7.4 The Body Effect (Substrate Bias Effect)
Table of Contents -
Study Aids -
Reading: Neamen 10.3.5 pp 466-448
The threshold voltage of a MOSFET is affected by the voltage which is
the back contact. The voltage difference between the source and the
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:
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
mosfetc1.xls - body.gif
Fig.7.4.1 Square root of ID versus the
gate-source voltage as calculated using the quadratic model
(green curves) and the variable depletion layer model (red curves) at
VBS = 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.
© Bart J. Van Zeghbroeck, 1996, 1997