Abstract
The exact analytical solution of the diffusion trapping model for defect profiling using the variable energy positron beam is reported. The solution is based on the Green’s function valid for the case of a discreet step-like vacancy distribution. The solution is applied to the description of experimental data from slow positron beam measurements for samples of stainless steel exposed to high-energy proton multi-implantation. This implantation ensured to obtain an approximate step-like vacancy distribution. The measured annihilation line shape parameter versus positron incident energy is well described by this solution. The determined positron trapping rate, which is proportional to the concentration of vacancies induced during proton implantation, increases linearly with the total dose. The comparison with the commonly used VEPFIT numerical code is also performed. The presented solution can be an alternative to other numerical codes commonly used for evaluation of data from positron beam experiments.
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References
P.J. Schultz, K.G. Lynn, Rev. Mod. Phys. 60, 701 (1988)
R. Krause-Rehberg, H.S. Leipner, Positron Annihilation in Semiconductors, Defect Studies (Springer, Berlin, Heidelberg, New York, 2000)
J. Dryzek, Nucl. Instrum. Methods Phys. Res. B 196, 186 (2002)
G.C. Aers, K.O. Jensen, A.B. Walker, in Slow Positron Beam Techniques for Solids and Surfaces, vol. 303, ed. by E. Ottewitte, A.H. Weiss, AIP Conference Proceedings (AIP Press, New York, 1994), p. 13
A. van Veen, H. Schut, J. de Vries, R.A. Hakvoort, W.R. Ijmpa, in Positron beam for solids and surfaces, vol. 218, ed. by J. Schultz, G.R. Massoumi, P.J. Simpson, AIP Conference Proceedings (AIP Press, New York, 1990), p. 171
A.S. Saleh, J.W. Taylor, P.C. Rice-Evans, Appl. Surf. Sci. 149, 87 (1990)
G.C. Ares, in Positron Beams for Solids and Surfaces, ed. by P.J. Schultz, G.R. Massoumi, P. Simpson (AIP, New York, 1991)
V.A. Stephanovich, J. Dryzek, Phys. Lett. A 377, 3038 (2013)
J. Dryzek, P. Horodek, Nucl. Instrum. Methods Phys. Res. B 266, 4000 (2008)
V.J. Ghosh, D.O. Welch, K.G. Lynn, in Positron Beam Techniques for Solids and Surfaces, vol. 303, ed. by E. Ottewite, A.H. WeissSlow, Jackson Hole, Wyoming, AIP Conference Proceedings, New York (1994), p. 37
D.T. Britton, P.C. Rice-Evans, J.H. Evans, Philos. Mag. Lett. 57, 165 (1988)
J. Dryzek, P. Horodek, M. Wróbel, Wear 294–295, 264 (2012)
A.A. Sidorin, I. Meshkov, E. Ahmanova, M. Eseev, A. Kobets, V. Lokhmatov, V. Pavlov, A. Rudakov, S. Yakovenko, The LEPTA facility for fundamental studies of positronium physics and positron spectroscopy. Mater. Sci. Forum 733, 291 (2013)
A.A. Sidorin, I. Meshkov, E. Ahmanova, M. Eseev, A. Kobets, V. Lokhmatov, V. Pavlov, A. Rudakov, S. Yakovenko, Positron annihilation spectroscopy at LEPTA facility. Mater. Sci. Forum 733, 322 (2013)
J. Dryzek, http://www.ifj.edu.pl/~mdryzek/page_r18.html. Accessed 1 Aug 2013
J.F. Ziegler, M.D. Ziegler, J.P. Biersack, Nucl. Instrum. Methods Phys. Res. B 268, 1818 (2010)
J.F. Ziegler, J.P. Biersack, http://www.srim.org/SRIM/SRIMINTRO.htm. Accessed 10 April 2012
A.S. Saleh, J. Theor. Appl. Phys. 7, 39 (2013)
F. Lukáč, J. Čižek, I. Procházka, Y. Jirásková, D. Janičkovič, W. Anwand, G. Brauer, J. Phys: Conf. Ser. 443, 012025 (2013)
A.P. Knights, F. Malik, P.G. Coleman, Appl. Phys. Lett. 75, 466 (1999)
H.-E. Schaefer, Phys. Status Solidi A 102, 47 (1987)
Acknowledgments
The authors express their gratitude to M. Kulik, M. Turek, K. Pyszniak and A. Drozdziel for their technical help assistance at ion implantation.
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Dryzek, J., Horodek, P. The solution of the positron diffusion trapping model tested for profiling of defects induced by proton implanted in stainless steel. Appl. Phys. A 121, 289–295 (2015). https://doi.org/10.1007/s00339-015-9433-4
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DOI: https://doi.org/10.1007/s00339-015-9433-4