MOSFET Body Effect Factor – Substrate Bias Effects

• The source and body may not be at the same potential. The curve represented as EFi is the Fermi level from the p substrate through the reverse biased source–substrate junction to the source contact.
• The space charge region width under the oxide increases from the original xd @ threshold value when a VSB  > 0 is applied.  Since the maximum depletion region depth Xd was due to 2Ef it is now due to 2Ef + Vsb and the maximum Xd is bigger before Vt is reached.

@Threshold with:   

With Vsb applied

And thus

Substituting from the identity table below:

Factoring

The change in the threshold voltage is

And here we find the body effect factor.  It is defined as:

 

The following is my work and needs to be verified

Substituting Identity

Since:

The following simple expression results

 

Identity Table

 

 

Research Links

• Introduction to Solid State Devices: Chapter 10   See page 6, Substrate Bias & Body Effect coefficient page 49  ( The whole book is here )
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