Density of states in finite-barrier quantum wells

Abstract

Density of states in finite-barrier quantum wells is examined critically. In the infinite barrier limit, the two-dimensional (2D) density of states (DOS) has been shown to correspond to the bulk case.1 When finite wells are considered, this correspondence may no longer hold. In this paper, we propose a modification to the finite-well DOS, which retains the elegance of the infinite-well case while preserving the effects of the finite barrier. This is accomplished by either defining an effective infinite-well width that matches the parameters of the finite well or by defining a new effective mass. Both approaches are based on rigorous calculations of the quantized wave vectors. In the spirit of the effective mass concept, we concentrate on the latter case, particularly in the limits of very thin and very thick wells. We investigate the relationship between the DOS and the quantum-well effective mass, based on the allowed wave vectors. Examples will be given illustrating the conventional definition of 2D DOS, the modified DOS, and their comparison with the bulk case.