# MOSFET Threshold Voltage Calculator (Body Effect)

URL: https://speedycalculator.com/calculators/physics/mosfet-threshold-voltage/
Last updated: 2026-10-30

> The MOSFET threshold voltage calculator finds the threshold voltage of an n-channel MOSFET including the body effect from the zero-bias threshold, oxide capacitance, substrate doping, temperature and source-body voltage.

## Inputs

- Zero-bias threshold V_T0 (V, mV, kV, µV, MV)
- Oxide capacitance C_ox (fF/µm²)
- Substrate doping N_A (cm⁻³)
- Temperature (K, °C, °F)
- Source-body voltage V_SB (V, mV, kV, µV, MV)
- Intrinsic carrier density n_i (cm⁻³)

## Results

- Fermi potential φ_F
- Body-effect coefficient γ
- Threshold voltage V_T

## 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))
```

## Explanation

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

FieldWhat to enterZero-bias threshold V_T0Units: V, mV, kV, µV, MVOxide capacitance C_ox (fF/µm²)A numberSubstrate doping N_A (cm⁻³)A numberTemperatureUnits: K, °C, °FSource-body voltage V_SBUnits: V, mV, kV, µV, MVIntrinsic 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)0.250.4830.3750.6080.50.7330.6250.8580.750.98311.233

## 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.

## FAQ

**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.


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)