Skip to main content
Erschienen in: Physics of Metals and Metallography 11/2018

01.11.2018 | STRUCTURE, PHASE TRANSFORMATIONS, AND DIFFUSION

On the Theory of Atomic Diffusion after Ion Implantation

verfasst von: A. G. Kesarev, V. V. Kondratyev, I. L. Lomaev

Erschienen in: Physics of Metals and Metallography | Ausgabe 11/2018

Einloggen

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

An analytical solution to the problem of atomic diffusion after ion implantation (taking into account the drift of impurity atoms) in a semi-infinite medium characterized by a nonuniform distribution of nonequilibrium vacancies is obtained using asymptotic methods in the theory of differential equations. This solution can be used at annealing times that are longer than the setting time for the steady-state nonuniform distribution of vacancies originating from the implantation region, but correspond to a diffusion length that is shorter than the characteristic scale of variation of the impurity diffusion coefficient. This work analyzes the applicability of this solution in the general form. It has been compared to the results of numerical calculations for an exponential coordinate dependence of the vacancy density with the drift of atoms, which results from the nonuniform distribution of nonequilibrium vacancies, either taken into account or neglected. The concentration profiles of implanted aluminum in silicon at the initial stage of diffusion are calculated within the proposed approach.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat T. Iton, T. Inada, and K. Kanekawa, “Doping of silicon by ion implantation,” Appl. Phys. Lett. 12, 244–246 (1968).CrossRef T. Iton, T. Inada, and K. Kanekawa, “Doping of silicon by ion implantation,” Appl. Phys. Lett. 12, 244–246 (1968).CrossRef
2.
Zurück zum Zitat T. Iton and I. Ohdomari, “Analysis of radiation-enhanced diffusion of aluminium in silicon,” J. Appl. Phys. 41, 434–436 (1970).CrossRef T. Iton and I. Ohdomari, “Analysis of radiation-enhanced diffusion of aluminium in silicon,” J. Appl. Phys. 41, 434–436 (1970).CrossRef
3.
Zurück zum Zitat M. Kurata, Y. Morikawa, K. Nagami, and H. Kuroda, “Remarks on the vacancy mechanisms in ion implantation,” Jpn. J. Appl. Phys. 12, 472–473 (1973).CrossRef M. Kurata, Y. Morikawa, K. Nagami, and H. Kuroda, “Remarks on the vacancy mechanisms in ion implantation,” Jpn. J. Appl. Phys. 12, 472–473 (1973).CrossRef
4.
Zurück zum Zitat V. M. Zelevinskaya, G. A. Kachurin, and N. B. Pridachin, “Acceleration of impurity diffusion by preliminary ion bombardment,” Fiz. Tekh. Poluprovodn. 8, 394–396 (1974). V. M. Zelevinskaya, G. A. Kachurin, and N. B. Pridachin, “Acceleration of impurity diffusion by preliminary ion bombardment,” Fiz. Tekh. Poluprovodn. 8, 394–396 (1974).
5.
Zurück zum Zitat J. Kowall, D. Peak, and J. W. Corbett, “Impurity–concentration profile for an exponentially decaying diffusion coefficient in irradiation enhanced diffusion,” Phys. Rev. B 13, 477–478 (1976).CrossRef J. Kowall, D. Peak, and J. W. Corbett, “Impurity–concentration profile for an exponentially decaying diffusion coefficient in irradiation enhanced diffusion,” Phys. Rev. B 13, 477–478 (1976).CrossRef
6.
Zurück zum Zitat E. W. Maby, “Bombardment-enhanced diffsusion of arsenic in silicon,” J. Appl. Phys. 47, 830–836 (1976).CrossRef E. W. Maby, “Bombardment-enhanced diffsusion of arsenic in silicon,” J. Appl. Phys. 47, 830–836 (1976).CrossRef
7.
Zurück zum Zitat V. L. Arbuzov, B. N. Goshchitskii, S. E. Danilov, A. V. Kozlov, V. D. Parkhomenko, N. L. Pecherkina and V. V. Sagaradze, “Interactions between radiation defects and interstitial impurities in nickel microalloyed with carbon and boron under electron and neutron irradiation,” Phys. Met. Metallogr. 118, 507–515 (2017).CrossRef V. L. Arbuzov, B. N. Goshchitskii, S. E. Danilov, A. V. Kozlov, V. D. Parkhomenko, N. L. Pecherkina and V. V. Sagaradze, “Interactions between radiation defects and interstitial impurities in nickel microalloyed with carbon and boron under electron and neutron irradiation,” Phys. Met. Metallogr. 118, 507–515 (2017).CrossRef
8.
Zurück zum Zitat V. A. Shabashov, V. V. Sagaradze, A. E. Zamatovskii, K. A. Kozlov and N. V. Kataeva, “Radiation-induced atomic redistribution in aging Fe–Ni Alloys upon neutron irradiation,” Phys. Met. Metallogr. 118, 846–858 (2017).CrossRef V. A. Shabashov, V. V. Sagaradze, A. E. Zamatovskii, K. A. Kozlov and N. V. Kataeva, “Radiation-induced atomic redistribution in aging Fe–Ni Alloys upon neutron irradiation,” Phys. Met. Metallogr. 118, 846–858 (2017).CrossRef
9.
Zurück zum Zitat A. E. Ermakov, V. L. Gapontsev, V. V. Kondrat’ev, and Yu. N. Gornostyrev, “Deformation-induced phase instability in nanocrystalline alloys,” Phys. Met. Metallogr. 88, 211–218 (1999). A. E. Ermakov, V. L. Gapontsev, V. V. Kondrat’ev, and Yu. N. Gornostyrev, “Deformation-induced phase instability in nanocrystalline alloys,” Phys. Met. Metallogr. 88, 211–218 (1999).
10.
Zurück zum Zitat A. G. Kesarev and V. V. Kondrat’ev, “On the phase separation in nanostructured solid solutions under the effect of a flux of nonequilibrium vacancies,” Phys. Met. Metallogr. 102, 10–17 (2006).CrossRef A. G. Kesarev and V. V. Kondrat’ev, “On the phase separation in nanostructured solid solutions under the effect of a flux of nonequilibrium vacancies,” Phys. Met. Metallogr. 102, 10–17 (2006).CrossRef
11.
Zurück zum Zitat V. V. Kondratyev, A. G. Kesarev, and I. L. Lomaev, “Grain boundary diffusion in nanocrystalline materials produced by severe plastic deformation,” Diffus. Found. 5, 129–143 (2015).CrossRef V. V. Kondratyev, A. G. Kesarev, and I. L. Lomaev, “Grain boundary diffusion in nanocrystalline materials produced by severe plastic deformation,” Diffus. Found. 5, 129–143 (2015).CrossRef
12.
Zurück zum Zitat A. G. Kesarev and V. V. Kondrat’ev, “To the theory of diffusion in inhomogeneous media: Short times of the process,” Phys. Met. Metallogr. 106, 327–331 (2008).CrossRef A. G. Kesarev and V. V. Kondrat’ev, “To the theory of diffusion in inhomogeneous media: Short times of the process,” Phys. Met. Metallogr. 106, 327–331 (2008).CrossRef
13.
Zurück zum Zitat A. G. Kesarev, V. V. Kondrat’ev and I. L. Lomaev, “On diffusion theory in inhomogeneous media: Thin-film source of diffusant,” Phys. Met. Metallogr. 118, 872–878 (2017).CrossRef A. G. Kesarev, V. V. Kondrat’ev and I. L. Lomaev, “On diffusion theory in inhomogeneous media: Thin-film source of diffusant,” Phys. Met. Metallogr. 118, 872–878 (2017).CrossRef
14.
Zurück zum Zitat A. Naife, Introduction to Perturbation Techniques (Wiley, New York, 1981; Mir, Moscow, 1984). A. Naife, Introduction to Perturbation Techniques (Wiley, New York, 1981; Mir, Moscow, 1984).
15.
Zurück zum Zitat G. N. Gaidukov and B. Ya. Lyubov, “Averaged equation of diffusion,” Fiz. Met. Metalloved. 39, 1097–1100 (1975). G. N. Gaidukov and B. Ya. Lyubov, “Averaged equation of diffusion,” Fiz. Met. Metalloved. 39, 1097–1100 (1975).
16.
Zurück zum Zitat R. Sh. Malkovich, “On the analysis of coordinate-dependent diffusion,” Tech. Phys. 51, 283–286 (2006).CrossRef R. Sh. Malkovich, “On the analysis of coordinate-dependent diffusion,” Tech. Phys. 51, 283–286 (2006).CrossRef
17.
Zurück zum Zitat V. A. Ditkin and A. P. Prudnikov, A Handbook of Operational Calculus (Vysshaya Shkola, Moscow, 1965). V. A. Ditkin and A. P. Prudnikov, A Handbook of Operational Calculus (Vysshaya Shkola, Moscow, 1965).
18.
Zurück zum Zitat Handbook of Special Functions, Ed. by M. Abramovits (Nauka, Moscow, 1979) [in Russian]. Handbook of Special Functions, Ed. by M. Abramovits (Nauka, Moscow, 1979) [in Russian].
19.
Zurück zum Zitat A. G. Kesarev and V. V. Kondrat’ev, “On the theory of diffusion in inhomogeneous media: Long times of the process,” Phys. Met. Metallogr. 108, 30–37 (2009).CrossRef A. G. Kesarev and V. V. Kondrat’ev, “On the theory of diffusion in inhomogeneous media: Long times of the process,” Phys. Met. Metallogr. 108, 30–37 (2009).CrossRef
Metadaten
Titel
On the Theory of Atomic Diffusion after Ion Implantation
verfasst von
A. G. Kesarev
V. V. Kondratyev
I. L. Lomaev
Publikationsdatum
01.11.2018
Verlag
Pleiades Publishing
Erschienen in
Physics of Metals and Metallography / Ausgabe 11/2018
Print ISSN: 0031-918X
Elektronische ISSN: 1555-6190
DOI
https://doi.org/10.1134/S0031918X18110078

Weitere Artikel der Ausgabe 11/2018

Physics of Metals and Metallography 11/2018 Zur Ausgabe