1. The Stopping and Range of Slow Heavy Ions in Light Targets Valery Kuzmin Center of Applied Physics Flerov Laboratory of Nuclear Reactions Joint Institute for Nuclear Research Dubna, Russia

2. Motivation Key element of many modern and promise future nanotechnologies Modification of surface properties: –mechanical –electrical –magnetic –optical Conclusion on quality and reliability of approximations of the underlying theory. Introduction Ion Beam Analysis: –Low Energy Ion Scattering (LEIS) Synthesis of new materials

3. Approaches Transport Theory (Boltzmann equations forward / backward type) Method Monte-Carlo Molecular Dynamics Ab-initio Molecular Dynamics (Car-Parrinello method) Introduction

4. [ Taken from http://www.srim.org/ ] Introduction SRIM / TRIM (implementation of Ziegler-Biersack-Littmark theory) Common (and free of charge) available 92x92 Ion-Target pairs User-friendly interface Good accuracy IN AVERAGE

5. Taken from the paper: “Range Parameters of Heavy-Ions implanted into C-Films” by P.L. Grande, P.F.P. Fichtner, M. Behar, F.C. Zawislak, Nucl. Instr. and Meth. B 33 (1988) 122. Introduction Experimental data by 1) P.L. Grande, F.C. Zawislak, D. Fink, M. Behar, Nucl. Instr. and Meth. B61 (1991) 282 [GZFB]; 2) E. Friedland S. Kalbitzer, M. Hayes, C. Klatt, G. Konac, C. Langpape, ibid B136-138 (1998) 147 [FKHKKL].

6. Considerable discrepancies (20-40%) between predictions of the standard theory by Ziegler, Biersack and Littmark (ZBL) and experimental data by :  P.L. Grande, P.F.P. Fichtner, M. Behar, R.P. Livi, F.C. Zawislak, J.P. Biersack, D. Fink, P. Mertens, Nucl. Instr. and Meth. B 19-20 (1987) 25.  P.L. Grande, P.F.P. Fichtner, M. Behar, F.C. Zawislak, Nucl. Instr. and Meth. B 33 (1988) 122.  P.L. Grande, M. Behar, J.P. Biersack and F.C. Zawislak, Nucl. Instr. and Meth. B45 (1990) 689.  M. Behar, P.L. Grande, L. Amaral, J.R. Kaschny, F.C. Zawislak, R.B. Guimaraes, J.P. Biersack, D. Fink, Phys. Rev. B 41 (1990) 6145.  M. Behar, P.L. Grande, R. Wagner de Oliveira, J.P. Biersack, Nucl. Instr. and Meth. B59/60 (1991) 1.  P.L. Grande, F.C. Zawislak, D. Fink, and M. Behar, Nucl. Instr. and Meth. B61 (1991) 282. (GZFB)  P.F.P. Fichtner, M. Behar, D. Fink, P. Goppelt, P.L. Grande, Nucl. Instr. and Meth. B 64 (1992) 668.  P.F.P. Fichtner, M.R. Herberts, P.L. Grande, M. Behar, D. Fink, F.C. Zawislak, Nucl. Instr. and Meth. B 80-81 (1993) 53.  P.F.P. Fichtner, M.C. Herberts, P.L. Grande, M. Behar, Nucl. Instr. and Meth. B 85 (1994) 579. Range parameters for ions with 29 ≤ Z 1 ≤ 83 implanted into targets: Be, B, C, Si, BN, SiC, SiO 2, AZ1350 photoresist have been measured Conclusion: origin of the discrepancies between predictions of the standard theory and experimental data is a correlation between the nuclear and electronic stopping. Introduction

7. J.H. Liang, Nucl. Instr. and Meth. B 132 (1997) 29. K.M. Wang, F. Lu, M.Q. Ming, B.R. Shi, D.Y. Shen, Y.G. Liu, D. Fink, Nucl. Instr. and Meth. B 145 (1998) 271. K. M. Wang, H. Hu, F. Lu, F. Chen, J.H. Zhang, X.D. Liu, B.R. Shi, Y.G.Liu, Nucl. Instr. and Meth. B 174 (2001) 65. K.M. Wang, B.R. Shi, N Cue, D.Yu. Shen, F. Chen, X.L. Wang, F. Lu, Nucl. Instr. and Meth. B 225 (2004) 503.  V. Schüle, R. Günzler, P. Oberschachtsiek, M. Weiser and S.Kalbitzer, Nucl. Instr. and Meth. B62 (1992) 338  E. Friedland, S.Kalbitzer, M. Hayes, Ch. Klatt, G. Konac, Ch. Langpape, Nucl. Instr. and Meth. B136-138 (1998) 147. Introduction

8. The GZFB model Critical review of the GZFB model [Taken from: “Range parameters study of medium-heavy ions implanted into light substrates” by P.L. Grande, F.C. Zawislak, D. Fink, and M. Behar, Nucl. Instr. and Meth. B61 (1991) 282.]

9. The present approach. Ion interaction with target’s atoms/ions is separated into elastic part (nuclear stopping) and inelastic part (electronic stopping) which are considered as independent. Elastic scattering is described by the classical theory. Interatomic interaction potential is determined from the self-consistent first-principles calculations. Inelastic stopping is suggested to be velocity-proportional and given by experiment / theory. Range parameters are obtained by solution of (second order) range- projection equations or from Monte-Carlo simulations. Outline

10. Experimental value a = a F * 0.69 by W. Takeuchi, N. Matsuda, “New method of evaluation for interatomic interaction potential in LEIS with large-angle scattering using the two-atom scattering model”, Nucl. Instr. and Meth. B 266 (2008) 877. Interatomic Potential HOMO orbital, contour value 0.05Difference between the quasimolecular and the atomic electron densities He - Cu

11. O.B. Firsov, Sov. JETP 36 (1959) 1517. J. Lindhard, M.Scharff, and K. Schiøtt, Mat. Fys. Medd. Dan. Vid. Selsk., 33, no. 14, (1963), (LSS). D.J. Land, J.G. Brennan, Atom. Dat. and Nucl. Dat. Tabl. 22 (1978) 236, (LB). J.F. Ziegler, J.P. Biersack, U. Littmark, “The Stopping and Range of Ions in Solids”, Pergamon, New York, 1985 (ZBL) [Taken from the paper by N.R. Arista, Nucl. Instr. and Meth. B 195 (2002) 91.] W.N. Lennard, H. Geissel, D.P. Jackson, D. Phillips, Nucl. Instr. and Meth. B 13 (1986) 127, (LGJP). Electronic Stopping

12. [ Taken from the paper by P.Sigmund, Eur. Phys. J. D 47 (2008) 45 ] Reciprocity Firsov, Sov. JETP 36 (1959) 1517. Lindhard and Scharff, Phys. Rev. 124 (1961) 128

13. Au – C V. Kuzmin, Nucl. Instr. and Meth. B 249 (2006) 13.

14. Au – C Experimental Data from Helmut Paul’s collection at http://www.exphys.uni- linz.ac.at/stopping/ and by W.N. Lennard, H. Geissel, D.P. Jackson, D. Phillips, Nucl. Instr. and Meth. B 13 (1986) 127.http://www.exphys.uni- linz.ac.at/stopping/

15. Au – C V. Kuzmin, Nucl. Instr. and Meth. B 249 (2006) 13. Experimental data by P.L. Grande, F.C. Zawislak, D. Fink, and M. Behar, Nucl. Instr. and Meth. B61 (1991) 282.

16. The Stopping and Range of Carbon in Gold V. Kuzmin, Nucl. Instr. and Meth. B 256 (2007) 105. Experimental data by E. Friedland, S.Kalbitzer, M. Hayes, Ch. Klatt, G. Konac, Ch. Langpape, Nucl. Instr. and Meth. B136-138 (1998) 147.

17. Cu – C Experimental data by P.L. Grande, F.C. Zawislak, D. Fink, and M. Behar, Nucl. Instr. and Meth. B61 (1991) 282.

18. Kr – C V. Kuzmin, Surf. Coat. Tech, 201 (2007) 8388. Experimental data by P.L. Grande, F.C. Zawislak, D. Fink, and M. Behar, Nucl. Instr. and Meth. B61 (1991) 282.

19. Xe – C V. Kuzmin, Surf. Coat. Tech, 201 (2007) 8388. Experimental data by P.L. Grande, F.C. Zawislak, D. Fink, and M. Behar, Nucl. Instr. and Meth. B61 (1991) 282.

20. Pb – C V. Kuzmin, Nucl. Instr. and Meth. B 249 (2006) 13. Experimental data by P.L. Grande, F.C. Zawislak, D. Fink, and M. Behar, Nucl. Instr. and Meth. B61 (1991) 282.

21. Bi – C Experimental data by P.L. Grande, F.C. Zawislak, D. Fink, and M. Behar, Nucl. Instr. and Meth. B61 (1991) 282.

22. Au – B V. Kuzmin, Nucl. Instr. and Meth. B 267 (2009) 2657. Experimental data by P.L. Grande, F.C. Zawislak, D. Fink, and M. Behar, Nucl. Instr. and Meth. B61 (1991) 282.

23. Au – Si Experimental data by P.L. Grande, P.F.P. Fichtner, M. Behar, F.C. Zawislak, Nucl. Instr. and Meth. B 33 (1988) 122. V. Kuzmin, Nucl. Instr. and Meth. B 267 (2009) 2657.

24. Au – BN Experimental data by P.F.P. Fichtner, M.R. Herberts, P.L. Grande, M. Behar, D. Fink, F.C. Zawislak, Nucl. Instr. and Meth. B 80-81 (1993) 53. V. Kuzmin, Nucl. Instr. and Meth. B 267 (2009) 2657.

25. Au – SiC Experimental data by P.F.P. Fichtner, M. Behar, D. Fink, P. Goppelt and P.L. Grande, Nucl. Instr. and Meth. B64 (1992) 668. V. Kuzmin, Nucl. Instr. and Meth. B 267 (2009) 2657.

26. In this work range parameters of Cu, Au, Pb and Bi ions implanted into elemental films of Be, B, C, Si and also into two- component films of BN and SiC at energies of about 10 – 400 keV are calculated and compared with available experimental data. Ab-initio level of theory as well as including of relativistic corrections in calculations of the interaction potentials do not change substantially final results. We can conclude that the origin of disagreements between the ZBL theory and available experimental data are inaccuracies of the ZBL potential and/or the ZBL electronic stopping power. At energy range in question correlation effects between the nuclear and electronic stopping can be neglected in range parameter calculations. Conclusions

27. Thank you