Below threshold the drain current is exponential in the gate voltage. Its slope, the subthreshold swing S = 2.3nφt, decides how well the transistor turns off. Change the oxide, doping, temperature and source bias and read S.
log ID versus VGS (red line: leakage floor, red dot: off current)
Subthreshold swing versus oxide thickness (dot: measured on your device)
What to look for
IDS ≈ I′M e(VGS − VM)/(nφt) (1 − e−VDS/φt), S = 2.3 n φt
In weak inversion every decade of current costs S volts of gate swing; S can never be below 2.3φt ≈ 60 mV at 300 K.
n = 1 + C′b/C′ox: a thin oxide or light doping brings n toward 1 and S toward the limit.
Temperature raises φt (and S) and, through ni, raises the off current. Leakage sets the floor below which the transistor cannot be turned off further.
Try this
Read S for tox = 10 nm and 2 nm. Compare with the analytical formula.
Raise T from 300 to 400 K. How do S and the off current change?
Raise VSB to 1.5 V. Why does S improve slightly, and what happens to the off current?
Raise the leakage to 10⁻¹⁰ A. Over how many decades is the subthreshold exponential still visible?