In a MOSFET, the current saturates at VGS-VT = VDS. Why does more current pass at higher values of VGS? Is it due to an increase in channel depth or more electrons in the channel? Is it due to higher VDS required for saturation, resulting in higher electric field pushing electrons through the point of pinch off?
As far as I am aware, a battery results in constant electric field, which means that no matter which value of voltage VGS-VT = VDS occurs at, the effect on channel effective length is the same, so it should have no effect on the current.