Calibrated Si Mobility and Incomplete Ionization Models with Field Dependent Ionization Energy for Cryogenic Simulations

Cryogenic silicon CMOS operating between 77K and 4.2K is becoming more popular in high-speed server applications and the periphery of quantum computers. In the cryogenic regime, dopant incomplete ionization and field enhanced ionization become dominating physical phenomena. Therefore, it is important to use accurate and well-calibrated mobility and incomplete ionization models in cryogenic TCAD simulations. In this paper, we present a Philips Unified Mobility Model (PhuMob) and Altermatt's incomplete ionization model calibrated between 300K and 20K for boron and arsenic dopants in silicon across 5 orders of magnitude in doping concentration. A novel method is proposed to include field-dependent ionization energy in Altermatt's model, which results in good convergence even in 3D TCAD simulations at 4K.