Abstract
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.
Highlights
In homoepitaxial crystal growth, four basic growth morphologies have been established that describe the deposition of atoms on single crystal surfaces: stepflow, layer-by-layer, mound formation, and random/self-affine growth
One often speaks about growth regimes or growth modes, strictly speaking, a growth mode is defined by thermodynamics and not kinetics[1]
When considering etching, the question arises if Considering the third growth mode, one realizes that the final surface contour looks rather similar for both adatom deposition and vacancy creation: in both cases mounds are formed, see Fig. 1
Summary
Four basic growth morphologies (idealized growth modes) have been established that describe the deposition of atoms on single crystal surfaces: stepflow, layer-by-layer, mound formation, and random/self-affine growth. We only consider homoepitaxial growth on single crystals, which is often referred to as thin film growth At slightly higher deposition fluxes, lower mobility, or wider terraces, adatoms meet each other during their random walk on the terraces leading to the nucleation of islands with a typical mean distance that scales with M=F6. As these islands serve as sinks for newly arriving adatoms, the local adatom pressure and, the surface chemical potential drops and further island nucleation stops. This leads to the layer-by-layer growth mode, Fig. 1a
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