[paper] Polylogarithms in MOSFET Modeling

A. Ortiz-Conde and F. J. García-Sánchez

Recent Applications of Polylogarithms in MOSFET Modeling

2023 IEEE 33rd International Conference on Microelectronics

MIEL, Nis, Serbia, 2023, pp. 1-8

DOI: 10.1109/MIEL58498.2023.10315897

Department of Electronics and Circuits, Universidad Simón Bolívar, Caracas, Venezuela

Abstract: We present a review of recent uses of the special mathematical function known as the polylogarithm for MOSFET modeling applications. We first summarize some basic properties of polylogarithms, with a particular focus on those with negative exponential argument. After examining cases of the use of first order polylogarithms pertinent to electron device modeling, we explain the reasons that motivate the use of polylogarithms of diverse orders for formulating mono- and poly-crystalline succinct compact MOSFET models. We then analyze a particular representative example: the modeling of polysilicon MOSFETs using the polylogarithm. Recalling that polylogarithms may be used to faithfully represent Fermi-Dirac Integrals in general, and considering that they are analytically differentiable and integrable, we describe a full Fermi–Dirac Statistics-based version of the usually approximate Boltzmann Statistics-based MOSFET Surface Potential Equation (SPE).

TABLE: Some Features of Polylogarithms with Negative Exponential Argument