Interaction of surface acoustic waves with a narrow electron channel in a piezoelectric material

Abstract

The interaction between a surface acoustic wave (SAW) of wave number $k$ and frequency $\ensuremath{\omega}$ and a two-dimensional electron gas in a piezoelectric semiconductor can be expressed in terms of the longitudinal conductivity ${\ensuremath{\sigma}}_{\mathrm{xx}}(k,\ensuremath{\omega})$ and an effective electromechanical coupling coefficient. The resulting velocity change and the attenuation of the transmitted SAW intensity are well known. In a recent paper, Simon [Phys. Rev. B 54, 13 878 (1996)] calculated the fractional energy change $\ensuremath{\Delta}U/U$ for a SAW interacting with a two-dimensional sheet embedded in a semi-infinite piezoelectric material and obtained a relationship with the results for the attenuation coefficient and the fractional velocity change. In this paper, $\ensuremath{\Delta}U/U$ is calculated for a narrow channel of width ${r}_{\ensuremath{\perp}}$ ${(kr}_{\ensuremath{\perp}}\ensuremath{\ll}1)$ at a distance $d$ below the surface of a slab of piezoelectric material of finite thickness when an elastic wave is launched on the surface. $\ensuremath{\Delta}U/U$ is given as a closed-form expression in terms of the velocity of the elastic wave, the elastic constants, and the piezoelectric tensor. Numerical results are presented for $\ensuremath{\Delta}U/U$ as a function of $\mathrm{kd}$ for several values of the thickness of a slab of ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$.