Channel length modulation: Difference between revisions

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Revision as of 17:22, 19 November 2015

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In the Shichman–Hodges model used above, output resistance is given as:

::<math>r_O = \begin{matrix} \frac {1 + \lambda V_{DS}}{\lambda I_D} \end{matrix} =\begin{matrix} \frac {1/\lambda + V_{DS}} {I_D} \end{matrix}=\begin{matrix} \frac {V_E L + V_{DS}} {I_D} \end{matrix}</math>,

where <math>V_{DS}</math> = drain-to-source voltage, <math>I_D</math> = drain current and <math>\lambda</math> = 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 ''r_O'':<ref name=Sansen>

{{Cite book

| author=W. M. C. Sansen

| title=Analog Design Essentials

| year= 2006

| publisher=Springer

| ___location=Dordrecht

| isbn=0-387-25746-2

| url=http://worldcat.org/isbn/0387257462

| pages=§0124, p. 13}}

}}</ref>

::<math>\lambda </math>\approx ≈ <math>\begin{matrix}\frac {\Delta L} {V_EL} \end{matrix}</math>,

where V_E = is a fitting parameter, although it is similar in concept to the [[Early effect|Early Voltage]] for BJTs. For a [[65nm|65 nm process]], roughly V_E ≈ 4 V/μm.<ref name=Sansen/> (A more elaborate approach is used in the EKV model.<ref name=Fjeldly>

{{Cite book

|author= Trond Ytterdal, Yuhua Cheng, Tor A. Fjeldly

|title=Device Modeling for Analog and RF CMOS Circuit Design

|year= 2003

|page=212

|publisher=Wiley

|___location=New York

|isbn=0-471-49869-6

|url=http://books.google.com/books?id=aMUBiiFJYtQC&pg=PA212&dq=%22channel+length+modulation%22&as_brr=0&sig=yNvT90etEzmJc8hqVkaUT8U-z-A}}

}}</ref >). However, no simple formula used for λ to date provides accurate length or voltage dependence of ''r_O'' 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: [[DIBL|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 [[DIBL|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 [[SPICE#Device models|computer models]].