Abstract
The threshold-voltage modulation ΔVr of m.o.s. transistors, due to substrate bias VR, is determined using a simple 2-dimensional approach. It is shown that, for a given substrate bias, the ΔVT of short-channel devices is less than that of long-channel devices. It is also shown that the intrinsic (zero substrate bias) threshold voltage of short-channel devices is less than that of long-channel devices. The functional dependence of ΔVT on VR is derived, and verified experimentally.

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