Strained coherent heteroepitaxy of III-V semiconductor films such as In$_x$Ga$_{1-x}$As/GaAs has potential for electronic and optoelectronic applications such as high density logic, quantum computing architectures, laser diodes, and other optoelectronic devices. Crystal symmetry can have a large effect on the morphology of these films and their spatial order. Often the formation of group IV strained heterostructures such as Ge deposited on Si is analyzed using analytic models based on the Asaro-Tiller-Grinfeld instability. However, the governing dynamics of III-V 3D heterostructure formation has different symmetry and is more anisotropic. The additional anisotropy appears in both the surface energy and the diffusivity. Here, the resulting anisotropic governing dynamics are studied to linear order. The resulting possible film morphologies are compared with experimentally observed In$_x$Ga$_{1-x}$As/GaAs films. Notably it is found that surface-energy anisotropy plays a role at least as important as surface diffusion anisotropy if not more so, in contrast to previous suppositions.
An efficient method for the simulation of strained heteroepitaxial growth with intermixing using kinetic Monte Carlo is presented. The model used is based on a solid-on-solid bond counting formulation in which elastic effects are incorporated using a ball and spring model. While idealized, this model nevertheless captures many aspects of heteroepitaxial growth, including nucleation, surface diffusion, and long range effects due elastic interaction. The algorithm combines a fast evaluation of the elastic displacement field with an efficient implementation of a rejection-reduced kinetic Monte Ca…
We study the equilibrium shape, shape transitions and optimal size of strained heteroepitaxial nanoislands with a two-dimensional atomistic model using simply adjustable interatomic pair potentials. We map out the global phase diagram as a function of substrate-adsorbate misfit and interaction. This phase diagram reveals all the phases corresponding to different well-known growth modes. In particular, for large enough misfits and attractive substrate there is a Stranski-Krastanow regime, where nano-sized islands grow on top of wetting films. We analyze the various terms contributing to the tot…
An off-lattice, continuous space Kinetic Monte Carlo (KMC) algorithm is discussed and applied in the investigation of strained heteroepitaxial crystal growth. As a starting point, we study a simplifying (1+1)-dimensional situation with inter-atomic interactions given by simple pair-potentials. The model exhibits the appearance of strain-induced misfit dislocations at a characteristic film thickness. In our simulations we observe a power law dependence of this critical thickness on the lattice misfit, which is in agreement with experimental results for semiconductor compounds. We furthermore in…
We introduce an off-lattice model with continuous particle distances and pair-potential interactions which allows for the efficient simulation of strained heteroepitaxial growth by means of kinetic Monte Carlo (KMC) simulations. We discuss in detail the application of our model to the simulation of three important strain relaxation mechanisms: First, the formation of misfit dislocations in strained adsorbate films is investigated. We find a power-law misfit dependence of the critical layer thickness, in agreement with various experimental studies. Second, we study the self-assembled island for…
We investigate the equilibrium properties of arrays of coherent strained islands in heteroepitaxial thin films of bidimensional materials. The model we use takes into account only three essential ingredients : surface energies, elastic energies of the film and of the substrate and interaction energies between islands via the substrate. Using numerical simulations for a simple Lennard-Jones solid, we can assess the validity of the analytical expressions used to describe each of these contributions. A simple analytical expression is obtained for the total energy of the system. Minimizing this en…
Using density functional theory within the LSDA + U method, we investigate the effect of strain on the spin state and magnetic ordering in perovskite lanthanum cobaltite, LaCoO3. We show that, while strain-induced changes in lattice parameters are insufficient to stabilize a non-zero spin state, additional heteroepitaxial symmetry constraints -- in particular the suppression of octahedral rotations -- stabilize a ferromagnetic intermediate-spin state. By comparing with experimental data for the bulk material, we calculate an upper bound on the Hubbard U value, and describe the role that the on…
A systematic study based on the self-consistent dynamical simulations is presented for the spontaneous evolution of flat solid droplets (bumps), which are driven by the surface drift diffusion induced by the capillary and mismatch stresses, during the development of the Stranski-Krastanow island morphology on a rigid substrate. The physico-mathematical model, which bases on the irreversible thermodynamics treatment of surfaces and interfaces with singularities (Ogurtani, T.O., J. Chem. Phys. 124, 144706, 2006) furnishes us to have auto-control on the otherwise free-motion of the triple junctio…
In the Ge on Si model heteroepitaxial system, metal patterns on the silicon surface provide unprecedented control over the morphology of highly ordered Ge islands. Island shape including nanorods and truncated pyramids is set by the metal species and substrate orientation. Analysis of island faceting elucidates the prominent role of the metal in promoting growth of preferred facet orientations while investigations of island composition and structure reveal the importance of Si-Ge intermixing in island evolution. These effects reflect a remarkable combination of metal-mediated growth phenomena …
A numerical method for computation of heteroepitaxial growth in the presence of strain is presented. The model used is based on a solid-on-solid model with a cubic lattice. Elastic effects are incorporated using a ball and spring type model. The growing film is evolved using Kinetic Monte Carlo (KMC) and it is assumed that the film is in mechanical equilibrium. The strain field in the substrate is computed by an exact solution which is efficiently evaluated using the fast Fourier transform. The strain field in the growing film is computed directly. The resulting coupled system is solved iterat…
We study the morphological evolution of strained heteroepitaxial films using a kinetic Monte Carlo method in three dimensions. The elastic part of the problem uses a Green's function method. Isolated islands are observed under deposition conditions for deposition rates slow compared with intrinsic surface roughening rates. They are semi-spherical and truncated conical for high and low temperature cases respectively. Annealing of films at high temperature leads to the formation of closely packed islands consistent with an instability theory. At low temperature, pits form via a layer-by-layer nu…
A systematic study based on the self-consistent dynamical simulations is presented for the spontaneous evolution of an isolated thin solid droplet on a rigid substrate, which is driven by the surface drift diffusion induced by the anisotropic capillary forces (surface stiffness) and mismatch stresses. In this work, we studied the affect of surface free energy anisotropies on the development kinetics of the 'Stranski-Krastanow' island type morphology. The anisotropic surface free energy and the surface stiffness were treated with well accepted trigonometric functions. Although, various tilt ang…
Nonlinear evolution of three-dimensional strained islands or quantum dots in heteroepitaxial thin films is studied via a continuum elasticity model and the development of a nonlinear dynamic equation governing the film morphological profile. All three regimes of island array evolution are identified and examined, including a film instability regime at early stage, a nonlinear coarsening regime at intermediate times, and the crossover to a saturated asymptotic state, with detailed behavior depending on film-substrate misfit strains but not qualitatively on finite system sizes. The phenomenon of…
The functional properties of devices based on perovskite oxides depend strongly on the growth modes that dramatically affect surface morphology and microstructure of the hetero-structured thin films. To achieve atomically flat surface morphology, which is usually a necessity for the high quality devices, understanding of the growth mechanism of heteroepitaxial thin film is indispensable. In this study, we explore heteroepitaxial growth kinetics of the SrRuO3 using intermittent growth scheme of pulsed laser epitaxy and ex-situ atomic force microscopy. Two significant variations in surface rough…
Heteroepitaxial growth of BaSnO$_3$ (BSO) and Ba$_{1-x}$La$_x$SnO$_3$ (x = 7 %) (LBSO) thin films on different perovskite single crystal (SrTiO$_3$ (001) and SmScO$_3$ (110)) substrates has been achieved by Pulsed Laser Deposition (PLD) under optimized deposition conditions. X-ray diffraction measurements indicate that the films on either of these substrates are relaxed due to the large mismatch and present a high degree of crystallinity with narrow rocking curves and smooth surface morphology while analytical quantification by proton induced x-ray emission (PIXE) confirms the stoichiometric L…
We study the formation and evolution of coherent islands on lattice mismatched epitaxially strained films. Faceted islands form in films with aniostropic surface tension. Under annealing, these islands ripen until a stable array is formed, with an island density which increases with film thickness. Under deposition, an island shape transition occurs, which leads to a bimodal island size distribution. In films with isotropic surface tension we observe continual ripening of islands above a certain film thickness. A stable wavy morphology is found in thinner films.
The formation of dislocation-free three-dimensional islands during the heteroepitaxial growth of lattice-mismatched materials has been observed experimentally for several material systems. The equilibrium shape of the islands is governed by the competition between the surface energy and the elastic relaxation energy of the islands as compared to the uniform strained film. As an exemplification we consider the experimentally intensively investigated growth of InAs quantum dots on a GaAs(001) substrate, deriving the equilibrium shape as a function of island volume. For this purpose InAs surface …
A continuum dynamical model is developed to determine the morphological and compositional instabilities on the free surface of heteroepitaxial alloy films in the absence of growth. We use linear stability analysis to study the early nonequilibrium processes of surface evolution, and calculate the stability conditions and diagrams for different cases of material parameters. There are two key considerations in our treatment: the coupling between top free surface of the film and the bulk phase underneath, and the dependence of both Young's and shear elastic moduli on local composition. The combin…
We investigate strained heteroepitaxial crystal growth in the framework of a simplifying (1+1)-dimensional model by use of off-lattice Kinetic Monte Carlo simulations. Our modified Lennard-Jones system displays the so-called Stranski-Krastanov growth mode: initial pseudomorphic growth ends by the sudden appearance of strain induced multilayer islands upon a persisting wetting layer.
Morphological properties of strained epitaxial films are examined through a mesoscopic approach developed to incorporate both the film crystalline structure and standard continuum theory. Film surface profiles and properties, such as surface energy, liquid-solid miscibility gap and interface thickness, are determined as a function of misfit strains and film elastic modulus. We analyze the stress-driven instability of film surface morphology that leads to the formation of strained islands. We find a universal scaling relationship between the island size and misfit strain which shows a crossover…
Complex surface patterning in homo- and heteroepitaxial contexts: (simultaneous) step bunching and step meandering
Faculty of Mathematics and Informatics, Sofia University（索非亚大学数学与信息学院）；Faculty of Physics, Sofia University（索非亚大学物理学院）；Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所）；Institute of Physical Chemistry, Bulgarian Academy of Sciences（保加利亚科学院物理化学研究所）
We demonstrate how first-principles calculations using density-functional theory (DFT) can be applied to gain insight into the molecular processes that rule the physics of materials processing. Specifically, we study the molecular beam epitaxy (MBE) of arsenic compound semiconductors. For homoepitaxy of GaAs on GaAs(001), a growth model is presented that builds on results of DFT calculations for molecular processes on the beta2-reconstructed GaAs(001) surface, including adsorption, desorption, surface diffusion and nucleation. Kinetic Monte Carlo simulations on the basis of the calculated ener…
We present a first-principles analysis of the strain renormalization of the cation diffusivity on the GaAs(001) surface. For the example of In/GaAs(001)-c(4x4) it is shown that the binding of In is increased when the substrate lattice is expanded. The diffusion barrier ΔE(e) has a non-monotonic strain dependence with a maximum at compressive strain values (e < 0), while being a decreasing function for any tensile strain (e > 0) studied. We discuss the consequences of spatial variations of both the binding energy and the diffusion barrier of an adatom caused by the strain field around a heteroe…
The mechanisms of stability or instability in the strained alloy film growth are of intense current interest to both theorists and experimentalists. We consider dislocation-free, coherent, growing alloy films which could exhibit a morphological instability without nucleation. We investigate such strained films by developing a nonequilibrium, continuum model and by performing a linear stability analysis. The couplings of film-substrate misfit strain, compositional stress, deposition rate, and growth temperature determine the stability of film morphology as well as the surface spinodal decomposi…
The heteroepitaxial growth of Re (0001) films on Nb (110) surfaces has been investigated. Nb/Re bilayers were grown on A-plane sapphire -- alpha-Al2O3 (11-20) -- by molecular beam epitaxy. While Re grew with a (0001) surface, the in-plane epitaxial relationship with the underlying Nb could be best described as a combination of Kurdjumov-Sachs and Nishiyama-Wassermann orientations. This relationship was true regardless of Re film thickness. However, an evolution of the surface morphology with increasing Re thickness was observed, indicative of a Stranski-Krastanov growth mode. Re (0001) layers …
The coupling between antiferrodistortion (AFD) and ferroelectric (FE) polarization, universal for all tilted perovskite multiferroics, is known to strongly correlate with domain wall functionalities in the materials. The intrinsic mechanisms of domain wall phenomena, especially AFD-FE coupling-induced phenomena at the domain walls, have continued to intrigue the scientific and technological communities because of the need to develop the future nano-scale electronic devices. Over the past years, theoretical studies often show controversial results, owing to the fact that they are neither suffic…
In-plane compressively strained $α$-Sn films have been theoretically predicted and experimentally proven to possess non-trivial electronic states of a 3D topological Dirac semimetal. The robustness of these states typically strongly depends on purity, homogeneity and stability of the grown material itself. By developing a reliable fabrication process, we were able to grow pure strained $α$-Sn films on InSb(100), without heating of the substrate during growth, nor using any dopants. The $α$-Sn films were grown by molecular beam epitaxy, followed by experimental verification of the achieved chem…
Morphological evolution of heteroepitaxial nanoislands toward equilibrium (coarsening) is computed using the detailed continuum model that incorporates the quantum size effect. Results reveal the metastability of the "magic" heights, show the morphological transitions and the surface diffusion routes by which a quantum island reaches its stable height, and provide the coarsening laws for the island density and area, thus clarifying the kinetic morphology pathways in the growth of an ultrathin metal films.
Small-Data Machine Learning Uncovers Decoupled Control Mechanisms of Crystallinity and Surface Morphology in $β$-Ga2O3 Epitaxy
State Key Laboratory of Information Photonics and Optical Communications & School of Physical Science and Technology, Beijing University of Posts and Telecommunications（北京邮电大学信息光子学与光通信国家重点实验室及物理科学与技术学院）；Centro de Física de Materiales (CFM-MPC), CSIC-UPV/EHU（材料物理学中心（CFM-MPC），西班牙科学研究中心-巴斯克国立大学）；Institute of Microelectronics and Key Laboratory of Science and Technology on Silicon Devices, Chinese Academy of Sciences（中国科学院微电子研究所及硅器件技术与科学重点实验室）
The linear dispersion relation for longwave surface perturbations, as derived by Levine et al. Phys. Rev. B 75, 205312 (2007) is extended to include a smooth surface energy anisotropy function with a variable anisotropy strength (from weak to strong, such that sharp corners and slightly curved facets occur on the corresponding Wulff shape). Through detailed parametric studies it is shown that a combination of a wetting interaction and strong anisotropy, and even a wetting interaction alone results in complicated linear stability characteristics of strained and unstrained films. PACS: 68.55.J, …
The grain boundary (GB) microstructure influences and is influenced by the development of residual stresses during synthesis of polycrystalline thin films. Recent studies have shown that the frustration between the preferred growth direction and rotations of abutting crystals to local cusps in GB energies leads to internal stresses localized within nanoscopic surface layers around the valleys and ridges that form at emergent boundaries (eGBs). Using a combination of continuum frameworks, numerical analyses and all-atom simulations of bicrystal $\langle 111\rangle$ copper films, we show that eG…
