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SIMNRA User's Guide - Max-Planck

1. e E 4 10 i HE 4 10 where this is the defining equation for e E the energy dependent stopping cross section x is the pathlength into the material measured in areal density 10 atoms cm SIMNRA uses the Ziegler stopping power data see section 4 4 de dE is the first and e d e dE the second derivative of e If incoming or outgoing particles with incident energy Ey traverse a layer of material with thickness Az then the particles energy Ej after the layer can be expanded into a Taylor series oe Ar Eo LAS y m LAS DIE 4 11 The terms in eq 4 11 look as follows G 4 12 cs Leg Cos 2 a eget ee 4 14 With e and e evaluated at Ep Ey Ey Ave waned Ar e e e 4 15 See ref 5 for a discussion of the accuracy of the above equations el and e are calculated by SIMNRA by numerical differentiation of the Ziegler stopping power data The stepwidth Az 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 15 Typical values for the stepwidth of outgoing particles are around 200 keV 39 4 4 Stopping power data 4 4 1 Hydrogen SIMNRA uses the electronic stopping power data by Andersen and Ziegler 13
2. The variance of the energy loss straggling o in eq 4 30 has two contributions nuclear 2 energy loss straggling 0 and electronic energy loss straggling o2 The total straggling c is given by quadratically adding the two independent contributions of electronic and nuclear straggling 9 cgi dg 4 31 The electronic energy loss straggling is calculated by applying Chu s theory 30 26 o H E Mi Ze Bohr 4 32 oi 1 the electronic energy loss straggling in Bohr approximation and is given by 25 26 oi keV 0 26 Z Za Ax 10 atoms cm 4 33 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 Mi Z3 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 30 26 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 Zo oscillations are clearly visible The Chu correction is mainly necessary for high Zs and low energies For high energies H approaches 1 and becomes independent of
3. 60 Bibliography 10 11 12 13 14 15 16 J R Tesmer and M Nastasi Eds Handbook of Modern Ion Beam Materials Analysis Materials Research Society Pittsburgh Pennsylvania 1995 M S Caceci and W P Cacheris Byte 5 1984 340 W Hosler and R Darji Nucl Instr Meth B85 1994 602 E Steinbauer P Bauer M Geretschl ger G Bortels J P Biersack and P Burger Nucl Instr Meth B 85 1994 642 R Doolittle Nucl Instr Meth B9 1985 344 R Doolittle Nucl Instr Meth B15 1986 227 J L Ecuyer J A Davies and N Matsunami Nucl Instr Meth 160 1979 337 M Hautala and M Luomajarvi Rad Effects 45 1980 159 H H Andersen F Besenbacher P Loftager and W Moller Phys Rev A21 6 1980 1891 M Bozoian K M Hubbard and M Nastasi Nucl Instr Meth B51 1990 311 M Bozoian Nucl Instr Meth B58 1991 127 M Bozoian Nucl Instr Meth B82 1993 602 H H Anderson 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 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 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 J F Ziegler J P Biersack
4. This affects the accuracy of the calculation but also the time necessary for the calculation of a simulated spectrum e Stepwidth incoming ion Stepwidth of the incoming ion in keV See chapter 4 for details The default is 10 keV The stepwidth of the incoming ion affects the time T necessary to perform a calculation heavily 7 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 For incident heavy ions with energies in the range of several ten MeV you can increase this stepwidth to several 100 keV Note 1 The stepwidth of the incident ions is an important parameter for the ac curacy 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 oscillations or steps in the simulated spectra may occur This is due to rounding er rors in the routine which calculates the contents of each channel If these oscillations occur you have to decrease the stepwidth of the incident ion Note 2 If the backscattering cross section contains narrow resonances the step width of the incoming ions should be lower than the width of the resonance e Stepwidth Outgoing Particle Stepwidth of outgoing particles in keV See chap ter 4 for details The default is 200 keV e Cutoff Energy All particles are calculated until their energy has
5. Be 158 7 200 1700 PBEMO56B RTR Mozer 1956 Be p p Be 170 5 2400 2700 PBELE94A RTR Leavitt 1994 TB pp UB 154 1000 3000 PB_OV62A RTR Overley 1962 TB p p B 150 500 2000 PB TA56A RTR Trautfest 1956 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 2C pp C 168 2 400 4500 PC_JA53A RTR Jackson 1953 TAN pp AN 150 800 1900 PN_TA56A RTR Tautfest 1956 BN pp AN 152 1035 1075 PN_HA57A RTR Hagedorn 1957 TN p p N 152 1450 1625 PN_HA57B RTR Hagedorn 1957 TAN pp AN 152 650 1800 PN_HA57E RTR Hagedorn 1957 TN p p N 155 2 1850 3000 PN_LA67A RTR Lambert 1967 TN p p N 158 7 1735 1760 PN_HA57C RTR Hagedorn 1957 HN p p 7N 158 7 1785 1815 PN_HA57D RTR Hagedorn 1957 TN p p N 159 5 600 4000 PN BAS59A RTR Bashkin 1959 TN p p N 165 1850 3000 PN LA67B RTR Lambert 1967 UN p p 7N 167 2 3600 4100 PN_OL58A RTR Olness 1958 TN p p N 170 1450 2300 PN_RAS5A RTR Rauhala 1985 159 p p O 149 5 2450 2850 PO_GO65A RTR Gomes 1965 O p p O 170 1000 3580 PO AM93A RTR Amirikas 1993 TF p p PF 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 TE p p F 160 500 1300 PF_DE56C RTR Dearnaly 1956 TF p p PF 160 1300
6. 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 17 W H Bragg and R Kleeman Philos Mag 10 1905 318 18 D Boutard W Moller and B M U Scherzer Phys Rev B38 5 1988 2988 19 J F Ziegler and J M Manoyan Nucl Instr Meth B35 1988 215 61 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 E Szil gy F P szti and G Amsel Nucl Instr Meth A4 B100 1995 103 M A Kumakhov and F F Komarov Energy Loss and Ion Ranges in Solids Gordon and Breach Science Publishers New York London Paris 1981 J R Bird and J S Williams Eds Jon Beams for Materials Analysis Academic Press Sydney New York Tokyo 1989 J Tirira Y Serruys and P Trocellier Forward Recoil Spectrometry Plenum Press New York London 1996 P V Vavilov Soviet Physics J E T P 5 1957 749 N Bohr Mat Fys Medd Dan Vid Selsk 18 8 1948 J W Mayer and E Rimini on Handbook for Material Analysis Academic Press New York San Francisco London 1977 M G Payne Phys Rev 185 2 1969 611 C Tschal r Nucl Instr Meth 61 1968 141 C Tschal r Nucl Instr Meth 64 1968 237 W K Chu Phys Rev 13 1976 2057 E Steinbauer P Bauer and J P Biersack Nucl Instr Meth B 45 1990 171 P Bauer E Steinbauer and J P Biersack Nucl Instr Meth B79 1993
7. 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 1 All files with this extension have been taken from SigmaBase The references of the original publications are found in 1 SIMNRA distinguishes between three different types of scattering events for each iso tope http ibaserver physics isu edu sigmabase This server is mirrored in New Zealand at http pixe gns cri nz 18 1 Backscattering of projectiles 2 Creation of recoils 3 Nuclear reactions 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
8. energy loss straggling Bohr s theory of nuclear straggling can be used without loss in precision Fig 4 4 compares the beam width FWHM of 2 5 MeV He ions in silicon calculated by SIMNRA using eq 4 30 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 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 Z2 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 49 1 0 MeV He in Au Straggling keV FWHM 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 30 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 m
9. for the stopping of incident protons deuterons and tritons in all elements The electronic stopping power S in eV 10 atoms cm for an incident hydrogen ion with energy mass E in keV amu is given by 1 1 1 4 16 Se Stow SHigh with S Low A Eo 4 17 and A3 A4 A2 As are fitting coefficients and tabulated in 13 They are stored in the file STOPH DAT Equations 4 16 4 18 are valid for 10 keV lt E 1 MeV For energies in the range 1 MeV 100 MeV the electronic stopping power Se is given by Se Ag A 4 gt 8 V Ais In Ey 4 19 E p i 0 Ag A1 are tabulated in 13 8 v c with v the ion velocity and c the speed of light Equation 4 19 is used only if the switch High energy stopping in the Setup Calculation menu is checked If unchecked the program will use Equations 4 16 4 18 at all energies The program default is checked The difference between eq 4 16 and eq 4 19 is small in most cases T he main problem using eq 4 19 is that the first and second derivatives of eq 4 16 and eq 4 19 do not fit smoothly together at 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 13 and is neglected by SIMNRA 4 4 2 Helium For incident He and He ions the electronic stopping power data by Ziegler 14 are used for all elements The electroni
10. 100 nm Au on Si scattering angle 165 Bottom Magnification of the low energy gold edge 51 Figure 4 7 Examples of ion trajectories with one two and three scattering events 4 5 2 Energy loss straggling in compounds For compounds a simple additivity rule for energy loss straggling is used 26 The strag gling in a compound consisting of elements with atomic concentration c is calculated with o y Go 4 36 i with 0 being the straggling in each element 4 6 Multiple and plural scattering 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 7 left This is only an approximation to physical reality because the particles on the ingoing and outgoing path suffer many small angle scatterings 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 7 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 20 Multiple scatter ing results in an angular spread of the particles and therefore in a spread of path lengths Due to the path length differences we get an energy spread of the particles in a given depth Multiple scattering is not treated by SIMNRA Plural scattering with
11. 1000 keV He incident on Au on top of silicon 0 165 56 Energy keV 100 200 300 400 rs 14000 Experimental Dual scattering 12000 Single scattering 10000 2 8000 c e le ZG 6000 4000 2000 100 200 ony 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 57 Energy keV 400 600 800 1000 1200 1400 14000 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 0 165 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 33 were used for the simulation The pronounced peak in the spectrum is due to the resonance in the C 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 34 were used for the simu
12. 1800 3600 PARBK61A RTR Barnhard 1961 T Ar p p Ar 166 CM 1000 2000 PARCO63A RTR Cohen Ganouna 1963 WAr p p Ar 166 CM 1825 1950 PARCO63B RTR Cohen Ganouna 1963 79 Ar p p Ar 155 1750 2750 PARFR58A RTR Frier 1958 Ca p p Ca 160 1800 3000 PCAWI74A RTR Wilson 1974 TTi p p Ti 160 1800 2150 PTIPR72A RTR Prochnow 1972 T pp Ti 160 2150 2500 PTIPR72B RTR Prochnow 1972 78 T i p p Ti 160 2500 2800 PTIPR72C RTR Prochnow 1972 TTi p p Ti 160 2900 3040 PTIPR72D RTR Prochnow 1972 T pp Ti 170 1000 2600 PTIRAS9A RTR Rauhala 1989 Li 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 ABETA65A 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 B a a B 170 5 975 3275 AB_MC92A RTR McIntyre 1992 B a a B 150 8 2000 4000 AB_RA72A RTR Ramirez 1972 B a a B 160 5 4000 8000 AB_OT72A RTR Ott 1972 T B o a B 170 5 980 3300 AB_MC92B RTR McIntyre 1992 C a a C 149 4000 12000 AC_MS72A RTR Marvin 1972 C a a C 165 1810 9050 AC_FE94A RTR Feng 1994 C a a C 167 4000 7500 AC BI54A RTR Bittner 1954 C a a C 170 5000 9000 AC CH94A RTR Cheng 1994 C a a C 170 5 1560 5000 AC LE89A RTR Leavitt 1989 BC a a C 165 2000 3500 AC_BA65A RTR Barnes 1965 BC a a C 165 3300 6500 AC KE68A RTR Kerr 1968 HN a o HN 163 7 2600 4700 AN_KA58A RTR Kashy 1958 N a a N 165 2000 6200
13. 2 MB free hard disk space At least 8 MB RAM are recommended 2 2 Installation Unzip the file SIMNRAxy ZIP into a directory of your choice for example C SIMNRA Use pkunzip s d switch to create the correct subdirectory structure After unzipping you should have obtained the files listed in table 2 1 Now run the program SIMNRA The name of the executable program is SIMNRA EXE When you run SIMNRA for the first time you will be prompted for the name of the di rectory where SIMNRA is installed for the above example enter CASIMNRA The names IWIN32S is a 32 bit extension for Windows 3 1 It is available from Microsoft http www microsoft com WIN32S is not needed for Windows 95 or Windows NT SIMNRA will not run with WIN32S Version 1 25 or lower xy is the version number 30 stands for version 3 0 Directory Files SIMNRA EXE executable program README Readme file MANUAL PS This manual ATOM ATOMDATA DAT atomic data STOP STOPH DAT stopping data STOPHE DAT LCORRHI DAT CHU_CORR DAT CRSEC CRSDA DAT cross section data R33 T RTR SAMPLES NRA examples Table 2 1 Directory structure and files used by SIMNRA of the sub directories will be created automatically Note If you encounter error messages File not found then check the entries in Options Directories Chapter 3 Using SIMNRA 3 1 Basic steps This section gives a quick overview about the basic steps necessar
14. 2000 9000 AO_CH93A RTR Cheng 1993 O a a O 170 1770 5000 AO_LE90A RTR Leavitt 1990 B0 a 5O 160 2400 3500 AO POGAA RTR Powers 1964 F a a F 165 1500 5000 AF_CH93A RTR Cheng 1993 PE a a PF 170 1500 2300 AF_CS84A RTR Cseh 1984 PE a a PF 170 2300 3700 AF_CS84B RTR Cseh 1984 F a a PF 170 1500 4000 AF_CS84C RTR Cseh 1984 Ne a a Ne 167 3 2400 3200 ANEGO54A RTR Goldberg 1954 Ne a a Ne 167 3 3200 4000 ANEGO54B RTR Goldberg 1954 Ne a a Ne 167 3 2400 4000 ANEGO54C RTR Goldberg 1954 Na a a Na 165 2000 6000 ANACH91A RTR Cheng 1991 Mg a a Mg 165 2000 9000 AMGCH93A RTR Cheng 1993 Mgl a a J Mg 162 5 3150 3900 AMGCS82A RTR Cseh 1982 Mg a a Mg 162 5 4200 4900 AMGCS82B RTR Cseh 1982 Mg a a Mg 164 3150 3900 AMGKA52A RTR Kaufmann 1952 Mgl a a Mg 165 5900 6250 AMGIK79A RTR Ikossi 1979 Mg a a Mg 165 6080 6140 AMGIK79B RTR Ikossi 1979 Si a a Si 170 2000 6000 ASICH93A RTR Cheng 1993 Si a a Si 170 6000 9000 ASICH93B RTR Cheng 1993 BSi a a PSi 165 2400 4000 ASILE72A RTR Leung 1972 BSi a a Si 165 4000 5000 ASILE72B RTR Leung 1972 BSi a a Si 165 5100 6000 ASILE72C RTR Leung 1972 BSi a a Si 165 2400 5000 ASILE72D RTR Leung 1972 77 Ala a Al 170 2000 9000 AALCH93A RTR Cheng 1993 Cl a a Cl 165 2000 9000 ACLCH93A RTR Cheng 1993 Ar a a Ar 170 1800 5200 AARLES6A RTR Leavitt 1986 PK a a K 175 5 6000 8000 AK FR82A RTR Frekers 1982 Ca a a Ca 166 2200 8800 ACAHU90A RTR Hubbard 1990 Ca a a Ca 145 5000 90
15. 3 4 Thickness Thickness of the layer in 101 atoms cm 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 He can be used Concentration Atomic concentration of the element in the actual layer The con centration c must be 0 0 lt c 1 0 The sum of the concentrations of all elements in one layer must be equal to 1 0 999 lt gt c 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 7 to 1 minus the sum of concentrations of all other elements c 1 57 2 Cj Isotopes You can use these buttons 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 C on top of C 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 Calculatio
16. 443 R Amirikas D N Jamieson and S P Dooley Nucl Instr Meth B77 1993 110 J Vorona J W Olness W Haeberli and H W Lewis Phys Rev 116 1959 1563 M Wielunski M Mayer R Behrisch J Roth and B M U Scherzer Nucl Instr Meth B122 1997 113 J E E Baglin A J Kellog M A Crockett and A H Shih Nucl Instr Meth B64 1992 469 F Besenbacher I Stensgaard and P Vase Nucl Instr Meth B15 1986 459 62
17. AN FE94A RTR Feng 1994 BN ao N 167 4550 6550 AN_FO93A RTR Foster 1993 HN a o HN 167 7090 9070 AN_FO93B RTR Foster 1993 BN 0 0 IN 167 8650 9000 AN_FO93C RTR Foster 1993 N a a N 167 2 2000 4000 AN_HE58A RTR Herring 1958 PN a a PN 165 2 1600 2600 AN_SM61A RTR Smothich 1961 BN a a N 165 2 2400 3800 AN SM61B RTR Smothich 1961 PN a a PN 165 2 3800 4800 AN SMOIC RTR Smothich 1961 PN a a PN 165 2 4700 5600 AN_SM61D RTR Smothich 1961 BN a a N 165 2 1600 5600 AN_SM61E RTR Smothich 1961 BN a a N 165 2 1600 5600 AN SM61F RTR Smothich 1961 PN a a PN 165 2 3800 4800 AN_MO72A RTR Mo 1972 TO a a O 158 6 6000 10500 AO_HUG7A RTR Hunt 1967 TO a a SO 165 2050 9000 AO_FE94A RTR Feng 1994 TO a a O 165 9200 9900 AO_CA85A RTR Caskey 1985 TO a a O 165 9600 10500 AO_CA85B RTR Caskey 1985 21 22 0 Lab Energy keV File Reference 1O0 a a PO 165 10320 10700 AO CASBC RTR Caskey 1985 TO a a O 165 10650 11100 AO_CAS5D RTR Caskey 1985 O a a O 165 11050 11600 AO_CAS5E RTR Caskey 1985 O0 a a O 165 11500 12500 AO_CA85F RTR Caskey 1985 TO a a O 165 12150 12750 AO_CAS5G RTR Caskey 1985 TO a a O 165 12500 13500 AO_CA85H RTR Caskey 1985 SO a a O 165 9150 12750 AO CASBLRTR Caskey 1985 TO a a O 165 7 5000 12500 AO_JO69A RTR John 1969 TO a a O 170
18. C 135 600 2950 13CDP R33 Marion 1956 1MN D a0 C 150 600 1400 14NDAO 1 R33 Amsel 1969 N D a1 C 150 600 1400 14NDA1_1 R33 Amsel 1969 TTN D po PN 150 500 1900 14NDP0_1 R33 Simpson 1984 N D pi 2 N 150 600 1400 14NDP12 R33 Amsel 1969 AN D ps N 150 800 1400 14NDP3 R33 Amsel 1969 UN D p45 N 150 600 1400 14NDP45 R33 Amsel 1969 IN D p N 150 600 1400 14NDP45 R33 Amsel 1969 ANCHe p1 2 0 90 1600 2800 14NTP1X1 R33 Terwagne 1994 ANCHe p1 2 O 135 1600 2800 14NTP1X2 R33 Terwagne 1994 TN FHe p3 0 90 1600 2800 14NTP3X1 R33 Terwagne 1994 N He p3 O 135 1600 2800 14NTP3X2 R33 Terwagne 1994 PNCHe pa O 90 1600 2800 14NTP4X1 R33 Terwagne 1994 TIN FHe pa1 0 135 1600 2800 14NTP4X2 R33 Terwagne 1994 1N He ps O 90 1600 2800 14NTP5X1 R33 Terwagne 1994 NC He ps 0 135 1600 2800 14NTP5X2 R33 Terwagne 1994 24 0 Lab Energy keV File Reference DN Dep UDO 90 1600 2800 14NTP7X1 R33 Terwagne 1994 N 7He p7 O 135 1600 2800 14NTP7X2 R33 Terwagne 1994 TAN 7He ao N 90 1600 2800 14NTAOX1 R33 Terwagne 1994 ANC He a0 PN 135 1600 2800 14NTAOX2 R33 Terwagne 1994 BN a po O 135 4000 5000 14NAP1 R33 Giorginis 1995 I5N p a C 140 900 2860 15NPA R33 Hagedorn 1957 BN D a C 150 800 1300 15NDA_1 R33 Sawicki 1985 I0 D a N 135 800 2000 160DA 2 R33 Amsel 1964 OD DAN 145 760 950 160DA_1 R33 Turos 1973 160 D a N 165 800 200
19. Li p a He 60 650 2900 6LIPA R33 Marion 1956 SLi D a He 150 400 1900 6LIDA_1 R33 Maurel 1981 8T i He po Be 165 900 5100 6LITPO R33 Schiffer 1956 T i He p Be 165 900 5100 6LITP1 R33 Schiffer 1956 TLi p a He 150 500 1500 7LIPA R33 Maurel Be D ao Li 165 500 1900 9BEDAO R33 Biggerstaff 1962 Be D a1 zm 165 500 1600 9BEDA1 R33 Biggerstaff 1962 Be He po 1 90 1800 5100 9BETPO 1 R33 Wolicki Be He pi e 90 1800 5100 9BETP1_1 R33 Wolicki Be He po 2 150 1800 5100 9BETPO 2 R33 Wolicki Be He pi 1 150 1800 5100 9BETP1_2 R33 Wolicki pac Be 50 1800 10800 10BPA0_1 R33 Jenkin 1964 DB p a 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 a0 Be 156 980 1800 10BDAO R33 Purser 1963 B D a1 Be 156 980 1800 10BDA1 R33 Purser 1963 B He po 7C 90 1300 5000 10BTPO R33 Schiffer 1956 B He p C 90 1300 5000 10BTP1 R33 Schiffer 1956 B a po C 135 4000 5000 10BAPO R33 Giorginis 1995 B a p1 C 135 4000 5000 10BAP1 R33 Giorginis 1995 HB He D 7C 90 3000 5400 11BTDO0 R33 Holmgren 1959 HB He po C 90 3000 5400 11BTPO R33 Holmgren 1959 HB He p 3 C 90 3000 5400 11BTP123 R33 Holmgren 1959 UO D p C 135 520 2950 12CDP_1 R33 Jarjis 1979 C D p 3C 165 800 1950 12CDP_2 R33 Kashy 1960 T7G He po N 90 2100 2300 12CTP0 R33 Tong 1990 2C He p1 N 90 2100 2400 12CTP1 R33 Tong 1990 2C He p2 N 90 2100 2400 12CTP2 R33 Tong 1990 BCO p
20. Z and energy For E M values in the range 100 1000 keV amu the data have been taken from ref 26 data for lower and higher E M values are based on an extrapolation performed in ref 20 Tabulated values for H are stored in the file CHU_CORR DAT For not tabulated values SIMNRA uses linear interpolation For the nuclear energy loss straggling 02 SIMNRA uses Bohr s theory of nuclear strag gling The nuclear energy loss straggling in Bohr s approximation is given by M 2 Az 10 atoms cm 4 34 47 E M ke V amu 5000 3000 2000 1500 e t 1000 i t 750 500 300 200 100 50 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 26 solid lines are extrapolated data taken from 20 48 2 5 MeV He in Si 10 20 Straggling keV FWHM Depth 10 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 30 the dashed line is the prediction 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 Because the nuclear energy loss straggling is generally much smaller than the electronic
21. 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 e Print This menu item will print all parameters of the calculation and plot the experimental and simulated curves Note 1 SIMNRA is not intended to produce high quality graphics and the plot looks quite ugly If you want to obtain high quality graphics 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 Note 2 Printing may not work properly if the program is used under Windows 3 1 Printing works properly under Windows 95 and Windows NT e Exit Terminates the program 3 3 The Edit menu e Copy Data This will copy the experimental and simulated data in ASCII format to the clipboard 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 Note 1 SIM
22. different straggling contributions The Number of counts N in each channel i is given by integrating S E over the channel width from the minimum to the maximum energy of each channel Emaz i j j Ne S E dE 4 3 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 10 4 The area Q of the brick in fig 4 1 is calculated by SIMNRA by using the cross section 35 at the mean energy E in the brick do Ax NAQ E Q qa pers 4 4 NAQ 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 4 2 Cross sections 4 2 1 Rutherford cross sections The Rutherford cross section for backscattering is given in the laboratory system by 2 2 Au 0 1 2 2 ZZ j m3 Mj sin 6 M3 cos d 4 5 6 or mb sr 5 18275 x 10 Elev nee i ey 0 is the s
23. file format 31 e A line containing the string THETA Theta should be given in degrees The value of theta is not used by SIMNRA however this line must be present and contain a value e A line containing the string NVALUES The value of nvalues is ignored however this line must be present SIMNRA assumes that the data will start after this line e The data are organised in 4 columns The first column is the energy in keV the second column is the energy error ignored by SIMNRA the third column is the differential cross section in the laboratory frame measured in mbarn sr and the fourth column is the cross section error ignored by SIMNRA SIMNRA expects the data to be arranged in order of ascending energy 32 3 11 Detector nonlinearity It is well known that the energy calibration of semiconductor detectors which are used in most ion beam experiments is not exactly linear This is due to the energy dependent energy loss in the top electrode and the dead layer of the semiconductor detector 3 4 which results in a nonlinearity of typically several channels To account for detector nonlinearities SIMNRA offers two possibilities 1 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 sili
24. in compounds SIMNRA uses Bragg s rule 17 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 elements with atomic concentrations c gt gt c 1 the total stopping power S is given by Sq 4 28 42 Si 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 containing heavier constituents such as oxides nitrides hydrocarbons etc The deviations from Bragg s rule predictions may be of the order of 10 20 18 Ziegler and Manoyan 19 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
25. 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 e A line containing the string QVALUE The Q value is the energy released in the nuclear reaction in keV 30 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 lon 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 NAME Gyorgy Vizkelethy ADDRESS1 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 REACTION 160 d a0 14N DISTRIBUTION Energy MASSES 2 16 4 14 QVALUE 3110 00 THETA 145 0 SIGFACTORS 1 00 0 00 ENFACTORS 1 00 0 00 0 00 0 00 NVALUES 5 761 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 Figure 3 5 Example for a cross section data file in the R33
26. reviewed by Szil gy et al 20 Multiple small angle scattering geometrical straggling and surface roughness are not calculated by SIMNRA The finite energy resolution of the detector is included in the calculations Plural scattering with two scattering events dual scattering can be calculated by SIMNRA 44 4 5 1 Electronic and nuclear energy loss straggling There are four main theories describing electronic and nuclear energy loss straggling 21 22 23 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 1096 Vavilov s Theory 24 22 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 25 26 As the number of collisions becomes large the distribution of particle energies becomes Gaussian 20 50 Symon s Theory 21 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 the
27. 0 160DA 3 R33 Amsel 1964 0D po O 135 20 3000 160DP0_1 R33 Jarjis 1979 OD pi O 135 500 3000 160DP12 R33 Jarjis 1979 1 0 D p1 7O 155 400 1100 160DP1 1 R33 Amsel 1967 TOC He a PO 90 1600 2600 160TA R33 Abel 80 p a PN 155 1500 1800 180PA_2 R33 Alkemada BO p a PN 165 500 1000 180PA_1 R33 Amsel 1967 180 D ao N 165 830 2000 180DA_1 R33 Amsel 1964 30 D 01 N 165 830 2000 180DA 2 R33 Amsel 1964 150 D 02 N 165 830 2000 180DA_3 R33 Amsel 1964 150 D a3 N 165 830 2000 180DA 4 R33 Amsel 1964 BE p a O 90 700 1900 19FPA_1 R33 Dieumegard 1980 PE p0a O 150 700 2000 19FPA 2 R33 Dieumegard 1980 E D 00 O0 150 700 1900 19FDAO 1 R33 Maurel 1981 U7F D o1 O 150 1000 1900 19FDA1_1 R33 Maurel 1981 25 3 7 The Calculate menu In the Calculate menu all commands for calculating spectra scattering kinematics stop ping powers and data fitting are located e Calculate Spectrum Calculates the simulated spectrum e Calculate Spectrum Fast Sets the detector resolution to 0 0 keV ignores strag gling and dual scattering and calculates the simulated spectrum The calculation of the spectrum is performed much faster than with Calculate Spectrum but the spectrum will contain kinks e Fit Spectrum Data fitting to experimental data See section 3 7 1 for details e Kinematics Calculation of scattering kinematics Allows the calculation of the energies of backscattered particles recoils and nuclear r
28. 0 180 0 degree Figure 4 2 Angular dependence of the correction factors for the Rutherford cross section by L Ecuyer eq 4 6 dashed lines and Andersen eq 4 7 solid lines for He backscattered from gold at different energies Ener is the energy at which the deviation from the Rutherford cross section is 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 choose 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 4 3 Evaluation of energy loss The energy E of a particle in the depth x is given by the integral equation x cosa dE Ba E Bla 2 dal 4 9 0 x Here we assume that the particle starts with initial energy Eo at the surface x 0 dE dx E x x is the energy and depth dependent stopping power In principle eq 4 9 38 can be evaluated directly however this consumes a lot of computing time For the evaluation of the energy loss SIMNRA uses the algorithm of Doolittle instead developed for RUMP 5 The beam loses energy according to the differential equation dE
29. 00 ACASEST7A RTR Sellschop 1987 Table 3 2 Non Rutherford ERDA cross sections 23 0 Lab Energy keV File Reference He H He 20 2000 3000 1H TP1X1 R33 Terwagne 1996 H He H He 30 1900 3000 1HTP1X2 R33 Terwagne 1996 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 30 900 3000 CRSDA DAT No 125 Baglin 1991 H a H a 30 2000 7000 CRSDA DAT No 3 D a D a 10 1000 2500 ERD10D R33 Quillet 1994 D a Dja 20 1000 2500 ERD20D R33 Quillet 1994 D a D a 30 1000 2500 ERD30D R33 Quillet 1994 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 3 Nuclear reactions cross sections 0 Lab Energy keV File Reference D He a p All 380 1000 CRSDA DAT No 1 D He a p All 700 2000 CRSDA DAT No 111 D He a p All 300 2000 CRSDA DAT No 129 D He p a All 380 1000 CRSDA DAT No 28 3He D o p All 250 660 CRSDA DAT No 2 He D p a All 250 660 CRSDA DAT No 46 Li p He He 60 650 2900 6LIP3HE R33 Marion 1956
30. 1 Overview 1 2 Installation 3 2 1 System requirements 3 2 2 Installation it Ka s An RR c 3 3 Using SIMNRA 5 31 Basic Steps iode As sl ti Mu La 5 3 2 The File ment s mosii gadi ane ai Ga oe A Echo Rogo 7 3 39 The Edit menu icon eke e di aid ms 9 S4 The Setup Menu a AA RE er 10 34 1 Setup Experiments re it a a bY 10 3 4 2 Setup Calculation s 4 34 62 tok Sew aS bakes ba Bs 12 3 9 Ehe Target men cx EE dE ans Rcx n rds 15 39 1 Target Target n u al ide Pan een ei 15 3 5 2 Target Foils a Ge fe Sr Bas ea da XE 17 3 6 The Reactions menu 18 3 7 The Calculate menu 26 SC EFUGJSpecUrumnisss anahi See e Sedo ete ates ee NE AT tek 26 370 CDhePlotgnent sas uv eeu Gade eae Bee be YR ERE Ee RE RE 28 3 9 CTTh ptions menu c nac a poe os WA SIR RE EE 29 3 10 Adding new cross section data 30 3 10 1 The R33 file format les 30 3 11 Detector nonlinearity 33 4 Physics 34 AL OVEIVIEW er AA E EE AE he RUN 34 A D CrOSS SECHIONS A ae dE E AE AA AAA Ee a 36 4 2 1 Rutherford cross sections 36 4 2 2 Non Rutherford cross sections 37 4 3 Evaluation of energy loss 38 4 4 Stoppingpowerdata 40 ZA Hydro u 222 8 Er wg de En ee LE IE ag 40 442 Helium 25550
31. 1550 PF DE56D RTR Dearnaly 1956 TF p p PF 165 850 1010 PF_KN89A RTR Knox 1989 TE p p PF 165 1000 1875 PF KN89B RTR Knox 1989 TF p p PF 165 1350 1550 PF_KN89C RTR Knox 1989 TF p p F 158 7 600 1800 PF WE55A RTR Webb 1955 PE pp F 158 7 1300 1500 PF_WE55B RTR Webb 1955 20Ne p p Ne 166 CM 1500 2800 PNELA7IA RTR Lambert 1971 WNa p p Na 156 5 550 1450 PNABA56A RTR Bauman 1956 Mg p p Mg 164 400 4000 PMGMOBIA RTR Mooring 1951 Mg p p Mg 164 792 856 PMGMOSIE RTR Mooring 1951 Meg p p Mg 164 1466 1501 PMGMOSIF RTR Mooring 1951 Mg p p Mg 164 1642 1671 PMGMOSIG RTR Mooring 1951 Mg p p Mg 164 1991 2026 PMGMO51H RTR Mooring 1951 Me p p Mg 164 2393 2431 PMGMOSILRTR Mooring 1951 20 0 Lab Energy keV File Reference Mg p p Mg 170 700 2540 PMGRASSA RTR Rauhala 1988 77 Al p p AI 170 1000 2450 PALRAS9A RTR Rauhala 1989 8Si p p Si 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 STP p p IP 165 1000 2000 PP_CO63A RTR Cohen Ganouna 1963 2S p p S 167 4 1300 4000 PS_OL58A RTR Olness 1958 S p p S 170 1500 2690 PS RAS8A RTR Rauhala 1988 Cl p p Cl 150 2000 5000 PCLBO93A RTR Bogdanovic 1993 20 Ar p p Ar 159 5
32. 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 31 32 SIMNRA is able to calculate dual scattering i e all particle trajectories with two scattering events 52 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 v see fig 4 8 After the first scattering event the scattered particles have the direction w 4 The scattering angle 01 of the first scattering event is given by cos 0 sina sin y sin cosa 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 particles after the first scattering is a 180 y The scattering angle 05 of the second scattering event is given by cos 05 sin B sin y sing cos 8 cos Y SIMNRA subdivides the whole sphere of 47 into 10 w intervals and 12 intervals resulting in 120 solid angle intervals SIMNRA considers only trajectories with scattering angles 91 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 s
33. 3 6 The 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 Addi tionally 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 during the last years at the IPP Garching and contains fitting coefficients to various cross section data A documen tation is not available and no guarantee is provided that the fits agree with the original data Data from this file should be used with care and 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
34. 60 one kon LES et ed a ata 40 449 Heavy IOUS ec sans la ei Das leek a aA ears A ee Sle puel d des 42 44 4 Stopping in compounds 42 4 5 Stragglinp n onde ee e dto On ep ee ak uk e grat 43 4 5 1 Electronic and nuclear energy loss straggling 45 4 5 2 Energy loss straggling in compounds 52 4 6 Multiple and plural scattering 52 5 Examples 55 5 1 RBS Rutherford cross sections 55 5 2 RBS Non Rutherford cross sections 58 5 3 ERDA Non Rutherford cross sections 60 i Chapter 1 Overview This report describes the use of the program SIMNRA and the physical concepts imple mented therein SIMNRA is a Microsoft Windows 95 Windows NT 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 backscat tering 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 He ions are included SIMNRA can calculate spectra for any ion target combination including incident heavy ions and any geometry including arbitrary foils in front of the detector SIMNRA uses the Andersen Ziegler values for the stopping powers of swift and heavy ions and Chu en
35. A Ax E Es e EsjAz By putting the above equations together we get the energy difference AE Ej E of the two particles after penetrating the layer AB 1 SE Eo An AE 4 29 If de dE is negative which is the case for all energies above the stopping power maximum the energy difference increases and the distribution function is broadened If de dE is positive the energy difference decreases and the distribution function gets skewed Because this is a linear Taylor expansion a Gaussian distribution remains gaussian but the width of the Gaussian is changed according to eq 4 29 To the non statistic broadening we have to add the statistical effects When the in cident beam with initial energy Eo and initial beam width og a is the variance of the energy distribution the full width at half maximum FWHM is 2V2In2o 2 355 0 penetrates a layer of matter with thickness Az then the beam width 0 after penetrating the layer is given by dE e E dE dx E is the stopping power of the material and c is the energy loss straggling 2 de 2 2 2 er zt Eg Ar og 0 4 30 in the layer including nuclear energy loss straggling in Bohr approximation and electronic 46 energy loss straggling according to Chu s theory The first term in eq 4 30 describes the non statistical broadening of the beam according to eq 4 29 due to the energy dependence of the stopping power the second term adds the statistical effects
36. Energy overlap in cross sections All available cross section data are listed in tables 3 1 3 3 If you want to add new cross section data files see section 3 10 Note 1 Files containing total cross sections in the R33 file format are ignored SIM NRA currently handles only differential cross section data 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 19 Table 3 1 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 SLi p p Li 164 1200 3100 PLIBASIA 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 PBEMOSGA RTR Mozer 1956 Be p p
37. MAX PLANCK INSTITUT FUR PLASMAPHYSIK GARCHING BEI MUNCHEN SIMNRA User s Guide Matej Mayer IPP 9 113 April 1997 Die nachstehende Arbeit wurde im Rahmen des Vertrages zwischen dem Max Planck Institut f r Plasmaphysik und der Europ ischen Atomgemeinschaft ber die Zusammenarbeit auf dem Gebiete der Plasmaphysik durchgef hrt IPP 9 113 Matej Mayer SIMNRA User s Guide April 1997 Abstract This report describes the use of the program SIMNRA and the physical concepts imple mented therein SIMNRA is a Microsoft Windows 95 Windows NT 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 backscat tering 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 He ions are included SIMNRA can calculate spectra for any ion target combination including incident heavy ions and any geometry including arbitrary foils in front of the detector SIMNRA uses the Andersen Ziegler values for the stopping powers of swift and heavy ions and Chu energy loss straggling Additionally SIMNRA can calculate the effects of dual scattering Data fitting layer thicknesses compositions etc is possible by means of the Simplex algorithm This manual describes SIMNRA version 3 0 Contents
38. NRA does not support OLE Note 2 Copy Data does not work properly under Windows 3 1 and is disabled Copy Data works properly under Windows 95 and Windows NT 3 4 The Setup menu 3 4 1 Setup Experiment In the Setup Experiment menu the global parameters of the backscattering experi ment are defined e Incident ion Selects the incident ions For incident protons H D T He or He 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 e Energy Energy of the incident ions in keV e Geometry Geometry of the experiment Incident angle a exit angle 8 and scattering angle 0 a and f are measured towards the surface normal see fig 3 2 All angles in degrees Note 0 lt 8 lt 90 Transmission geometry is not possible e 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 E 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 i
39. ace 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 incident 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 31 32 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 55 Counts Energy keV 200 400 600 800 1000 experimental simulated 100 200 300 400 500 600 700 800 Channel Figure 5 1
40. c stopping power Se in eV 10 atoms cm for incident 40 He ions with energy E in keV is given by a Qm SEH with Stow A Ef 4 21 and SHigh a In a A 458 4 22 A As are fitting coefficients and tabulated in 14 They are stored in the file STOPHE DAT Equations 4 20 4 22 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 14 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 15 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 1 2 M M3 zi 2 Sn is the reduced nuclear stopping and Zi M are the nuclear charge and mass of the helium ion and Z2 Ma are the nuclear charge and mass of the target element The reduced nuclear stopping Sn has the simple form In 1 4 4 24 i c 0 10718 c037544 4 24 e is the reduced energy and is given by 32 53 M2 E c 2 4 25 E 1 2 2122 Mi M zi 2 Nuclear stopping is only important at incident energies E lt 100 keV at higher energies nuclea
41. cattering angle Zj and M are the nuclear charge and the mass of the projectile respectively and Z and M are the nuclear charge and the mass of the target atom respectively cg 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 7 8 9 1 This screening is taken into account by a correction factor F o Fog For 0 gt 90 the correction factor by L Ecuyer et al 7 is widely used _ 0 049 Z Z7 Es 4 6 FL Ecuyer 1 Ecm is the energy in the center of mass system in keV Tabulated values of FL Ecuyer can be found for example in 1 The correction for backscattering angles 0 gt 90 at 36 typical energies used in ion beam analysis usually is small For 1 MeV He ions on gold the correction is only about 3 5 The correction factor by L Ecuyer eq 4 6 is a first order correction and does not take into account the influence of the scattering angle 0 For 0 lt 90 eq 4 6 will underestimate the necessary correction to the Rutherford cross section SIMNRA uses the angular and energy dependent correction factor by Andersen et al 9 2 1 V 1 5507 2 2 Vi V 1 Eb ep E scs cm is the scattering angle in the center of
42. con 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 2 SIMNRA offers the possibility 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 33 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 5 6 However RUMP uses many 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 i
43. cribed below 2 Copy this file into the directory where all other cross section data files are This directory is displayed in Options Directories 3 Recreate the reaction list by clicking Options Create Reaction List Note If your file will be ignored then SIMNRA was not able to read or understand the file Carefully read the section about the R33 file format and try again 3 10 1 The R33 file format The R33 file format is described in full detail in a proposal by I C Vickridge The proposal can be obtained from SigmaBase An example for a valid file in the R33 format is shown in fig 3 5 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 must be present in the file in the given order The file may additionally contain an arbitrary number of other information All other lines than the ones listed below are ignored by the program e A line containing the string REACTION Uppercase characters are important SIMNRA will interpret the nuclear reaction string written in that line In the exam ple of fig 3 5 160 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 parti cles from this line Please note that the first mass is the mass of the
44. 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 e 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 12 e Straggling If checked electronic and nuclear energy loss straggling will be taken into account Default is checked Note Straggling due to multiple small angle scattering is not calculated by the program See chapter 4 for details e High energy stopping If checked the program will use the high energy stop ping formula by Andersen and Ziegler for incident protons and heavy ions for E gt 1 MeV amu If 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 is very small in most cases 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 Not
45. e If you use high energy stopping you may obtain kinks in the spectra be cause the two stopping power formulas do not fit absolutely smoothly together The derivative of the stopping power jumps at 1 MeV amu e 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 3 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 elements 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 13 Figure 3 3 Examples of ion trajectories with one two and three scattering events Note 1 Dual scattering should be used only if all cross sections are Rutherford For the calcu
46. eaction products e Stopping Calculation of stopping powers for any projectile in any target element and of energy loss in the different layers Note The result of a stopping power calculation for E gt 1 MeV amu depends on the setting of Setup Calculation High energy stopping see section 3 4 2 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 x J w i Neapli Nsim 3 2 i is minimised by varying the input parameters of the calculation Nezp i is the number of counts in channel i of the measured spectrum and Nsim i is the number of counts in channel 1 of the simulated spectrum w i is the weight 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 2 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 26 SIMNRA uses equal weighting of each data point this means w i 1 for all points You can fit 1 Energy calibration 2 Particles sr 3 Thickness of a layer 4 Composition of a layer independently or all at once Check which pa
47. ean energy of the beam has decreased to the energy of the stopping power maximum 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 fits the measured curve relatively well except of the multiple scattering contribution The straggling of outgoing particles is calculated with eq 4 30 as well Outgoing particles always start with an energy distribution with variance gout which is given by 2 2 2 Cop K mm 4 35 with K the kinematic factor and Erd the variance of the energy distribution of the incident beam 50 Energy keV 900 950 1000 700 750 800 850 Za Experimental f We E e Chu 6000 4000 Counts 2000 O i 500 eu 700 z Channel Energy keV gt 740 750 760 770 780 790 6000 4000 2000 600 0 AAA se oe 580 Channel Figure 4 6 Measured and simulated spectra using Bohr and Chu straggling of 1 0 MeV He ions incident on
48. ental data Deletes the experimental data from the plot e Delete simulated data Deletes all simulated data from the plot e Scaling the axis To scale the x or y axis double click with the left mouse button on the desired axis Enter the axis minimum and maximum e 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 Release the left mouse button Now double click with the left mouse button into the rectangle to zoom in e Zooming out Click the right mouse button to zoom out 28 3 9 The Options menu e Directories Directories where atomic data file ATOMDATA DAT stopping data the files STOPH DAT and STOPHE DAT and cross section data are located 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 Note Some data files contain total cross sections These files are ignored by SIM NRA The program displays a list of all ignored files 29 3 10 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 file format is des
49. ergy loss straggling Additionally SIMNRA can calculate the effects of dual scattering Data fitting layer thicknesses compositions etc is possible by means of the Simplex algorithm In contrast to other programs for the simulation of backscattering spectra SIMNRA is easy to use due to the Microsoft Windows user interface 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 SIMNRA is a native 32 bit program for Windows 95 or Windows NT and requires at least a 386 processor with math coprocessor or a higher processor 486 Pentium A fast processor 100 MHz 486 or higher is highly recommended SIMNRA will run un der Windows 3 1 with WIN32S Version 1 30 or higher However using SIMNRA with Windows 3 1 is not recommended and may result in global protection faults SIMNRA does not run under OS 2 Warp 3 Super VGA resolution of 800 x 600 pixels or higher is recommended SIMNRA requires about
50. is not implemented in SIMNRA 4 5 Straggling 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 statistical fluctuations in the transfer of energy to electrons 2 Nuclear energy loss straggling due to statistical fluctuations in the nuclear energy loss Though the contribution of the nuclear energy loss to the total energy loss is usually negligible at high energies it contributes to the total energy loss straggling The contribution of the nuclear energy loss straggling is however always smaller than the contribution of the electronic energy loss straggling 3 Straggling due to plural scattering and multiple small angle scattering resulting in different path lengths and energy and angular spread of the incident beam 4 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 43 particles 5 Straggling due to surface and interlayer roughness An additional contribution to the energy broadening visible in experimental spectra is the energy resolution of the detector The different straggling contributions have been recently
51. lation 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 to the experimentally determined cross section data which contain these structures 58 Energy keV 400 600 800 1000 1200 1400 1600 1800 experimental simulated 2000 Counts 400 500 600 700 800 Channel Figure 5 4 2000 keV protons backscattered from silicon a 5 0 165 59 Energy keV 600 800 1000 1200 1400 1600 1800 PEN Exp SIMNRA 200 ar we 150 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 3 75 0 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 35 Both recoil cross sections are non Rutherford The cross section data of Baglin et al 36 for H He H He and of Besenbacher et al 37 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
52. lation of dual scattering the cross sections for all possible scattering 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 Element Spectra If checked individual spectra for each element in the target will be calculated and plotted If unchecked only the total spectrum will be calculated and plotted Default is unchecked Logfile If checked a file named SIMNRA LOG will be created This file contains additional information about each step of the calculation The logfile is intended for debugging the program Default is unchecked 14 3 5 The 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
53. lues are normally sufficient and you should change these values only if you know what you are doing 7 With File Read data a measured spectrum can be imported for comparison with the simulated one and for data fitting 3 2 The File menu In the File menu all necessary commands for reading and 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 will be deleted Open This menu item will read a saved calculation from disk Save This menu item will save all current parameters target and foil definitions experimental and simulated data to disk The data are saved as an ASCII file The default file extension is NRA Save as Like Save but you will be prompted for the name of the file Read Data This menu item allows the import of experimental data Read Data IPP Reads experimental data stored in the data file format used at the IPP Garching This data file format will not be described here Read Data ASCIT 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 firs
54. mass system The increase in the kinetic 4 7 F Andersen energy V is given by 1 2 Vi keV 0 04873 Zi Zo 22 2319 The dependence of the correction factor FA ndersen from the scattering angle 0 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 Zi Zo Mi M3 2M3E keV cos 0 c PP mb sr 2 0731 x 107 4 8 0 is the recoil angle in the lab system SIMNRA applies the correction to the Rutherford cross section from eq 4 7 also for the recoil cross section 4 2 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 10 11 12 M Ma Z Enr MeV 38 for Zi 1 M Ma ZZ Enr MeV nn for Z gt 1 2 37 1 00 2000 keV Se 1000 keV 500 keV 0 90 250 keV 0 85 0 80 L 0 75 0 70 0 65 0 60 0 30 60 90 120 15
55. n menu must be checked to manipulate individual isotopes 15 Incident beam Target 19Ae7 Figure 3 4 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 To manipulate layers use the buttons in the Layer manipulation box e 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 Attention If a layer is pasted the current layer is overwritten 16 3 5 2 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 4 The default is no foil in front of the detector 17
56. n 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 Attention If a non linear energy calibration is used then the energy scale which is plotted at the top axis is only approximately valid This scale remains linear even for non linear energy calibrations 10 Figure 3 2 Geometry of a scattering experiment Incident angle a exit angle and scattering angle 0 e Particles sr Number of incident particles times the solid angle of the detector Solid angle in steradians e Detector Resolution Energy resolution of the detector in keV The energy res olution is measured as full width at half maximum FWHM 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 distrib ution of the incident beam with a full width at half maximum which can be entered in the Energy spread of incident beam field The energy distribution of the inci dent beam depends on the experimental setup typical values for this energy spread are several keV in many experiments If this field is set to 0 0 SIMNRA assumes a monoenergetic incident beam 11 3 4 2 Setup Calculation In the Setup Calculation menu the parameters for the calculation can be altered
57. ncident 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 3 and the calculation of straggling in section 4 5 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 1A backscattered particle may be a recoil or a product in a nuclear reaction as well 34 Energy Figure 4 1 Notation used for a single 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 E 0 with width P ee 2 7 OStraggling Out Detector 4 1 OStrapeling Out 18 the variance of the energy distribution of the outgoing particles due to energy loss straggling and on etector I the energy resolution of the detector The final contribution to the energy spectrum of each isotope in each sublayer is given by oo S B SE f E dE 42 0 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
58. ory is significantly higher than predicted by Bohr s theory The distribution of particle energies is still Gaussian 50 9096 Payne s and Tschal rs Theory 27 28 29 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 24 22 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 calculates the non statistic broadening or skewing of the energy distribution in the following way 45 Assume two particles with energies E and Es AE AE x ee Sages centered around a mean energy Eg The energy difference E Es of the two particles is AE To evaluate the stopping power e dE dx at E and Es we can apply a Taylor expansion of the stopping power e E and considering only the linear term Et Bo 55 Eo AR E Eo 5 S5 Ho AB The energies E and E after penetrating a thin layer with thickness Az are then given by E E e F
59. pectrum 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 05 is calculated Fig 4 9 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 with dual scattering are slightly lower than the experimental results This is due to trajectories with more than two scattering events 53 Figure 4 8 Geometry used for the calculation of dual scattering Energy keV 100 200 300 400 Sg 14000 Experimental Dual scattering 12000 Single scattering 10000 2 8000 c 9 3 6000 4000 2000 A 100 200 e Channel Figure 4 9 500 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 54 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 surf
60. r stopping becomes negligible 41 4 4 3 Heavy ions The electronic stopping power of heavy ions in all elements is derived from the stopping power of protons using Brandt Kitagawa theory 16 The formalism is described in detail in ref 16 The screening length A eq 3 29 of ref 16 is multiplied by an empirical correction factor which has been digitised from fig 3 25 of ref 16 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 16 The reduced nuclear stopping sn with the universal potential is given by In 1 1 1383 e 4 26 Sn 2 Te 0 01321 21226 0 19593 ES for e lt 30 For e gt 30 sn is given by In e 4 2 Sn de 7 The reduced energy e in eqs 4 26 and 4 27 is calculated using the universal screening length ay which is o 1 Z0 Z9 3 instead of the Firsov screening length ap wae SECHS which is used in eq 4 25 The difference between eq 4 24 and 4 26 is only some percent The nuclear stopping component is only important at ion energies below about 200 keV amu Nuclear stopping becomes very small at higher energies typically below 1 of the electronic stopping component 4 4 4 Stopping
61. rameters should be varied Only one layer at a time can be fitted e Fitting range The range in channels in which x is calculated e Max Iterations The maximum number of iterations Fitting will be performed until the desired accuracy is reached or the maximum number of iterations is reached e Max Error The desired accuracy of the fit The fit has converged if the relative change of all fitted parameters and of x is below Max Error 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 x e fast and accurate fit If fast fit is selected the fit will be performed with zero detector resolution and without calculation of straggling and dual scattering see Calculate Spectrum Fast This will speed up the fit significantly but is less ac curate If accurate fit is selected the actual detector resolution straggling if checked in the Setup Calculation menu and dual scattering if checked in the Setup Calculation menu are used for the calculation 27 3 8 The Plot menu This section describes all plot related commands including all commands which are not accessible via menus e Autoscaling If 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 e Delete experim
62. t 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 column 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 Write 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 lt CR gt means Carriage Return 13 decimal lt LF gt means Line Feed 10 decimal 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 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
63. y 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 calculation 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 2 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 3 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 4 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 5 Now the spectrum can be calculated Click Calculate Calculate Spectrum for a simulation of the spectrum 6 With Setup Calculation the parameters for the calculation can be altered The default va

SIMNRA User's Guide - Max-Planck

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