From spiral growth to kinetic roughening in molecular-beam epitaxy of GaN(0001)

Surface roughening of GaN layers grown by molecular-beam epitaxy using ${\mathrm{NH}}_3$ as a nitrogen source on Si(111) substrates has been studied by ex situ atomic force microscopy. Mound formation is observed and analyzed using scaling concepts. The surface roughness evolution as a function of the growth time exhibits two distinct behaviors. Above a certain thickness, the growth leads to a kinetic roughening characterized by the roughness exponent $\alpha \approx 0.92$ and the dynamic exponent $\beta \approx \mathrm{0.3.}$ However, in the first stages of the heteroepitaxial growth, a coarsening of the mounds without an increase of the roughness is observed. This behavior is inconsistent with the scaling relationship of the surface width predicted by most kinetic roughening models. Results are interpreted considering a crossover between screw dislocation induced spiral growth and kinetic roughening.