Chapter 2 · Animation 4 of 4 · Sections 2.7 and 2.8

What a C–V Measurement Wiggles

Add a small signal to the gate voltage and see which charge answers it: holes at the surface, ions at the depletion edge, or electrons in the inversion layer. That decides the capacitance.

where the signal charge changes (pulsing)electronhole⊖ acceptor ion

Gate-body capacitance per unit area: low and high frequency (dot: this bias)

What to look for

Watch the amber box: it marks where the small-signal charge appears in the silicon. Its distance from the gate is the 'plate spacing' of the capacitor.
In accumulation and in low-frequency inversion it is at the surface, so C′ ≈ C′_ox. In depletion and in high-frequency inversion it is at the depletion edge, so C′ is smaller.
The signal on screen is greatly exaggerated (about 0.2 V); real C–V measurements use a few tens of millivolts.

The physics behind it

Small-signal capacitance: C′_gb = dQ′_G/dV_GB = C′_oxC′_c/(C′_ox + C′_c), with C′_c = −dQ′_C/dψ_s (Section 2.7).
In depletion C′_c ≈ ε_s/x_d; the minimum high-frequency capacitance uses the maximum depletion width at the onset of strong inversion.
C–V curves give C′_ox (hence t_ox), the doping from the depletion part, and V_FB (Section 2.8).