Chapter 2 · Visualization 2 of 6 · Sections 2.4 to 2.6

Surface Potential and Charge

See how the surface potential ψS and the silicon charge respond to the gate voltage. The shaded bands mark accumulation, depletion, and weak, moderate and strong inversion.

Surface potential versus gate voltage

Silicon charge (total, depletion part, inversion part) versus gate voltage

What to look for

VGB = VFB + ψS − Q′C / C′ox

  • ψS follows VGB closely in depletion and weak inversion, then flattens: in strong inversion it is nearly pinned near ψ0 = 2ΦF + 6φt.
  • |Q′B| grows slowly like √ψS. |Q′I| grows exponentially and overtakes it around the end of moderate inversion.
  • In accumulation Q′C is positive (holes) and |Q′C| rises almost linearly with the gate voltage.

Try this

  1. Drag the marker through each shaded region and watch which of the two charge curves dominates.
  2. Make the oxide thicker (10 nm). The pinned value of ψS hardly changes. What changes instead?
  3. Raise NA: how do γ and VT − VFB change?