Converse piezoelectric effect in [111] strained-layer heterostructures

Abstract

Strained-layer heterostructures grown along the [111] crystal direction, such as GaAs-${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As-GaAs, are often embedded in the intrinsic region of a p-i-n diode so that an electric field can be applied during the study of their optical properties. The layers comprising the heterostructure are usually lattice matched to a crystal substrate that provides in-plane mechanical constraints on the heterostructure. We investigate the effect of these constraints on the magnitude of the converse piezoelectric effect in the strained layer. Minimizing the free energy of a strained layer that is in an external electric field and subject to mechanical constraints, we obtain the equation of state for the strained layer that relates the internal electric field to the strain along the [111] growth axis. For the GaAs-${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As-GaAs system grown on a (111) B GaAs substrate, the mechanical constraints on the ${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum well decrease the magnitude of the converse piezoelectric effect 24% below that of a free ${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As film with the same internal electric field.