Enter device and process data
Single-column page layout, with a responsive three-column form on large screens.
Core equations
The calculator uses the flat-band term, Fermi potential, oxide capacitance, and body-effect contribution to estimate the threshold voltage.
Cox = εox / tox
Vfb = φms - (Qox / Cox)
φF = (kT / q) ln(Nsub / ni)
γ = √(2 q εsi Nsub) / Cox
NMOS: Vth = Vfb + 2φF + γ √(2φF + |VSB|)
PMOS: Vth = Vfb - 2φF - γ √(2φF + |VSB|)
For PMOS, the sign of φms and the threshold result depends on the chosen convention. This page keeps the common signed result form for quick engineering estimates.
Steps
- Select NMOS or PMOS.
- Enter the gate-semiconductor work-function difference, φms.
- Provide substrate doping and intrinsic carrier concentration values.
- Enter oxide thickness and material permittivities.
- Add temperature, body-bias magnitude, and fixed oxide charge density.
- Press the calculate button to show results above the form.
- Review Vth, Vth0, Vfb, φF, γ, Cox, and the body-effect shift.
- Use the CSV or PDF buttons to save the result.
Sample scenarios
| Device | φms (V) | Nsub (cm⁻³) | tox (nm) | |VSB| (V) | Temp (K) | Vth (V) |
|---|---|---|---|---|---|---|
| NMOS | -0.900 | 1.000e+16 | 8.00 | 0.00 | 300 | -0.072870 |
| NMOS | -0.900 | 5.000e+16 | 5.00 | 1.00 | 300 | 0.142994 |
| PMOS | 0.900 | 8.000e+15 | 9.00 | 0.75 | 300 | 0.039509 |
FAQs
1. What does threshold voltage mean in a MOS device?
It is the gate voltage level where strong inversion begins and a conductive channel can form. Designers use it to estimate switching behavior, bias margins, and process sensitivity.
2. Why does body bias change threshold voltage?
Body bias changes the depletion charge that the gate must balance. A larger body-bias magnitude usually increases the required gate voltage magnitude, shifting the threshold.
3. Why is oxide thickness important?
Oxide thickness controls oxide capacitance. A thinner oxide increases Cox, strengthens gate control, and usually reduces the threshold contribution from depletion and fixed charge terms.
4. What role does substrate doping play?
Higher substrate doping increases the Fermi potential and body-effect coefficient. That often raises the threshold magnitude and changes how strongly body bias affects the device.
5. Should NMOS and PMOS results have different signs?
Yes. NMOS threshold is commonly positive, while PMOS threshold is commonly negative under usual sign conventions. This calculator reports signed results based on the selected device type and entered parameters.
6. What is φms in this calculator?
φms is the gate-semiconductor work-function difference. It strongly affects flat-band voltage and therefore shifts the calculated threshold voltage before body-bias effects are added.
7. Why include fixed oxide charge density?
Fixed oxide charge changes the flat-band voltage through Qox/Cox. Even modest trapped charge can shift threshold voltage, which matters in process comparison and reliability studies.
8. Can I use this for final fabrication signoff?
Use it for estimation, education, and quick comparison. Final signoff should rely on foundry models, measurement data, detailed device simulation, and the exact sign conventions used by your process documentation.