RBS - Rutherford Backscattering Spectrometry M. Mayer

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3 RBS - Rutherford Backscattering Spectrometry M. Mayer Max-Planck-Institut für Plasmaphysik, EURATOM Association, Garching, Germany History Scattering geometry and kinematics Rutherford cross section and limitations RBS spectra from thin and thick films Stopping power and energy loss Detector resolution Energy loss straggling Cross sections from selected light elements - incident 1 H - incident 4 He 1

4 Introduction RBS - Rutherford Backscattering Spectrometry Widely used for near-surface layer analysis of solids Elemental composition and depth profiling of individual elements Quantitative without reference samples ( SIMS, sputter-xps,...) Non-destructive ( SIMS, sputter-xps,...) Analysed depth: µm (He-ions); 0 µm (protons) Very sensitive for heavy elements: ppm Less sensitive for light elements NRA E 0 MeV Energy sensitive detector E Sample

5 Introduction () Rutherford Backscattering (RBS) is Elastic scattering of protons, 4 He, 6,7 Li,... Nuclear Reaction Analysis (NRA): Inelastic scattering, nuclear reactions Detection of recoils: Elastic Recoil Detection Analysis (ERD) Particle Induced X-ray Emission (PIXE) Particle Induced γ-ray Emission (PIGE) RBS is a badly selected name, as it includes: - Scattering with non-rutherford cross sections - Back- and forward scattering Sometimes called Particle Elastic scattering Spectrometry (PES) Ion beam Analysis (IBA) acronyms: G. Amsel, Nucl. Instr. Meth. B118 (1996) 5 3

6 History Sir Ernest Rutherford ( ) 1911: Rutherford s scattering experiments: 4 He on Au Atomic nucleus, nature of the atom RBS as materials analysis method 1957: S. Rubin, T.O. Passell, E. Bailey, Chemical Analysis of Surfaces by Nuclear Methods, Analytical Chemistry 9 (1957) 736 Nuclear scattering and nuclear reactions induced by high energy protons and deuterons have been applied to the analysis of solid surfaces. The theory of the scattering method, and determination of O, Al, Si, S, Ca, Fe, Cu, Ag, Ba, and Pb by scattering method are described. C, N, O, F, and Na were also determined by nuclear reactions other than scattering. The methods are applicable to the detection of all elements to a depth of several µm, with sensitivities in the range of 10-8 to 10-6 g/cm. 4

7 History () 1970 s: RBS becomes a popular method due to invention of silicon solid state detectors 1977: H.H. Andersen and J.F. Ziegler Stopping Powers of H, He in All Elements 1977: J.W. Mayer and E. Rimini Ion Beam Handbook for Materials Analysis 1979: R.A. Jarjis Nuclear Cross Section Data for Surface Analysis 1985: M. Thompson Computer code RUMP for analysis of RBS spectra 1995: J.R. Tesmer and M. Nastasi Handbook of Modern Ion Beam Materials Analysis 1997: M. Mayer Computer code SIMNRA for analysis of RBS, NRA spectra 5

8 Index History Scattering geometry and kinematics Rutherford cross section and limitations RBS spectra from thin and thick films Stopping power and energy loss Detector resolution Energy loss straggling Cross sections from selected light elements - incident 1 H - incident 4 He 6

9 Scattering Geometry α β θ α: incident angle β: exit angle θ: scattering angle Often (but not exclusive): 160 θ 170 optimised mass resolution α β θ IBM geometry Incident beam, exit beam, surface normal in one plane α + β + θ = 180 Advantage: Simple Cornell geometry Incident beam, exit beam, rotation axis in one plane cos(β) = cos(α) cos(θ) Advantage: large scattering angle and grazing incident + exit angles good mass and depth resolution simultaneously General geometry α, β, θ not related 7

10 Scattering Kinematics 1.0 θ = K 0.4 Elastic scattering: E 0 = E 1 + E 0. 1 H 4 He 7 Li Kinematic factor: E 1 = K E 0 K = ( M M sin θ ) 1/ 1 + M1 cos M 1 + M θ E M dk 1 = E0 M dm E 1 : Energy separation M : Mass difference 8

11 Scattering Kinematics: Example (1) ,000 11,000 10,000 9,000 8,000 7,000 Energy [kev] Au: kev 4 He, θ = 165 backscattered from C, O, Fe, Mo, Au Atoms/cm each on Si substrate Counts 6,000 5,000 4,000 3,000 C: 1 O: 16 Si: 8 Mo: 96 light elements may overlap with thick layers of heavier elements,000 Fe: 56 1, ,000 Channel 1,00 1,400 1,600 1,800,000 9

12 Scattering Kinematics: Example () 000 kev 4 He, θ = 165 Energy [kev] ,000 19,000 18,000 17,000 16,000 15,000 14,000 13,000 1,000 Au 197 Hg 01 Counts 11,000 10,000 9,000 8,000 7,000 6,000 5,000 4,000 3,000,000 1,000 C 1 O 16 Cr Fe 5 56 Au 197 Hg 01 Cr Fe ,000 Channel 1,00 1,400 1,600 1,800,000 Decreased mass resolution for heavier elements 10

13 Mass Resolution E dk 1 = E0 M dm δm = δe E0 dk dm 1 δm : Resolvable mass difference δe: Energy resolution of the system Improved mass resolution with increasing M 1 But: For surface barrier detectors δe = δe(m 1 ) δe(1): 1 kev δe(4): 15 kev δe(1): 50 kev optimum mass resolution for M 1 = 4 7 J.R. Tesmer and M. Nastasi, Handbook of Modern Ion Beam Materials Analysis, MRS, 1995 Heavier M 1 only useful with magnetic analysers, time-of-flight detectors 11

14 Index History Scattering geometry and kinematics Rutherford cross section and limitations RBS spectra from thin and thick films Stopping power and energy loss Detector resolution Energy loss straggling Cross sections from selected light elements - incident 1 H - incident 4 He 1

15 Rutherford Cross Section Neglect shielding by electron clouds Distance of closest approach large enough that nuclear force is negligible Rutherford scattering cross section Note that: σ Z Z R E 1 Sensitivity increases with increasing Z 1 increasing Z decreasing E 13

16 Rutherford Cross Section: Example ,000 11,000 10,000 9,000 8,000 7,000 Energy [kev] Au: kev 4 He, θ = 165 backscattered from C, O, Fe, Mo, Au Atoms/cm each on Si substrate Counts 6,000 5,000 4,000 3,000 C: 6 O: 8 Si Mo: 4 Increased sensitivity for heavier elements Z Good for heavier elements on lighter substrate,000 Fe: 6 Less good for lighter 1,000 elements on heavier substrate ,000 Channel 1,00 1,400 1,600 1,800,000 14

17 Shielded Rutherford Cross Section Shielding by electron clouds gets important at low energies low scattering angles high Z Shielding is taken into account by a shielding factor F(E, θ) σ ( E, θ ) = F( E, θ ) σ R ( E, θ ) F(E, θ) close to unity F(E, θ) is obtained by solving the scattering equations for a shielded interatomic potential: Z1Ze V ( r) = ϕ( r / a) r ϕ: Screening function Use Thomas-Fermi or Lenz-Jenssen screening function a: Screening radius a 0 : Bohr radius 0 /3 /3 ( Z + ) a = 0.885a Z 1 1/ 15

18 Shielded Rutherford Cross Section () σ Z =1 σ R E CM 1 Z For 90 θ 180 : L Ecuyer et al. (1979) Wenzel and Whaling (195) 4/3 σ Z =1 σ R E CM 1 Z 7 / For all θ: Andersen et al. (1980) 4 He backscattered from Au F(E, θ) kev 1000 kev 500 kev 50 kev L Ecuyer 1979 Andersen θ (degree) 16

19 Non-Rutherford Cross Section Cross section becomes non-rutherford if nuclear forces get important high energies high scattering angles low Z Energy at which the cross section deviates by > 4% from Rutherford at 160 θ 180 Bozoian (1991) 1 H: E NR Lab = 0.1 Z [MeV] 4 He: E NR Lab = 0.5 Z [MeV] Linear Fit to experimental values ( 1 H, 4 He) or optical model calculations ( 7 Li) Accurate within ± 0.5 MeV J.R. Tesmer and M. Nastasi, Handbook of Modern Ion Beam Materials Analysis, MRS,

20 Index History Scattering geometry and kinematics Rutherford cross section and limitations RBS spectra from thin and thick films Stopping power and energy loss Detector resolution Energy loss straggling Cross sections from selected light elements - incident 1 H - incident 4 He 18

21 RBS-Spectrum of a thin layer A layer is thin, if: Energy loss in layer < experimental energy resolution Negligible change of cross section in the layer Energy E of backscattered particles: α β E = K E 0 θ Number Q of backscattered particles: x Q = N0Ωσ ( E) cosα Q: Number of counts in detector N 0 : Number of incident particles Ω: Detector solid angle σ(e): Differential scattering cross section (Barns/sr) x: Layer thickness (Atoms/cm ) α: Angle of incidence Counts/channel Energy Q 19

22 RBS-Spectrum of a thin layer () Convolution with experimental energy resolution Assume Gaussian energy resolution function f(x) with standard deviation w f ( x x 1 w ( x) = e π w 0 ) 300 Count density function Counts N i in channel i n ( E K E Q w ( ) E = High i e π w N = n( E) de i E E Low i 0 ) Counts/channel Energy 0

23 RBS-Spectrum of a thick layer Target is divided into thin sublayers ( slabs ) Calculate backscattering from front and back side of each sublayer taking energy loss into account Energy at front side E 1 = E 0 - E in E E 1 Starting energy from front side E 1 = K E 1 Energy at surface E out 1 = E 1 - E out 1 Energy at back side E = E 1 - E Starting energy from back side E = K E Energy at surface E out = E - E out For each isotope of each element in sublayer Brick E out E 1 out 1

24 RBS-Spectrum of a thick layer () Area Q of the brick: Q = x N0Ωσ ( E) cosα Q: Number of counts N 0 : Number of incident particles Ω: Detector solid angle σ(e): Differential scattering cross section x: Thickness of sublayer (in Atoms/cm ) α: Angle of incidence E E 1 E out E 1 out How to determine σ(e)? Mean energy approximation: Use σ(<e>), with <E> = E 1 - E/ Mean cross section <σ>: < σ >= E 1 σ ( E) de E E 1 E More accurate, but time consuming

25 RBS-Spectrum of a thick layer (3) Shape of the brick: Height of high energy side σ(e 1 ) Height of low energy side σ(e ) use linear interpolation E E 1 Better approximations: Height of high energy side σ(e 1 )/S eff (E 1 ) Height of low energy side σ(e )/S eff (E ) S eff : Effective stopping power, taking stopping on incident and exit path into account use quadratic interpolation with additional point <E> E out E 1 out 3

26 RBS-Spectrum of a thick layer (4) Convolution of brick with energy broadening Detector resolution Energy straggling Depth dependent E E 1 E out E 1 out 4

27 RBS-Spectrum of a thick layer: Example 000 kev 4 He, θ = 165 backscattered from Au on Si substrate Counts Au-thickness [x10 17 at/cm ] Energy [kev] 5

28 RBS-Spectra: Example (1) 800. MeV 6 Li Nb Counts Co Nb Co Nb Co Nb MeV 4 He Experiment SIMNRA Co Nb Nb: at/cm Co: at/cm Counts Energy [kev] M. Mayer et al., Nucl. Instr. Meth. B190 (00) 405 6

29 RBS-Spectra: Example () 3980 kev 4 He, θ = Initial 550 C 650 C Simulation Ag Ag 1.x10 18 TiN 1.0x10 17 Si substrate Counts Si Ti Channel M. Balden, unpublished 7

30 RBS-Spectra: Example (3) 1.9 MeV 4 He, 170 backscattered from ceramic glass 8000 O 64 Na 11 Si K Zn Cd O Counts 4000 Na Si K Zn Cd Channel 8

31 Index History Scattering geometry and kinematics Rutherford cross section and limitations RBS spectra from thin and thick films Stopping power and energy loss Detector resolution Energy loss straggling Cross sections from selected light elements - incident 1 H - incident 4 He 9

32 Stopping Power 4 He in Ni Electronic stopping power: - Andersen, Ziegler (1977): H, He in all elements - Ziegler, Biersack, Littmarck (1985): All ions in all elements - Several SRIM-versions since then - Additional work by Kalbitzer, Paul,... - Accuracy: 5% for H, He 10% for heavy ions Nuclear stopping power: - Only important for heavy ions or low energies - Ziegler, Biersack, Littmarck (1985): All ions in all elements using ZBL potential J.F. Ziegler, Helium - Stopping Powers and Ranges in All Elements, Vol. 4, Pergamon Press,

33 Stopping Power () Stopping in compounds: consider compound A m B n, with m + n = 1 S A is stopping power in element A S B is stopping power in element B What is stopping power S AB in compound? Bragg s rule (Bragg and Kleeman, 1905): S AB = m S A + n S B Bragg s rule is accurate in: Metal alloys Bragg s rule is inaccurate (up to 0%) in: Hydrocarbons Oxides Nitrides... Other models for compounds Hydrocarbons: Cores-and-Bonds (CAB) model Ziegler, Manoyan (1988) Contributions of atomic cores and chemical bonds between atoms Large number of experimental data, especially for hydrocarbons, plastics,... 31

34 Evaluation of Energy Loss Question: Energy E(x) in depth x? Taylor expansion of E(x) at x = 0: 0 x E( x) = E(0) + de dx de x dx 1 d E x + x 3 x= 0 dx dx x= 0 x= 0 d E +... = S S: Stopping power E d E dx 3 d E x dx = = d dx d dx ds de de dx ( S ) = = S S ds dx ds dx ( S S ) = S + S = S S S S ( S S + S ) E( x) = E 0 xs + x SS x S + S, S, S evaluated at x = 0 6 3

35 Evaluation of Energy Loss () 3 MeV 4 He in Pt L.R. Doolittle, Nucl. Instr. Meth. B9 (1985)

36 Index History Scattering geometry and kinematics Rutherford cross section and limitations RBS spectra from thin and thick films Stopping power and energy loss Detector resolution Energy loss straggling Cross sections from selected light elements - incident 1 H - incident 4 He 34

37 Silicon Detector Resolution Principle of operation: Creation of electron-hole pairs by charged particles Separation of electron-hole pairs by high voltage V Number of electron-hole pairs Particle energy Charge pulse Particle energy Limited energy resolution due to: Statistical fluctuations in energy transfer to electrons and phonons Statistical fluctuations in annihilation of electron-hole pairs V Additional energy broadening due to: Preamplifier noise Other electronic noise 35

38 Silicon Detector Resolution () Typical values (FWHM): H MeV: 10 kev He MeV: 1 kev Li 5 MeV: 0 kev Ad-hoc fit to experimental data: Ne C B Li He H J.F. Ziegler, Nucl. Instr. Meth. B (1998) 141 Better energy resolution for heavy ions can be obtained by: Electrostatic analyser (Disadvantage: large) Magnetic analyser (Disadvantage: large) Time-of-flight (Disadvantage: length, small solid angle) 36

39 Index History Scattering geometry and kinematics Rutherford cross section and limitations RBS spectra from thin and thick films Stopping power and energy loss Detector resolution Energy loss straggling Cross sections from selected light elements - incident 1 H - incident 4 He 37

40 Energy Straggling Slowing down of ions in matter is accompanied by a spread of beam energy energy straggling Electronic energy loss straggling due to statistical 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 Multiple small angle scattering Surface and interlayer roughness 38

41 Electronic Energy Loss Straggling Due to statistical fluctuations in the transfer of energy to electrons statistical fluctuations in energy loss Energy after penetrating a layer x: <E> = E 0 -S x <E> mean energy S stopping power only applicable for mean energy of many particles 39

42 E/E 0 Electronic Energy Loss Straggling () Shape of the energy distribution? < 10% Vavilov theory Low number of ion-electron collisions Non-Gaussian 10% 0% Bohr theory Large number of ion-electron collisions Gaussian 0% 50% Symon theory Non-stochastic broadening due to stopping Almost Gaussian 50% 90% Payne, Tschalär Energy below stopping power maximum theory Non stochastic squeezing due to stopping Non-Gaussian Vavilov Gaussian 40

43 Vavilov Theory Vavilov 1957 P.V. Vavilov, Soviet Physics J.E.T.P. 5 (1957) 749 Valid for small energy losses Low number of ion-electron collisions Non-Gaussian energy distribution with tail towards low energies Mostly replaced by Bohr s theory and approximated by Gaussian distribution Total energy resolution near the surface usually dominated by detector resolution due to small energy loss straggling Only necessary in high resolution experiments 41

44 Bohr Theory Bohr 1948 N. Bohr, Mat. Fys. Medd. Dan. Vid. Selsk. 18 (1948) Valid for intermediate energy losses Large number of ion-electron collisions Gaussian energy distribution Approximations in Bohr s theory: Ions penetrating a gas of free electrons Ions are fully ionised Ion velocity >> electron velocity stationary electrons Stopping power effects are neglected σ Bohr = 0.6 Z1 Z x σ Bohr variance of the Gaussian distribution [kev ] x depth [10 18 atoms/cm ] Z 1 atomic number of incident ions atomic number of target atoms Z 4

45 Bohr Theory: Example 80.5 MeV 4 He in Si Straggling (kev FWHM) x 10% 0% 50% Max Vavilov Depth (10 19 atoms/cm ) 43

46 Improvements to Bohr Theory Chu 1977 J.W. Mayer, E. Rimini, Ion Beam Handbook for Material Analysis, 1977 Approximations in Chu s theory: Binding of electrons is taken into account Hartree-Fock electron distribution Stopping power effects are neglected σ Chu = H E M, Z σ Bohr 1 Smaller straggling than Bohr H(E/M, Z ) E/M [kev/amu] Z 44

47 Straggling in Compounds Additive rule proposed by Chu 1977 J.W. Mayer, E. Rimini, Ion Beam Handbook for Material Analysis, 1977 consider compound A m B n, with m + n = 1 σ A is variance of straggling in element A σ B is variance of straggling in element B σ AB = σ A + σ B σ A σ B Straggling in element A in a layer m x Straggling in element B in a layer n x 45

48 Propagation of Straggling in Thick Layers Consider particles with energy distribution 80 Energy above stopping power maximum higher energetic particles smaller stopping 60 non-stochastic broadening Energy below stopping power maximum higher energetic particles larger stopping non-stochastic squeezing Stopping Power 40 0 E C. Tschalär, Nucl. Instr. Meth. 61 (1968) 141 M.G. Payne, Phys. Rev. 185 (1969) Energy [kev] 46

49 Propagation of Straggling in Thick Layers () E E * = E 1 = E + δe δx 0 S( E( y)) dy x δx S( E( y)) dy δe S i S f 0 x δe* = E 1 x δx S( E( y)) dy E 1 E E 1 * E * δe δx S i Select δx so, that E decreases to E 1 δx x δx x δx * E1 = E1 S( E( y)) dy S( E( y)) dy 0 x x δx δe * = E = x x δx S * f E S( E( y)) dy δx * 1 * δ E = S S f i δe S f S i Final stopping power Initial stopping power 47

50 Propagation of Straggling in Thick Layers (3) 80 S max Stopping Power S S f i <1 S S Squeezing f i >1 Broadening Energy [kev] Adding stochastic and non-stochastic effects: Statistically independent S i S f S f σ f = σ i + σ S i Chu σ i σ f 48

51 Propagation of Straggling: Examples 80.5 MeV 4 He in Si MeV 4 He in Au Straggling (kev FWHM) % Chu + Propagation Bohr 0% 50% Max Straggling (kev FWHM) Max 0% Chu + Propagation Bohr 50% 90% Depth (10 19 atoms/cm ) Depth (10 18 atoms/cm ) S f σ f = σ i + σ S i Chu 49

52 Multiple and Plural Scattering Multiple small angle deflections Path length differences on ingoing and outgoing paths energy spread Spread in scattering angle energy spread of starting particles P. Sigmund and K. Winterbon, Nucl. Instr. Meth. 119 (1974) 541 E. Szilagy et al., Nucl. Instr. Meth. B100 (1995) kev 4 He, 100 nm Au on Si, θ = 165 Energy (kev) Large angle deflections (Plural scattering) For example: Background below high-z layers Experimental Dual scattering Single scattering Au W. Eckstein and M. Mayer, Nucl. Instr. Meth. B153 (1999) 337 Counts etc Si Channel 50

53 Index History Scattering geometry and kinematics Rutherford cross section and limitations RBS spectra from thin and thick films Stopping power and energy loss Detector resolution Energy loss straggling Cross sections from selected light elements - incident 1 H - incident 4 He 51

54 Threshold for Non-Rutherford Scattering Thresholds for non-rutherford scattering [MeV] For 1 H: E 0.1 Z -0.5 For 4 He: E 0.5 Z Z for Non-Rutherford scattering 1 H 4 He 1 MeV 1 3 MeV 1 6 J.R. Tesmer and M. Nastasi, Handbook of Modern Ion Beam Materials Analysis, MRS,

55 Non-Rutherford Scattering: Example 1.5 MeV H, θ = 165 6x10 17 at/cm Be, C, O on Si Typical problem for light elements: Overlap with thick layers of heavier elements High cross sections wishful 3,400 3,00 3,000,800 Energy [kev] C,600,400,00 Be O Counts,000 1,800 1,600 1,400 1,00 1,000 Si Channel M. Mayer, unpublished 53

56 Cross Section Data Sources Many non-rutherford scattering cross sections were measured in the years for nuclear physics research goal was nuclear physics, not materials analysis most data published only in graphical form Since to now non-rutherford scattering cross sections are measured for RBS analysis some data published in graphical form and tabular form for typical angles of RBS Data compilation by R.A. Jarjis, Nuclear Cross Section Data for Surface Analysis, University of Manchester, UK 1979 volumes, 600 pages unpublished still the most comprehensive compilation of cross section data (RBS + NRA) 54

57 Cross Section Data Sources () Data compilation by R.P. Cox et al. for J.R. Tesmer and M. Nastasi, Handbook of Modern Ion Beam Analysis, MRS 1995 Digitised (or tabulated) data from original publications in RTR file format These data are available at SigmaBase: ibaserver.physics.isu.edu/sigmabase/ or Also included in the computer code SIMNRA Data compilation by M. Mayer since 1996 Digitised (or tabulated) data from original publications (or authors) in R33 file format Most of these data are available at SigmaBase Included in the computer code SIMNRA 55

58 Index History Scattering geometry and kinematics Rutherford cross section and limitations RBS spectra from thin and thick films Stopping power and energy loss Detector resolution Energy loss straggling Cross sections from selected light elements -incident 1 H - incident 4 He 56

59 1 C(p,p) 1 C High to very high cross section 100 C(p,p)C, θ = above 500 kev Typical energies for RBS: 1500 or 500 kev smooth cross section easy data evaluation, thick layers 1740 kev maximum sensitivity Cross Section [Ratio to Rutherford] Amirikas 170 Amirikas Fit 170 Mazzoni 170 Liu 170 Rauhala 170 Jackson 168. Amirikas Fit 165 Mazzoni 165 Gurbich E [kev] SIMNRA Home Page 57

60 14 N(p,p) 14 N High to very high cross section N(p,p) 14 N but: large scatter of data Cross Section [Ratio to Rutherford] Ramos 178 Rauhala 170 Guohua 170 Olness 167 Lambert E [kev] SIMNRA Home Page 58

61 16 O(p,p) 16 O 16 O(p,p) 16 O High to very high cross section Typical energies for RBS: 1500 or 500 kev smooth cross section together with C 3470 kev maximum sensitivity Cross Section [Ratio to Rutherford] Ramos 178 Amirikas 170 Gurbich E [kev] SIMNRA Home Page 59

62 7 Al(p,p) 7 Al 7 Al(p,p) 7 Al Small cross section 4 Many resonances complicated spectrum Not useful for RBS with protons Cross Section [Ratio to Rutherford] 3 1 Rauhala 170 Chiari 170 Chiari E [kev] SIMNRA Home Page 60

63 Si(p,p)Si Small cross section advantageous if used as substrate Typical energies for RBS: kev small background from substrate 1670 or 090 kev maximum sensitivity Cross Section [Ratio to Rutherford] Si(p,p)Si Amirikas 170 Amirikas Fit Rauhala 170 Vorona 167. Salomonovic 160 Salomonovic 170 Gurbich E [kev] SIMNRA Home Page 61

64 Index History Scattering geometry and kinematics Rutherford cross section and limitations RBS spectra from thin and thick films Stopping power and energy loss Detector resolution Energy loss straggling Cross sections from selected light elements - incident 1 H -incident 4 He 6

65 1 C(α,α) 1 C Small cross section at E < 3000 kev not suitable for RBS High and smooth cross section around 4000 kev Maximum sensitivity at 470 kev J.R. Tesmer and M. Nastasi, Handbook of Modern Ion Beam Materials Analysis, MRS,

66 14 N(α,α) 14 N Small cross section at E < 3000 kev not suitable for RBS Several useful resonances at higher energies J.R. Tesmer and M. Nastasi, Handbook of Modern Ion Beam Materials Analysis, MRS,

67 16 O(α,α) 16 O Widely used resonance at 3040 kev J.R. Tesmer and M. Nastasi, Handbook of Modern Ion Beam Materials Analysis, MRS,

68 7 Al(α,α) 7 Al nat Si(α,α) nat Si Many resonances and small cross sections not suitable for RBS J.R. Tesmer and M. Nastasi, Handbook of Modern Ion Beam Materials Analysis, MRS,

69 Computer Simulation Codes Spectrum simulator Depth resolution Depth profile Program Author Since RUMP M. Thompson 1983 Cornell University USA RBX E. Kótai 1985 Research Institute for Particle and Nuclear Physics Hungary SIMNRA M. Mayer 1996 Max-Planck-Institute for Plasma Physics Germany DEPTH E. Szilágyi 1994 Research Institute for Particle and Nuclear Physics Hungary WINDF N. Barradas 1997 Technological and Nuclear Institute Sacavem Portugal 67