Effects of uniaxial stress on hole subbands in semiconductor quantum wells. I. Theory

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Abstract
The valence subbands and the corresponding wave functions in semiconductor quantum wells under uniaxial stress are analyzed by solving a 4×4 Luttinger-Kohn Hamiltonian together with a 4×4 strain Hamiltonian in the spin J=(3/2 basis. Appropriate boundary conditions are obtained by integrating the total Hamiltonian across the interfaces of the quantum wells and, if a proper unitary transformation is made, yield eight linear equations that determine the eigenenergies and eigenfunctions. The results of our general formalism can be greatly simplified for some special cases which are used as examples in order to explore the underlying physics. The causes of the valence-band mixing, the effect of the valence-band warping, and the behavior of the hole effective masses under uniaxial stress are discussed. The numerical results are presented in a paper to follow.