PHT.301 Physics of Semiconductor Devices

## 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.

 $\phi_m$ = eV $\chi_s$ = eV $t_{ox}$ = nm $\epsilon_{ox}$ = $N_c(300)$ = 1/cm³ $T$ = K $E_g$ = eV $\epsilon_{semi}$ = $N_v(300)$ = 1/cm³ $N_A$ = 1/cm³

Q - V

 $Q$ [C/m²] $V$ [V]

C - V

 $C$ [F/m²] $V$ [V]
 $E_g=$  eV $n_i=$  1/cm³ $\phi_s=$  eV $V_{fb}=\phi_m-\phi_s=$  V $C_{\text{ox}}=\frac{\epsilon_{\text{ox}}}{t_{\text{ox}}}=$  F/m² $V_T=$  V

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.