Consider the nMOS for simplicity, even in saturation,
Ids grows with
Vds because the depletion region around the drain grows too with
Vds and then the effective length of the channel is shorter.
What i don't understand is that, why we consider the depletion region around the drain a good conductor ?
For example, usually we want to work with a
Vgs higher than
Vt so that the channel is 'filled of' electrons (
0 < Vgs < Vt we have that the channel is made by a depletion region and we just have some leakage of current...! but we don't use the MOSFET in this region...)