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Journal of Computational Electronics

, Volume 13, Issue 1, pp 338–351 | Cite as

Scattering of electrons by ionized impurities in semiconductors: quantum-mechanical approach to third body exclusion

  • Dmitry Pozdnyakov
Article
  • 208 Downloads

Abstract

As applied to the numerical simulation of electron transport and scattering processes in semiconductors an efficient model describing the scattering of electrons by the ionized impurities is proposed. On the example of GaAs at 77 and 300 K and Si at 300 K the dependencies of low-field electron mobility on the donor impurity concentration in the semiconductors are calculated in the framework of proposed model as well as in the framework of such most frequently used applied models as the Conwel-Weisskopf model and the Brooks-Herring one. After comparing the calculation results with the well-known experimental data it has been ascertained that the best agreement between the theory and experiment is achieved with application of the proposed model.

Keywords

Ionized impurity Scattering Electron mobility Monte Carlo simulation 

Notes

Acknowledgements

This work was funded by Belarusian State University within the project “Development of physico-mathematical models, algorithms and software for Monte Carlo simulation of submicron SOI MOSFETs” which is the part of Belarusian State Research Program “Electronics and Photonics”, under Grant No. 1.1.03.

References

  1. 1.
    Conwell, E.M., Weisskopf, V.F.: Theory of impurity scattering in semiconductors. Phys. Rev. 77, 388–390 (1950) CrossRefMATHGoogle Scholar
  2. 2.
    Brooks, H.: Scattering by ionized impurities in semiconductors. Phys. Rev. 83, 879 (1951) Google Scholar
  3. 3.
    Ridley, B.K.: Reconciliation of the Conwell-Weisskopf and Brooks-Herring formulae for charged-impurity scattering in semiconductors: Third-body interference. J. Phys. C, Solid State Phys. 10, 1589–1593 (1977) CrossRefGoogle Scholar
  4. 4.
    Chattopadhyay, D., Queisser, H.J.: Electron scattering by ionized impurities in semiconductors. Rev. Mod. Phys. 53, 745–768 (1981) CrossRefGoogle Scholar
  5. 5.
    Ridley, B.K.: Quantum Processes in Semiconductors. Oxford University Press, New York (1999) Google Scholar
  6. 6.
    Kopf, Ch., Kaiblinger-Grujin, G., Kosina, H., Selberherr, S.: Reexamination of electron mobility dependence on dopants in GaAs. In: Grünbacher, H. (ed.) Proceedings of 27th European Solid-State Device Research Conference, Stuttgart, pp. 304–307 (1997) Google Scholar
  7. 7.
    Kosina, H.: Efficient evaluation of ionized-impurity scattering in Monte Carlo transport calculations. Phys. Status Solidi A 163, 475–489 (1997) CrossRefGoogle Scholar
  8. 8.
    Kaiblinger-Grujin, G., Kosina, H., Selberherr, S.: Influence of the doping element on the electron mobility in n-silicon. J. Appl. Phys. 83, 3096–3101 (1998) CrossRefGoogle Scholar
  9. 9.
    Sotoodeh, M., Khalid, A.H., Rezazadeh, A.A.: Empirical low-field mobility model for III–V compounds applicable in device simulation codes. J. Appl. Phys. 87, 2890–2900 (2000) CrossRefGoogle Scholar
  10. 10.
    Poklonski, N.A., Kocherzhenko, A.A., Vyrko, S.A., Vlassov, A.T.: A comparison of two-particle models for conduction electron scattering on hydrogen-like impurity ions in non-degenerate semiconductors. Phys. Status Solidi B 244, 3703–3710 (2007) CrossRefGoogle Scholar
  11. 11.
    Jacaboni, C., Reggiani, L.: The Monte Carlo method for the solution of charge transport in semiconductors with applications to covalent materials. Rev. Mod. Phys. 55, 645–705 (1983) CrossRefGoogle Scholar
  12. 12.
    Jacaboni, C., Lugli, P.: The Monte Carlo Method for Semiconductor Device Simulation. Springer, Wien (1989) CrossRefGoogle Scholar
  13. 13.
    Hess, K. (ed.): Monte Carlo Device Simulation: Full Band and Beyond. Kluwer Academic, Boston (1991) MATHGoogle Scholar
  14. 14.
    Ivaschenko, V.M., Mitin, V.V.: Simulation of Kinetic Phenomena in Semiconductors. The Monte Carlo Method. Naukova Dumka, Kiev (1990) (in Rusian) Google Scholar
  15. 15.
    Bonch-Bruevich, V.L., Kalashnikov, S.G.: The Physics of Semiconductors. Nauka, Moscow (1990) (in Russian) Google Scholar
  16. 16.
    Davydov, A.S.: Quantum mechanics. Pergamon, New York (1991) Google Scholar
  17. 17.
    Newton, R.G.: Scattering Theory of Waves and Particles. Dover, New York (2002) MATHGoogle Scholar
  18. 18.
    Pozdnyakov, D.V., Galenchik, V.O., Borzdov, V.M., Komarov, F.F., Zhevnyak, O.G.: Ionized impurity and surface roughness scattering rates of electrons in semiconductor structures with one-dimensional electron gas and broadened energy levels. Phys. Low-Dimens. Struct. 1, 19–24 (2006) Google Scholar
  19. 19.
    Mensky, M.B.: Quantum Measurements and Decoherence: Models and Phenomenology. Kluwer Academic, Dordrecht (2000) CrossRefGoogle Scholar
  20. 20.
    Querlioz, D., Nguyen, H.-N., Saint-Martin, J., Bournel, A., Galdin-Retailleau, S., Dollfus, Ph.: Wigner-Boltzmann Monte Carlo approach to nanodevice simulation: from quantum to semiclassical transport. J. Comput. Electron. 8, 324–335 (2009) CrossRefGoogle Scholar
  21. 21.
    Moore, E.J.: Quantum-transport theories and multiple scattering in doped semiconductors, II: mobility of n-type gallium arsenide. Phys. Rev. 160, 618–626 (1967) CrossRefGoogle Scholar
  22. 22.
    Van de Roer, T.G., Widdershoven, F.P.: Ionized impurity scattering in Monte Carlo calculations. J. Appl. Phys. 59, 813–815 (1986) CrossRefGoogle Scholar
  23. 23.
    Meyer, J.R., Bartoli, F.J.: Phase-shift calculation of ionized impurity scattering in semiconductors. Phys. Rev. B 23, 5413–5427 (1981) CrossRefGoogle Scholar
  24. 24.
    Kuchar, F., Fantner, E., Hess, K.: Ionized impurity scattering in semiconductors: InSb doped by neutron irradiation. J. Phys. C, Solid State Phys. 9, 3165–3171 (1976) CrossRefGoogle Scholar
  25. 25.
    Sarker, A.Q.: Localized states in semiconductors: isocoric impurities in Si and Ge. J. Phys. C, Solid State Phys. 10, 2617–2632 (1977) CrossRefGoogle Scholar
  26. 26.
    Pantelides, S.T.: The electronic structure of impurities and other defects in semiconductors. Rev. Mod. Phys. 50, 797–858 (1978) CrossRefGoogle Scholar
  27. 27.
    Pantelides, S.T., Sah, C.T.: Theory of localized states in semiconductors, I: new results using an old method. Phys. Rev. B 10, 621–637 (1974) CrossRefGoogle Scholar
  28. 28.
    Pantelides, S.T., Sah, C.T.: Theory of localized states in semiconductors, II: the pseudo impurity theory application to shallow and deep donors in silicon. Phys. Rev. B 10, 638–658 (1974) CrossRefGoogle Scholar
  29. 29.
    Mansour, N.S., Diff, K., Brennan, K.F.: Comparison of different formulations of the electron–plasmon scattering rate and the dispersion relation on bulk semiconductor transport. J. Appl. Phys. 69, 6506–6509 (1991) CrossRefGoogle Scholar
  30. 30.
    Pop, E., Dutton, R.W., Goodson, K.E.: Analytical band Monte Carlo model for electron transport in Si including acoustic and optical phonon dispersion. J. Appl. Phys. 96, 4998–5005 (2004) CrossRefGoogle Scholar
  31. 31.
    Fischetti, M.V.: Effect of the electron-plasmon interaction on the electron mobility in silicon. Phys. Rev. B 44, 5527–5534 (1991) CrossRefGoogle Scholar
  32. 32.
    Sernelius, B.E.: Temperature-dependent resistivity of heavily doped silicon and germanium. Phys. Rev. B 41, 3060–3068 (1990) CrossRefGoogle Scholar
  33. 33.
    Meyer, J.R., Bartoli, F.J.: Ionized-impurity scattering in the strong-screening limit. Phys. Rev. B 36, 5989–6000 (1987) CrossRefGoogle Scholar
  34. 34.
    Stringfellow, G.B.: Electron mobility in AlXGa1−XAs. J. Appl. Phys. 50, 4178–4183 (1979) CrossRefGoogle Scholar
  35. 35.
    Yanchev, I.Y., Arnaudov, B.G., Evtimova, S.K.: Electron mobility in heavily doped gallium arsenide due to scattering by potential fluctuations. J. Phys. C, Solid State Phys. 12, L765–L769 (1979) CrossRefGoogle Scholar
  36. 36.
    Baccarani, G., Ostoja, P.: Electron mobility empirically related to the phosphorus concentration in silicon. Solid-State Electron. 18, 579–580 (1975) CrossRefGoogle Scholar
  37. 37.
    Li, S.S., Thurber, W.R.: The dopant density and temperature dependence of electron mobility and resistivity in n-type silicon. Solid-State Electron. 20, 609–616 (1977) CrossRefGoogle Scholar
  38. 38.
    Jacoboni, C., Canali, C., Ottaviani, G., Quaranta, A.A.: A review of some charge transport properties of silicon. Solid-State Electron. 20, 77–89 (1977) CrossRefGoogle Scholar
  39. 39.
    Masetti, G., Solmi, S.: Relationship between carrier mobility and electron concentration in silicon heavily doped with phosphorus. Solid-State Electron Dev. 3, 65–68 (1979) CrossRefGoogle Scholar
  40. 40.
    Masetti, G., Severi, M., Solmi, S.: Modeling of carrier mobility against carrier concentration in arsenic-, phosphorus-, and boron-doped silicon. IEEE Trans. Electron Devices 30, 764–769 (1983) CrossRefGoogle Scholar
  41. 41.
    Fistul, V.I., Omelyanovskii, E.M., Pelevin, O.V., Ufimtsev, V.B.: Influence of impurity individuality on impurity scattering and polytropy in gallium arsenide. Izv. Akad. Nauk SSSR, Neorg. Mater. 2, 657–658 (1966) (in Russian) Google Scholar
  42. 42.
    Bohm, D.: Quantum Theory. Dover, New York (1989) Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Faculty of Radiophysics and Computer TechnologiesBelarusian State UniversityMinskBelarus

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