Chapter 4 · Animation 2 of 4 · Sections 4.3 and 4.7

The Channel at Work

Electrons enter from the source and leave at the drain. The current must be the same at every point of the channel, so where the gate induces fewer electrons they move faster. Push the drain voltage up and watch the channel pinch off.

electron in the channel (density ∝ |Q′I|)→local electron velocity relative to the source (log length; capped near a pinched-off drain)⊖ acceptor ion (bold: depleted)

Output characteristic at this VGS (dot: now)

Inversion charge along the channel

What to look for

  • The density of dots follows |Q′I(x)| from the complete model; their speed is IDS/(W|Q′I|), so the flux of dots is the same at every x.
  • Below V′DS the drain end still holds many electrons; at V′DS it is nearly empty, and further drain voltage changes almost nothing upstream.
  • The depletion region (dashed) is deeper toward the drain because the reverse bias of the field-induced junction grows along the channel.

The physics behind it

  • Continuity: IDS = W|Q′I(x)|v(x) = constant (4.3.4).
  • Strong inversion: IDS = (W/L)µC′ox[(VGS − VT)VDS − (α/2)VDS²] up to V′DS = (VGS − VT)/α, then constant (4.7.24).
  • The real electrons near a pinched-off drain cannot move infinitely fast: diffusion takes over and, in short devices, velocity saturation (Chapter 5).