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 an AlxGa1-xAs heterostructure with a 2DEG a distance d from a (100) surface of the crystal where the SAW's are propagated in the [011] direction at wave vector q. It is found that the velocity shift Delta upsilon(s) and the attenuation coefficient kappa satisfy the well known equation (Delta upsilon(s)/upsilon(s)) - (i kappa/q) = (alpha(2)/2)/[1 + i sigma(xx)(q,omega)/sigma(m)], where sigma(xx)(q,omega) is the complex conductivity at wave vector q and frequency omega = upsilon(s)q with upsilon(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.