Coupling of Surface Acoustic Waves to a Two Dimensional Electron Gas

TL;DR

This paper investigates how surface acoustic waves interact with a two-dimensional electron gas in an AlGaAs heterostructure, revealing how the velocity shift and attenuation relate to the 2DEG's conductivity and how these effects depend on the system's parameters.

Contribution

It provides a detailed theoretical analysis of the coupling between surface acoustic waves and a 2DEG, including explicit formulas and the dependence of coupling coefficients on system parameters.

Findings

Velocity shift and attenuation are related to the 2DEG conductivity.

The coupling coefficient α depends nontrivially on the product qd.

Explicit expressions for the velocity shift and attenuation are derived.

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 $\Delta v_s$ 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 $qd$.