"Atomistic" Dopant Profiling Using Scanning Capacitance Microscopy

Abstract

In this article we investigate the possibility to use scanning capacitance microscopy (SCM) for 3-D dopant profiling. It is shown that SCM with probes that have a radius under 10 nm, could be potentially used to determine the x-y-z coordinates of the doping atoms (or ionized impurities) in a layer of a thickness equal to the width of the depletion region. An inversion algorithm that computes the locations of the dopants from the experimental capacitance-voltage (C-V) measurements is presented for the first time. The algorithm is based on the evaluation of the doping sensitivity functions of the differential capacitance and uses a gradient-based iterative method to compute the locations of the dopants.

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“…Most of the existing work related to the analysis of RDF effects in semiconductor devices focuses on the study of the variability of threshold voltages [10], current characteristics [11], and small-signal parameters [12] in field-effecttransistors and there are practically no studies related to the variability of C-V curves besides a few recent conference presentations [6,13,14]. Next, we present a number of simulation studies that show the substantial effect that the discrete nature of dopant impurities has on the lowfrequency differential capacitance in SCM measurements.…”

“…where we have used (4). In order for system (14) to have unique solution, we need in general K M  . Ideally, basis functions   k  r should be selected in such a way to form a complete set in the space of the possible dopant profiles.…”

“…r . In this case we need to compute the superposition coefficients by solving system (14) where: (18) This choice of the basis functions is appropriate for the case when we need to compute the 3-D doping profile, where the doping concentration can be approximated as a continuous function (for instance in large devices).…”