Chapter 4 · Animation 1 of 4 · Sections 4.1 and 4.3 (Fig. 4.2)
Electrons Over the Source Barrier
The gate controls a barrier between the source and the channel; the drain voltage tilts the channel. Watch thermally agitated electrons cross the barrier, diffuse along a flat channel in weak inversion and drift down a sloping one in strong inversion.
electron (drawn at its energy)━ EC along the surface- - -Fermi level in the source and drain
Real transfer characteristic of the device (dot: your VGS)
What to look for
Each dot moves by random thermal steps plus a push down the slope of EC: diffusion and drift in one picture.
The number of electrons in the channel follows e−barrier/kT, which is why the weak-inversion current is exponential in VGS.
In weak inversion the drain voltage only stops the return flow; once that is negligible (a few kT/q) the current saturates.
The physics behind it
The surface EC(x) is computed from ψS(x) of the complete all-region model, with n⁺ regions at φbi (source) and φbi + VDS (drain).
Electron density at the top of the barrier ∝ e−q(φbi − ψs0)/kT: the gate lowers the barrier, as in a bipolar transistor's emitter junction (Sec. 4.3, 'An energy barrier point of view').
At the barrier top the field is zero, so electrons cross by diffusion; inside the channel they drift if there is a field.