In this paper, a metal-oxide-semiconductor-field-effect-transistor modeling methodology for cryogenic conditions has been extensively verified through device measurements performed on a cryogenic probe station that was cooled by liquid nitrogen (-196 °C). The approach is valid for all operating regions (including the sub-threshold mode). The developed model can estimate I _D - V _GS and I _D-V _DS curves of transistors having different channel lengths and widths with an error of less than 5%. Statistical analysis of cryogenic measurements is used to introduce the variation levels around the nominal cryogenic operation to identify the impact of process variations at cryogenic conditions. Models adjusted to various temperatures between -196 °C and -40 °C have been developed for applications requiring different cryogenic operation conditions. Experimental data collected from a ring oscillator is employed to visualize the model performance in estimating the cryogenic characteristics of a typical integrated circuit. It is shown that the frequency of the ring oscillator is correctly simulated using the proposed cryogenic models.

Conventional transistor models are unable to capture the electrical behavior of transistors at cryogenic temperatures. In this paper, a methodology has been developed to calibrate temperature dependence parameters of Berkeley Short-Channel Insulated Gate Field Effect Transistor Model (BSIM3). Rather than modifying BSIM3 equations, the algorithm only changes the values of relevant parameters through noniterative, analytic operations; therefore, it can be implemented in typical circuit simulation tools. Proposed methodology allows to estimate I_D-V_GS and I_D-V_DS curves of the transistors having different channel lengths and widths even under various operating voltages, including the body bias. The parameter extraction algorithm runs with a reasonable computation cost and can compute parameter sets for transistors at user-defined cryogenic conditions.