Solving Poisson's Equation using Deep Learning in Particle Simulation of PN Junction

Abstract

Simulating the dynamic characteristics of a PN junction at the microscopic level requires solving the Poisson's equation at every time step. Solving at every time step is a necessary but time-consuming process when using the traditional finite difference (FDM) approach. Deep learning is a powerful technique to fit complex functions. In this work, deep learning is utilized to accelerate solving Poisson's equation in a PN junction. The role of the boundary condition is emphasized in the loss function to ensure a better fitting. The resulting I-V curve for the PN junction, using the deep learning solver presented in this work, shows a perfect match to the I-V curve obtained using the finite difference method, with the advantage of being 10 times faster at every time step.

Enhancing Computational Fluid Dynamics with Machine Learning

“…It is also possible to accelerate CFD by solving the Poisson equation with deep learning, as proposed by several research groups in various areas [108,133]. The Poisson equation is frequently used in operator-splitting methods to discretize the Navier-Stokes equations [17], where first the velocity field is advected, and the resulting field u * does not satisfy the continuity equation (i.e.…”

Solving 1D non‐linear magneto quasi‐static Maxwell's equations using neural networks

“…FENN was successfully used to solve inverse problem based on Poisson's equation. Also the works presented in [20,22] concern electrostatic problems, here by making use of CNNs. Tang et al [20] highlighted the flexibility of CNNs in case of complex distributions of excitation sources and dielectric constants.…”

“…The use of NNs and CNNs for solving PDEs in engineering applications has been mainly focused to fluid dynamics [9,[15][16][17][18]. However, few works dealing with electromagnetism do exist [19][20][21][22]. However, almost all of them are limited to electrostatics.…”

“…FENN was successfully used to solve inverse problem based on Poisson's equation. Also the works presented in [20, 22] concern electrostatic problems, here by making use of CNNs. Tang et al.…”

“…Zhang et al. [22] could decrease, in comparison to FD method, the calculation time of factor 10 in determining the I–V curve for a PN junction. Finally, Bartlett [21] solved Maxwell's equations in frequency domain in case of a non‐magnetic, linear material.…”