Temperature dependence of thermal expansion and elastic constants of single crystals of ZrB2 and the suitability of ZrB2 as a substrate for GaN film

Abstract

Coefficients of thermal expansion (CTE) and elastic constants of single crystals of ZrB2 have been determined in the temperature ranges from room temperature to 1073 K and from room temperature to 1373 K, respectively. The elastic constants of ZrB2 are best characterized by the large value of the Young modulus (as high as 500 GPa) and the small values of the Poisson ratio (0.13–0.15), indicating the high stiffness and hardness and the brittleness, respectively. The values of CTE along the a- and c-axis directions are 6.66×10−6 and 6.93×10−6 K−1, respectively, when averaged over the temperature range from room temperature to 1073 K. The CTE value along the a-axis direction of ZrB2 is only moderately larger than the corresponding value for GaN. This together with the small lattice mismatch along the a-axis direction between ZrB2 and GaN in the heteroepitaxial orientation relationship of (0001)GaN//(0001)ZrB2 and 〈112̄0〉GaN//〈112̄0〉ZrB2 indicate that only a small compressive stress develops in the GaN thin-film crystal grown on the (0001) surface of the ZrB2 substrate. The stresses developed in the GaN thin-film crystal are evaluated with the values of CTE and elastic constants of ZrB2 determined in the present study. The evaluation verifies the suitability of ZrB2 as a substrate for heteroepitaxial growth of GaN.