Monte Carlo - Finite Element Mixed Model for Heat Transport on Electronic Devices at The 20 nm Scale

Simulation of the thermal evolution of actual electronic devices is a very challenging topic. Heat transport at the nanoscale does not behave as in the macroscale [1-2]. This is a problem for engineers, as they cannot predict the thermal response of their devices with accuracy.<br/><br/>In the last years, the Kinetic Collective Model (KCM) has been used to develop a finite element tool to describe the thermal evolution of electronic devices with great accuracy using the Guyer and Krumhansl hydrodynamic equation. The results obtained from this approach fit extraodinarily to experiment with characteristic scales up to 400 nm using only ab initio parameters [1-2], but for smaller devices, effective values for the parameters are required. In that situations, some corrections are required in order to predict the experiments.<br/><br/>We present the Higher Order Perturbation (HOPE) an improvement of the KCM-hydrodynamic approach [4-5]. This new method allows to obtain a full predictive finite element model for thermal transport at the 20nm scale. The model is obtained from the split of the Boltzmann Transport Equation (BTE) in two terms, a first one that describes the hydrodynamic behavior and a second one with the residual terms that describes the evolution of the perturbations of higher order. From the solution of the residual term using a Monte Carlo approach we derive a boundary correction term that modifies the hydrodynamic boundary conditions. With this correction, the applicability of our finite element tool is significantly improved. We compare the results obtained from our simulations with experimental data of devices in the 200-20 nm range.<br/><br/><br/><b>Bibliography</b><br/><br/>[1] Beardo, A. et al. (2021) <i>Observation of second sound in a rapidly varying temperature field in Ge.</i> Science Advances, 7(27), eabg4677. https://doi.org/10.1126/sciadv.abg4677<br/><br/>[2] Beardo, A. et al. (2021) <i>A General and Predictive Understanding of Thermal Transport from 1D-and 2D-Confined Nanostructures: Theory and Experiment.</i> ACS NANO, 15(8), 13019–13030. https://doi.org/10.1021/acsnano.1c01946<br/><br/>[3] Alajlouni, S. et al. (2021). Geometrical quasi-ballistic effects on thermal transport in nanostructured devices. NANO RESEARCH, 14(4), 945–952. https://doi.org/10.1007/s12274-020-3129-6<br/><br/>[4] Sendra, L. et al. (2021). Derivation of a hydrodynamic heat equation from the phonon Boltzmann equation for general semiconductors. Phys Rev B, 103(14). https://doi.org/10.1103/PhysRevB.103.L140301<br/><br/>[5] Sendra, L. et al. (2022). <i>Hydrodynamic heat transport in dielectric crystals in the collective limit and the drifting/driftless velocity conundrum. </i>Phys Rev B, 106(15). https://doi.org/10.1103/PhysRevB.106.155301