Multivalley Effective-Mass Approximation for Donor States in Silicon. II. Deep-Level Group-VI Double-Donor Impurities

Abstract

It is suggested that the recently proposed two-parameter model impurity potentials of the shallow-level group-V donors in silicon may be scaled to give the model impurity potentials of the deep-level group-VI donors of the same row in the Periodic Table. It is shown that in the case of sulfur this suggestion follows naturally from examining the behavior of the true impurity potential in the central-cell region. By extending the multivalley effective-mass approximation (EMA) to singly ionized sulfur donors in silicon, using recently available optical data, it is found that indeed the potential parameters of sulfur are essentially identical to those of phosphorus, as expected from this model. A heliumlike model in the multivalley EMA is also developed and applied to the two-electron neutral group-VI donors in silicon. The calculated energy of neutral sulfur agrees well with observed thermal activation energy. Using the scaled model impurity potentials of As, Sb, and Bi, the energies of substitutional Se, Te, and Po in Si are predicted. It is also suggested that the same procedure may be applied to acceptor states. Holes bound to deep-level acceptors may be described simply by scaling the impurity potentials of the shallow-level group-III acceptors. The effects of the ${\Delta }_5$ valence band and the ${{\Delta }_2}^{\prime }$ conduction band on the deep-level donors are discussed. These effects are found to be small for singly ionized sulfur in silicon.