How this calculator works
Reverse source-to-body bias widens the depletion region in a p-type substrate and raises the enhancement nMOS threshold. The body-effect coefficient describes how strongly that depletion charge couples through the gate oxide. The material modes use SI carrier densities and oxide capacitance per area, not a total gate capacitance. Intrinsic carrier density must correspond to the entered temperature. The model neglects short-channel and quantum corrections.
Formula
Vt = Vt0 + gamma[sqrt(2 phiF+Vsb)-sqrt(2 phiF)]. gamma = sqrt(2 q epsilon_s NA)/Cox. phiF = (kB T/q) ln(NA/ni).
Worked example
For Vt0 = 1 V, gamma = 0.5 sqrt(V), phiF = 0.5 V and Vsb = 3 V, the threshold is 1.5 V. Inverting the same values gives a 3 V source-body bias.
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Frequently asked questions
Why is oxide capacitance entered per unit area?
The body-effect coefficient compares depletion charge density with oxide capacitance density. A total gate capacitance has different units and cannot be substituted directly.
Can I use substrate density in 1/cm³?
Convert it to 1/m³ first by multiplying by one million. The field is explicitly labelled in SI density units.
Does this include forward body bias?
No. The offered bias domain is nonnegative reverse bias for an nMOS device. Junction conduction and other limits require a fuller model.