PHT.301 Physics of Semiconductor Devices

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Electrons in crystals

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pn junctions

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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.