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How does a substrate bias (a.k.a. back-gate bias) on a MOS transistor affect Vt?
A back-gate bias increases the magnitude of Vt. The mechanism is an increase in the depletion width of the induced p-n junction under the gate. This uncovers more fixed charge in the channel region. (The mobile charge gets "pulled" to the substrate contact.) Since the uncovered fixed charge has the same sign as the channel inversion charge, not as much channel inversion charge is needed to balance the charge on the gate. As a result, some of the inversion charge flows out the source terminal, so the channel isn't as inverted as it was prior to applying the substrate bias. Therefore, the gate voltage needs to increase in magnitude to restore the previous level of channel inversion.
Generally speaking, it is the so called body effect. For NMOS, with the decrease of VB, VTH increases.
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