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

We investigate the tunneling shot noise limits on the sensitivity of a micromechanical displacement detector based on a metal junction, radio-frequency single-electron transistor (rf-SET). In contrast with the charge sensitivity of the rf-SET electrometer, the displacement sensitivity improves with increasing gate voltage bias and, with a suitably optimized rf-SET, displacement sensitivities of ${10}^{-6}\mathring{\mathrm{A}}\mathrm{/}\sqrt{\mathrm{H}\mathrm{z}}$ may be possible.