A Physics-Based Temperature-Dependent Scalable Model for CMOS On-chip Spiral Inductors for Quantum Computing Applications

This paper presents a physical-based temperature-dependent scalable 2-π equivalent circuit model of spiral inductors for cryo-CMOS circuit design. A physical-based modeling method is purposed to include temperature dependency, enabling accurate prediction of inductance and quality factor from 300 K to 4 K with different geometric parameters. The resistivity of metal decreases as temperature decreases, which affects the dc resistance and dc inductance in the scalable model. This effect can be modeled by Bloch-Grüneisen theory. Moreover, the conductivity and relaxation time constant (RTC) of substrate change with the temperature due to carrier freeze-out. The behavior of each three important terms at different temperature can be predicted by fitting existing physical formulas. The model has been validated by comparing the data of the modeling and measurements at different temperatures with different geometric parameters.