Gated-charge force microscopy for imaging a surface-acoustic-wave-induced charge in a depleted one-dimensional channel

Gated-charge force microscopy (GCFM) generates images of subsurface induced charge with single-electron charge resolution and zero sensitivity to background charge, for the noninvasive study of confined quantum electronic systems. By gating the radio-frequency signal applied to transducers, which generate surface-acoustic waves (SAWs), we use GCFM to generate images of a GaAs depleted one-dimensional channel and provide insight to SAW-induced transport. Unexpected SAW-induced subsurface charge was imaged at points of high potential gradient. This suggests that electrons depopulating a SAW minimum due to a high potential gradient rapidly lose energy and interact with following SAW minima.

Figure 1

(Color online) Illustration of experimental setup. Surface acoustic waves were generated by applying a RF signal to the interdigitated-finger transducer at the left-hand end of the device. The SAW channel was defined from the 2DES by applying a negative bias to the central gate electrodes. Source and drain ohmic contacts connect to the 2DES.

Figure 2

(a) SGM (device conductance) image of the SAW channel made with $V_{\text{tip}}=-1.6\text{V}$ and $V_{\text{gate}}=-0.9\text{V}$. The contour outlines the gate electrodes. Four crosses locate spots of charge seen in subsequent GCFM images. (b) Conductance profile along the length of the SAW channel, following the line shown in (a). Data were taken at 400 mK in the absence of SAWs. Scale bars are $1\mu \text{m}$.

Figure 3

Series of GCFM images for $V_{\text{gate}}$ from $-1.00$ to $-1.30\text{V}$ with $V_{\text{tip}}=-0.6\text{V}$. A small background level has been subtracted from each image independently. The range of electric potential is the same in all images. The contour outlines the gate electrodes and four crosses locate points where SAW-induced charge is prevalent. Data were taken at 400 mK. Scale bars are $1\mu \text{m}$.

Figure 4

Plot of SAW current and device conductance as a function of $V_{\text{gate}}$ made with the tip retracted $\left(V_{\text{tip}}=-0.6\text{V}\right)$. The plus symbols plot the relative range (signal to noise) from the GCFM images of Fig. 3 (the signal-to-noise ratio is 0 at $V_{\text{gate}}=-1.00\text{V}$ and is maximum at 4.4 at $V_{\text{gate}}=-1.14\text{V}$). Data were taken at 400 mK.