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We developed device simulators that predict MOSFET current-voltage characteristics for temperatures as low as 20 K. This is achieved through the development of novel physics-based modeling techniques, and verified by low temperature current-voltage measurements. Our numeric simulations indicated that all the observed device and IC temperature characteristics can be self-consistently explained. Our investigations showed that carrier freeze-out was not detrimental for MOSFET direct-current and transient operations. We also observed that the DC transconductance as well as the threshold voltage rose several percent as the temperature decreased within the aforementioned range. Our modeling showed that any effects of freeze-out are mitigated by impurity band formation, larger mobilities are achieved at low temperatures due to suppressed phonon-limited scattering, and cut-off frequency of devices as well as circuits are expected to increase with decreasing temperatures.