Chapter 3 · Visualization 2 of 6 · Section 3.2

Surface Potential and Charges Versus Gate Voltage

Solve the three-terminal charge-sheet equation for any VGB and VCB. See how VCB postpones inversion and shifts every curve to the right.

Surface potential ψS versus VGB (Fig. 3.7)

Inversion and depletion charge versus VGB, log scale (Fig. 3.6)

What to look for

VGB = VFB + ψS + γ√(ψS + φte(ψS−2ΦF−VCB)/φt) (3.2.21)

  • All curves share the dashed ψsa(VGB) until electrons become important, at ψS ≈ 2ΦF + VCB; then ψS flattens.
  • In accumulation and depletion VCB has no effect at all: it acts only through the electrons.
  • On the log plot weak inversion is a straight line of the same slope for every VCB; the curves are shifted by slightly more than ΔVCB (body effect).

Try this

  1. Set VCB = 0 and VCB = 1 V. Read VH in both cases. Is the difference larger than 1 V?
  2. Find VGB where the weak-inversion approximation departs from the exact curve. Compare with VM.
  3. Reduce tox to 2 nm. What happens to the spacing between the grey curves, and why?
  4. Switch the gate to p⁺ polysilicon. Which features move and which keep their shape?