Theory of signal and noise in double-gated nanoscale electronic pH sensors

The maximum sensitivity of classical nanowire (NW)-based pH sensors is defined by the Nernst limit of 59 mV/pH. For typical noise levels in ultra-small single-gated nanowire sensors, the signal-to-noise ratio is often not sufficient to resolve pH changes necessary for a broad range of applications. Recently, a new class of double-gated devices was demonstrated to offer apparent "super-Nernstian" response (>59 mV/pH) by amplifying the original pH signal through innovative biasing schemes. However, the pH-sensitivity of these nanoscale devices as a function of biasing configurations, number of electrodes, and signal-to-noise ratio (SNR) remains poorly understood. Even the basic question such as "Do double-gated sensors actually resolve smaller changes in pH compared to conventional single-gated sensors in the presence of various sources of noise?" remains unanswered. In this article, we provide a comprehensive numerical and analytical theory of signal and noise of double-gated pH sensors to conclude that, while the theoretical lower limit of pH-resolution does not improve for double-gated sensors, this new class of sensors does improve the (instrument-limited) pH resolution.