Efficient spectrally-resolved electron transport for thermal property prediction

Predicting thermal conductivity from the transport of electrons is a complex challenge which must be addressed for the design and production of nano- and microscale devices. In this work, we describe our progress in simulating thermal electron transport in silicon for the purposes of thermal conductivity prediction. We describe a new approach to solve the Boltzmann transport equation for electrons, using the self-adjoint angular flux formulation coupled with a novel approach in computing electron temperature and Fermi energy which does not require the combination of linear “inner” and nonlinear “outer” iterations. The electron Boltzmann transport equation is discretized in space by the continuous finite element method, and in angle by discrete ordinates, using the Multiphysics Object Oriented Simulation Environment, implemented in the radiation transport code Griffin . We rely on density functional theory calculations to provide material properties such as electron density of states, energy, wavevector, mean free path, and more. Our method couples the discrete electron groups through temperature and Fermi energy, to simulate thermal electron transport (in the absence of electric fields) for the prediction of thermal conductivity, thermal and electrical flux, and heat capacity. We show effective thermal conductivity and temperature results for different sized 2D slabs of Si at 300 K, which agree with other studies in the literature. Additionally, we report Fermi energy and efficiency of this method using the generalized minimal residual method. • Fully coupled (in temperature and Fermi energy) method for thermal electron transport, without using non-linear iterations. • Self-adjoint angular flux formulation of Boltzmann transport equation allows efficient simulation with well-known linear algebra solvers. • Material property discretization consistent with angular discretization of the transport system.