Coupling of Surface Acoustic Waves to a Two Dimensional Electron Gas

Abstract

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 $Δv_s$ and the attenuation coefficient $κ$ satisfy the well known equation $(Δv_s/v_s) - (i κ/q) = (α^2/2)/\left(1 + \frac{i σ_{xx}(q,ω)} {σ_m}\right)$ where $σ_{xx}(q,ω)$ is the complex conductivity at wavevector $q$ and frequency $ω= v_s q$ with $v_s$ the velocity of the SAW. The coefficients $α$ and $σ_m$ are calculated and it is found that $α$ has a nontrivial dependence on the product $qd$.