Channel length modulation

In textbooks, channel length modulation in active mode usually is described using the Shichman–Hodges model, accurate only for old technology: where I_\text{D} = drain current, K'_n = technology parameter sometimes called the transconductance coefficient, W, L = MOSFET width and length, V_\text{GS} = gate-to-source voltage, V_\text{th} = threshold voltage, V_\text{DS} = drain-to-source voltage, V_\text{DS,sat} = V_\text{GS} - V_\text{th}, and λ = channel-length modulation parameter. In the classic Shichman–Hodges model, V_\text{th} is a device constant, which reflects the reality of transistors with long channels. ==Output resistance==

Channel-length modulation is important because it decides the MOSFET output resistance, an important parameter in circuit design of current mirrors and amplifiers. In the Shichman–Hodges model used above, output resistance is given as: ::\begin{align} r_\text{O} &= \frac{1 + \lambda V_\text{DS}}{\lambda I_\text{D}} \\ &= \frac{1}{I_\text{D}}\left(\frac{1}{\lambda} + V_\text{DS}\right) \\ &= \frac{V_\text{E} L/{\Delta L} + V_\text{DS}}{I_\text{D}} \end{align} where V_\text{DS} = drain-to-source voltage, I_\text{D} = drain current and \lambda = channel-length modulation parameter. Without channel-length modulation (for λ = 0), the output resistance is infinite. The channel-length modulation parameter usually is taken to be inversely proportional to MOSFET channel length L, as shown in the last form above for rO: ::\lambda \approx \frac{\Delta L}{V_EL}, where VE is a fitting parameter, although it is similar in concept to the Early Voltage for BJTs. For a 65 nm process, roughly VE ≈ 4 V/μm.). However, no simple formula used for λ to date provides accurate length or voltage dependence of rO for modern devices, forcing use of computer models, as discussed briefly next. The effect of channel-length modulation upon the MOSFET output resistance varies both with the device, particularly its channel length, and with the applied bias. The main factor affecting the output resistance in longer MOSFETs is channel length modulation as just described. In shorter MOSFETs additional factors arise such as: drain-induced barrier lowering (which lowers the threshold voltage, increasing the current and decreasing the output resistance), velocity saturation (which tends to limit the increase in channel current with drain voltage, thereby increasing the output resistance) and ballistic transport (which modifies the collection of current by the drain, and modifies drain-induced barrier lowering so as to increase supply of carriers to the pinch-off region, increasing the current and decreasing the output resistance). Again, accurate results require computer models. ==See also==