Analitical modeling for square gate-all-around MOSFETs

Abstract

Two analytical models for square Gate All Around (GAA) MOSFETs has been introduced. The first part of this report include a quantum viewpoint and this first work has been published, while the second part approach a classical developed. With the model developed in the first part, it is possible to provide an analytical description of the 2D inversion charge distribution function (ICDF) in square GAA MOSFETs of difeerent sizes and for all the operational regimes. The accuracy of the model is verified by comparing the data with that obtained by means of a 2D numerical simulator that self-consistently solves the Poisson and Schrödinger equations. The expressions presented here are useful to achieve a good description of the physics of these transistors; in particular, of the quantization effects on the inversion charge. The analytical ICDF obtained is used to calculate important parameters from the device compact modeling viewpoint, such as the inversion charge centroid and the gate-to-channel capacitance, which are modeled for different device geometries and biases. The model presented accurately reproduces the simulation results for the devices under study and for different operational regimes. Anyway the second part of this report is focus on square GAA MOSFETs with a classical view point, which have not been analytically described in depth due to their particular geometrical complexity. The analytical description of cylindrical GAA MOSFETs is simpler since the symmetry of the structure around the rotation angle allows a 1D description, accounting just for the radial component. In the case of square GAA MOSFETs other modeling strategies are necessary, as will be shown below. Firstly, a technique to obtain analytical functions which are solutions of the 2D Poisson equation where the charge density in the silicon channel has been calculated, and the total inversion charge is introduced. Among all these functions a simple one for the electric potential in the silicon core of the square GAA MOSFETs was proposed. Secondly, the model introduced has been used to calculate the total inversion charge making use of Gauss's Law. The models obtained are finally validated with simulations data obtained with a 2D simulator developed in our group for Multiple-gate MOSFETs.