Roughness scaling in cyclical surface growth - art. no. 051604

The scaling behavior of cyclical growth (e.g., cycles of alternating deposi tion and desorption primary processes) is investigated theoretically and pr obed experimentally. The scaling approach to kinetic roughening is generali zed to cyclical processes by substituting the number of cycles n for the ti me. The roughness is predicted to grow as n(beta) where beta is the cyclica l growth exponent. The roughness saturates to a value that scales with the system size L as L-alpha, where alpha is the cyclical roughness exponent. T he relations between the cyclical exponents and the corresponding exponents of the primary processes are studied. Exact relations are found for cycles composed of primary linear processes. An approximate renormalization group approach is introduced to analyze nonlinear effects in the primary process es. The analytical results are backed by extensive numerical simulations of different pairs of primary processes, both linear and nonlinear. Experimen tally, silver surfaces are grown by a cyclical process composed of electrod eposition followed by 50% electrodissolution. The roughness is found to inc rease as a power law of n, consistent with the scaling behavior anticipated theoretically. Potential applications of cyclical scaling include accelera ted testing of rechargeable batteries and improved chemotherapeutic treatme nt of cancerous tumors.