Sensitivity of a piezoelectric micromechanical displacement detector based on the radio-frequency single-electron transistor

We investigate the displacement and force sensitivity of a micromechanical detector in which a GaAs cantilever is capacitively coupled to a radio-frequency single-electron transistor (rf-SET). The piezoelectric effect in GaAs is utilized to convert the displacement signal into an electrical signal which is read out using the rf-SET. We analyze the input displacement noise due to the tunneling current shot-noise and back-action displacement noise due to the SET island voltage noise, and show, as an example, that a displacement sensitivity of ${\text{1.2×10}}^{\text{−3}}\mathrm{\hspace{0.17em}\AA }$ and a force sensitivity of ${\text{73×10}}^{\text{−18}}\hspace{0.17em}\mathrm{N}$ in a 6 KHz bandwidth are possible for a detector design with a resonant frequency of 38.4 MHz.