Model database for determining dopant profiles from scanning capacitance microscope measurements

Abstract

To help correlate scanning capacitance microscope measurements of silicon with uniformly doped concentrations, model capacitance curves are calculated and stored in a database that depends on the probe-tip radius of curvature, the oxide thickness, and the dopant density. The oxide thicknesses range from 5 to 20 nm, the dopant concentrations range from 10 17 to 10 20 cm Ϫ3 , and the probe-tip radius of curvature is set to 10 nm. The cone-shaped probe is oriented normal to the sample surface, so that the finite-element method in two dimensions may be used 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 512ϫ512 point image takes less than 2 min. ͓S0734-211X͑98͒02401-9͔

One- and two-dimensional dopant/carrier profiling for ULSI

“…A fast algorithm has been developed by Kopanski et a1. [87] using interpolation on the stored solutions of the three-dimensional Poisson equation [88] for various tip-sample bias voltages, oxide thicknesses, dopant concentrations and tip radii. The probe is modeled in this case as a cone with a hemispherical shape which does include the effect of stray fields.…”

Shape dependence of the capacitance of scanning capacitance microscope probes

“…It can be used to arbitrary tip shapes as well as surface morphology. However, until now axially symmetric cases, sections of three-dimensional problems in Cartesian coordinates [31,32] and combination of both have been analysed [33][34][35][36].…”

Calibrated Scanning Capacitance Microscopy for Two-Dimensional Carrier Mapping of n-type Implants in p-doped Si-Wafers

“…Most of the work related to samples containing pn-junctions was carried out in regards to junction delineation. Especially on small structures, a quantitative determination of the 2D doping distribution is obviously impossible without inverse modeling [14] or intensive simulations using empirical databases [15]. In addition, rather sophisticated calibration schemes had to be applied, which usually required intensive simulation [13].…”