**7.4 The Body Effect (Substrate Bias Effect)
**

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Table of Contents -
Glossary -
Study Aids -
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Reading: Neamen **10.3.5** pp 466-448

The threshold voltage of a MOSFET is affected by the voltage which is
applied to
the back contact. The voltage difference between the source and the
bulk, *V*_{BS}
changes the width of the depletion layer and therefore also the voltage
across the oxide due to the change of the charge in the depletion region.
This results in a difference in threshold voltage which equals the difference
in charge in the depletion region divided by the oxide capacitance, yielding:
(mf21b)

The variation of the threshold voltage with the applied bulk-to-source
voltage is typically observed by plotting the square root of the drain current
as a function of the source-to-drain voltage for different values of the applied
bulk-to-source voltage while the device is in saturation.
The expected characteristics as calculated using the
quadratic model and the variable depletion layer model are shown in the figure
below.

mosfetc1.xls - body.gif
**Fig.7.4.1** *Square root of **I*_{D} versus the
gate-source voltage as calculated using the quadratic model
(green curves) and the variable depletion layer model (red curves) at
*V*_{BS} = 0 , -2.5, -5 and -7.5 Volt.

A first observation is that the threshold shift is the same for both models
since at threshold saturation is obtained at zero drain-to-source voltage
so that the depletion layer width is constant along the channel. As the
drain-source voltage at saturation is increased there is an increasing difference
between the drain current as calculated with each model. The difference
however reduces as a more negative bulk-source voltage is applied. This is
due to the larger depletion layer width which reduces the relative variation of
the depletion layer charge along the channel.

7.3
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© Bart J. Van Zeghbroeck, 1996, 1997