Chapter 4 · Animation 3 of 4 · Sections 4.3 and 4.8

Drift or Diffusion?

Each walker takes random thermal steps plus a push from the lateral field. Nothing else is programmed in, yet their density settles onto the inversion-charge profile of the complete model, and you can see which mechanism carries the current.

electron (random walker)→local drift current→local diffusion current (both ∝ value / IDS)

What to look for

  • In weak inversion the bars form a straight line from source to drain: Fick's law with no field.
  • In strong inversion the bars are nearly flat across the channel: the field carries the current.
  • The bars match the model line because the walkers obey exactly the drift-diffusion equation (4.3.4) with the model's ψS(x) and end charges.

The physics behind it

  • Each walker: Δx = D (dψS/dx)/φt Δt + √(2DΔt)·N(0,1), i.e. drift with µE plus diffusion with D = µφt (Einstein relation, Section 1.3).
  • Their steady density solves I = µW(−Q′IdψS/dx + φtdQ′I/dx) = const, the same equation as the charge-sheet model.
  • IDS1 and IDS2 are the channel averages of the local drift and diffusion currents (Section 4.3).