Self-consistent calculation of a two-dimensional electron gas in narrow and wide quantum wells of n-InGaAsP bounded by n-InP

Abstract

We present a self-consistent density-functional calculation of a two-dimensional electron gas (2DEG) in In x Ga 1−x As y P 1−y InP (x = 0.75, y = 0.5 and x = 0.53, y = 1) quantum wells, under the realistic assumption that both well and barrier consists of n-type material. Exchange and correlation effects are taken into account within the local-density approximation. We examine the effect of temperature on both the formation of the 2DEG and the width of the depletion layer, which, contrary to the assumption of the so-called quasi-accumulation approximation, is small in the system under study. As a function of material parameters, we calculate the density of the 2DEG and the energy eigenvalues. We give conditions which must be met by the donor concentration in the barrier, the acceptor concentration in the (partly compensated) well, and by the temperature in order to have a 2DEG in the well. We place special emphasis on the dependence of the results on the width of the quantum well. In narrow wells, the 2DEG is centered in the middle of the well, as is in the simple square-well approximation. With increasing well width, the density of the 2DEG does not change remarkably, but, as expected, the electrons are attracted to the InGaAsP/InP interfaces, and the electron density in the center of the well becomes negligibly small. Besides, in a wide quantum well at least two Subbands, if any, are filled, instead of one in a narrow well. These findings are of general interest, since they give evidence about the validity of the square-well or the single-interface approximation, which is interesting also for heterostructures of different materials.