Phonon Frequencies and Thermal Expansion of III-V Compounds
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Phonon Frequencies and Thermal Expansion of III-V Compounds Robert R. Reeber North Carolina State University Department of Materials Science and Engineering Raleigh, NC 27695-7919 ABSTRACT: Thermal expansion is an important parameter for the design and manufacturing of dimensionally thermally stable opto-electronic integrated circuits and superlattices. In earlier work1,2 we established the quantitative relationships between phonon frequencies and thermal expansion for Group IV semiconductors. In this paper we extend this approach to the III-V compounds GaAs, GaP, InP, GaSb, InAs, AlSb and InSb.
INTRODUCTION: Thermal expansion causes a vibrational response of crystals to the thermal stresses induced by changing temperature. The phonon distribution of a crystal is a function of its symmetry and can be determined by resonant neutron studies. In this paper we empirically correlate a comprehensive collection of thermal expansion and expansivity data (lattice parameters) for Group III -V compounds, all with the zincblende structure. Corresponding states relationships were first derived by Einstein, Lindemann, Debye and Grüneisen during the early part of the 20th century. The application of characteristic temperatures to thermophysical property correlation has been comprehensively reviewed by Blackman3. In earlier work4,5,6 this author has utilized corresponding states relationships to correlate melting of alkali halides, phase, and brittle-ductile transitions in II-VI and III-V compounds. When a corresponding states relationship exists it provides a method for predicting thermophysical properties for compounds having minimal data from the larger group of isostructural materials that are well characterized. Melting points can also be correlated with thermal expansion as shown earlier by Straumanis7 for a wide variety of cubic elements. Our earlier model1 provided an iterative thermal expansion fitting procedure with multiple Einstein frequencies that quantitatively implemented Blackman’s lattice theory of thermal expansion.8 In addition to diamond9 and the other group IV semiconductors mentioned earlier, it has been applied to ten II-VI and III-V compounds10, beta-SiC, GaP and InP11, GaN12 and InN.13 The objective here is to correlate the cubic III-V compounds and provide a data set for them that is consistent with the principle of corresponding states. Comparisons with available data are made for selected materials and a table of predicted thermal expansions and lattice parameters is provided over extended temperatures ranges (cryogenic to near melting) for AlSb and InP.
COMPUTATIONAL METHODS:
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The earlier method1 utilized a table of sets of temperatures, to identify a best least squares set of Einstein and Planck functions that reproduced the thermal expansion and expansivity, respectively. This best set was then iteratively changed to improve the fitting. When the data was exceptionally accurate, i.e. as in the case of Ge and Si, the determined frequencies correspond well with a simple approximation
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