Quantum resonances in the valence bands of zinc-blende semiconductors. I. Theoretical aspects

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Abstract
Quantum resonances in the valence bands of semiconductors under uniaxial stress provide very detailed information on the band parameters if the experimental data can be analyzed on the basis of an adequate theoretical model. Such a model has been developed for and applied to Ge by Hensel and Suzuki and yielded high-precision band parameters for this material. The theory which is based on the invariant expansion of the valence-band Hamiltonian and makes use of the symmetry of the diamond lattice fails, however, to explain similar experiments for InSb. The reason for this failure is twofold: The reduced symmetry of the zinc-blende lattice makes it necessary to consider inversion-asymmetry-induced contributions to the effective Hamiltonian; the small gap of InSb requires an exact treatment of the couplings between valence band and lowest conduction band. Here we present a theory to overcome these difficulties. An effective Hamiltonian, acting in the eightfold space of the valence band and the lowest conduction band of a zinc-blende-type material, is constructed by invariant expansion. For this purpose the method of invariants is extended to the cross space between valence band and conduction band on the basis of the angular momentum calculus. The Hamiltonian describes the Landau levels of valence and conduction bands under uniaxial stress for magnetic fields (parallel to the stress) along the high-symmetry [001], [111], and [110] directions. Since the Hamiltonian is constructed on group-theoretical grounds, the eigenstates can be classified according to their transformation properties, and selection rules are given for both inter- and intraband transitions.