Numerical investigation of a piezoelectric surface acoustic wave interaction with a one-dimensional channel

We investigate the propagation of a piezoelectric surface acoustic wave (SAW) across a $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructure surface, on which there is a fixed metallic split gate. Our method is based on a finite element formulation of the underlying equations of motion, and is performed in three dimensions fully incorporating the geometry and material composition of the substrate and gates. We demonstrate attenuation of the SAW amplitude as a result of the presence of both mechanical and electrical gates on the surface. We show that the incorporation of a simple model for the screening by the two-dimensional electron gas (2DEG), results in a total electric potential modulation that suggests a mechanism for the capture and release of electrons by the SAW. Our simulations suggest the absence of any significant turbulence in the SAW motion which could hamper the operation of SAW based quantum devices of a more complex geometry.

Figure 1

(a) A schematic diagram showing the experimental setup in acoustic charge transport experiments. A transducer on the left excites a SAW wave that propagates towards the split gate on the right. (b) The acoustoelectric current versus split-gate voltage. The current exhibits a steplike behavior as the gate voltage is varied.

Figure 2

A schematic diagram showing the device geometry. A split gate, composed of a $\mathrm{Ti}∕\mathrm{Al}$ alloy, is placed on the surface $(z=z0)$ of the $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ substrate. The SAW, generated by the three membranes separated $1.0\mu \mathrm{m}$ apart, propagates along the $x$ axis. The $x_0$, $y_0$, and $z_0$ parameters are chosen to be $12000\mathrm{nm}$, $3000\mathrm{nm}$, and $8000\mathrm{nm}$, respectively. The depletion parameter $d$ is $300\mathrm{nm}$. The gate is centered along the $x$ axis at $x=x_g=9850\mathrm{nm}$.

Figure 3

Time development of SAW induced electric potential $\varphi$ as a function of the $x$ axis (without gates on the surface and without the 2DEG). For clarity, the inset shows that the amplitude of the SAW is $\sim 20\mathrm{mV}$.

Figure 4

The SAW potential $\varphi$ at $t=2.0\mathrm{ns}$, (a) directly under the gates $(y=500\mathrm{nm})$ and (b) in between the gates at the center of the split-gate constriction $(y=1500\mathrm{nm})$. The curves were taken $100\mathrm{nm}$ below the surface. The SAW amplitude is reduced directly below the gate as much as $\sim 30\%$ but less than $\sim 1\%$ at the center of the constriction.

Figure 5

Time development of SAW induced electric potential $\varphi$ as a function of the $x$ axis. The simulation includes the screening by the 2DEG, in the source and drain regions.

Figure 6

The time development of a rear potential barrier showing the mechanism by which electrons from the source 2DEG could be captured.

Figure 7

Surface plots showing the time development of the SAW induced electric potential $\varphi$ in the $x\text{−}y$ plane.

Figure 8

(a) Time development of the total electric potential $\varphi$ as a function of the $y$ coordinate. (b) The electric potential $\varphi$ directly under the gate and in between the gate.