Piezoelectric displacement sensing with a single-electron transistor

We propose a displacement sensing scheme for rf mechanical resonators made from GaAs, based on detecting the piezoelectrically induced charge. By using a single-electron transistor to detect the charge, we calculate that a significantly higher displacement sensitivity can be achieved than by using capacitive displacement sensing, primarily due to the strong piezoelectric coupling strength. We estimate a displacement sensitivity of order ${10}^{\text{−17}}\hspace{0.17em}{\mathrm{m/Hz}}^{\text{1/2}}$ for a 1 GHz GaAs resonator. Our model solves the coupled electromechanical response self-consistently, including the effects of both dissipative and reactive electronic circuit elements on the resonator behavior.