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Do you understand "sub"?
Does a submarine dive below the surface of the water or does it fly above the water?
The Mosfet biased in deep subthreshold is not in triode mode, instead it is cutoff.
If the transistor is in subthreshold, this means (VGS-Vth)< 0, so VDS is always > (VGS-Vth) so the transistor cannot be in triode and subthreshold at the same time. Nevertheless, the concept of saturation and triode is not valid at subthreshold operation and the transistor follows the diode exponential current curve (to some extend of course). The best way to characterise it at subthreshold, is to use gm/ID charts.
At subthreshold V* >0 but "Vov= VGS-Vth" can be less than zero.
If the transistor is in subthreshold, this means (VGS-Vth)< 0, so VDS is always > (VGS-Vth) so the transistor cannot be in triode and subthreshold at the same time.
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