On the grain size-thickness correlation for thin films

Abstract

A meta-analysis of published data in combination with measurements on Al, Cu, CuO, CoCrCuFeNi, Ni90Cr10, TiN, and V sputter deposited thin films, demonstrates that the grain size is correlated to the film thickness by a power law. The growth exponent depends on the homologous temperature which is defined as the ratio between the deposition and the melting temperature of the studied material. An average value of the growth exponent close to 0.4 was found for the growth exponent for a homologous temperature between 0.14 and 0.31. Film growth models that depict an evolutionary overgrowth mechanism obtain the same growth exponent. Above a homologous temperature of approximately 0.3, a slightly higher exponent is observed which agrees with the general idea that at higher homologous temperatures the grain size is also influenced by restructuring mechanisms occurring during film growth. At low homologous temperatures (<0.14), a substantially lower exponent was noticed. From a theoretical point of view the growth exponent’s value should be close to zero. The aforementioned boundaries of the homologous temperatures correspond with those observed in published structure zone models that describe the microstructure of physical vapor deposited thin films. The good agreement suggests that the underlying mechanism for the observed boundaries is the atom mobility. This hypothesis was further investigated by a study on the influence of intentionally added impurities on the power law behavior for Al and Cu thin films. For both materials, a similar decrease of the grain size as a function of an increasing impurity-to-metal impingement flux ratio on the substrate was observed. No change of the growth exponent is observed for Al, while the growth exponent becomes almost zero for Cu at sufficiently high impurity-to-metal flux ratios.