When the source of a MOSFET sits above the substrate, the threshold voltage rises – the body effect. It matters in stacked transistors, pass gates and analogue circuits, and is captured by the body-effect coefficient γ.
How to use the MOSFET Threshold Voltage Calculator
- Zero-bias threshold V_T0
- Oxide capacitance C_ox (fF/µm²)
- Substrate doping N_A (cm⁻³)
- Temperature
- Source-body voltage V_SB
- Intrinsic carrier density n_i (cm⁻³)
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the zero-bias threshold voltage, the oxide capacitance per area, the substrate doping, temperature, source-body voltage and intrinsic carrier density.
Inputs explained
| Field | What to enter |
|---|---|
| Zero-bias threshold V_T0 | Units: V, mV, kV, µV, MV |
| Oxide capacitance C_ox (fF/µm²) | A number |
| Substrate doping N_A (cm⁻³) | A number |
| Temperature | Units: K, °C, °F |
| Source-body voltage V_SB | Units: V, mV, kV, µV, MV |
| Intrinsic carrier density n_i (cm⁻³) | A number |
What each result means
- Fermi potential φ_F = 1.380649e-23×[Temperature]÷1.602176634e-19×ln([Substrate doping N_A (cm⁻³)]÷[Intrinsic carrier density n_i (cm⁻³)])
- Body-effect coefficient γ = sqrt(2×1.602176634e-19×11.7×8.8541878128e-12×[Substrate doping N_A (cm⁻³)]×1e6)÷([Oxide capacitance C_ox (fF÷µm²)]×1e-3)
- Threshold voltage V_T = [Zero-bias threshold V_T0] + [Body-effect coefficient γ]×(sqrt(2×[Fermi potential φ_F] + [Source-body voltage V_SB]) – sqrt(2×[Fermi potential φ_F]))
Example values
How the main result changes when Zero-bias threshold V_T0 changes and everything else stays at the example values above:
| Zero-bias threshold V_T0 (V) | Threshold voltage V_T (V) |
|---|---|
| 0.25 | 0.483 |
| 0.375 | 0.608 |
| 0.5 | 0.733 |
| 0.625 | 0.858 |
| 0.75 | 0.983 |
| 1 | 1.233 |
Formula
φ_F = (kT/q)·ln(N_A/n_i), γ = √(2q·ε_Si·N_A)/C_ox, V_T = V_T0 + γ·(√(2φ_F + V_SB) − √(2φ_F))
Worked example
Inputs — Zero-bias threshold V_T0: 0.5 V; Oxide capacitance C_ox (fF/µm²): 3.45; Substrate doping N_A (cm⁻³): 1e+17; Temperature: 300 K; Source-body voltage V_SB: 1 V; Intrinsic carrier density n_i (cm⁻³): 10,000,000,000.
Results — Fermi potential φ_F = 0.41669 V; Body-effect coefficient γ = 0.5281 √V; Threshold voltage V_T = 0.73296 V.
Key terms
- Body effect
- Threshold shift due to source-body bias.
Frequently asked questions
What is the body effect?
An increase in threshold voltage when V_SB > 0.
Why does doping matter?
Higher doping increases the depletion charge and γ.
What is a typical γ?
0.3–0.6 √V for older CMOS processes.
Why does temperature change V_T?
φ_F and n_i vary with temperature.