The fluctuations of steps on crystal surfaces, driven by edge diffusion and by attachment, are treated exactly for the linear regime by considering the mobility of the representative point in the configuration space of the Fourier components. Langevin kinetics are avoided. An accurate treatment of terrace diffusion shows that relaxation modes remain Gaussian with fluctuation amplitudes determined almost entirely by step stiffness, modified by step-step energetic interactions, but not by surface defect mechanisms or diffusion. The attachment model is examined in detail for linear diffusion models, and a straightforward extension of the results is identified for arbitrarily complex diffusion in linear regimes near equilibrium. Relaxation modes, their amplitudes, and characteristic decay times are treated for steps near sinks, including other steps, and a connection is made to results for step arrays. An analysis of correlated step motions suitable for the interpretation of experimental observations is given. The fast (square root) limit of fluctuation dissipation at which terrace diffusion can no longer compete with edge diffusion is treated self-consistently.

• Received 15 April 2002

DOI:https://doi.org/10.1103/PhysRevB.66.155405