Chapter 4 · Animation 4 of 4 · Sections 4.4.4 and 4.5 (Fig. 4.17)

The Current as an Area, in Motion

The drain current equals (W/L)µ times the area under the Chapter 3 curve −Q′I(VCB) between VSB and VDB. Watch the area and the I–V curve grow together, and stop growing at the pinch-off voltage.

▮area ∝ IDS (red if negative)|VSB|VDB- -VP

What to look for

  • The curve depends only on VGB; VSB and VDB only choose the limits of the area.
  • Saturation needs no special assumption: past VP there is simply no charge left to add.
  • Forward and reverse currents: the area from VSB to ∞ is IF, from VDB to ∞ is IR, and IDS = IF − IR.

The physics behind it

  • IDS = (W/L)µ ∫VSBVDB (−Q′I) dVCB (4.5.2), where VCB is the local quasi-Fermi potential split along the channel.
  • In strong inversion −Q′I ≈ C′ox(VGB − VTB(VCB)), which integrates to the complete strong-inversion model (4.7.2).
  • The pinch-off voltage VP = ψsa(VGB) − φ0 is where the strong-inversion line reaches zero (Chapter 3).