Early voltage in mosfets

[123elctro]

What is the reason for the Early Voltage? Can someone tell me in terms of the physical events happening there..... like the depletion region change etc...?

 

[LvW]

I think, the term "Early voltage" applies to bipolar transistors only. It is a measure for the slope of the output chracteristics Ic=f(Vce) for Ib=const.

Of course, the output characteristics for mosfets show a similar slope, which is a measure for the so-called "channel length modulation".
However, as mentioed, I think it is not appropriate to describe this property using the term "Early voltage"

 

[dick_freebird]

The same effect (qualitatively) is called Early voltage by
some when referrinf to MOSFETs, even though Mr. Early
did his work on BJTs. Also referred to by its old-school
LEVEL= models "lambda" param, which fitted the channel-
shortening effects of Vds.

The drain depletion region pushes laterally toward the
source, shortening the channel and enhancing drain
current over the long-channel (as-drawn) expected
value.

 

[123elctro]

Thanks for the reply... but could you tell why does this Early voltage come into picture? I understand that when we interpolate the graphs the Drain current in saturation depends upon the voltage... but why does this physically happen?Could you please explain the relation between the channel length modulation (which decreases the length) and Early voltage?

 

[Dominik Przyborowski]

The formula for channel length modulation factor:
\[\lambda_M = \dfrac{1}{V_M} = \frac{1}{I_D}\frac{d I_D}{d V_{DS}} \approx \frac{1}{L} \sqrt{\frac{\epsilon_{Si}}{2 q N_b \left ( \Phi_B + V_{DS} - \frac{V_{GS} - V_{Th}}{n} \right )}},\]
And we modelling that \[I_D \propto \lambda_M V_{DS}\]
The Phi_B is a built in potential, N_b bulk doping, n slope factor.
Some peoples identifies Early voltage with modulation voltage V_M