Stark shift and field-induced tunneling in ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs quantum-well structures

Within the framework of the effective-mass approximation, a method is developed using the time-dependent and the time-independent Schrödinger equations to describe electron behavior in quantum wells in both low- and high-field regions. In low-field regions, the energy states are determined by the time-independent Schrödinger equation, which is applicable if the electron is confined. In high-field regions, field-induced tunneling occurs and the tunneling of the particles must be described by the time-dependent Schrödinger operator because of the lack of energy eigenstates. This method improves upon the time-independent analysis of other works which do not adequately describe the high-electric-field regions.