Dynamics of rough Ge(001) surfaces at low temperatures

Mass transport by surface diffusion on rough Ge(001) surfaces is characterized using in situ scanning tunneling microscopy. Rough starting surfaces with nearly constant step densities are prepared by low-energy ion etching at 270 degrees C; the characteristic in-plane length scale of the roughness is varied from 37 to 118 nm. These surfaces are subsequently annealed at 245-325 degrees C for times between 10 min and 6 h and imaged at room temperature. The activation energy for surface smoothing is 1.9 +/- 0.25 eV. The dependence of the relaxation rate on the in-plane length scale is inconsistent with the continuum model of Mullins: the time constant tau of the smoothing process increases with increasing lateral length scale L as tau proportional to L(n), n = 2.2 +/- 0.4.