A theoretical model for the electrical properties of chromium thin films sputter deposited at oblique incidence

Chromium thin films are prepared by magnetron sputtering using the glancing angle deposition (GLAD) method. The electrical conductivity of the films exhibiting an inclined columnar structure is investigated. An analytical three-dimensional model is proposed in order to predict the evolution of the electrical conductivity as a function of the columns' orientation. This model is based on two types of electron scattering mechanisms, which are simultaneously operational: the isotropic background scattering at the grain boundary and the scattering due to electron dispersion at the column boundary. The developed analytical expressions enable systematic studies of different processes and film parameters, especially the column angle β as well as the sputtering pressure used during the GLAD deposition. The theoretical and experimental results are compared. It is found that the column angle β must reach a threshold value to significantly reduce the electrical conductivity of chromium thin films close to one order of magnitude. The effect of the sputtering pressure on the structure of films and their electrical behaviours are also studied and well predicted by the proposed model. Finally, a comprehensive discussion of the applicability of the model is presented.