Jeremiah R. Lowney

Majority and minority electron and hole mobilities in heavily doped GaAs

The majority electron and minority hole mobilities have been calculated in GaAs for donor densities between 5×1016 and 1×1019 cm−3. Similarly, the majority hole and minority electron mobilities have been calculated for acceptor densities between 5×1016 and 1×1020 cm−3. All the important scattering mechanisms have been included. The ionized impurity and carrier–carrier scattering processes have been treated with a phase‐shift analysis. These calculations are the first to use a phase‐shift analysis for minority carriers scattering from majority carriers. The results are in good agreement with experiment, but predict that at high dopant densities minority mobilities should increase with increasing dopant density for a short range of densities. This effect occurs because of the reduction of plasmon scattering and the removal of carriers from carrier–carrier scattering because of the Pauli exclusion principle. Some recent experiments support this finding. These calculations do not treat the density‐of‐states m...

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.

Models for heavy doping effects in gallium arsenide

Klauder’s self‐energy method is used in a self‐consistent calculation of the effects due to the interactions between carriers and dopant ions in GaAs at 300 K. The many‐body effects due to the interactions among the carriers themselves, exchange, and correlation, are estimated by evaluating expressions similar to those of Abram et al. at 300 K. When densities exceed about 5×1016 cm−3 in n‐type GaAs and 1018 cm−3 in p‐type GaAs, carrier‐dopant ion interactions and carrier‐carrier interactions become significant and should be included in calculations of band structure changes and of properties which depend on the density of states such as carrier transport, effective intrinsic carrier concentrations, and coefficients for optical absorption.

Scanning electron microscope analog of scatterometry

Optical scatterometry has attracted a great deal of interest for linewidth measurement due to its high repeatability and capability of measuring sidewall shape. We have developed an analogous and complementary technique for the scanning electron microscope. The new method, like scatterometry, measures shape parameters (e.g., wall angles) as well as feature widths. Also like scatterometry, it operates by finding a match between the measured signal from an unknown sample and a library of signals calculated for known samples. A physics-based model of the measurement is employed for the calculation of libraries. The method differs from scatterometry in that the signal is an image rather than a scattering pattern, and the probe particles are electrons rather than photons. Because the electron-sample interaction is more highly localized, isolated structures or individual structures within an array can be measured. Results of this technique were compared to an SEM cross section for an isolated polycrystalline silicon line. The agreement was better than 2 nm for the width and 0.2{degrees} for wall angles, differences that can be accounted for by measurement errors arising from line edge roughness.

Temperature and Composition Dependence of the Energy Gap of Hg1-xCdxTe by Two-Photon Magnetoabsorption Techniques

Accurate determinations of the energy gap Eg at liquid helium temperatures in alloys of 0.24≤x≤0.30 have been made by two‐photon magnetoabsorption techniques. They are shown to help verify the use of the Hansen–Schmit–Casselman (HSC) relation over the range 0<x<0.30 at these temperatures. In contrast, the observed temperature dependence of Eg below 77 K is nonlinear and thus cannot be described accurately by the HSC relation. Analysis of Eg (T) data for three samples with 0.24≤x≤0.26 has allowed the deduction of a new relationship for Eg (x,T) that more properly accounts for the nonlinear temperature dependence below 77 K and the linear behavior above 77 K, while still accurately describing the x dependence Eg(x,T) =−0.302 +1.93x +5.35(1−2x)(10−4) [(−1822+T 3)/(255.2+T 2)] −0.810x2 +0.832x3, for Eg in eV and T in K. This relation should apply to alloys with 0.2<x<0.3. The maximum change from the HSC relation in this range is 0.004 eV for x=0.2 at ∼10 K.

A model for the charge-pumping current based on small rectangular voltage pulses

Abstract The charge-pumping current results from recombination associated with the SiO2Si interface traps under the gate of a MOSFET when a voltage pulse is applied to the gate. A model is proposed which predicts this current as a function of the frequency, amplitude, and average voltage of pulses with peak-to-peak amplitudes less than the difference between the flatband and inversion voltages and with pulse transistions fast enough so that negligible capture or emission occurs during the transition. The model is based on Shockley-Read-Hall traps segregated by energy and capture cross section into traps which capture only and traps which tend to emit before capture. It predicts the dominant behavior of the measured current and with the inclusion of surface potential fluctuations and a distribution of cross sections it agrees well with experiment. Thus, the charge-pumping current due to these small rectangular pulses can be used to determine the density, the electron capture cross section, and the hole capture cross section of interface traps near midgap.

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.

Effect of donor impurities on the conduction and valence bands of silicon

The energy shifts of valence and conduction band states in silicon due to the interaction of electrons and holes with ionized donors have been calculated by performing a partial wave analysis. The potential is modeled by the Yukawa form with the screening radius determined self‐consistently by the Friedel sum rule. The results show that this effect is an important part of the optically measured band‐gap narrowing. The variation of the Fermi energy due to this phenomenon is also calculated.

Intrinsic carrier concentration of narrow‐gap mercury cadmium telluride based on the nonlinear temperature dependence of the band gap

The intrinsic carrier concentrations of narrow‐gap Hg1−xCdxTe alloys have been calculated as a function of temperature between 0 and 300 K for x values between 0.17 and 0.30. The new and more accurate relation for the temperature dependence of the energy gap, which is based on two‐photon magnetoabsorption data, is used. This relation is further supported here by additional one‐photon magnetoabsorption measurements for x=0.20 and 0.23, which were made with a CO2 laser. In this range of composition and temperature, the energy gap of mercury cadmium telluride is small, and very accurate values for the gap are needed to obtain reliable values for the intrinsic carrier density. Kane’s k⋅p theory is used to account for the conduction‐band nonparabolicity. Large percentage differences occur between our new calculations and previously calculated values for ni at low temperatures. A nonlinear least‐squares fit was made to the results of our calculations for ease of use. The implications of these results for Hg1−xC...