An analytical model for the inversion charge distribution in square GAA MOSFETs with rounded corners

Abstract

In this work we introduce an analytical model for square Gate All Around (GAA) MOSFETs with rounded corners including quantum effects. With the model developed it is possible to provide an analytical description of the 2D inversion charge distribution function (ICDF) in devices of different sizes and for all the op erational regimes. The accuracy of the model is verified by comparing with data obtai ned by means of a 2D numerical simulator that self-consistently solves the Poi sson and Schr ̈odinger equations. The expressions presented here are useful to achieve a good d escription of the physics of these transistors; in particular, of the quantization effect s on the inversion charge. The analytical ICDF obtained is used to calculate important par ameters from the device compact modeling viewpoint, such as the inversion charge ce ntroid and the gate-to- channel capacitance, which are modeled for different device g eometries and biases.