AD-NEGF: AN END-TO-END DIFFERENTIABLE QUANTUM TRANSPORT SIMULATOR FOR SENSITIVITY ANALYSIS AND INVERSE PROBLEMS Anonymous

Abstract

Quantum transport theory describes transport phenomena from first principles, which is essential for domains such as semiconductor fabrication. As a representative, the Non-Equilibrium Green Function (NEGF) method achieves superiority in numerical accuracy. However, its tremendous computational cost makes it unbearable for high-throughput simulation tasks such as sensitivity analysis, inverse design, etc. In this work, we propose AD-NEGF, to the best of our knowledge the first Automatic Differentiation (AD) based quantum transport simulator. AD-NEGF calculates gradient information efficiently by utilizing automatic differentiation and implicit layer techniques, while guaranteeing the correctness of the forward simulation. Such gradient information enables accurate and efficient calculation of differential physical quantities and solving inverse problems that are intractable by traditional optimization methods.

1. INTRODUCTION

The strong and lasting demand for higher computing power and lower energy consumption urges the downscale of semiconductor devices. Over the last 40 years, the microelectronics industry has successfully made the transistor feature size scale from 10µm to near 20nm, of which size the quantum mechanical effect starts to dominate (Anantram et al., 2008; Wang et al., 2008; Datta, 1997) . Therefore, device simulators facing the future need to take a quantum theory oriented formulation, while NEGF, as a representative, is one of the most rigorous approaches among existing quantum transport methods (Jacoboni, 2010) . Although NEGF shows superiority in simulation accuracy, it is also extremely time and computation consuming. Recently, many works successfully integrate machine learning techniques to resolve the accuracy-efficiency dilemma of scientific simulations. A typical paradigm is to build up learningbased surrogate models (e.g., a neural network) (Li et al., 2020; Bürkle et al., 2021; Pimachev & Neogi, 2021) . By learning from data generated with highly accurate simulations beforehand, the surrogate model is expected to maintain first-principle accuracy while performing much faster in usage. A fatal problem of such methods is that there is no guarantee for prediction accuracy, especially for input out of the distribution of the training dataset. Such drawback limits the application of machine learning based surrogates in quantum transport scenarios. An alternative is to utilize automatic differentiation to make the computation process differentiable. In quantum transport simulations, practically useful information is often related to calculating derivatives. For instance, the thermoelectric property measured by the Seebeck coefficient; the sub-threshold swing of MOSFET that is related to the derivative of the drain current I D with respect to the applied gate voltage V g , etc. Compared to traditional numerical differentiation, automatic differentiation can overcome the trade-off between the round-off error and the truncation error when choosing the step-size (Gautschi, 1997, Chap. 3) , and also can be numerically more efficient when the input dimension is high. Moreover, in theoretical inverse problems, an end-to-end differentiable solver is also extremely useful and in fact, critical. The availability of gradients makes it possible to conduct efficient gradient-based optimization, which can outperform black-box optimization methods such as Bayesian optimization, genetic algorithm, etc., and can conduct optimization on a scale that black-box methods cannot. Recent advances have also shown the value to apply differentiable

