Optical absorption coefficient of quantum wires in strain and electric fields with intermixing interfaces

Abstract

We have theoretically studied the optical absorption coefficient of quantum wires in electric and strain fields with intermixing interfaces. The potential profiles are governed by the intermixing heterojunctions, internal strain due to the lattice mismatch, the external electric field and stress. The second Fick's law describes the wires' intermixing heterojunctions due to the alloy interdiffusion. We adopt the Green's function method to solve the Poisson equation for the displacement to determine the internal strain due to the lattice mismatch. The single-band Schr\"odinger equation in the effective mass approximation is used to describe the conduction subband structures while the four-band Kohn-Luttinger Hamiltonian is used to describe the valence subband structures. In solving the Schr\"odinger equation and the Kohn-Luttinger Hamiltonian, we expand the wave functions for the electrons and holes by using linear combinations of the two-dimensional harmonic oscillator wave functions to yield two matrix equations. These matrix equations are numerically solved for their eigen-energies and their corresponding eigenfunctions. We investigate some physical properties of the unstrained quantum wire $(\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{As})$ and the strained wire $(\mathrm{Cd}\mathrm{Se}∕\mathrm{Zn}\mathrm{Se})$ as examples. When the interdiffusion becomes stronger, on one hand, the internal strain is relaxed leading to the band gap shrinkage (if the initial strain ${\ensuremath{\epsilon}}_{0}<0$) and, on the other hand, the potential profiles are deformed and the effective band gap becomes wider. Variations of the transition energies with external stress show the anticrossing effect and variations of the transition energies with external electric field show the field emission effect. The hole effective masses can be enhanced or become electronlike by applying stress to the wire. The oscillator strengths of the dipole-allowed intersubband transitions for the $y$ and $z$ polarizations are calculated to infer possible optical transitions. The optical absorption coefficients together with the joint density of states are calculated.