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 degrees 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 degrees C and -40 degrees 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.