Physically constrained learning of MOS capacitor electrostatics

Govind Indani, T and Narayan Chaudhury, K and Guha, S and Mahapatra, S (2023) Physically constrained learning of MOS capacitor electrostatics. In: Journal of Applied Physics, 134 (18).

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Abstract

In recent years, neural networks have achieved phenomenal success across a wide range of applications. They have also proven useful for solving differential equations. The focus of this work is on the Poisson-Boltzmann equation (PBE) that governs the electrostatics of a metal-oxide-semiconductor capacitor. We were motivated by the question of whether a neural network can effectively learn the solution of PBE using the methodology pioneered by Lagaris et al. IEEE Trans. Neural Netw. 9 (1998). In this method, a neural network is used to generate a set of trial solutions that adhere to the boundary conditions, which are then optimized using the governing equation. However, the challenge with this method is the lack of a generic procedure for creating trial solutions for intricate boundary conditions. We introduce a novel method for generating trial solutions that adhere to the Robin and Dirichlet boundary conditions associated with the PBE. Remarkably, by optimizing the network parameters, we can learn an optimal trial solution that accurately captures essential physical insights, such as the depletion width, the threshold voltage, and the inversion charge. Furthermore, we show that our functional solution can extend beyond the sampling domain. © 2023 Author(s).

Item Type:	Journal Article
Publication:	Journal of Applied Physics
Publisher:	American Institute of Physics Inc.
Additional Information:	The copyright for this article belongs to American Institute of Physics Inc.
Keywords:	Boltzmann equation; Charge coupled devices; Dissociation; Electrostatics; MOS capacitors; Oxide semiconductors; Poisson equation; Threshold voltage, Dirichlet boundary condition; Generic procedures; Governing equations; Learn+; Metal-oxide- semiconductorcapacitors; Neural-networks; Novel methods; Poisson-Boltzmann equations; Robin boundary conditions; Trial solutions, Boundary conditions
Department/Centre:	Division of Electrical Sciences > Electrical Engineering Division of Interdisciplinary Sciences > Centre for Nano Science and Engineering
Date Deposited:	28 Feb 2024 12:49
Last Modified:	28 Feb 2024 12:49
URI:	https://eprints.iisc.ac.in/id/eprint/83658

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