MOSFET Threshold Voltage Calculator

How to use this MOSFET threshold voltage calculator

What this calculator does

This calculator estimates the threshold voltage of a simplified long-channel enhancement-mode n-channel MOSFET. It first evaluates a zero-source-body-bias threshold and then applies the classical body-effect correction. The purpose is to make the influence of oxide capacitance, substrate doping, surface potential, and source-to-body bias easy to inspect numerically. It is an analytical estimate rather than a compact-model replacement: it does not include work-function differences, fixed oxide charge, interface traps, short-channel effects, drain-induced barrier lowering, or process-specific extraction rules. For a device-physics derivation of threshold behavior, see the Engineering LibreTexts threshold-voltage chapter.

When to use it

Use the tool to check hand calculations for coursework, compare the effect of substrate bias in a long-channel model, sanity-check a set of semiconductor parameters before a more detailed SPICE simulation, or study how changing oxide capacitance and doping changes the body-effect coefficient. It is especially useful when you want the intermediate values, not only a final voltage.

How to calculate

1. The calculator opens with a complete demonstration set and a validated example workbook ready for immediate download. Replace the sample values with values for your device or exercise.
2. Enter Capacitance of the insulator (C₀), Doping of the substrate (Nₐ), Surface potential (φF), Temperature (T), Source-body voltage (Vsb), and Intrinsic concentration (nᵢ). Results update live.
3. Open Other parameters only if you need to change the silicon relative permittivity, elementary charge, vacuum permittivity, or Boltzmann constant. The supplied constants are suitable for ordinary silicon calculations in the units shown.
4. Read Threshold voltage (VT) first, then use Zero-bias threshold (VT0), Body-effect shift (ΔVT), Body-effect coefficient (γ), and Surface potential from T, Nₐ, nᵢ to understand how the result was assembled.
5. Select Download Excel to export the current typed inputs and calculated results as a real XLSX workbook. Reset clears the demonstration and all entered numeric data; Excel export is then disabled until a complete valid state is entered again.

Input guide

Capacitance of the insulator (C₀) is required, in F/cm², and must be positive. A sample value is 1e-7 F/cm². Higher C₀ reduces γ and therefore reduces the depletion-charge contribution to the threshold estimate. Do not enter a total gate capacitance; this field is capacitance per unit area. Doping of the substrate (Nₐ) is required, in cm⁻³, must be positive, and must exceed nᵢ in this model; 1e17 cm⁻³ is the demonstration value. Increasing Nₐ increases γ through a square-root dependence. Surface potential (φF) is required in volts and must be positive; the sample is 0.3 V. It directly enters both square-root terms and the zero-bias expression, so confusing φF with the full 2φF surface potential will materially change the answer.

Temperature (T) is required in kelvin and must be positive; 300 K is the sample. Intrinsic concentration (nᵢ) is required in cm⁻³ and must be positive; the demonstration uses 1e10 cm⁻³. These two fields, together with Nₐ, generate the displayed thermal surface-potential check φF,calc = (kT/q) ln(Nₐ/nᵢ). They do not overwrite the explicit φF input. Source-body voltage (Vsb) is required in volts and is restricted here to nonnegative values for the nMOS reverse-bias body-effect case; the sample is 0.5 V. Increasing Vsb raises the threshold estimate in this model. A common mistake is to reverse the voltage definition and enter Vbs instead of Vsb.

Under Other parameters, Silicon relative permittivity (εr) is a required positive dimensionless value; 11.7 is used initially. Elementary charge (q) is required in coulombs and starts at 1.602176634e-19 C. Vacuum permittivity (ε₀) is required in F/cm and starts at 8.8541878128e-14 F/cm. Boltzmann constant (k) is required in J/K and starts at 1.380649e-23 J/K. The q and k values agree with the NIST-listed physical constants. Scientific notation is accepted; commas and unit symbols inside the input boxes are rejected to prevent ambiguous parsing.

Output guide

Threshold voltage (VT) is the primary estimate, in volts. It is driven by C₀, Nₐ, φF, Vsb, εr, q, and ε₀. Zero-bias threshold (VT0) is the same model evaluated before the body-bias increment. Body-effect shift (ΔVT) is the difference VT – VT0; it is zero when Vsb is zero and grows with reverse body bias. Body-effect coefficient (γ), in √V, describes the strength of substrate coupling; it rises with the square root of doping and falls as oxide capacitance increases. The University of Toronto's MOS transistor body-effect notes show the same classical dependence of threshold voltage on Vsb and γ. Surface potential from T, Nₐ, nᵢ is a separate consistency estimate in volts. A mismatch between it and your entered φF does not automatically mean the threshold calculation is invalid; it indicates that the explicit φF and the simple thermal relation represent different assumptions.

The Calculation detail table repeats the canonical model values with six significant decimal places where useful: Silicon permittivity, Body-effect coefficient, Zero-bias threshold, Body-effect shift, Threshold voltage, and Thermal surface-potential check. These are estimates from the simplified equations, not measured device parameters or design guarantees.

Worked example

With the startup values C₀ = 1e-7 F/cm², Nₐ = 1e17 cm⁻³, φF = 0.3 V, T = 300 K, Vsb = 0.5 V, nᵢ = 1e10 cm⁻³, εr = 11.7, q = 1.602176634e-19 C, ε₀ = 8.8541878128e-14 F/cm, and k = 1.380649e-23 J/K, the silicon permittivity is 1.0359399740976e-12 F/cm. The model gives γ = 1.821954 √V and VT0 = 0.811280 V. The body term adds 0.499602 V, producing VT = 1.310882 V, displayed as 1.3109 V in the primary result. Independently, (kT/q) ln(Nₐ/nᵢ) gives φF,calc = 0.416685 V.

Learn more

Threshold voltage is model-dependent in real devices, especially as channel lengths shrink. For context on practical MOSFET switching and the meaning of threshold as a channel-formation condition, the University of Maryland MOSFET laboratory notes provide a concise device-level introduction. Use manufacturer data and a process-appropriate compact model when the result will drive real hardware design.