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One other question that you might ask is, this approach works for bipolars but what happens when you need to characterize a MOS transistor. Nothing changes, use the same testbench and measurements, see figure 1. In this testbench a MOS transistor is being compared to a bipolar transistor.
The simulation results are shown in Figure 2. The difference in the results is that the low frequency bipolar transistors current gain is limited by the base current, while the MOS transistor current gain is not limited. Note, in advanced node processes, MOS transistors do have significant gate leakage and the plot for the MOS transistor would look more like the plot for the bipolar transistor.
So the same techniques that you would to characterize a bipolar transistor and also be applied to MOS transistor.