SIZE QUANTIZATION OF HOLES IN A THIN FILM

Abstract

We describe a new method for determining the energy eigenstates of a quantum well in the multiple band envelope function approximation. A unitary transformation is used to diagonalize the 4×4 Luttinger-Kohn Hamiltonian into 2×2 blocks, making it more efficient to calculate the quantum well subband structure in both cases of infinite and finite quantum well models. Valence subbands of GaAs/Ga_1-xAl_xAs quantum wells are found by solving exactly the multiband effective mass equation for the envelope function, and then we impose boundary conditions for solutions of 2×2 block Hamiltonian. It is shown that the boundary conditions can change the sequence of energy subbands.