Sub-threshold MOSFET operation

One thing that all of these circuits have in common is that they operate in the sub-threshold region of the MOS transistor. That is, they use the MOS transistor's characteristics with the gate biased below the transistor's threshold voltage. This is rare for MOS circuits, in which the fact that they have a sharp transition from cutoff to conducting is the most useful of the transistor's properties. However, subthreshold operation also has its benefits.

Firstly, in the subthreshold region, the currents through the transistor are extremely low, orders of magnitude lower than in normal operation. Subthreshold circuits consume extremely small amounts of power, which is important when you are trying to cram many thousands of these circuits onto a single integrated circuit. Secondly, in the subthreshold region, a MOS transistor has an exponential characteristic like a bipolar transistor. This exponential characteristic can be used to produce very useful effects.

The best example of this is in the differential pair, used by most of the above resistive fuses. If the normal simplified model for a transistor were used, the differential pair would have a simple characteristic as shown in Figure 4.13. The circuit is acting as a simple comparator, with an output that is either high or low. However, if the subthreshold operation is taken into account, the transfer characteristic changes to:

$$I_1 - I_2 = I_b\tanh{\kappa(V_1 - V_2)\over 2}$$

Figure 4.13: Simple differential pair model.

This is shown in Figure 4.10. Over a small range of voltages the characteristic is almost linear. The range of this linear region is about $\pm 4V_{TH}$V, where $V_{TH}$ is the thermal voltage of a transistor. Past this region, the differential pair saturates. Both of these features are useful in the application being considered in this thesis. The linear region has a very high resistance, of the order of hundreds of k$\Omega$. This means that it can be used for any of the resistors required in this project. Furthermore, the saturating behaviour at fairly small currents means that no matter what erroneous input the circuit has to deal with, it never draws too much current. This is important for power considerations, and also limits the inpact of freak pixels in the input image.