Coupling of Surface Acoustic Waves to a Two Dimensional Electron Gas

When a surface acoustic wave (SAW) is coupled piezoelectrically to a two dimensional electron gas (2DEG), a velocity shift and attenuation of the SAW are induced that reflect the conductivity of the 2DEG. This paper considers the case of a AlGaAs heterostructure with a 2DEG a distance $d$ from a (100) surface of the crystal where the SAWs are propagated in the [011] direction at wavevector $q$. It is found that the velocity shift $\Delta v_s$ and the attenuation coefficient $\kappa$ satisfy the well known equation $(\Delta v_s/v_s) - (i \kappa/q) = (\alpha^2/2)/\left(1 + \frac{i \sigma_{xx}(q,\omega)} {\sigma_m}\right)$ where $\sigma_{xx}(q,\omega)$ is the complex conductivity at wavevector $q$ and frequency $\omega = v_s q$ with $v_s$ the velocity of the SAW. The coefficients $\alpha$ and $\sigma_m$ are calculated and it is found that $\alpha$ has a nontrivial dependence on the product $qd$.