Chapter 4 · Visualization 2 of 6 · Section 4.3 (Fig. 4.11) and 4.7

Inside the Channel

Follow the surface potential, the charges and the two current components from the source to the drain. The total current is the same at every point; how it is carried is not.

Cross-section drawn from the profile: inversion layer thickness ∝ |Q′I(x)|, depletion depth ∝ |Q′B(x)|

Surface potential along the channel

Inversion and depletion charge per unit area

Local drift and diffusion currents, as fractions of IDS

Mean electron velocity IDS/(W|Q′I|) (log scale)

What to look for

x/L = F(ψS(x), ψs0) / F(ψsL, ψs0) (4.3.20); Idrift = µW(−Q′I)dψS/dx, Idiff = µWφt dQ′I/dx

  • Strong inversion, small VDS: ψS rises almost linearly, the channel is nearly uniform, drift carries everything.
  • Toward saturation the channel thins at the drain; to carry the same current there the electrons move faster and diffusion takes over near the drain end.
  • Weak inversion (VGS ≈ 0.2 V): ψS is flat, Q′I(x) is a straight line and the current is pure diffusion.

Try this

  1. Set VGS = 1.5 V and slide VDS from 0.05 to 2 V. Watch the drain end of the inversion layer and the velocity plot.
  2. At VDS = 2 V, what fraction of the current is diffusion at the last point? Is the device 'in strong inversion'?
  3. Set VGS = 0.2 V. Why is the drift curve almost zero everywhere?
  4. With VDS = 2 V, at which x does the mean velocity reach 10⁷ cm/s? What does this suggest for short channels?