Jf. Marchiando et al., MODEL DATABASE FOR DETERMINING DOPANT PROFILES FROM SCANNING CAPACITANCE MICROSCOPE MEASUREMENTS, Journal of vacuum science & technology. B, Microelectronics and nanometer structures processing, measurement and phenomena, 16(1), 1998, pp. 463-470
To help correlate scanning capacitance microscope measurements of sili
con with uniformly doped concentrations, model capacitance curves are
calculated and stored in a database that depends on the probe-tip radi
us of curvature, the oxide thickness, and the dopant density. The oxid
e thicknesses range from 5 to 20 nm, the dopant concentrations range f
rom 10(17) to 10(20) cm(-3), and the probe-tip radius of curvature is
set to 10 nm. The cone-shaped probe is oriented normal to the sample s
urface, so that the finite-element method in two dimensions may be use
d to solve Poisson's equation in the semiconductor region and Laplace'
s equation in the oxide and ambient regions. The equations are solved
within the semi-classical quasistatic approximation, where capacitance
measurement depends only on the charge due to majority carriers, with
inversion and charge trapping effects being ignored. Comparison with
one-dimensional-related models differs as much as 200% over the given
doping range. For shallow gradient profiles satisfying quasiuniformity
conditions, the database is used directly to find the doping profile.
Converting a 512x512 point image takes less than 2 min.