Scaling of surface roughness in a heterogeneous film growth system: Ge_xSi_1-x on Si

We examine how the roughness of compositionally graded, relaxed GeSi/Si(001) films can be understood in terms of theoretical ideas based on continuum descriptions of surface growth. The roughness of all samples shows a universal behavior; it increases linearly with length at small length scales and becomes constant at large length scales. Remarkably, all data can be collapsed onto one universal curve. These results can be described by a linear model composed of Laplacian and surface diffusion terms. We also examine the nonuniversal amplitudes and the up-down symmetry to investigate rigorously the linearity of the model.