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

Depth Profiles

Look inside the silicon: carrier densities, electric field and potential versus depth, from the exact solution of Poisson's equation. Zoom to the first nanometres to see the inversion layer.

Electron and hole densities versus depth (log scale)

Electric field versus depth

Potential versus depth

What to look for

dE/dy = ρ/εs, E(ψ) = √(2 q NA F(ψ) / εs)

  • In depletion, p(y) drops far below NA over a width xd and the field falls roughly linearly to zero.
  • In inversion a thin electron layer, only a few nanometres thick at the surface, sits on top of the depletion region (try the 5 nm range).
  • In accumulation hole density rises exponentially toward the surface within a few Debye lengths.

Try this

  1. Set the depth range to 5 nm in strong inversion. How far does the electron layer extend before n(y) falls below NA?
  2. Compare the surface field at VT for NA = 10¹⁶ and 10¹⁸ cm⁻³.
  3. In accumulation, which length sets the width of the hole layer?