Influence of strain on confined electronic states in semiconductor quantum structures

A continuum finite element technique is adopted to study electronic properties of submicron electronic devices where function hinges on quantum mechanical effects. Of particular interest is the influence of mechanical strain on confined electronic states. The steady state Schrodinger equation, which governs the electronic behavior of such devices, is modified to include the potential induced by a strain field which is present as a consequence of the fabrication. The governing equation is cast in a variational form, and it is discretized on a standard finite element mesh which is more refined in regions where large quantum mechanical wave function gradients are expected. Multiple energy bands and three-dimensional structures can be considered, and effects including strain enhanced charge confinement and strain induced energy band mixing are studied. As examples, a Ge [5 0 1] faceted island, or quantum dot, on a Si substrate and a Ge v-groove quantum wire on a Si substrate are considered. The technique is used to determine size ranges in which these devices are expected to be most useful. The nonuniform mismatch strain field in the structures is found to affect the energies of experimentally accessible confined states and in some cases to enhance quantum mechanical confinement.