After reading online, I have modeled this as an relation between the threshold voltage and the doping concentration:
For a N-channel MOSFET on a P-type substrate: $$ V_{T,N} \propto \sqrt{N_{A}} $$
For a P-channel MOSFET on a N-type substrate:
$$ V_{T,P} \propto - \sqrt{N_{D}} $$
which would then mean that an increase in substrate doping concentration leads to a higher magnitude threshold voltage (more positive for N-channel and more negative for P-channel).
How accurate is this? Does this qualitatively describe how the threshold voltage is affected by the semiconductor doping?
