Dependence of valence-subband dispersion relations on heterointerface boundary conditions in InxGa1−xAsyP1−y/InP narrow quantum wells

Abstract

In the framework of envelope function approximation, the dependence on heterointerface boundary conditions of valence-band dispersion relations in InP-based quantum-well structures is investigated. Under conventional boundary conditions, the root-finding calculation for the eigenvalue problem of quantum well structures is carried out while taking into account a large difference in the effective-mass parameters (the Luttinger parameters) among the constituting bulk materials. In spite of a decreasing interband mixing between heavy- and light-hole states due to strain and the quantum size effect, hole subband structure of a compressive-strained quantum well with a narrow well width is found to form an anomalous dispersion curve. It is clarified that the requirement for envelope continuity at interfaces is responsible for anomaly in the dispersion curves through off-diagonal terms with an additional δ-function-like interface potential in the valence-band effective-mass Hamiltonian. We present the results of dispersion relations and envelope functions related to a newly derived connection rule based on the tight-binding bond-orbital description, under which the envelopes are free from continuity restrictions at the interfaces regardless of any difference in the effective-mass parameters.