MOS capacitor explorer
The oxide capacitance of a MOS stack (Cox = εox/tox) and the accumulation, depletion, and inversion regions.
Inputs
Result
Enter values and calculate to see the result.
Interpretation
The oxide capacitance Cox = εox/tox is the maximum capacitance of the MOS stack (reached in accumulation). A thinner oxide gives a larger Cox, which gives the gate stronger control over the channel — the main reason gate oxides were scaled aggressively (and why high-k dielectrics were introduced to keep Cox high without an impractically thin film).
Accumulation
Gate bias attracts majority carriers to the surface; capacitance ≈ the full oxide capacitance Cox.
Depletion
Opposite bias pushes majority carriers away, growing a depletion layer in series with the oxide; total capacitance falls below Cox.
Inversion
Strong bias forms a minority-carrier channel at the surface — the condition a MOSFET turns on in.
Formula
Per unit area; εox ≈ 3.9·ε₀ for SiO₂.
Variables
| Symbol | Variable | Unit |
|---|---|---|
| Cox | Oxide capacitance per area | F/m² |
| εox | Oxide permittivity | F/m (≈ 3.9·ε₀) |
| tox | Oxide thickness | m |
Assumptions & validity
This tool assumes:
- SiO₂ gate dielectric (εr ≈ 3.9); Cox is per unit area.
- Educational — no full C–V curve, high-k, poly depletion, or quantum effects.
Worked example
tox = 5 nm (SiO₂).
Cox = 3.9·ε₀ / 5 nm ≈ 6.9 mF/m² (≈ 0.69 µF/cm²)