The parameter is called the channel length modulation coefficient, having a value in the range 0.02V -1 to 0.005V -1 . Assuming that , the saturation current given in (2.11) can be written as

The simplified equation (2.13) points to a linear dependence of the saturation current on the drain-to-source voltage. The slope of the current-voltage characteristic in the saturation region is determined by the channel length modulation factor .

Impact ionization :An electron traveling from the source to the drain along the channel gains kinetic energy at the cost of electrostatic potential energy in the pinch-off region, and becomes a “hot” electron. As the hot electrons travel towards the drain, they can create secondary electron-hole pairs by impact ionization. The secondary electrons are collected at the drain, and cause the drain current in saturation to increase with drain bias at high voltages, thus leading to a fall in the output impedance. The secondary holes are collected as substrate current. This effect is called impact ionization . The hot electrons can even penetrate the gate oxide, causing a gate current. This finally leads to degradation in MOSFET parameters like increase of threshold voltage and decrease of transconductance. Impact ionization can create circuit problems such as noise in mixed-signal systems, poor refresh times in dynamic memories, or latch-up in CMOS circuits. The remedy to this problem is to use a device with lightly doped drain. By reducing the doping density in the source/drain, the depletion width at the reverse-biased drain-channel junction is increase and consequently, the electric filed is reduced. Hot carrier effects do not normally present an acute problem for p -channel MOSFETs. This is because the channel mobility of holes is almost half that of the electrons. Thus, for the same field, there are fewer hot holes than hot electrons. However, lower hole mobility results in lower drive currents in p -channel devices than in n -channel devices.