Subthreshold slope and transconductance

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TL;DR
I'm trying to understand the difference between subthreshold slope and transconductance. The subthreshold slope is the change in drain current / change in gate voltage. The transconductance of a MOSFET is proportional to the drain current / VGS - Vth. It would seem the subthreshold slope is proportional to the transconductance? I'm trying to understand the physical significance and distinctions between subthreshold slope and transconductance. Thank you for any thoughts
I'm trying to understand the difference between subthreshold slope and transconductance. The subthreshold slope is the change in drain current / change in gate voltage. The transconductance of a MOSFET is proportional to the drain current / VGS - Vth. It would seem the subthreshold slope is proportional to the transconductance? I'm trying to understand the physical significance and distinctions between subthreshold slope and transconductance. Thank you for any thoughts
 
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As far as I can ascertain (regarding myself as a vacuum tube engineer!), the MOSFET has a gate voltage corresponding to cut-off, where the drain current is nominally zero. Above this gate voltage the drain current increase exponentially - it is like a square law device. The transconductance is the slope when biased above cut off and in normal operarting conditions.
For gate voltages below cut off, the drain current is not actually zero but is small. As bias is reduced further, the current reduces rapidly and if plotted as a log it is a straight line. This is similar to a diode. The slope of this line is the sub threshold slope.
 
Ah, so transconductance is always the relation above Vth for a MOSFET!

tech99 said:
increase exponentially - it is like a square law device

increases quadratically?