Dynamic input capacitance of single-electron transistors and the effect on charge-sensitive electrometers

We examine the “input capacitance,” $C_{\mathrm{SETT}},$ of a single-electron tunneling (SET) transistor. We note that this quantity is crucial in quantifying the sensitivity of a SET transistor used as a charge electrometer. Further, we point out that $C_{\mathrm{SETT}}$ is not the same as the “gate capacitance,” $C_G,$ usually taken to be ${\mathrm{e/\Delta V}}_G,$ where ${\mathrm{\Delta V}}_G$ is the period of the oscillation in current versus gate voltage. While $C_G$ is indeed the average value of $C_{\mathrm{SETT}}$ over one period, $C_{\mathrm{SETT}}$ can in fact differ substantially from that value, depending on the applied voltages. This has important consequences for maximizing the sensitivity of SET charge electrometers when a large stray capacitance is present.