# 2D - MOS Capacitor & MOSFET¶

Section author: Daryoush Nosraty Alamdary

The purpose of this tutorial is to show how the results of our simulation software (which solves the Poisson and drift-diffusion current equations numerically) compare with analytical equations given in standard text books on MOSFETs. The analytical equations use certain approximations and assumptions which limit their applicability. Nevertheless, in most cases the agreement is very good as demonstrated in this tutorial.

## Contents¶

### Part 1: Capacitance-voltage characteristics of a 2D MOS capacitor¶

In the first part of this tutorial we discuss the capacitance-voltage (C-V) characteristics of the MOS capacitor in a 2D simulation. (For a 1D simulation of the C-V characteristics, see also this tutorial: “Capacitance-Voltage curve of a “metal”-insulator-semiconductor (MIS) structure”). Our MOS has the same dimensions and properties (channel length, doping profiles and gate contact type) as the corresponding MOSFET discussed in Part 2.

### Part 2: Current-voltage characteristics of a 2D n-Channel MOSFET¶

In the second part of the tutorial, we start with the design of the MOSFET based on its 2D MOS capacitor, and then discuss its input and output characteristics and their respective conductances, namely transconductance and channel conductance.

### Part 3: Mobility models and pinch-off in a 2D n-Channel MOSFET¶

In this part we discuss and compare the effect of different mobility models on the output characteristics of the MOSFET and how they affect properties such as pinch-off, saturation, etc.