Subject :- VLSI Design

Topic :- Technology Trend

Difficulty :- Medium

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:

$\Delta V_T=\frac{\sqrt{2\epsilon_s qN_a}}{C_{OX}}(\sqrt{2\phi_F+V_{SB}}-\sqrt{2\phi_F})$

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.

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 $V_{BS}$ = 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.