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 ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As 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 Δ${\mathit{v}}_{\mathit{s}}$ and the attenuation coefficient κ satisfy the well known equation (Δ${\mathit{v}}_{\mathit{s}}$/${\mathit{v}}_{\mathit{s}}$)-(iκ/q)=(${\mathrm{\alpha }}^2$/2)/[1+i${\mathrm{\sigma }}_{\mathit{xx}}$(q,ω)/σ ${}_{\mathit{m}}{}^{}{}_{}{}^{}]$, where ${\mathrm{\sigma }}_{\mathit{xx}}$(q,ω) is the complex conductivity at wave vector q and frequency ω=${\mathit{v}}_{\mathit{sq}}$ with ${\mathit{v}}_{\mathit{s}}$ the velocity of the SAW. The coefficients α and ${\mathrm{\sigma }}_{\mathit{m}}$ are calculated and it is found that α has a nontrivial dependence on the product qd. © 1996 The American Physical Society.