Method of envelope functions and intervalley Γ-Xz interaction of states in (001) III-V semiconductor heterostructures

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The kp method is used to analyze the problem of intervalley Γ-Xz interaction of conduction band states in the (001) lattice-matched III-V semiconductor heterostructures. A convenient basis for expansion of the wave function is systematically selected and a multiband system of equations is derived for the envelope functions which is then reduced to a system of three equations for three valleys (Γ₁, X₁, and X₃) by using a unitary transformation. Intervalley Γ-Xz mixing is described by short-range potentials localized at heterojunctions. The expressions for the parameters determining Γ-Xz mixing strength explicitly contain the chemical composition profile of the structure since mixing is naturally stronger for abrupt heterojunctions than for structures with a continuously varying chemical composition. It is shown that the direct Γ₁-X₁ interaction of comparable strength to Γ₁-X₃ interaction exists. This must be taken into account when interpreting tunnel and optical experiments since X₁ valley is substantially lower in energy than X₃ valley.