The MOSFET channel forms when gate voltage bends bands enough to create inversion at the semiconductor surface. The threshold voltage depends on oxide thickness, work-function difference, fixed charge, substrate doping, and body effect. In strong inversion, long-channel current is often approximated by square-law expressions, though modern devices depart substantially from this ideal.

In the linear region, channel charge is approximately proportional to overdrive, while in saturation the channel pinches off near the drain. The long-channel saturation law is $I_D \approx \frac{1}{2} \mu C_{ox} \frac{W}{L}(V_{GS}-V_T)^2$ for ideal conditions. Mobility degradation, velocity saturation, and channel-length modulation all reduce accuracy in scaled nodes.

Short-channel effects include threshold-voltage roll-off, drain-induced barrier lowering, punch-through, velocity saturation, hot-carrier injection, and subthreshold slope degradation. These effects motivate finFETs, gate-all-around transistors, high-$k$ dielectrics, and strain engineering. Advanced compact models such as BSIM incorporate these phenomena for circuit simulation.