The dualism between adatom- and vacancy-based single crystal growth models

In homoepitaxial crystal growth, four basic growth morphologies (idealized growth modes) have been established that describe the deposition of atoms on single crystal surfaces: step-flow, layer-by-layer, mound formation, and random/self-affine growth. Mound formation leads to nano-scale surface patterning. However, the formation of (nano)-islands, patterns, and roughness occurs also during ion bombardment, electrochemical etching and oxidation/reduction cycling. Here we show, in analogy to many particle/anti-particle formalisms in physics, the existence of the dualism between individual adatom and single vacancy growth modes. We predict that all standard adatom growth modes do exist also in their counter, vacancy version. For the particular case of mound formation, we derive the theoretical equations and show the inverse similarity of the solution. We furthermore treat simultaneous growth by adatoms and vacancies, and derive the analytical solution of the growth shape evolution of the mounds. Finally, we present an experimental verification, in which both adatom and vacancy mound formation are active. The theoretically predicted mound shape nicely fits the experimental observation.