Chapter 3 · Animation 2 of 4 · Sections 2.5 and 3.2

The n⁺ Contact Fills the Channel Fast

Step the gate voltage on two structures at once. With an n⁺ region next to the gate the inversion layer forms in nanoseconds; without it, thermal generation needs minutes.

electronhole⊖ acceptor ion (bold: uncovered)○generation event

Inversion charge versus real time, both structures (vertical line: now)

What to look for

  • Same gate, same silicon, same final state: only the supply of electrons differs.
  • Both start in deep depletion; the depletion region shrinks back as the inversion layer forms.
  • The times differ by about eleven orders of magnitude, which is why the time axis is logarithmic.

The physics behind it

  • Contacted: the inversion layer charges like a distributed RC line from the n⁺ end. Its effective diffusivity is μ|Q′I|/C′ox, so the fill time grows as L²/(μ(VGB − VT)).
  • Isolated: Zerbst model, dQ′I/dt = q ni(xd − xd,final)/τg, with ψS from the charge balance at fixed Q′I (as in Chapter 2, Animation 3).
  • In equilibrium both reach the same Q′I, from the exact model with VCB = 0.