Mechanisms of defect pairing in semiconductors: A study for chalcogens in silicon

Carl M. Weinert; Matthias Scheffler

doi:10.1103/PhysRevLett.58.1456

Access by Xinjiang University

Mechanisms of defect pairing in semiconductors: A study for chalcogens in silicon

Carl M. Weinert and Matthias Scheffler

Physikalisch-Technische Bundesanstalt, D-3300 Braunschweig, Federal Republic of Germany

PDF

Phys. Rev. Lett. 58, 1456 – Published 6 April, 1987

DOI: https://doi.org/10.1103/PhysRevLett.58.1456

Abstract

Electronic-structure and total-energy calculations are reported for the vacancy and the substitutional and interstitial S, Se, and Te impurities in Si. We identify several mechanisms of impurity-impurity interactions. This theoretical study also serves to determine the dominant defect site of chalcogen pairs as two substitutionals.

References (18)

O. Madelung, Festkörpertheorie III (Springer-Verlag, Berlin, 1972).
W. E. Krag, W. H. Kleiner, H. J. Zeiger and S. Fischler, J. Phys. Soc. Jpn., Suppl. 21, 230 (1966).
G. W. Ludwig, Phys. Rev. 137, A1520 (1965).
P. Wagner, C. Holm, E. Sirtl, R. Oeder, and W. Zulehner, in Festkörperprobleme: Advances in Solid State Physics, edited by P. Grosse (Vieweg, Braunschweig, 1984), Vol. 24, p. 191.
E. Janzen, R. Stedman, G. Grossmann and H. G. Grimmeiss, Phys. Rev. B 29, 1907 (1984).
P. Wagner and C. Holm, in Proceedings of the Thirteenth International Conference on Defects in Semiconductors, Coronado, California, August 1984, edited by L. C. Kimerling and J. M. Parsey, Jr. (The Metallurgical Society of AIME, Warrendale, Pennsylvania, 1985), p. 677.
G. Pensl, G. Roos, C. Holm, and P. Wagner, in Defects in Semiconductors, edited by H. J. von Bardeleben, Materials Science Forum Vols. 10 – 12 (Trans Tech Publications, Rockport, Massachusetts, 1986), p. 911.
R. Wörner and O. F. Schirmer, Solid State Commun. 51, 665 (1984).
O. Gunnarsson, O. Jepsen and O. K. Andersen, Phys. Rev. B 27, 7144 (1983).
F. Beeler, M. Scheffler, O. Jepsen and O. Gunnarsson, Phys. Rev. Lett. 54, 2525 (1985).
For isolated substitutional S, Se, and Te impurities the lattice relaxation energies have been calculated to be between 0.1 and 0.8 eV [see M. Scheffler, in Proceedings of the Second International Conference on Shallow Impurity Centers, edited by A. Baldereschi (Elsevier, Amsterdam, to be published); C. M. Weinert and M. Scheffler, to be published]. For a defect pair we assume here (as a first approximation) that the lattice relaxation energy equals the sum of that of the isolated constituents. In particular for Te pairs this is likely an underestimate because of the strong short-distance repulsion between two Te atoms if forced at a 2.35- Å distance.
If the designation in Figs. 1(a) and 1(b) were made according to the $D_{3 d}$ point group, the $a_{1}$ states labeled as u would be $a_{2 u}$ and those labeled by g would be $a_{1 g}$ states.
The self-consistent calculations were performed within the pure density-functional, local-density-approximation theory. Thus, we have not modified the density-functional-theory, local-density-approximation band gap. As a consequence, the energy range $E_{v}$ < $E_{F}$ <= $E_{v}$ + 0.5 eV (Fig. 3) is truly calculated but the range $E_{F}$ > $E_{v}$ + 0.5 eV is an extrapolation.
The divacancy has two levels of $e_{u}$ and $e_{g}$ symmetry in the gap and resonances of symmetry $a_{1 g}$ and $a_{2 u}$ at the top of the valence band [see also S. T. Pantelides et al., Physica (Amsterdam) 116B, 18 (1983)]. The pair-binding energy of two isolated vacancies forming a divacancy is calculated as \(mi0.5, \(mi1.6, and \(mi1.7 eV in p-type, intrinsic, and n-type Si (Weinert and Scheffler, Ref. 11).
Alternatively, the electronic structure of a pair may be described as that of a perturbed isolated impurity atom. This picture was developed recently by O. F. Sankey and J. D. Dow, Solid State Commun. 51, 705 (1984).
Weinert and Scheffler, Ref. 11.
J. Bernholc, N. O. Lipari, S. T. Pantelides and M. Scheffler, Phys. Rev. B 26, 5706 (1982).
J. Bourgoin and M. Lannoo, Point Defects in Semiconductors I (Springer-Verlag, Berlin, 1982).

[c1] O. Madelung, Festkörpertheorie III (Springer-Verlag, Berlin, 1972).

[c2] W. E. Krag, W. H. Kleiner, H. J. Zeiger and S. Fischler, J. Phys. Soc. Jpn., Suppl. 21, 230 (1966).

[c3] G. W. Ludwig, Phys. Rev. 137, A1520 (1965).

[c4] P. Wagner, C. Holm, E. Sirtl, R. Oeder, and W. Zulehner, in Festkörperprobleme: Advances in Solid State Physics, edited by P. Grosse (Vieweg, Braunschweig, 1984), Vol. 24, p. 191.

[c5] E. Janzen, R. Stedman, G. Grossmann and H. G. Grimmeiss, Phys. Rev. B 29, 1907 (1984).

[c6] P. Wagner and C. Holm, in Proceedings of the Thirteenth International Conference on Defects in Semiconductors, Coronado, California, August 1984, edited by L. C. Kimerling and J. M. Parsey, Jr. (The Metallurgical Society of AIME, Warrendale, Pennsylvania, 1985), p. 677.

[c7] G. Pensl, G. Roos, C. Holm, and P. Wagner, in Defects in Semiconductors, edited by H. J. von Bardeleben, Materials Science Forum Vols. 10 – 12 (Trans Tech Publications, Rockport, Massachusetts, 1986), p. 911.

[c8] R. Wörner and O. F. Schirmer, Solid State Commun. 51, 665 (1984).

[c9] O. Gunnarsson, O. Jepsen and O. K. Andersen, Phys. Rev. B 27, 7144 (1983).

[c10] F. Beeler, M. Scheffler, O. Jepsen and O. Gunnarsson, Phys. Rev. Lett. 54, 2525 (1985).

[c11] For isolated substitutional S, Se, and Te impurities the lattice relaxation energies have been calculated to be between 0.1 and 0.8 eV [see M. Scheffler, in Proceedings of the Second International Conference on Shallow Impurity Centers, edited by A. Baldereschi (Elsevier, Amsterdam, to be published); C. M. Weinert and M. Scheffler, to be published]. For a defect pair we assume here (as a first approximation) that the lattice relaxation energy equals the sum of that of the isolated constituents. In particular for Te pairs this is likely an underestimate because of the strong short-distance repulsion between two Te atoms if forced at a 2.35- Å distance.

[c12] If the designation in Figs. 1(a) and 1(b) were made according to the $D_{3 d}$ point group, the $a_{1}$ states labeled as u would be $a_{2 u}$ and those labeled by g would be $a_{1 g}$ states.

[c13] The self-consistent calculations were performed within the pure density-functional, local-density-approximation theory. Thus, we have not modified the density-functional-theory, local-density-approximation band gap. As a consequence, the energy range $E_{v}$ < $E_{F}$ <= $E_{v}$ + 0.5 eV (Fig. 3) is truly calculated but the range $E_{F}$ > $E_{v}$ + 0.5 eV is an extrapolation.

[c14] The divacancy has two levels of $e_{u}$ and $e_{g}$ symmetry in the gap and resonances of symmetry $a_{1 g}$ and $a_{2 u}$ at the top of the valence band [see also S. T. Pantelides et al., Physica (Amsterdam) 116B, 18 (1983)]. The pair-binding energy of two isolated vacancies forming a divacancy is calculated as \(mi0.5, \(mi1.6, and \(mi1.7 eV in p-type, intrinsic, and n-type Si (Weinert and Scheffler, Ref. 11).

[c15] Alternatively, the electronic structure of a pair may be described as that of a perturbed isolated impurity atom. This picture was developed recently by O. F. Sankey and J. D. Dow, Solid State Commun. 51, 705 (1984).

[c16] Weinert and Scheffler, Ref. 11.

[c17] J. Bernholc, N. O. Lipari, S. T. Pantelides and M. Scheffler, Phys. Rev. B 26, 5706 (1982).

[c18] J. Bourgoin and M. Lannoo, Point Defects in Semiconductors I (Springer-Verlag, Berlin, 1982).

Physical Review Letters

Export citation

Export citation

Mechanisms of defect pairing in semiconductors: A study for chalcogens in silicon

Abstract

References (18)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation