MOS Capacitor - Capacitance voltage
In capacitance-voltage profiling, the capacitance of a MOS capacitor is measured as a function of the bias voltage. The app below solves the Poisson equation to determine the charge-voltage and capacitance voltage characteristics of a MOS capacitor with a p-type substrate. This is the low-frequency result. At high frequencies, the charge at the oxide interface does not change fast enough and the characteristics take on another form.
The page: MOS Capacitor - Solving the Poisson Equation, describes how to solve the Poisson equation for the charge per square meter $Q$ on a MOS capacitor for any voltage $V$. This app uses the same routine to calculate the charge for many bias voltages and plots the $Q-V$ characteristic of a MOS capacitor. This is then numerically differentiated to plot the capacitance- voltage ($C-V$) characteristic. Due to a numerical error in the code, there is a small peak in the $C-V$ characteristic at the flatband voltage.