Power law scaling during physical vapor deposition under extreme shadowing conditions

Abstract

A qualitative model that relates the period of the surface roughness to the vertical and spherical growth rates of glancing angle deposited (GLAD) nanorods suggests that rod self-shadowing is responsible for the previously reported temperature dependence in the rod width. Atomic shadowing interactions between neighboring rods as well as surface islands on the rod growth fronts control the morphological evolution which is quantified by the growth exponent p that relates the rod width w (=Ahp) to their height h. An analytical formalism predicts linear dependences of p and A on the average island separation and provides an explanation for reported anomalous p values. Experimental validation using new and previously published GLAD data for Al, Cr, Nb, and Ta shows quantitative agreement for all metallic systems under consideration and confirms the predicted dependences. In addition, a discontinuity in the p versus homologous deposition temperature θ suggests a critical value θc=0.24±0.02 for a transition from two-dimensional to three-dimensional island growth, which is independently confirmed by a discontinuity in the measured island width.