Hole subbands in strained GaAs-Ga1-xAlxAs quantum wells: Exact solution of the effective-mass equation

Valence subbands of uniaxially stressed GaAs-Ga1-xAlxAs quantum wells are found by solving exactly the multiband effective-mass equation for the envelope function; as in the particle in a box problem, we first solve the effective-mass equation in each bulk material, and then we impose boundary conditions on the linear combinations of bulk solutions. Discrete symmetries of the effective-mass Hamiltonian are used to decouple the spin-degenerate subbands; the energy levels are obtained as the zeros of an 8×8 determinant. The functional form of the wave functions is given analytically, and is used in order to discuss the heavy-hole light-hole mixing at finite values of the in-plane vector k?; the mixing greatly increases when the applied stress reduces the energy separation at k?=0. Resonances are shown to arise and are due to the degeneracy of discrete levels with states of the continuum at different values of k?. © 1987 The American Physical Society