Thermally Induced Strains in Diamond Cubic, Tetragonal, Orthorhombic, and Hexagonal Films

Abstract

When thin films adhere to a substrate which has a different thermal expansion coefficient, changing the temperature of the composite will induce strains in both film and substrate. Calculations of strain and strain energy have been made for various polycrystalline diamond cubic, tetragonal, orthorhombic, and hexagonal films on substrates which are assumed to be undeformable and to have isotropic thermal expansion and elastic properties in directions parallel to the surface of the substrate. Computer programs were developed to calculate the above quantities for the diamond cubic semiconductors Ge and Si, the tetragonal metals Sn and In, the orthorhombic metal Ga, and the hexagonal metals Be, Cd, Co, Mg, Ti, Zn, and Zr. Each film was assumed to have been deposited on glass or on sodium chloride at room temperature and cooled to approximately liquid air temperature. The induced thermal strains and strain energies for many different crystallographically oriented grains were calculated. The particular (hkl) orientations chosen corresponded to the lowest order x-ray reflections from crystal planes parallel to the surface of the substrate. These calculations extend the authors' earlier work on adhering cubic metal films. Finally, in the case of nonadhering films having more than one thermal expansion coefficient, strains due to thermal expansion alone were calculated as a function of crystal orientation. Various applications of these results are discussed in the text.