The in ̄uence of strain on con®ned electronic states in semiconductor quantum structures

A continuum ®nite element technique is adopted to study electronic properties of submicron electronic devices where function hinges on quantum mechanical e€ects. Of particular interest is the in ̄uence of mechanical strain on con®ned electronic states. The steady state Schr odinger equation, which governs the electronic behavior of such devices, is modi®ed to include the potential induced by a strain ®eld 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 ®nite element mesh which is more re®ned in regions where large quantum mechanical wave function gradients are expected. Multiple energy bands and three-dimensional structures can be considered, and e€ects including strain enhanced charge con®nement 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 ®eld in the structures is found to a€ect the energies of experimentally accessible con®ned states and in some cases to enhance quantum mechanical con®nement. Ó 2001 Elsevier Science Ltd. All rights reserved.