Interaction of surface acoustic waves with a narrow electron channel in a piezoelectric material

The interaction between a surface acoustic wave (SAW) of wave number k and frequency ω and a two-dimensional electron gas in a piezoelectric semiconductor can be expressed in terms of the longitudinal conductivity σₓₓ(k,ω) and an effective electromechanical coupling coefficient. The resulting velocity change and the attenuation of the transmitted SAW intensity are well known. In a recent paper, Simon [Phys. Rev. B 54, 13 878 (1996)] calculated the fractional energy change ΔU/U for a SAW interacting with a two-dimensional sheet embedded in a semi-infinite piezoelectric material and obtained a relationship with the results for the attenuation coefficient and the fractional velocity change. In this paper, ΔU/U is calculated for a narrow channel of width r_⊥ (kr_⊥1) at a distance d below the surface of a slab of piezoelectric material of finite thickness when an elastic wave is launched on the surface. ΔU/U is given as a closed-form expression in terms of the velocity of the elastic wave, the elastic constants, and the piezoelectric tensor. Numerical results are presented for ΔU/U as a function of kd for several values of the thickness of a slab of GaAs/AlₓGa_1-xAs.