This article presents an intelligent operator learning approach for the rapid prediction of the thermal field in a block of transistors within an integrated circuit. Phonon Boltzmann transport equation (BTE) simulations were conducted to analyze the thermal field in a single dual-fin field-effect transistor. The nanoscale heat flux profile from the top of the substrate was used as an input to simulate a large substrate containing 100 transistors using the Fourier heat conduction equation. Multiple Fourier simulations were performed with randomly varying on/off switching patterns of the surrounding transistors to assess their impact on the thermal field of the central transistor. The substrate side wall temperature profile of the central transistor, obtained from the Fourier simulations, was then used as a boundary condition for a BTE simulation of the same transistor with fins. The resulting BTE data, consisting of mesh coordinates, sidewall temperature profiles, and temperature at each mesh nodes was used to train and test a deep operator network (DeepONet) capable of predicting the thermal field of any arbitrarily chosen transistor. The trained DeepONet was also tested for a large block of 5000 transistors and effectively predicts the thermal field of any arbitrarily selected transistor. The proposed approach enables the prediction of thermal fields in integrated circuits within seconds and can be readily extended for large-scale circuits containing thousands of transistors. These findings underscore DeepONet’s potential as a highly efficient and scalable tool for rapid thermal field prediction in integrated circuits, facilitating real-time thermal management and optimization. By enabling fast and accurate thermal modeling, this approach bridges the gap between detailed phonon transport physics and large-scale circuit analysis, paving the way for advancements in digital twin technology for semiconductor thermal design.
Panda et al. (Fri,) studied this question.