Inverse Design of Thermal Transport with Auxiliary Physics-Informed Neural Networks for Ultra-Wide-Bandgap Semiconductor Materials

The traditional formulation for the inverse design of complex electronic devices consists of determining desired material properties and device geometrical and doping characteristics from a limited set of measured data. The rigorous solution of this problem based on the inversion of the Boltzmann transport equation would enable the predictive design of desired novel functionalities in a large frequency range. However, such inverse problems are notoriously high dimensional, intrinsically ill-posed, and strongly nonlinear. Under these circumstances, traditionally numerical techniques fail to predict the desired systems’ parameters to a reasonable degree of precision. Motivated by these limitations, a new class of mesh-free numerical solvers based on artificial neural networks (ANNs), known as physics-informed neural networks (PINNs), have recently gained popularity due to their inherent ability to regularize and efficiently handle the solution of inverse problems. In particular, using only a single training dataset, PINNs leverage both the physical constraints and the desired engineered output to restrict the space of potential solutions and inversely solve for a realistic set of parameters for a desired structure. We have already successfully employed this methodology for the inverse design of scattering nanostructures and photonic metamaterials based on the inversion of the dynamic Maxwell’s equations. Here, we describe our recent advances in developing auxiliary physics-informed neural networks (APINNs) for the forward and inverse solution of the phonon Boltzmann transport equation (BTE) applied to a class of ultra-wide-bandgap (UWBG) semiconductor alloys. Specifically, we focus on Al_xGa_1-xN, materials at different Al concentrations and obtain APINN solutions for arbitrary temperature gradients in different relevant device geometries. The APINN framework avoids discretization errors due to the quadrature evaluations of integral terms, mapping an integro-differential transport problem into an equivalent differential one. Our work provides a new path to efficiently design UWBG materials with desired thermal transport properties for applications to high-frequency and high-power microelectronics devices.