Multivalley Effective-Mass Approximation for Donor States in Silicon. I. Shallow-Level Group-V Impurities
- 15 November 1971
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 4 (10), 3468-3481
- https://doi.org/10.1103/physrevb.4.3468
Abstract
Following the procedures of the Kohn-Luttinger one-valley effective-mass approximation (EMA), but without neglecting the intervalley overlap terms, a multivalley EMA is developed within the pseudopotential formalism for shallow-level group-V donors in silicon. A phenomenological two-parameter model impurity potential is proposed which behaves like a square well at small and a screened Coulomb potential at large . The relative smoothness of the model impurity potential compared with the true impurity potential justifies the use of the EMA. Within the EMA, the valley-orbit interaction can be incorporated completely in the energy calculations, instead of treated as a perturbation. The effects of the higher-energy subsidiary valleys and the coupling etc. can also be estimated quantitatively in this EMA. The energy levels of the group- donor impurities in silicon are calculated using the variation method. The two potential parameters are adjusted to fit the observed and transition energies. It is shown that the proposed potential describes well the central-cell effects. For the states, it is found that the usual one-valley approximation is adequate. It is also found that in the multivalley approximation the valley-orbit interaction shifts the level downward and the and levels upward relative to the one-valley level. The effects of the uncertainty in the position of the conduction-band valleys and of the coupling between the and states on the ground-state energy are shown to be negligible. The contribution from wave-function components of an valley of the conduction band to the ground-state energy is computed to be less than 1% of that from wave-function components of valley. It indicates that the higher-energy subsidiary conduction-band valleys may be neglected. The ground-state-model wave function is used to calculate the photo-ionization cross section and to predict the Fermi contact hyperfine constants. These results are compared with reported experimental and theoretical results.
Keywords
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