Keithley 4200A-SCS Reference Manual page 1199

Appendix D: Using a Model 82 C-V System
Flatband voltage shift method
The primary method for measuring oxide charge density is the flatband voltage shift or temperature-
bias stress method (Snow, et al). In this case, two high-frequency C-V curves are measured, both at
room temperature. Between the two curves, the device is biased with a voltage at 200-300° to drift
mobile ions across the oxide. The flatband voltage differential between the two curves is then
calculated, from which charge density can be determined.
From Nicollian and Brews (426, Eq. 10.9 and IO. lo), we have:
Where:
•
Q = the first moment of the charge distribution
O
•
= charge centroid
•
W = metal semiconductor work function (constant)
MS
•
ε
= oxide dielectric constant
OX
•
X = oxide thickness
O
•
C = oxide capacitance
OX
So that:
For the common case of thermally grown oxide, x (before) = X
Where Q is the effective charge. Divide Q
O
unit area.
D-58
Model 4200A-SCS Parameter Analyzer Reference Manual
and x (after) = 0, so that
O
by the gate area to obtain mobile ion charge density per
O
4200A-901-01 Rev. C / February 2017