Quantum wells

A quantum well (QW) is a heterostructure in which one thin-well layer is surrounded by two barrier layers. This layer is so thin that both electrons and holes are quantized. The electronic and the optical properties of quantized states offer new opportunities in developing practical devices, such as QW infrared photo-detectors, quantum cascade lasers, all-optical switches, modulators, and many others [1,2,3,4]. Hence, it is very important to obtain eigenvalues and wave functions for the design of the active region in these optoelectronic devices based on QW structures. In this chapter, we review theoretical formalism to calculate eigenvalues and wave functions of (001)-oriented zinc-blende and (0001)-oriented wurtzite QW structures [5,6,7,8,9,10]. We block diagonalize zinc-blende and wurtzite Luttinger-Kohn 6 × 6 Hamiltonians for the valence bands to two 3 × 3 Hamiltonians, which have analytical solutions for eigenvalues and eigenvectors. We derive several important forms such as interband optical matrix elements and optical gains [11,12,13,14,15]. Also, as a numerical example, we calculate eigenvalues and wave functions for zinc-blende and wurtzite Hamiltonians using a finite-difference method (FDM) [4]. On the basis of this information, we discuss crystal orientation effects on electronic and optical properties of strained zinc-blende and wurtzite QW structures, including the Hamiltonian for nonpolar wurtzite QW structures.