Section 4: Multi-frequency capacitance-voltage unit
Model 4200A-SCS Parameter Analyzer Reference Manual
4-46
4200A-901-01 Rev. C / February 2017
Depletion region
For a p-type MOS capacitor, as the gate voltage moves toward positive values, the MOS capacitor
starts to differ from a parallel-plate capacitor. Roughly at the point where the gate voltage becomes
positive, the following occurs:
•
The positive gate electrostatically repels holes from the substrate-to-oxide/well-to-oxide interface.
•
A carrier-depleted area forms beneath the oxide, creating an insulator (recall that the absence of
free-moving charges distinguishes an insulator from a conductor).
As a result, the high-frequency 4210-CVU measures two capacitances in series: the oxide
capacitance and the depletion capacitance. As the gate voltage becomes more positive, the following
occurs:
•
The depletion zone penetrates more deeply into the semiconductor.
•
The depletion capacitance becomes smaller, and consequently, the total measured capacitance
becomes smaller.
Therefore, the C-V curve slope is negative in the depletion region.
Inversion region
For a p-type MOS capacitor, as the gate voltage increases beyond the threshold voltage, dynamic
carrier generation and recombination move toward net carrier generation. Although the average net
concentration of carriers in a semiconductor is stable at equilibrium, carrier generation and
recombination occur dynamically.
The positive gate voltage both generates electron-hole pairs and attracts electrons (the minority
carriers) toward the gate. Again, because the oxide is a good insulator, these minority carriers
accumulate at the substrate-to-oxide / well-to-oxide interface. The accumulated minority-carrier layer
is called the inversion layer, because the carrier polarity is inverted. Above a certain positive gate
voltage, most available minority carriers are in the inversion layer, and further gate-voltage increases
do not further deplete the semiconductor. That is, the depletion region reaches a maximum depth.
However, inversion-charge generation is slower than the 1 MHz or 100 kHz frequency of the high
frequency-CV (HF-CV) measurement. The average time to generate an inversion charge is
~10
τ
g
N
a
/n
i
, where
τ
g
is the generation lifetime (seconds), N
a
is the doping concentration (cm
-3
), and n
i
is the intrinsic carrier concentration (cm
-3
). For a 10
15
cm
-3
doping concentration and microsecond
generation lifetime, electron-hole-pair (ehp) generation cannot keep up with the high frequency
measurement signal. Therefore, once the depletion region reaches a maximum depth, the
capacitance that is measured by the HF-CV analyzer is still based on the majority carrier position and
distribution. The following applies:
•
The capacitance that is measured by the HF-CV analyzer is the oxide capacitance in series with
maximum depletion capacitance. This capacitance is often referred to as minimum capacitance.
•
The C-V curve slope is almost flat.
The measured inversion-region capacitance at the maximum depletion depth depends on the
measurement frequency. Therefore, C-V curves measured at different frequencies may have
different appearances. Generally, such differences are more significant at lower frequencies and less
significant at higher frequencies.
