Evolution of surface waviness in thin films via volume and surface diffusion

Deformation mechanisms involving mass transport by stress driven diffusion influence a large number of technological problems. We study the formation of undulations on surfaces of stressed films at high temperature by exploring the deformation kinetics governed by volume and surface diffusion. A governing equation is derived that gives the amplitude change of such surfaces as a function of time. A parametric study is then carried out using a range of practically important input values of the film material properties. The results show that at the dominant instability wavelength, under high average stresses (giga pascal range), only surface diffusion contributes to film surface morphology evolution whereas under low stress and high-temperature conditions, both surface diffusion and volume diffusion contribute to film surface morphology evolution. Furthermore, the contribution of volume diffusion depends on the sign of the film stress, with compressive stress promoting surface roughening and tensile stress promoting surface smoothing.