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Stopping power of different ions in Si measured with a bulk sample method and Bayesian inference data analysis

N.P. Barradas1,2, E. Alves1,2, Z. Siketić3, I. Bogdanović Radović3

(1)Instituto Tecnológico e Nuclear, E.N. 10 , Sacavém 2686-953, Portugal (2) Centro de Física Nuclear da Universidade de Lisboa, Av. Prof. Gama Pinto 2, Lisboa, Portugal (3)Ruđer Bošković Institute, P.O. Box 180, Zagreb 10002 , Croatia

Abstract. The accuracy of ion beam analysis experiments depends critically on the stopping power values available. While for H and He ions accuracies normally better than 5% are achieved by usual interpolative schemes such as SRIM, for heavier ions the accuracy is worse. One of the main reasons is that the experimental data bases are very sparse, even for important materials such as Si. New measurements are therefore needed. Measurement of stopping power is often made with transmission in thin films, with the usual problems of film thickness homogeneity. We have previously developed an alternative method based on measuring bulk spectra, and fitting the yield by treating the stopping power as a fit parameter in a Bayesian inference Markov chain Monte Carlo procedure included in the standard IBA code NDF. We report on improvements of the method and on its application to the determination of the stopping power of 7Li in Si. To validate the method, we also apply it to the stopping of 4He in Si, which is known with 2% accuracy. Keywords: electronic stopping, RBS, silicon PACS: 06.20.Fn, 02.50.Ga, 34.50.Bw, 61.18.Bn

INTRODUCTION method based on measuring bulk spectra, and fitting the yield by treating the stopping power as a fit Quantification of the depth scale in ion beam parameter in a Bayesian inference Markov chain analysis techniques such as Rutherford backscattering Monte Carlo procedure included in the standard IBA 4,5 (RBS), Elastic Recoil Detection Analysis, or Nuclear code NDF. We report on improvements of the Reaction Analysis depends on knowledge of the method and on its application to the determination of 7 stopping powers involved. The accuracy of the the stopping power of Li ions in Si. To validate the 4 experiments thus depends crucially on the stopping method, we first apply it to the stopping of He in Si, 6 power values available. Given that not all ion/target which is known with a 2% accuracy , and with 0.6% 7 pairs have been measured, interpolative schemes such accuracy at a 1.5 MeV beam energy. as SRIM1 or MSTAR2 are often used. The accuracy of SRIM is 4.2% for H and 4.1% for EXPERIMENTAL DETAILS He ions. However, for Li and heavier ions the accuracy is only 5.1% and 6.1%, respectively.3 These We self-amorphised Si by implanting Si at liquid numbers are averages, and are not the uncertainty for a nitrogen temperature, with 5×1015 at/cm2 at 340 keV given system. For instance, for heavy ions 42% of and 5×1015 at/cm2 at 100 keV. This leads to an stopping power values calculated with SRIM2008 are amorphous Si layer 300 nm thick (see Figure 1a). off from the experimental ones by more than 5%. Then an Au marker layer around 20 nm thick was One of the main reasons is that the experimental deposited. data bases are sparse, even for important materials The 4He RBS experiments at 0.5, 1.0, 1.5, 2.0 and such as Si. Therefore, new measurements are needed 2.4 MeV were done at ITN at an 179.9º scattering to improve experimental data bases. Stopping power angle using an annular detector. The 7Li RBS measurements are most often performed using thin experiments at 1.0, 1.5, 2.0, 2.5 and 3.0 MeV were transmission films, with the usual problems of film done at the Ruđer Bošković Institute using three thickness homogeneity. detectors simultaneously, at 118º, 150º and 165º We have previously developed an alternative scattering angles. The energy calibration was made using the narrow 991.88 keV resonance in 27Al(p,γ)28S, samples.14 We have also used these methods to analyse and the neutron threshold reaction 7Li(p,n)7Be at the ambiguity of ellipsometry data.15 1880.6 keV. Basically, the method consists in treating the The exact Au areal density was determined to be stopping power function as a free parameter, and 116.8(1.1)×1015 at/cm2 from the 1.5 MeV 4He fitting the energy spectra. In our case, the a1-a8 experiment (see Figure 1b). At this energy, a careful parameters of the ZBL85 parameterisation16 are the analysis of the certified standard free parameters, ensuring that the shape of the IRMM0001/BAML003 released by IRMM, Geel8,9, stopping curve is realistic. A large number of different has shown that SRIM2008 stopping power of 4He in Si simulations are made, all with a different stopping is correct with an uncertainty of 0.6%.7 The total power curve, but all leading to simulations consistent 0.97% error in the Au content includes errors from with the data within the experimental uncertainties. statistics, background determination (namely pile-up), Other parameters such as the energy calibration or the and from the uncertainty in the angle of incidence. detector dead layer thickness (which leads to changes in the calculated yield17,18), are also varied during the procedure. In the end, a consistent estimate of the

20000 errors can be made taking the average and standard a) 2 MeV 4He in Si - channelled Au deviation of all stopping curves that led to a good fit. 10000 Note that the Au areal density was fixed during the )

s BI/MCMC at the value determined from the 1.5 MeV t

n 6000 4 u c-Si a-Si He experiment. The corresponding 0.97% error was o c

then added to the BI/MCMC error. d

l 4000 e i Y 2000 RESULTS

4 0 For the He data, we constructed a Markov chain 50 100 150 200 250 300 350 400 with 60000 elements, that is, 60000 stopping power Channel data sets in the energy range up to 3 MeV. Each of Au 150000 b) 1.5 MeV 4He in Si - SRIM2008 these data sets leads to RBS spectra that simultaneously fit the five experimental spectra well, 100000 i.e. within experimental errors. The final results are ) s t shown in Figure 2, where the BI/MCMC is given as

n 50000 u

o the two curves, corresponding to the average plus c

d minus one standard deviation. l e

i 20000 Y

4 0 80 He in Si 50 100 150 200 250 300

Channel ) 2 60 m c / t

FIGURE 1. a) Channelled He spectrum. The 1

4 1 40

amorphised region is clearly seen. b) 1.5 MeV He /

V e spectrum. The simulations use SRIM2008 stopping. ( SRIM2008

S 20 KKKNS [ BI/MCMC BAYESIAN INFERENCE 0 Full details of the Bayesian inference (BI) method 0 500 1000 1500 2000 E (keV) with Markov chain Monte Carlo (MCMC) integration as applied to stopping power determination is given in.4 The improvements reported in Ref. 10 were also FIGURE 2. Confidence limits (± 1) obtained for the 4He in Si stopping power with BI/MCMC. SRIM20081 used. We have previously reported a similar Bayesian 6 approach to the determination of the error of the depth and KKKNS stopping are also shown. profiles extracted from IBA spectra11 for high 12 13 The results agree very well both with SRIM2008 resolution data , RBS/ERD data and to extract 6 scattering cross sections from bulk and thin film and with KKKNS stopping values, which validates the present approach. Note that at low energies, below 500 keV, the deviation seen is within two standard The final results are shown in Fig. 4, together with deviations, so it is statistically not significant. The SRIM2008 and other experimental measurements.22-27 deviation might be due to the notorious difficulties in The results indicate a slightly lower maximum than simulating the yield at low energies19, even when given by SRIM2008, and slightly higher stopping at double scattering20 and pile-up21 were included in the low energies, but always within three standard simulations. deviations. This shows that SRIM2008 is For the 7Li data, we constructed a Markov chain fundamentally correct. with 15000 elements. The smaller length of the Markov chain is justified because 15 spectra (3 per beam energy, corresponding to the three detectors) 7 120 Li in Si were collected, leading to more information in the data. We show three of the spectra in Fig. 3, together 100 ) 2 with simulations using SRIM2008 stopping and the m c 80 / t a

average value determined in this work. An 5 1

0 60 1

improvement in the simulation is seen particularly at / Ap70 [22] low energies. Note that the minimum energy probed is V e Hof76 [23]

] Sa84 [24]

around 0.3 MeV, corresponding to the way out in the 1 S

[ Liu96 [25] MeV experiment. 20 SRIM2008 Jia99 [26] BI/MCMC Aze02 [27] 0

0 500 1000 1500 2000 2500 3000 20000 Au E (keV) 7 Li 2.5 MeV,  =150º 10000 scatt ) s

n FIGURE 4. Confidence limits (± 1) obtained for the Li in u

( 4000 Si stopping power with BI/MCMC. SRIM2008 and c-Si a-Si d

l 22-77

e different experimental stopping values are also shown. i

Y 2000 DS+PUP 0 100 200 300 740 760 780 800 SUMMARY 20000 7 Li 1.5 MeV,  =150º Au scatt

10000)

s We reported on a method to determine the stopping t n

u c-Si a-Si o of ions in matter using bulk samples. We validated the c (

4000 4 d

l method by determining the stopping of He in Si and e i Y 2000 comparing the results with the highly accurate current DS+PUP knowledge. We then applied to the determination of 0 7 50 100 150 400 420 440 460 the stopping power of Li in Si in the 0.3-3 MeV

20000 range. 7 Li 1 MeV,  =150º Au 10000 scatt ) s t

n 4000 ACKNOWLEDGMENTS u

o a-Si c (

d l e i 2000 We would like to thank the International Atomic Y DS+PUP Energy Agency for support under the Research 0 Contracts No. 14635 and 14580. 60 80 100 240 260 280 300 Channel REFERENCES FIGURE 3. Three of the 15 spectra collected with the 7Li beam. Simulations using SRIM2008 stopping and 1. J.F. Ziegler, Nucl. Instrum. Methods Phys. Res. B 219, the average value found in this work are also shown. 1027 (2004). The vertical dashed lines indicate, for 1.5 and 2.5 2. N.P. Barradas, C. Jeynes, R.P. Webb, E. Wendler, Nucl. MeV, where the a-Si layer begins. For 1 MeV, only Instrum. Methods Phys. Res. B 194, 15 (2002). the a-Si layer is probed, and the vertical dashed line 3. C. Pascual-Izarra, N. P. Barradas, G. García, A. Climent.Font, Nucl. Instrum. Methods Phys. Res. B 239, indicates the ROI for the fit. DS+PUP indicate the 135 (2005). calculated double scattering and pile-up. 4. G. Konac, S. Kalbitzer, C. Klatt, D. Niemann, R. Stoll, Nucl. Instrum. Methods Phys. Res. B136-138, 159 (1998). 5. N.P. Barradas, K. Arstila, G. Battistig, M. Bianconi, N. Dytlewski, C. Jeynes, E. Kótai, G. Lulli, M. Mayer, E. Rauhala, E. Szilágyi, M. Thompson, Nucl. Instrum. Methods Phys. Res. B 262, 281 (2007). 6. K.H.Ecker, A.Berger, R.Grötzschel, L.Persson, U. Wätjen, Nucl. Instrum. Methods Phys. Res. B 175, 797 (2001). 7. K. H. Ecker, U. Wätjen, A. Berger, L. Persson, W. Pritzcow, M. Radtke, H. Riesemeier, Nucl. Instrum. Methods Phys. Res. B 188, 120 (2002). 8. N.P. Barradas, C. Jeynes, Nucl. Instrum. Methods Phys. Res. B 266, 1875 (2008). 9. N.P.Barradas, C.Jeynes, M.Jenkin, P.K.Marriott, Thin Solid Films 343-344, 31 (1999). 10. N.P.Barradas, A.P.Knights, C.Jeynes, O.A.Mironov, T.J.Grasby, E.H.C.Parker, Phys. Rev. B59, 5097 (1999). 11. N.P.Barradas, S.A.Almeida, C.Jeynes, A.P.Knights, S.R.P.Silva, B.J.Sealy, Nucl. Instrum. Methods Phys. Res. B 148, 463 (1999). 12. N.P. Barradas, A.R. Ramos, E. Alves, Nucl. Instrum. Methods Phys. Res. B 266, 1180 (2008). 13. N.P.Barradas, J.L.Keddie, R.Sackin, Phys.Rev.E 59, 6138 (1999). 14. J. F. Ziegler, J. P. Biersack, and U. Littmark, in Stopping and Ranges of Ions in Solids Publisher, Pergamon, New York, 1985. 15. W.N. Lennard, H. Geissel, K.B. Winterbon, D. Phillips, T.K. Alexander, J.S. Forster, Nucl. Instrum. Methods Phys. Res. A 248, 454 (1986). 16. C. Pascual-Izarra, N. P. Barradas, Nucl. Instrum. Methods Phys. Res. B 266, 1866 (2008). 17. N. P. Barradas, Nucl. Instrum. Methods Phys. Res. B 261, 418 (2007). 18. N.P. Barradas, Nucl. Instrum. Methods Phys. Res. B 225, 318 (2004). 19. N.P. Barradas, M. Reis, X-Ray Spectrometry 35, 232 (2006). 20. F.Apel, U.Mueller-Jahrreiss, G.Rockstroh, S.Schwabe, Phys.stat.solidi(a) 3, K173 (1970). 21. I.Hoffmann, E.Jäger, U.Müller-Jahreis, Rad.Effects 31, 57 (1976). 22. D.C.Santry, R.D.Werner, Nucl. Instrum. Methods Phys. Res. B 1, 13 (1984). 23. Jiarui Liu, Zongshuang Zheng, Wei-Kan Chu, Nucl. Instrum. Methods Phys. Res. B 118, 24 (1996). 24. W.Jiang, R.Grötzschel, W.Pilz, B.Schmidt, W.Möller, Phys.Rev. B59, 226 (1999). 25. G.de M.Azevedo, M.Behar, J.F.Dias, P.L.Grande, D.L.da Silva, Phys. Rev. B65, 075203 (2002).