7.4 The Body Effect (Substrate Bias Effect)

Table of Contents - Glossary - Study Aids - Ź Ž

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:

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 Ź Ž 7.

Š Bart J. Van Zeghbroeck, 1996, 1997