Jay F. Marchiando

Scanning capacitance microscopy measurements and modeling: Progress towards dopant profiling of silicon

A scanning capacitance microscope (SCM) has been implemented by interfacing a commercial contact‐mode atomic force microscope with a high‐sensitivity capacitance sensor. The SCM has promise as a next‐generation dopant‐profiling technique because the measurement is inherently two dimensional, has a potential spatial resolution limited by tip diameter of at least 20 nm, and requires no current carrying metal–semiconductor contact. Differential capacitance images have been made with the SCM of a variety of bulk‐doped samples and in the vicinity of pn junctions and homojunctions. Also, a computer code has been written that can numerically solve Poisson’s equation for a model SCM geometry by using the method of collocation of Gaussian points. Measured data and model output for similar structures are presented. How data and model output can be combined to achieve an experimental determination of dopant profile is discussed.

Scanning capacitance microscopy measurement of two-dimensional dopant profiles across junctions

Cross-sectioned p+/p and p–n junction test structures were imaged with a scanning capacitance microscope (SCM). To maintain a constant difference capacitance, our SCM utilizes an electronic attenuator circuit with a dynamic range of 20 V to less than 1 mV. Dopant profiles are extracted from SCM images using a formalism, which rapidly determines the theoretical SCM response from a database of calculated C–V curves. A dopant profile from a p+/p junction determined via constant difference capacitance SCM is compared to a secondary ion mass spectroscopy profile from similar structures.

Carrier concentration dependence of the scanning capacitance microscopy signal in the vicinity of p–n junctions

Scanning capacitance microscopy (SCM) was used to image (1) boron dopant gradients in p-type silicon and (2) identical boron dopant gradients in n-type silicon. The bias voltage dependence of the apparent p–n junction location in the (SCM) images was measured. The theoretical bias voltage dependence of the apparent p–n junction location of the same structures was determined using a two-dimensional, numerical Poisson equation solver. The simulations confirm that, for symmetric step p–n junctions, the apparent junction coincides with the electrical junction when the bias voltage is midway between the voltage that produces the peak SCM response on the p-type side and the voltage that produces the peak response on the n-type side. This rule is only approximately true for asymmetrically doped junctions. We also specify the extent of the region on the junction high and low sides from which valid carrier profiles may be extracted with a simple model.

Model database for determining dopant profiles from scanning capacitance microscope measurements

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 1017 to 1020 cm−3, 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 sa...

Scanning capacitance microscopy applied to two-dimensional dopant profiling of semiconductors

Abstract Scanning capacitance microscope (SCM) images of a semiconductor have contrast that is sensitive to variations in dopant density and spatial resolution on the order of the tip radius, approximately 10 nm. SCMs can be operated in a direct-capacitance, a constant-voltage-difference (open loop), or a constant-capacitance-difference (closed loop) mode. A fast and accurate formalism to convert SCM images to quantitative two-dimensional (2-D) dopant profiles, using either a 1-D model extended to 2-D (quasi-2-D model) or a full 2-D, finite element, numerical solution of Poissons equation, has been developed. Measurements on silicon junctions are used to illustrate the effect of the SCM operating conditions on the quality of the image. For the first time with the SCM, dopant variations of GaAs pn-junctions have been imaged.

Factors influencing the capacitance–voltage characteristics measured by the scanning capacitance microscope

A scanning capacitance microscope (SCM) can measure the local capacitance–voltage (C–V) characteristics of a metal-oxide-semiconductor structure formed by the SCM probe tip and a doped semiconductor sample. A common realization of the SCM depends on a parallel atomic force microscope, which includes a laser focused on the end of the cantilever to monitor the position of the probe tip. In this configuration, it is found that the stray light from the laser can dramatically affect the measured C–V curve. The difference between the SCM C–V curves measured in this high stray light condition and those measured in the true dark condition are shown and discussed. Also discussed is the distortion of the measured C–V curves caused by the SCM method of measuring the differential capacitance using a capacitance-modulating ac voltage and a lock-in amplifier. After reducing and accounting for these effects, the SCM C–V curves show markedly different behavior from that of conventional one-dimensional C–V curves. The mea...

Regression procedure for determining the dopant profile in semiconductors from scanning capacitance microscopy data

A regression procedure has been developed to correlate scanning capacitance microscope (SCM) data with dopant concentration in three dimensions. The inverse problem (calculation of the dopant profile from SCM data) is formulated in two dimensions as a regularized nonlinear least-squares optimization problem. For each iteration of the regression procedure, Poisson’s equation is numerically solved within the quasistatic approximation. For a given type model ion-implanted dopant profile, two cases are considered; the background doping is either the same or the opposite type as that ion-implanted. Due to the long-range nature of the interactions in the sample, the regression is done using two spatial meshes: a coarse mesh and a dense mesh. The coarse mesh stepsize is of the order of the probe-tip size. The dense mesh stepsize is a fraction of the coarse mesh stepsize. The regression starts and proceeds with the coarse mesh until the spatial wavelength of the error or noise in the estimated dopant density profile is of the order of the coarse mesh stepsize. The regression then proceeds in like manner with the dense mesh. Regularization and filtering are found to be important to the convergence of the regression procedure.

Comparison of experimental and theoretical scanning capacitance microscope signals and their impact on the accuracy of determined two-dimensional carrier profiles

The accuracy with which two-dimensional carrier profiles can be extracted from scanning capacitance microscopy (SCM) images of doped structures in silicon depends on the model used to interpret the SCM differential capacitance data. This work validates models of the SCM by comparing the calculated SCM signal to the measured signal for a variety of sample parameters, measurement conditions, and capacitance sensors from different manufacturers. The magnitude of the capacitance sensor high-frequency voltage is measured and its effect on ΔC–V curves and extracted carrier profiles is quantified. Two nonidealities commonly observed in SCM signals, U-shaped C–V curves and double zero crossing in the SCM signal at the p–n junctions, are related to the measurement parameters and explained.

Limitations of the calibration curve method for determining dopant profiles from scanning capacitance microscope measurements

The calibration or conversion curve method (CCM) refers here to using a database of calculations of the capacitance done for a matrix set of model parameters, such as oxide thickness, uniform dopant density, etc., as one method for interpreting scanning capacitance microscope (SCM) measurements. The method was originally intended to help analyze SCM data for slowly varying dopant profiles, where the condition of quasi charge neutrality could be suitably maintained during SCM measurement. However, when the dopant gradient becomes sufficiently large, the quasi charge neutrality condition becomes less satisfied, and the CCM becomes less accurate (unless the gradient is taken into account in some manner). To help evaluate the limitations of the CCM (without gradient correction) in extracting two-dimensional dopant profiles from simulated SCM data, we analyze two representative ion-implanted steep-gradient dopant profiles currently used in device fabrication. The dopant profiles are derived from Monte Carlo si...

Towards reproducible scanning capacitance microscope image interpretation

Scanning capacitance microscope (SCM) images, and the two-dimensional (2D) dopant profiles extracted from them, show poor reproducibility from laboratory to laboratory. Major factors contributing to SCM image variability include: poor sample surface and oxide quality, excess carrier generation from stray light, reduced sensor dynamic range from stray capacitance, and use of nonoptimal SCM operating voltages. This article discusses the sources of SCM image variability, how they affect the measured SCM images, and possible approaches for mitigating their effects. Recommended procedures for extracting quantitative 2D are discussed. Finally, a set of informal research materials is introduced consisting of a complementary metal-oxide-semiconductor transistor pair, an identical pair without metallization, and a pair of transistor-like structures with the conductivity type of the source/drains reversed. These structures are intended for use with the FASTC2D software to help improve laboratory-to-laboratory dopan...