Power Spectral Density of Thermal Noise at High Frequencies in Thermal Conductance for Semiconductor Devices

Abstract

We previously derived the power spectral density (PSD) of thermal flux fluctuations at low frequencies for a thermal conductor under non-equilibrium conditions, which is relevant for device modeling due to self-heating effects. In this work, we extend the analysis to include frequency dependence. A closed-form expression is obtained for the case of temperature-independent thermal conductivity and heat capacity. The thermal flux PSD can be accurately approximated as $S_{i,T}(f)\approx 4k[(T^{2}+T_{a}^{2})\Re (Y_{th})/2-(T-T_{a})^{2}G_{th}/6]$ where $k$ is the Boltzmann constant, $Y_{th}$ and $G_{th}$ is the AC and DC thermal admittances, and $T$ and $T_{a}$ are the device and ambient temperatures, respectively. We further demonstrate that a simple one-node RC model, combined with a frequency-independent flux PSD, provides a reasonable approximation for the frequency dependence of the temperature fluctuation PSD.