Chapter 3 · Visualization 3 of 6 · Sections 3.3 and 3.4.2

Body Effect Lab

Reverse-bias the field-induced junction between the inversion layer and the body. The depletion region widens, the gate must hold more charge, and the threshold rises as a square root.

Threshold voltage versus VCB (square-root law) and its tangent at VCB = 0

Inversion charge versus VGC at VCB = 0 and at your VCB (exact model; vertical lines: VT)

Depletion width at the onset of strong inversion (to scale in depth)

What to look for

VT = VT0 + γ(√(φ0 + VCB) − √φ0), VTB = VT + VCB

  • The inversion layer is the n side of a junction whose p side is the body. VCB reverse-biases it, exactly like VR in Chapter 1.
  • A wider depletion region holds more acceptor charge γC′ox√(φ0+VCB); the gate must image it, so VT rises.
  • The rise slows down at large VCB: the tangent ('linear body effect') overestimates it.

Try this

  1. Read ΔVT at VCB = 1 V for tox = 2, 10 and 20 nm. Is it proportional to tox? Why?
  2. Raise NA from 10¹⁶ to 10¹⁸ cm⁻³ at tox = 10 nm. How does γ change?
  3. On the second plot, are the two curves parallel above threshold? What is their slope?
  4. At what VCB does the tangent overestimate VT by 50 mV?