High Temperature Elastic Constant Prediction of Some Group III-Nitrides
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High Temperature Elastic Constant Prediction of Some Group III-Nitrides Robert R. Reeber and Kai Wang MRS Internet Journal of Nitride Semiconductor Research / Volume 6 / January 2001 DOI: 10.1557/S1092578300000156, Published online: 13 June 2014
Link to this article: http://journals.cambridge.org/abstract_S1092578300000156 How to cite this article: Robert R. Reeber and Kai Wang (2001). High Temperature Elastic Constant Prediction of Some Group III-Nitrides . MRS Internet Journal of Nitride Semiconductor Research, 6, pp e3 doi:10.1557/S1092578300000156 Request Permissions : Click here
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MRS
Internet Journal Nitride Semiconductor Research
High Temperature Elastic Constant Prediction of Some Group IIINitrides Robert R. Reeber1 and Kai Wang1 1Department
of Materials Science and Engineering, North Carolina State University,
(Received Tuesday, January 9, 2001; accepted Thursday, January 25, 2001)
Thermoelastic properties are important for modeling thermal residual stresses and for optimizing the growth conditions of semiconductor thin films. Thermal expansions of AlN and GaN have been evaluated and predicted by us earlier [1] [2]. Here, high temperature elastic constants are estimated empirically from corresponding state relationships and data from other hexagonal GrimmSommerfeld compounds. This information together with our earlier thermal expansion data will further improve capabilities for calculating thermal residual stresses in various semiconductor thin films.
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Introduction and Methods
A material at absolute zero is uniquely represented by the nature of its atoms, their spatial arrangement and the forces between them. In the rigid ion model it is assumed that the electron distribution is locked to the nuclei and is not affected by the lattice dynamics induced by increases in temperature and pressure. As one explores the state of matter at higher temperatures and pressures it is anticipated that most models will have increasing inaccuracies as interatomic interactions responsible for materials behavior are complex, generally non-linear, and are not well understood. Shell representations provide qualitative results for this difficult problem. First principle theories for calculating high temperature elastic constants have many approximations and assumptions and, as indicated earlier [3] [4], have difficulty in reproducing thermal expansion measurements over extended temperature ranges. Calculations of high temperature elastic constants [5] based upon the central force model of Keating [6] [7] also have been questioned on theoretical grounds [8]. Most of the theoretical work provides zero K results for the temperature dependence of assumed quasi-harmonic cubic semiconductors. It is well known that the thermophysical properties of crystal-chemically similar
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