Device physicsMVP
MOSFET threshold voltage
An educational long-channel nMOS threshold-voltage model from substrate doping, oxide thickness, and flatband voltage.
Inputs
Result
Enter values and calculate to see the result.
Interpretation
Enter the substrate doping, oxide thickness, flatband voltage, and temperature.
Formula
Vth = Vfb + 2φF + √(2·εSi·q·Na·2φF) / Cox
Cox = εox/tox; φF = Vt·ln(Na/ni).
Variables
| Symbol | Variable | Unit |
|---|---|---|
| Vth | Threshold voltage | V |
| Vfb | Flatband voltage (parameter) | V |
| φF | Fermi potential | V |
| Na | Substrate (acceptor) doping | m⁻³ |
| Cox | Oxide capacitance per area | F/m² |
Assumptions & validity
This tool assumes:
- Educational long-channel nMOS model.
- Uniform substrate doping; complete ionization; non-degenerate.
- Ignores short-channel effects, poly depletion, quantum effects, and interface traps.
Worked example
Na = 1×10¹⁷ cm⁻³, tox = 5 nm, Vfb = −0.9 V, 27 °C.
Cox = εox/tox; φF = Vt·ln(Na/ni); Vth = Vfb + 2φF + √(…)/Cox