This review describes recent progress in the understanding of the emergence of scale invariance in far-from-equilibrium growth. The first section is devoted to ‘solvable’ needle models which illustrate the relationship between long-range competition mediated, for example, through shadowing or a Laplacian field, and scale invariance. The following three sections, which comprise the bulk of the article, develop the theory of kinetic surface roughening in a comprehensive manner. The two large classes of kinetic roughening processes, characterized by non-conserved (Kardar-Parisi-Zhang) and conserved (ideal molecular beam epitaxy (MBE)) surface relaxation, respectively, are treated separately. For the former case, which has been extensively reviewed elsewhere, the focus is on recent developments. For the case of ideal MBE we give a systematic derivation of the various universality classes in terms of microscopic processes, and compare the predictions of continuum theory to computer simulations and exp...

/pdf/origins-of-scale-invariance-in-growth-processes-4jpthvkz7r.pdf

Origins of scale invariance in growth processes

Morphological evolution during epitaxial thin film growth: Formation of 2D islands and 3D mounds

The evolution of the surface potential during homoepitaxial growth of Fe(001) is studied by scanning tunneling microscopy and reflection high energy electron diffraction. The observed morphology exhibits a non-self-affine collection of moundlike features that maintain their shape but coarsen as growth proceeds. The characteristic feature separation $L$ is set in the submonolayer regime and increases with thickness $t$ as $L(t)\ensuremath{\sim}{t}^{0.16\ifmmode\pm\else\textpm\fi{}0.04}$. During the coarsening phase, the mounds are characterized by a magic slope and a lack of reflection symmetry. These observations are shown to be described by a continuum growth equation without capillarity.

/pdf/coarsening-of-unstable-surface-features-during-fe-001-395apxnc5y.pdf

Coarsening of Unstable Surface Features during Fe(001) Homoepitaxy

This Review chronicles over two decades of research into creating a genetic code for crystal engineering. Rather than directing biological processes, this code uses synthetic forms of DNA to programme the assembly of nanoparticles and microparticles into 1D, 2D and 3D crystalline architectures, in which almost every aspect of the resultant structures can be systematically controlled. Within this conceptual framework, the structural and functional advances are described in an effort to define the present level of sophistication and to predict future directions of the platform. These advances include exotic structures with programmable lattice symmetries and well-defined crystal habits, responsive materials that leverage the intrinsic properties of nucleic acids to manipulate structures on demand, nanoparticle superlattices grown epitaxially from surfaces and colloidal crystals that offer insights into light–matter interactions. Looking forward, we challenge the community to leverage the extraordinary structural control afforded by crystal engineering with DNA to synthesize classes of functional materials that push beyond what has been possible with naturally occurring crystalline materials or those made by more conventional strategies. This Review outlines the ability of DNA to direct the organization of particle-based building blocks into crystalline architectures. These advancements permit programmable control of each structural element of colloidal crystalline materials and enable the design of functional and responsive behaviours.

Crystal engineering with DNA

Fast edge diffusion leads to a diffusion bias during molecular beam epitaxy. Kinetic Monte Carlo simulations on a solid-on-solid model incorporating fast edge diffusion clearly show pattern formation. Fast edge diffusion combined with an excess barrier to go past the outer corner of an island results in wavy steps, similar to the Bales-Zangwill instability, in the step flow growth regime. The evolution of surface morphology with fast edge diffusion and corner diffusion barriers is discussed in terms of the surface diffusion current.

Instability in Molecular Beam Epitaxy due to Fast Edge Diffusion and Corner Diffusion Barriers

A model for metal (100) homoepitaxy is developed which describes irreversible submonolayer nucleation and growth of 2D square islands, and the subsequent transition to multilayer growth Roughness is sensitive to the additional barrier to descend a step, which is estimated for Fe/Fe(100) We find oscillatory height-height correlations and non-Gaussian height and height-difference distributions, necessitating refinement of existing diffraction theory We predict the disappearance of a diffraction ring during growth, and a nonmonotonic variation of roughness with temperature {copyright} {ital 1995} {ital The} {ital American} {ital Physical} {ital Society}

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1037&context=math_pubs

Transition to Multilayer Kinetic Roughening for Metal (100) Homoepitaxy

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Transition to Multilayer Kinetic Roughening for Metal (100) Homoepitaxy