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Evaluation of Transport Properties Using Quantitative Mobility Spectrum Analysis (Special Feature Characterization)

Hall effect measurements are the most commonly used method for determining the carrier type, concentration, resistivity, and mobility of semiconductor materials. Measurements made at a single applied field usually provide enough information to characterize transport properties of single carrier semiconductors. Variable field measurements provide the data needed to characterize semiconductor materials with multiple populations of distinct carrier species such as quantum wells, multilayer device structures (i.e. heterostructures), HBTs and HEMTsby acquiring detailed information about transport properties of the individual carriers that make up a multi-carrier material. This is important for both research and development of new materials and industrial characterization and process control. This article looks at the use of the Quantitative Mobility Spectrum Analysis (QMSA) of magnetic field-dependent Hall data to characterize transport properties of multilayer semiconductor structures. We also comment on the use of QMSA to characterize novel materials fabricated in R&D environments and to evaluate deposition products in quality control applications. Hall Effect Measurements Single field Hall effect measurements provide only the Hall coefficient and a weighted average of mobilities of all available carriers at the measurement temperature. Data collected include the measurement temperature, applied magnetic field (B), Hall coefficient (RH) and resistivity (r), from which the mobility and density (or concentration) can readily be measured. Because both of these measurements refer only to the bulk average of all available carriers that make up the material, this data is of limited value. Furthermore, in the absence of measurements at other applied fields, it is impossible to determine whether more than one carrier species is present in the sample. The measurement of Hall data from variable fields can provide additional information about multiple carrier semiconductors. shows the Hall coefficient and resistivity as a function of field for three different samples. Although the raw data does not allow extraction of any individual carrier s behavior, it may be used to distinguish one material from another. In a, the RH vs. B plots suggest that samples A and B are similar, while C is dissimilar. And in fact, A and B are closely related structures. In b, the resistivity data show that samples A and B differ in conductance, although more specific characteristics cannot be inferred. Thus, Hall coefficient and resistivity measurements provide general qualitative information about multi-carrier samples but do not identify individual carrier properties. To correctly characterize transport properties, a more sophisticated analysis, known as Mobility Spectrum Analysis, is required. Quantitative Mobility Spectrum Analysis Mobility Spectrum Analysis was developed by Beck and Anderson in 1987 [1] and was further expanded to Quantitative Mobility Spectrum Analysis (QMSA) by Meyer and Hoffman [2] of the Naval Research Laboratory and Antoszewski et al [3, 4] at the University of Western Australia in 1997. Lake Shore licensed the analytic method, and developed a QMSA software calculation package for use with its own Hall effect measurement systems [5]. This software may also be used to analyze Hall effect data from other systems. Due to the nature of the analysis, however, QMSA results are very sensitive to inherent RH and r measurement errors, so that a high performance system such as the Lake Shore 7500 or 9500 series is required for the most reliable results. In essence, QMSA correlates the measured Hall coefficient and resistivity to a unique mobility spectrum. The Hall coefficient and resistivity measurements in different applied magnetic fields are analyzed to extract a corresponding set of carrier mobilities and concentrations. QMSA takes as its input values the measured Hall coefficient and resistivity at various values of magnetic field. The elements of the field-dependent conductivity matrix are then calculated, and by numerically fitting these elements, QMSA is able to extract a spectrum of mobilities and densities for the individual carriers. QMSA can be used to demonstrate that samples A and B contain low mobility carriers (see : Mobility 1, Density 1) with mobilities of
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