Chapter 2 · Animation 2 of 4 · Sections 2.4 to 2.6

Sweeping the Gate: Accumulation to Inversion

Move the gate voltage and watch the charges in the silicon and the energy bands respond together, from hole accumulation through depletion to an inversion layer of electrons.

holeelectron⊖ acceptor ion (bold when uncovered)depletion region+ / − gate charge

Surface potential versus gate voltage (exact)

Charges per unit area (log scale): electrons explode, ions saturate

What to look for

  • The gate charge always equals the opposite of all charge in the silicon (plus the small oxide charge): count the + signs on the gate and compare with the ions and carriers.
  • In depletion the band bending grows quickly with VGB; in strong inversion it hardly moves while the electron layer grows. That pinning of ψs is why VT is well defined.
  • On the log plot the electron charge rises by a decade every n·60 mV in weak inversion and then becomes linear in VGB in strong inversion.

The physics behind it

  • Potential balance: VGB = VFB + ψox + ψs (eq. 2.3.5); charge balance: Q′G + Q′o + Q′C = 0 (2.3.7).
  • Exact relation: Q′C = −sgn(ψs)γC′ox√F(ψs), from Poisson's equation with Boltzmann statistics (Section 2.4).
  • Regions by ψs: accumulation < 0 < depletion < ΦF < weak inversion < 2ΦF < moderate < ψ0 < strong inversion (Section 2.6).