Thermal strain in indium thin films deposited on GaAs substrates

Thermal strains in indium thin films deposited on GaAs substrates, which were introduced into the films upon cooling from 293 to 25 K, were measured using the conventional X-ray diffraction technique. Since the thermal expansion coefficients and the elastic constants of indium have strong dependences on the crystal orientation, we studied intensively the crystal orientation dependence of the strains perpendicular to the film surface. The strains measured for films with 60 nm thickness agreed well with those calculated based on a biaxial strain model using the difference in thermal expansions between the indium and the GaAs. The present strain analysis indicated that the anisotropy in the thermal expansion of indium is the prinary cause of different strains measured in grains with various crystal orientations. For the thicker films the strains were observed to deviate from the theoretical values owing to strain relaxation upon cooling.