Note: This software is no longer supported by the Berkeley Device Group. Use at your own risk.

Introduction

This software calculates the capacitance-voltage characteristics of an MOS capacitor considering the electron/hole distributions in both inversion and accumulation. These distributions are calculated by solving Schroedinger's and Poisson's equations self-consistently with the Fermi-Dirac distribution using the physical parameters for (100) Si. Electron and hole masses may be found in the source code.

User Agreement

By using this software, you agree to acknowledge the UC Berkeley Device Group when disseminating or publishing the software or results derived from it.

Installation

The simulator is written in Matlab. Download these three files to your local machine.
cmos.m shelec.m shhole.m

Operation

Before starting Matlab, edit cmos.m with the appropriate parameters. The user-defined parameters are all contained in the section labeled INPUT PARAMETERS; the comments indicate the meaning of each parameter. It is worthwhile to note that changing the number of 'voltage steps' does not significantly impact the simulation time. This is because the simulation converges more quickly for smaller voltage steps.

Start matlab and run cmos.m. (The other two files contain functions that are called by cmos.m.)
While the simulation is running, it will give updates of the current bias point, iteration number, and convergence indicator.
The simulation takes around 30 minutes, based on the processor type.

Note: The simulation input parameters Vstart and Vend refer to the potential at the silicon surface (not the gate voltage or oxide voltage). Typical parameters for sweeping from accumulation to inversion are given.

Note: Poly gate depletion is calculated after the quantum simulation using the electric field calculated in the simulation to reduce the effective gate potential. This option can be turned off.

Output File

The results are stored in plain text in a file whose name is specified as a parameter in the program. The results can be imported into your favorite graphing program (such as Microsoft Excel) as 'space delimited' text.

The columns in the output file are (from left to right): Si surface potential, gate voltage, gate capacitance, electron centroids (dc,ac), hole centroids (dc,ac), Si surface electric field, total charge, and inversion charge.

Fitting Physical Oxide Thickness

Run the simulation repeatedly, changing doping and oxide thickness until the simulated results match the measured results well. After a good fit is obtained, particularly in the accumulation regime, subtract 0.2nm from the final oxide thickness to compensate for the accumulation charge centroid in the gate. This value is obtained from an independent simulation for highly-doped silicon.