Cryogenic MOSFET Subthreshold Current: From Resistive Networks to Percolation Transport in 1-D Systems

Abstract

Small area MOSFETs are known to exhibit oscillations in subthreshold current at deep cryogenic temperatures. This feature becomes more pronounced as the drain bias is lowered down, even if its footprint is still recognizable in saturation regime. In this article, we restrict the analysis to the linear operation of cryogenic MOSFETs, where transistors can be regarded as simple resistors. In order to reproduce the main aspects of the experimental behavior, we first propose a model based on the concept of “resistive networks.” The resistors’ conductivity is initially described by drift–diffusion transport. Afterward, this model is provided with a physical background, given by the so-called “percolation transport theory.” In this context, the inversion channel conductivity is affected by the potential fluctuations induced by the presence of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{Si--\text{Si}}\text{O}_{\text{2}}$</tex-math> </inline-formula> interface trap charges. An example of such percolative current is simulated for a Gaussian-like potential. Finally, the negative transconductance often observed in the experimental curves is modeled by introducing a more advanced model for resistors’ conductivity, which relies on the Kubo–Greenwood integral.