MOSFET: Subthreshold Characteristics
This section explains the Subthreshold Characteristics of the MOSFET in details.
If we look at the drain current expression in this equation
it appears that the current abruptly goes to zero as soon as VG is reduced to VT. In reality, there is still some drain conduction below threshold, and this is known as subthreshold conduction.
This current is due to weak inversion in the channel between flat band and threshold (for band-bending between zero and 2ΦF), which leads to a diffusion
current from source to drain. The drain current in the subthreshold region is equal to
It can be seen that ID depends exponentially on gate bias, VG. However, VD has little influence once VD exceeds a few kT/q. Obviously, if we plot In ID as a function of gate bias VG, we should get a linear behavior in the subthreshold regime, as shown in Fig.(a). The slope of this line (or more precisely the reciprocal of the slope) is known as the subthreshold slope, S, which has typical values of -70 mV/decade at room temperature for state-of-theart MOSFETs.This means that a change in the input VG of 70 mV will change the output ID by an order of magnitude. Clearly, the smaller the value of S, the better the transistor is as a switch. A small value of S means a small change in the input bias can modulate the output current considerably.
It can be shown that the expression for S is given by
Here, the factor In 10 (= 2.3) is introduced to change from log10 to natural logarithm, In. This equation can be understood by looking at the electrical equivalent circuit of the MOSFET in terms of the capacitors (Fig.b).
Between the gate and the substrate, we find the gate capacitance, Q, in series with the parallel combination of the depletion capacitance in the channel,
Cd, and the fast interface state capacitance, Cit = qDit.