Chapter 3 · Visualization 1 of 6 · Section 3.2

The Surface Barrier and the n⁺ Contact

An n⁺ region touches the surface under the gate. Its potential, set by VCB, decides how high a barrier the electrons must climb to reach the surface, and so how many of them are there.

Conduction and valence band edges along the surface, from the n⁺ region into the region under the gate (dots: electrons, more dots = higher density on a log scale)

Surface electron density nsurface = n0e(ψS−VCB)/φt (dot: your bias)

What to look for

barrier = φbi + VCB − ψS, nsurface = n0 e(ψS − VCB)/φt

  • The electron quasi-Fermi level EFn (gold) is pinned to the n⁺ region, qVCB below the body Fermi level EFp. The electrons at the surface share it.
  • The surface electron density falls by e for every φt of barrier, i.e. 10× for every 60 mV.
  • Raising VCB raises the barrier by the same amount; the gate must lift ψS by VCB to bring the electrons back.

Try this

  1. Set VGB = 0.4 V, VCB = 0. Read the barrier and nsurface. Now set VCB = 0.6 V. By how many decades does nsurface fall?
  2. Keep VCB = 0.6 V and raise VGB until the barrier is back where it was. How much did VGB have to rise? Why more than 0.6 V?
  3. Lower VGB into depletion (about 0 V). Does VCB still change ψS?
  4. Increase tox to 20 nm and repeat the first step. What changes and what does not?