Electronic States in Quantum Wells and Superlattices

Abstract

In this contribution we are mainly interested in the electronic states of semiconductors quantum wells and superlattices. Such structures are simply viewed as a sequence of different semiconductor layers grown sucessively along a well defined crystalline growth direction. The carriers’ motion along this growth direction of the heterostructure (hereafter called the z direction) is then strongly modified by the presence of the various thin (≈100A) layers, whereas the translation symmetry (at the level of the bulk unitary cells) remains for the in-plane (x,y) directions. Single quantum wells present states which are localized in space around the well region for the z motion. Double quantum wells (DQW) consist of two well layers separated by a finite barrier layer. The localized states of the isolated quantum wells interact through the barrier region (tunnel interaction) to form the DQW eigenstates. The resulting new states are delocalized over the DQW region. For example, two identical wells (same thickness and material composition) give rise to symmetrical and antisymmetrical z-dependent DQW wavefunctions (with respect to the center of the central barrier). For wells of different thicknesses (asymmetrical DQW) the tunnel coupling is less efficient and each resulting DQW state presents a preferential localization around one of the two wells, reminiscent of the localized states of the isolated wells. In other words, the tunnel coupling is less effective to mix states of distinct quantum wells wich are misaligned in energy. Semiconductor superlattices (SL) consist of a periodic repetition of a fundamental cell composed by a sequence of wells and barriers. The simplest one consists of a well and a barrier (with eventually different thicknesses).