# Deep Impurity Levels in Semiconductors, Semiconductor Alloys, and Superlattices

## Abstract

Impurity levels determine the electrical properties of semiconductors and often strongly influence the optical properties as well. Until rather recently it was widely believed that “shallow impurities,” namely those impurities that produce energy levels within ≃0.1 eV of a band edge, were well understood in terms of hydrogenic effective-mass theory [1]. However “deep impurities” were regarded as more mysterious, having levels more than 0.1 eV deep in the gap; and several theoretical attempts were made to understand why their binding energies were so large. While specific deep levels were explained rather well by the early theories, most notably the pioneering work of Lannoo and Lenglart on the deep level in the gap associated with the vacancy in Si [2], numerous attempts to explain why the binding energy of a particular level might be large (making the level deep), rather than small, continued until recently, when it was realized that this basic picture of impurity levels was incomplete [3,4].

## Keywords

Alloy Composition Deep Level Band Edge Shallow Level Valence Band Maximum## Preview

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## References

- [1]W. Kohn, in Solid State Physics (edited by F. Seitz and D. Turnbull, Academic Press, New York, 1957) Vol. 5, p. 258–321Google Scholar
- [1a]J. M. Luttinger and W. Kohn, Phys. Rev. 97, 969 (1955).ADSCrossRefGoogle Scholar
- [2]M. Lannoo and P. Lenglart, J. Phys. Chem. Solids 30, 2409 (1969).ADSCrossRefGoogle Scholar
- [3]H. P. Hjalmarson, P. Vogl, D. J. Wolford, and J. D. Dow, Phys. Rev. Letters 44, 810 (1980); see also Ref. [4] for the concepts that form the foundation of this work.ADSCrossRefGoogle Scholar
- [4]W. Y. Hsu, J. D. Dow, D. J. Wolford, and B. G. Streetman, Phys. Rev. B 16, 1597 (1977).ADSCrossRefGoogle Scholar
- [5]S. Y. Ren, W. M. Hu, O. F. Sankey, J. D. Dow, Phys. Rev. B 26, 951 (1982).ADSCrossRefGoogle Scholar
- [6]S. Y. Ren, Scientia Sinica 27, 443 (1984).Google Scholar
- [7]D. J. Wolford, W. Y. Hsu, J. D. Dow, and B. G. Streetman, J. Lumin. 18/19, 863 (1979).CrossRefGoogle Scholar
- [8]A. A. Maradudin, E. W. Montroll, and G. H. Weiss, Solid State Phys. Suppl. 3, 132 (1963).MathSciNetGoogle Scholar
- [9]H. P. Hjalmarson and T. J. Drummond, Appl. Phys. Letters 48, 657 (1986); see also Ref. [10].ADSCrossRefGoogle Scholar
- [10]J. C. M. Henning and J. P. M. Ansems, Mat. Sci. Forum 10–12, 429 (1986)CrossRefGoogle Scholar
- [10a]J. C. M. Henning and J. P. M. Ansems, Semicond. Sci. Technol. 2, 1 (1987)ADSCrossRefGoogle Scholar
- [10b]A. K. Saxena, Solid State Electron. 25, 127 (1982).ADSCrossRefGoogle Scholar
- [11]See also, J. W. Farmer, H. P. Hjalmarson, and G. A. Samara, Proc. Mater. Res. Soc, 1987, to be published.Google Scholar
- [12]S. Y. Ren, J. D. Dow, and J. Shen, “Deep impurity levels in semiconductor superlattices,” to be published. See also Ref. [21].Google Scholar
- [13]J. D. Dow, in Highlights of Condensed Matter Theory (Proc. Intl. School of Phys. “Enrico Fermi” Course 89, Varenna, 1983) ed. by F. Bassani, F. Fumi, and M. P. Tosi (Societa Italiana di Fisica, Bologna, Italy, and North Holland, Amsterdam, 1985), pp. 465 et seq.Google Scholar
- [14]J. S. Nelson, C. Y. Fong, I. P. Batra, W. E. Pickett, and B. M. Klein, unpublished.Google Scholar
- [15]P. Vogl, H. P. Hjalmarson, and J. D. Dow, J. Phys. Chem. Solids 44, 365 (1983).ADSCrossRefGoogle Scholar
- [16]The tight-binding formalism we use here is hybrid-based. For bulk semiconductors the hybrid-based tight-binding formalism is equivalent to the widely used atomic-orbital based tight-binding formalism. But for superlattices these two formalisms are different: because the atomic-orbital based tight-binding parameters are obtained by fitting to the band structure of bulk GaAs and bulk AℓAs, the tight-binding parameters for the As atom at
*ß*=0 (which is considered to be an As atom in GaAs) are usually different from the corresponding tight-binding parameters for the atom at*ß*=2N_{1}(which is considered to be an As atom in AℓAs). But both of these As atoms are interfacial As atoms and physically are completely equivalent to each other. The way we correct for this problem is that we consider the hybrids h_{1}and h_{4}of the As atom at*ß*=0 to be hybrids of GaAs, while h_{2}and h_{3}are taken to be AℓAs hybrids. Similarly, h_{2}and h_{3}of the As atom at*ß*=2N_{1}are considered to be hybrids in GaAs, and h_{1}and h_{4}, are AℓAs hybrids. We believe that this properly accounts for the correct physics and the nature of interfacial bonds.Google Scholar - [17]D. J. Wolford, T. F. Kuech, J. A. Bradley, M. A. Grell, D. Ninno, and M. Jaros, J. Vac. Sci. Technol. B4, 1043 (1986).Google Scholar
- [18]In our model, which uses low-temperature band gaps, we take the valence band offset for Aℓ
_{0.7}Ga_{0.3}As to be 0.334 eV below the valence band edge of GaAs.Google Scholar - [19]S. Y. Ren and J. D. Dow, “Special points for superlattices and strained bulk semiconductors,” Phys. Rev. B, in press.Google Scholar
- [20]The defect potential matrix elements are related to the difference in atomic energies of the impurity and the host atom it replaces: \( {V_\ell } = {\beta _\ell }\left( {{w_{impurity}}\left( \ell \right) - {w_{host}}\left( \ell \right)} \right) + {C_\ell } \) where we have ℓ = s or p,
*ß*= 0.8, and*ß*_{P}= 0.6, and the atomic orbital energies w can be found in Table 3 of Ref. [15]. The constant C_{ℓ}is zero in Ref. [3], but here we take C_{S}= 1.434 eV in order to have the Si deep level in GaAs appear 0.234 eV above the conduction band minimum, where it is observed [12], instead of 0.165 eV below it, thereby compensating for the small theoretical uncertainty.Google Scholar - [21]R.-D. Hong, D. W. Jenkins, S. Y. Ren, and J. D. Dow, Proc. Materials Research Soc. 77, 545–550 (1987), Interfaces, Superlattices, and Thin Films, ed. J. D. Dow and I. K. Schuller.CrossRefGoogle Scholar