[paper] Modeling a 2D Electrostatic Potential in MOS Devices

Francois Lim, Benjamin Iñiguez, Alexander Kloes

A new analytical method for modeling a 2D electrostatic potential in MOS devices, 

applicable to compact modeling

J. Appl. Phys. 28 January 2024; 135 (4): 044501

DOI: 10.1063/5.0188863

Abstract: This paper presents a new conformal mapping method to solve 2D Laplace and Poisson equations in MOS devices. More specifically, it consists of an analytical solution of the 2D Laplace equation in a rectangular domain with Dirichlet boundary conditions, with arbitrary values on the boundaries. The advantages of the new method are that all four edges of the rectangle are taken into account and the solution consists of closed-form analytical expressions, which make it fast and suitable for compact modeling. The new model was validated against other similar methods. It was found that the new model is much faster, easier to implement, and avoids many numerical issues, especially near the boundaries, at the cost of a very small loss in accuracy.

FIG: (a) The calculated 2D potential from the closed-form analytic model,
for a Double Gate MOSFET with tsc=12nm, tox=1.6nm, and L=25nm.
(b) Corresponding equipotentials. 

Acknowledgments: This work was funded by the Spanish Ministry of Science through Contract No. PRX21/00726.

[paper] Compact Model for Electrostatics of III–V GAA Transistors

Mohit D. Ganeriwala, Francisco G. Ruiz*, Enrique G. Marin* and Nihar R. Mohapatra

A unified compact model for electrostatics of III–V GAA transistors with different geometries

Journal of Computational Electronics (2021)

Published: 07 August 2021

DOI: 10.1007/s10825-021-01751-2

 
Department of Electrical Engineering, Indian Institute of Technology Gandhinagar, Gandhinagar, Gujarat, 382355, India
*Department of Electronics, University of Granada, Granada, Spain

Abstract: In this work, a physics-based unified compact model for III-V GAA FET electrostatics is proposed. The model considers arbitrary cross-sectional geometry of GAA FETs viz. rectangular, circular and elliptical. A comprehensive model for cuboid GAA FETs is developed first using the constant charge density approximation. The model is then combined with the earlier developed model for cylindrical GAA FETs to have a unified representation. The efficacy of the model is validated by comparing it with simulation data from a 2D coupled Poisson-Schrödinger solver. The proposed model is found to be accurate for GAA FETs with different geometries, dimensions and channel materials and computationally efficient.

Fig: III–V GAA transistors with different geometries

Acknowledgements: This work is supported by the Visvesvaraya PhD scheme by MeitY, Gover nment of India Enrique G. Marin gratefully acknowledges Juan de la Cierva Incorporation IJCI-2017-32297 (MINECO/AEI).