface Ka T f D SL y 4 Yo 2S
149. rosoft Windows program for the simulation of back or forward scattering spectra for ion beam analysis with MeV ions SIMNRA is mainly intended for the simulation of spectra with non Rutherford backscattering cross sections nuclear reactions and elastic recoil detection analysis ERDA About 300 different non Rutherford and nuclear reaction cross sections for incident protons deuterons He and 4He ions are included SIMNRA can calculate spectra for any ion target combination in cluding incident heavy ions and any geometry including transmission geometry Arbitrary multi layered foils in front of the detector can be used SIMNRA uses the Ziegler Biersack values for the electronic stopping powers of swift and heavy ions and the universal ZBL potential for the calculation of nuclear stopping Alternatively the Andersen Ziegler values for electronic stopping powers may be used Energy loss straggling is calculated including the corrections by Chu to Bohr s theory Energy loss straggling propagation in thick layers is considered correctly Additionally the effects of plural large angle scattering and surface roughness can be calculated approximately Data fitting layer thicknesses compositions etc is possible by means of the Simplex algorithm OLE automation allows automated analysis of large numbers of spectra In contrast to other programs for the simulation of backscattering spectra SIMNRA is easy to use due to the Microsoft Windows user interfa
150. rties and Methods 117 App WriteSpectrumData 119 Restore Procedure Restore Description Restores the minimized application to its normal size Parameters None Return Value None Related Properties and Methods App Active 111 App BringToFront 113 App Minimize 116 SaveAs Function SaveAs FileName WideString Boolean Description Save a NRA file Parameters FileName The name of the NRA file including path If the file already exists it will be overwritten Return Value Returns true if the file was saved successfully Related Properties and Methods App Open 117 118 Show Procedure Show Description Shows SIMNRA if it was hidden Parameters None Return Value None Related Properties and Methods App Hide 115 WriteSpectrumData Function WriteSpectrumData FileName WideString Boolean Description Writes all spectra experimental simulated in ASCII format to a file See File Write Spectrum Data in section 3 2 for a description of the file format Parameters FileName The name of the data file including path If the file already exists it will be overwritten Return Value Returns true if the file was written successfully Related Properties and Methods App ReadSpectrumData 117 App CopySpectrumData 114 119 A 3 Simnra Setup The Simnra Setup object represents the experimental setup A 3 1 Properties Alpha Get Set Property Alpha Double D
151. ry for the server to start WScript Sleep 1000 Open a NRA file Success App Open c temp test nra Some error reported by App Open Display last error message and exit If Not Success Then WScript Echo App LastMessage Exit End If Calculate a spectrum Success App CalculateSpectrum A 10 Programming examples Sample program in Borland Delphi showing the use of the OLE automation objects Var App Variant Result Boolean Begin Create the application object App Create OLEObject Simnra App Wait 1000 ms May be necessary for the server to start Sleep 1000 Open a NRA file Result App Open c temp test nra Calculate a spectrum Result App CalculateSpectrum 145 Save the NRA file Result App SaveAs c temp test nra End Sample program in Visual Basic Script showing the use of the OLE automation objects Create the application object Set App CreateObject Simnra App Wait 1000 ms May be necessary for the server to start WScript Sleep 1000 Open a NRA file Result App Open c temp test nra Calculate a spectrum Result App CalculateSpectrum Save the NRA file Result App SaveAs c temp test nra Sample program in Visual Basic Script showing the use of the Fit object Create the application object Set App CreateObject Simnra App Create the fit object Set Fit Create
152. s a as aaae eg ba ee ee a aY Agd ESE BORIS lt a EAS A a 4 3 2 Wuclest reactions e o c s wr wen Ge ew de A a AA CUOBSEECUION dala s s e o soros a bee Re Re OR a Re eR EE 4 4 1 Rutherford cross sections e 4 4 2 Non Rutherford cross sections e 4 5 Evaluation of energy Joss 4 6 Stopping power data s oa s sas es c da nas s bo Padu kesa 4 6 1 Andersen Ziegler stopping o e e 4 6 2 Ziegler Biersack stopping e 40 3 SOpping n COMPOUNGS e mos pp E DA e be ae A Ee RE e A ONARE ENEE LGL SOVERVIBW sais a Se ee EN e a e ieren ee ke 4 7 2 Electronic energy loss straggling e 4 7 3 Nuclear energy loss straggling 4 7 4 Energy loss straggling in compounds 4 7 5 Geometrical straggling e 4 8 Multiple and plural scattering e o AST CBE cs a A A A a a 4 8 2 Multiple small angle scattering 4 8 3 Plural large angle scattering 4 9 Burlace roughness a s cesi so one ee sare aee kae a a 4 9 1 Rough film on a smooth substrate aa 4 9 2 Smooth film on a rough substrate s sc ss s eaae aos anata 5 Examples 5 1 RBS Rutherford cross sections gt o ss sa o e e e phs 5 2 RBS Non Rutherford cross sections 5 3 ERDA Non Rutherford cross sections 6 Acknowledgements 52 52 54 55 55 Di 57 57 58 60 61 61 63 65 67 67 68 73 73 75 78 78 78 85 90 90 96 104 104 107 109 110 A O
153. s line All masses in amu The first mass is the mass of the incident particle the second mass is the mass of the target particle the third mass is the mass of the outgoing particle for which the cross section is valid and the fourth mass is the mass of the other reaction product The masses may be rounded to the nearest integer value SIMNRA will replace the given masses by the exact values The original specification can be found in DSIR Physical Sciences Report 33 by I C Vickridge 43 COMMENT These cross sections have been digitised from the publication cited below No error of either the energy and or the sigma is given Some errors may be among the data we are recently checking then The Los Alamos Ion Beam Handbook also will contain these data as soon as it is ready If you use this data please refer to the paper below Source A Turos L Wielunski and a Batcz NIM 111 1973 605 Special comment WARNING THIS IS MAINLY FOR TEST NO GUARANTY IS PROVIDED FOR EVEN AGREEMENT WITH THE ORIGINAL PUBLICATION File created by R33 Manager version 0 1 Version R33 Source A Turos L Wielunski and a Batcz NIM 111 1973 605 Name Gyorgy Vizkelethy Addressi Department of Physics Address2 Idaho State University Address3 Campus Box 8106 Address4 Pocatello ID 83209 8106 Address5 208 236 2626 Address6 vizkel physics isu edu Serial Number 0 Reaction 160 d a0 14N Distribution Energy Composition Masses 2 000 1
154. s plotted at the top of the plot is obtained with the major energy calibration from the Calibration fields of the Setup Experiment form The energy scale is not valid for particles with individual energy calibrations e Particles sr Number of incident particles times the solid angle of the detector Solid angle in steradians The number of incident particles is obtained from the collected charge and the charge state Calculate Particles sr can be used for the calculation e Detector Resolution Energy resolution of the detector in keV The energy res olution is measured as full width at half maximum FWHM This energy resolution is used for all ion species if no specific resolution for that ion is supplied see below SIMNRA can use different detector energy resolutions for different ion species By pressing the button detector energy resolutions for each ion species may be entered If no energy resolution for an ion species is supplied the default resolution see above is used Note SIMNRA uses a constant energy independent detector resolution for each ion species This is more or less true for swift ions protons and He but for heavy ions the detector resolution depends on the particle energy Currently energy dependent detector resolutions are not implemented in SIMNRA e Energy spread of incident beam Usually the incident ion beam is not monoen ergetic but has an energy distribution SIMNRA assumes a gaussian energy dist
155. s provided that the fits agree with the original data The use of these data is highly discouraged and they should be used only if no other data are available 2 The R33 file format Cross sections for nuclear reaction are stored in the R33 file format in the SigmaBase data repository for ion beam analysis Most files with this extension have been taken from SigmaBase a few ones were added by the au thor The majority of these files has been digitised from the original publications by G Vizkelethy from Idaho State University No guarantee is provided for agreement with the original publication The references of the original publications are found in the file headers 3 The RTR Ratio To Rutherford file format These files contain non Rutherford cross sections for backscattering of protons and a particles The files contain the ratio of measured to Rutherford cross sections The majority of the data has been digitised from the original publications by R P Cox J A Leavitt and L C McIn tyre Jr from Arizona University These cross section data have been published in 5 All files with this extension have been taken from SigmaBase The references of the original publications are found in 5 SIMNRA distinguishes between three different types of scattering events for each iso tope 1 Backscattering of projectiles 2 Creation of recoils 3 Nuclear reactions 3http ibaserver physics isu edu sigmabase This server is mirrored
156. sections Parameters lay Number of the layer with 1 lt lay lt NumberOfLayers 127 el Number of the element with 1 lt el lt NumberOfElements lay HasLayerRoughness Get Set Property HasLayerRoughness lay Integer Boolean Description Specifies if the layer number lay is rough or not The FWHM of the roughness is specified by Target LayerRoughness If HasLayerRoughness is false the layer is treated as smooth and Target LayerRoughness is ignored Parameters lay Number of the layer with 1 lt lay lt NumberOfLayers Related Properties and Methods Target LayerRougness 128 HasSubstrateRoughness Get Set Property HasSubstrateRoughness Boolean Description Specifies if the substrate is rough or not The FWHM of the roughness is spec ified by Target SubstrateRoughness If HasSubstrateRoughness is false the substrate is treated as smooth and Target SubstrateRoughness is ig nored Related Properties and Methods Target SubstrateRougness 130 LayerRoughness Get Set Property LayerRoughness lay Integer Double Description 128 FWHM of the roughness of layer number lay 101 atoms cm Target HasLayerRoughness lay must be true otherwise LayerRoughness has no effect Parameters lay Number of the layer with 1 lt lay lt NumberOfLayers Related Properties and Methods Target HasLayerRougness 128 LayerThickness Get Set Property LayerThickness lay Integer Double
157. see fig 3 3 g and gq take into account the shapes of the beam and the detector aperture For circular detectors or circular beams with uniform current density g 0 59 g 0 68 for rectangular shapes as in the case of narrow slits 44 SIMNRA calculates geometrical straggling by calculating the energy at the surface of particles with exit angles AG 2 and G AG 2 and corresponding scattering angles 0 A0 2 and 6 A0 2 We therefore need the relation between AG and Ad In Cornell geometry the relation between the angles a 4 and 0 is given by cos sina sin D sin ch cosa cos 3 4 58 where is the azimuth angle defined in fig 4 15 Because a 3 and 0 are known eq 4 58 gives the azimuth angle The spread of 0 is given by 00 OB which yields from eq 4 58 z e in b singo in 3 4 60 Gi s n Q cos p s cosa S a In IBM geometry the incident and outgoing trajectories are in the same plane with 90 Equation 4 58 simply reduces to 180 a 8 0 4 61 Note that the beam spot size on the sample surface is d cosa Note that the incident particles have 90 79 and for the spread in 0 we get from eqs 4 59 and 4 60 A0 AB 4 62 Note the minus sign If 8 increases then 0 decreases and vice versa Energy loss straggling geometrical straggling and the detector resolution are indepen dent and are added quadratically Fig 4 7 gives as examples the different stragglin
158. t RegionMaxChannel 136 Fit RegionMinChannel 136 A T Simnra Spectrum The Simnra Spectrum object represents experimental and simulated spectra and allows to change plot parameters A 7 1 Input parameter The properties and methods of Simnra Spectrum require the input parameter spID which specifies if the experimental or simulated spectrum is accessed The possible values for spID are 137 spID Selected spectrum 1 Experimental data 2 Simulated data Other values are not allowed A 7 2 Properties AutoScale Get Set Property AutoScale Boolean Default Value true Description If AutoScale is true the plot is scaled automatically if experimental data are imported or a new calculation is performed If false the axis scales remain fixed BottomAxisMax Get Set Property BottomAxisMax Double Description Bottom axis maximum Related Properties and Methods BottomAxisMin 138 BottomAxisMin Get Set Property BottomAxisMin Double Description Bottom axis minimum Related Properties and Methods BottomAxisMax 138 138 Left AxisMax Get Set Property LeftAxisMax Double Description Left axis maximum Related Properties and Methods LeftAxisMin 139 Left AxisMin Get Set Property LeftAxisMin Double Description Left axis minimum Related Properties and Methods LeftAxisMax 139 NumberOfChannels Get Property NumberOfChannels spID Integer Integer D
159. teger differential integer are fully implemented 2 Each RBS file may contain only one spectrum Record type 20h is allowed but may contain only one row 3 Only one record 120h RBS spectrum type or 121h FRES spectrum type may be present i e simultaneous RBS and FRES ERD are not allowed 4 Record types 01h printed comments 02h unprinted comments 101h identifier for the data set 102h MCA information and 103h collection date time are recognized but ignored 40 RESET LAYER OPEN NEXT COMPOSITION THICKNESS ABSORBER Partly implemented Only elements are recognised but no isotopes The command Composition Si 1 0 2 will be recognised and the natural isotopic ratios for Si and O will be used The command Composition 28Si 1 160 2 will not be recognised properly RUMP allows to enter SiOz as Si 1 O 2 SIMNRA will convert this to Si 0 33333 O 0 66666 As units for thickness are possible CM2 M CM2 A NM If A for or NM for nm are used SIMNRA will use the weighted atomic densities of all elements in the layer to convert or nm to 10 atoms cm It is highly recommended to use the units CM2 or M CM2 instead Table 3 6 RUMP sample description commands which are supported by SIMNRA 5 Record type 111h accelerator parameters Beam current is ignored by SIMNRA and pile up is not calculated 6 Record type 112h data collection parameters Starting c
160. tep width of the incoming ions should be lower than the width of the resonance Automatic stepwidth control should not be used with narrow resonances Stepwidth outgoing ions Stepwidth of outgoing particles used in the calculation See chapter 4 for details Automatic or Fixed can be selected If automatic is selected the program will choose the stepwidth automatically This is usually the best choice for obtaining high accuracy and small computing times Automatic is the program default The automatically determined stepwidth is large at high energies where the stopping power shows only small variations to decrease computing time The step width is decreased near the stopping power maximum and at low energies where the stopping power varies strongly to increase accuracy Fixed stepwidth The program uses a fixed stepwidth for the calculation of outgoing particles The stepwidth will remain constant at all energies and for all outgoing 14 particles If Fixed is selected the default for the stepwidth is 200 keV For incident heavy ions with energies in the range of several ten MeV this stepwidth can be increased If a small fixed stepwidth is used this may increase the accuracy of the calculation but will slow down the calculation A very small fixed stepwidth may be even more accurate than automatic stepwidth control In contrast a large fixed stepwidth decreases the accuracy of the calculation but will speed up the calculation There is
161. th 168 1980 163 90 J R Bird P Duerden D D Cohen G B Smith and P Hillery Nucl Instr Meth 218 1983 53 90 C P Hobbs J W McMillan and D W Palmer Nucl Instr Meth B30 1988 342 90 M Wiiest and P Bochsler Nucl Instr Meth B71 1992 314 90 I M Yesil Einflu der Oberfl chenrauhigkeit auf ERDA Tiefen Profile Master s thesis Lud wig Maximilian Universitat Miinchen 1995 In german 90 90 I M Yesil W Assmann H Huber and K E G L bner Nucl Instr Meth B136 138 1998 623 90 90 90 A Kitamura T Tamai A Taniike Y Furuyama T Maeda N Ogiwara and M Saidoh Nucl Instr Meth B134 1998 98 90 R Behrisch S Grigull U Kreissig and R Gr tschel Nucl Instr Meth B136 138 1998 628 90 V S Shorin and A N Sosnin Nucl Instr Meth B72 1992 452 90 90 H Metzner M Gossla and Th Hahn Nucl Instr Meth B124 1997 567 90 90 90 H Metzner Th Hahn M Gossla J Conrad and J H Bremer Nucl Instr Meth B134 1998 249 90 90 90 M Mayer R Behrisch P Andrew and A T Peacock J Nucl Mater 241 243 1997 469 94 M Mayer R Behrisch C Gowers P Andrew and A T Peacock Change of the optical reflectivity of mirror surfaces exposed to JET plasmas In Diagnostics for Experimental Ther monuclear Fusion Reactors 2 P Stott G Gorini P Prandoni and E Sindoni Eds Plenum Press New York London 1998 p 279 94 94 M Kistner W Eckstein E
162. ths of the incident beam and detector diaphragm shall be calculated For RBS geometrical straggling usually is negligeable See section 3 4 2 for details Calibration Conversion from channels to energy To account for detector nonlin earities SIMNRA can use a non linear energy calibration with a quadratic term of the form E keV A B x channel C x channel 3 1 F is the particle energy in keV The calibration offset A must be entered in the Calibration Offset field A in keV The energy per channel B must be entered in the Energy per Channel field B in keV channel C is the quadratic correction term C in keV channel For a linear energy calibration C 0 0 A linear calibra tion is appropriate in most cases and only if a high accuracy is intended a non linear calibration should be used More energy calibration options An individual energy calibration may be used for each ion species This is mainly useful for ERDA measurements with incident heavy ions where each recoil species may require an individual calibration By clicking the button an individual nonlinear energy calibration for each ion species 10 Figure 3 2 Geometry of a scattering experiment Incident angle a exit angle and scattering angle 6 may be supplied If no individual energy calibration is defined the major energy calibration entered in the Calibration fields of the Setup Experiment form see above is used Attention The energy scale which i
163. tion have to be chosen 1 Click Setup Experiment Here you choose the incident ions the ions energy define the scattering geometry see fig 3 2 and you enter the energy calibration of the experiment Click Target Target Here you create the target Each target consists of layers Each layer consists of different elements with some atomic concentration which does not change throughout the layer and each layer has a thickness If there is a foil in front of the detector then click Target Foil for the definition of a foil The default is no foil in front of the detector Like the target the foil can consist of different layers and the layers can have different compositions Click Reactions Here you have to choose which cross section data should be used for the simulation The default are Rutherford cross sections for all elements You can select non Rutherford cross sections instead and you can add nuclear reactions Now the spectrum can be calculated Click Calculate Calculate Spectrum for a simulation of the spectrum With Setup Calculation the parameters for the calculation can be altered The default values are normally sufficient and you should change these values only if you know what you are doing With File Read Spectrum Data a measured spectrum can be imported for com parison with the simulated one and for data fitting 3 2 File menu In the File menu all necessary commands for reading a
164. to the experimentally determined cross section data which contain these structures 107 Energy keV 400 600 800 1000 1200 1400 1600 1800 e experimental simulated 2000 Counts 100 200 300 400 500 600 700 800 Channel Figure 5 4 2000 keV protons backscattered from silicon a 5 0 165 108 Energy keV 600 800 1000 1200 1400 1600 1800 Exp SIMNRA 200 Re 150 100 Counts 50 100 200 300 Channel Figure 5 5 ERDA with 2 6 MeV He ions incident on a soft amorphous hydrocarbon layer a C H layer containing both H and D The recoiling H and D atoms were separated with a AE E telescope detector the backscattered He ions are not shown a 8 75 6 30 5 3 ERDA Non Rutherford cross sections Fig 5 5 shows the measured and simulated spectra for ERDA with 2 6 MeV incident He ions on a soft amorphous hydrocarbon layer a C H layer containing both H and D The recoiling H and D atoms were separated with a AE E telescope detector 71 Both recoil cross sections are non Rutherford The cross section data of Baglin et al 72 for H He H He and of Besenbacher et al 73 for D He D He were used for the simulation The peak in the deuterium spectrum is due to a resonance at a He energy of 2130 keV The measured and simulated data agree very well 109 Chapter 6 Acknowledgements Many cross section data files included with SIMNRA have been taken from SigmaBase http ibaserver physi
165. uch as protons or helium ions nuclear energy loss straggling is small compared to electronic energy loss straggling and can be neglected For heavy ions nuclear straggling becomes more important and may exceed electronic straggling see eqs 4 53 and 4 55 However it has been shown experimentally for 60 MeV Ni ions in different target materials that the width of the straggling distribution is only somewhat larger than electronic energy loss straggling alone 43 The nuclear straggling energy distribution is broad with a long tail towards low energies which cannot be described by a Gaussian distribution However the tail contains only a small fraction of all particles and the width of the total energy distribution electronic plus nuclear straggling is still dominated by electronic energy loss straggling 43 This justifies to neglect nuclear straggling for all ion species 4 7 4 Energy loss straggling in compounds For compounds a simple additivity rule for energy loss straggling is used 38 The strag gling in a compound consisting of elements i with atomic concentration c is calculated with c 5 Go 4 56 i with 0 being the straggling in each element SSIMNRA versions before 4 70 used a quadratic addition of the nuclear and electronic energy loss straggling contributions i e 0 0 02 with 0 the variance of the nuclear straggling and o the variance of the electronic straggling Due to the different shape of the two
166. ve and requires a slightly thicker W layer 3 6 um for best fit The dashed line is calculated for a rough W layer characterized by a Gamma distribution of layer thicknesses with a mean thickness of 3 5 ym and standard deviation o 0 3 um on a rough carbon substrate characterized by a Lorentz distribution of tilt angles with FWHM 20 The roughnesses of the layer and the substrate are assumed to be independent and plural scattering is not taken into account The W peak channels gt 650 is already well described but the low energy tail below the peak is underestimated The solid line uses the same roughness parameters but takes additionally plural scattering into account Now the whole experimental spectrum is reproduced well Compared to the smooth layer the contribution of plural scattering has increased strongly which is due to an enhancement of plural scattering at inclined incidence The height and shape of the low energy tail below the W peak in channels lt 650 are determined by the wings of the tilt angle distribution with inclination angles gt 45 The observed tilt angle distribution see Fig 4 24 is best described by a FWHM of 26 6 while the best fit to the measured spectrum yields a FWHM of about 20 It is assumed that inaccuracies in the measurement of the tilt angle distribution at high inclinations due to the apex angle of the profiler tip and the constant step width together with uncertainties in the calculation of t
167. weighting factor due to the projection of the surface element onto the incident beam with w w 7i w a This is a 2 5 dimensional model We use the fully 97 Xx Figure 4 23 Rotation of the xy plane around d by Y 3 dimensional surface for the calculation of lt 3 gt but we use only one local exit angle lt 6 gt for each local incident angle as in the 2 dimensional model If we have a local tilt angle y then the local incident and exit angles and lt B gt are calculated according to Eqs 4 74 and 4 76 Which distribution has to be used as tilt angle distribution A line profile of the surface of a carbon fibre composite CFC material manufactured by Dunlop is shown in Fig 4 24 top Due to its high thermal conductivity this material is used for high heat flux components in the tokamak experiment JET The standard deviation of the surface roughness is about o 8 2 ym A histogram of the tilt angle distribution p y obtained with a profiler from several line scans in different sample directions is shown in Fig 4 24 bottom Tilt angles larger than about 60 are not observed due to the apex angle of the profiler tip The tilt angle distribution is fairly well described by a Lorentz distribution for the tilt angles p p dashed line while a Gaussian distribution underestimates strongly the wings of the distribution dotted line The full width at half maximum FWHM of the Lorentz distribution is 26 6 Having the inci
168. wer and upper channels of the regions are specified by the Fit RegionMinChannel and Fit RegionMaxChannel properties Related Properties and Methods 135 Fit RegionMaxChannel 136 Fit RegionMinChannel 136 ParticlesSr Get Set Property ParticlesSr Boolean Default Value false Description Specifies if the number of incident particles times solid angle is fitted The number of incident particles times solid angle is fitted if ParticlesSr is true RegionMaxChannel Get Set Property RegionMaxChannel reg Default Value 8192 Description Upper channel of fit region number reg Related Properties and Methods Fit NumberOfRegions 135 Fit RegionMinChannel 136 RegionMinChannel Get Set Property RegionMinChannel reg Default Value 1 Description Lower channel of fit region number reg 136 Integer Integer Integer Integer Related Properties and Methods Fit NumberOfRegions 135 Fit RegionMaxChannel 136 A 6 2 Methods Chi2 Function Chi2 Double Description Quadratic deviation x between the simulated and measured data points see Section 3 7 1 x is weighted with the statistical error of the experimental data x is calculated only in the fit regions defined by NumberOfRegions RegionMaxChannel and RegionMinChannel Chi2 can be used to develop your own fit algorithms Parameters None Return Value Returns x Related Properties and Methods Fit NumberOfRegion 135 Fi
169. y In this case a Q value is required for each particle contributing to the cross section R CEnergy lt String gt Note Allowed values are Energy and Angle This entry says whether the data contained in this file are for a cross section as a function of laboratory energy Energy or laboratory angle Angle M1 R 0 0 lt r gt M1 R 1 0 lt r gt Note Theta gives the laboratory angle with respect to the incident beam so that backscattering would be 180 Energy gives the laboratory energy of the incident beam If both entries are present an illegal condition then only the entry corresponding to the keyword in the Distribution entry will be used 152 Sigfactors Units Enfactors Nvalues Data Enddata O 1 0 0 0 lt r r gt Note Scale conversion factor and its associated error common to all the cross section data See original R33 publication in Appendix 1 for discussion O Cmb lt String gt Note Valid values are mb rr and jot R33 files are always in mb sr or units proportional to mb sr for differential cross sections and mb for total cross sections The constant of proportionality given in the enfactors entry is inde pendent of energy Some users find it preferable to have elastic scattering cross sections relative to the Rutherford cross section Since the conversion factor is no longer energy independent the enfactors entry can no longer cater for th
170. y is small For 1 MeV He ions on gold the correction is only about 3 5 The correction factor by L Ecuyer eq 4 13 is a first order correction and does not take into account the influence of the scattering angle 6 For 0 lt 90 eq 4 13 will underestimate the necessary correction to the Rutherford cross section SIMNRA uses the angular and energy dependent correction factor by Andersen et al 18 A 2 Eom 4 14 FAndersen e 5 91 2 f T Eom sow Sys four is the scattering angle in the center of mass system The increase in the kinetic energy Vi is given by 1 2 Vj keV 0 04873 Z1 Z2 LST 231 For M gt M there may exist two different solutions of the kinematic equation 4 5 The cross section given by eq 4 12 applies for the solution with the plus sign The cross section for the second solution of eq 4 5 is obtained by calculating the scattering angle in the centre of mass system 0cm from bcm 0 arcsin M Ma sin 9 rr calculating the Rutherford backscattering cross section in the centre of mass system and transforming into the laboratory system 57 1 00 2000 keV aa 1000 keV 500 keV 0 90 250 keV 0 85 0 80 ul H 075 0 70 0 65 0 60 L A i 0 30 60 90 120 150 180 9 degree Figure 4 2 Angular dependence of the correction factors for the Rutherford cross section by L Ecuyer eq 4 13 dashed lines and Andersen eq 4 14 solid lines for He backscatt

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