Roughness scaling in cyclical surface growth

The scaling behavior of cyclical growth (e.g., cycles of alternating deposition and desorption primary processes) is investigated theoretically and probed experimentally. The scaling approach to kinetic roughening is generalized to cyclical processes by substituting the number of cycles n for the time. The roughness is predicted to grow as $n^{\beta }$ where $\beta$ is the cyclical 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. The 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 processes. The analytical results are backed by extensive numerical simulations of different pairs of primary processes, both linear and nonlinear. Experimentally, silver surfaces are grown by a cyclical process composed of electrodeposition followed by 50% electrodissolution. The roughness is found to increase as a power law of n, consistent with the scaling behavior anticipated theoretically. Potential applications of cyclical scaling include accelerated testing of rechargeable batteries and improved chemotherapeutic treatment of cancerous tumors.