Linewidths of quantum well eigenstates with finite barriers

Abstract

The linewidth of quasi-bound eigenstates in quantum wells is an important parameter in understanding interband absorption in quantum confined Stark effect modulators, intersubband absorption in quantum well infrared detectors, tunneling phenomena in resonant tunneling diodes, and transport in quantum well transistors. We investigate the linewidths for the quasi-bound energy levels of a quantum well with finite barrier height and width as the barrier width is varied. For a GaAs/Al xGa 1−xAs quantum well with a barrier height of 240 meV, well width of 80 Å, and barrier widths varying from 30 to 80 Å, we find a linewidth for the ground state that increases from 0.06 meV at barrier width of 60 Å to 2.03 meV at 30 Å; for the excited state, the linewidth is significantly larger, increasing from 0.49 meV for a barrier width of 80 Å to 21.71 meV at 30 Å. The ground eigenstate has a narrow linewidth, less than 0.2 meV, for barrier widths greater than 50 Å indicating the applicability of the quasi-bound approximation, whereas the excited state is broad at all barrier widths less than 80 Å signifying large errors in the use of the quasi-bound approximation. The linewidths of both the ground and excited states are shown to be directly proportional to the transmission coefficient as determined by the Wentzel-Kramers-Brillouin (WKB) approximation, justifying its use in linewidth analysis in the literature.