where I_on is the current in strong inversion for V_GS =V_on .

Sub-threshold conduction is also observed in long-channel device and is due to the diffusion of minority carriers when the gate voltage is several thermal voltages less than V_T . Interestingly, in the sub-threshold region, the MOS transistor behaves more like a lateral bipolar transistor for which the substrate mimics the base region, whereas the source and the drain act like the emitter and the collector respectively .

Channel length modulation : so far one has not considered the variations in channel length due to the changes in drain-to-source voltage V_DS . For long-channel transistors, the effect of channel length variation is not prominent. With the decrease in channel lenghth, however, the variation matters. Figure 2.5 shows that the inversion layer reduces to a point at the drain end when V_DS = V_DSAT = V_GS -V_th . That is, the channel is pinched off at the drain end. The onset of saturation mode operation is indicated by the pinch-off event. If the drain-to-source voltage is increased beyond the saturation edge (V_DS > V_DSAT ), a still larger portion of the channel becomes pinched off. Let the effective channel (that is, the length of the inversion layer) be .

where L : original channel length (the device being in non-saturated mode), and : length of the channel segment where the inversion layer charge is zero. Thus, the pinch-off point moves from the drain end toward V_DS the source with increasing drain-to-source voltage . The remaining portion of the channel between the pinch-off point and the drain end will be in depletion mode. For the shortened channel, with an effective channel voltage of V_DSAT , the channel current is given by