Study of the ideal-vacancy-induced neutral deep levels in III-V compound semiconductors and their ternary alloys

A study of the behavior of ideal-vacancy-induced deep levels in six III-V compound semiconductors (GaSb, GaAs, GaP, InSb, InAs, and InP) and some of their ternary alloys is presented. The aim is to explore and expose (via a comparative study of a series of materials) the important ingredients necessary for a quantitatively reliable calculation of such levels. The Koster-Slater Green's-function technique is employed in conjunction with a linear combination of atomic orbitals description of the electronic structure of the perfect solid. It is established that a reliable description of the bulk-solid charge distribution, in addition to the bulk band energies, is essential for a quantitatively reliable calculation of the deep-level energies. This is true regardless of the particular method of description of the solid employed in such calculations. Here, the simplicity and flexibility of the empirical tight-binding description is used to establish the above-noted results. The established correlation between the photothreshold and ionicity of these materials is exploited to impose additional constraints on the empirically determined tight-binding parameters employed here for the different materials. This ensures a correct qualitative trend in the ionicity of the materials, and consequently in the overall charge distribution, implied by the tight-binding parameters employed. It is found that with increasing ionicity of the material, the anion and cation vacancy-induced deep levels move towards conduction and valence bands, respectively. Focusing attention on GaAs, a material for which differing results employing the empirical tight-binding method have been reported, we show that the differing nature of these and the present results is a consequence of the differences in the perfect-solid charge distribution implied by the tight-binding parameters employed, even though the band energies are equally well reproduced in all cases. This fact manifests itself in the same systematic trend, as noted above, found when the GaAs vacancy levels are plotted against the ionicity of GaAs implied by these different tight-binding parameters. The importance of the need for a correct charge distribution is confirmed via a calculation which employs a significantly different set of parameters for GaAs but which maintains the same ionicity and accuracy in the band energies and is found to produce essentially the same vacancy levels. A critical examination of the contributions of individual bands to the appropriate Green's function which determine the vacancy levels is presented. This analysis further underscores the need for an accurate determination of the band energies and eigenfunctions of the perfect solid for a quantitatively reliable calculation of deep levels. Results for the behavior of the vacancy-induced deep levels in some ternary alloys are obtained in the virtual-crystal approximation (VCA). The levels are found not to track the band extrema, revealing the true nature of the deep level. It is pointed out, however, that the VCA results can be substantially modified in systems where quantitative (alloy) disorder may be significant. Finally, a discussion of the results is provided in light of the few experimental results which serve as a guideline on the correctness of the ideal-vacancy-level positions obtained here. In particular, the recently proposed model for pinning of Fermi energy in Schottky barriers and metal-insulator-semiconductor structures by defect-induced states near surfaces is discussed in light of the results of the present study.