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Álvarez-Cuartas JD, González-Cabrera DL, Camargo M. Epitaxial growth in one dimension. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:463001. [PMID: 39111342 DOI: 10.1088/1361-648x/ad6c98] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2024] [Accepted: 08/07/2024] [Indexed: 08/24/2024]
Abstract
The final structure and properties of layers grown by epitaxy techniques are determined in the very early stage of the process. This review describes one-dimensional models for epitaxial growth, emphasizing the basic theoretical concepts employed to analyze nucleation and aggregation phenomena in the submonolayer regime. The main findings regarding the evolution of quantities that define the properties of the system, such as monomer and island densities, and the associated island size, gap length, and capture zone distributions are discussed, as well as the analytical tools used to evaluate them. This review provides a concise overview of the most widely used algorithms for simulating growth processes, discusses relevant experimental results, and establishes connections with existing theoretical studies.
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Affiliation(s)
| | | | - Manuel Camargo
- DCA & CICBA, Universidad Antonio Nariño-Campus Farallones, Km 18 vía Cali-Jamundí, 760030 Cali, Colombia
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2
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Álvarez-Cuartas JD, Camargo M, González-Cabrera DL. Colloidal model for nucleation and aggregation in one dimension: Accessing the interaction parameters. Phys Rev E 2024; 109:064604. [PMID: 39020952 DOI: 10.1103/physreve.109.064604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2024] [Accepted: 05/02/2024] [Indexed: 07/20/2024]
Abstract
Through a one-dimensional colloidal model for epitaxial growth, we characterize the nucleation and aggregation processes occurring in a gap between adjacent islands. The timescales associated with deposition, diffusion, aggregation, and nucleation inside the gap are studied in terms of the parameters defining the interaction between colloidal particles. Numerical results from molecular-dynamics (MD) simulations are compared with analytical models and good agreement is found between both data sets. The results for the timescales are used to calculate the associated rates to generate kinetic Monte Carlo (KMC) simulations, which allow exploring larger systems and longer timescales in comparison with MD simulations. The KMC simulations reproduce the global behavior of the densities of islands and monomers as well as the gap length distribution between adjacent islands.
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3
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Smirnov O, Amar JG. Island density scaling in reversible submonolayer growth with attachment barriers. Phys Rev E 2024; 109:034803. [PMID: 38632733 DOI: 10.1103/physreve.109.034803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2023] [Accepted: 02/19/2024] [Indexed: 04/19/2024]
Abstract
Island nucleation and growth play an important role in thin-film growth. One quantity of particular interest is the exponent χ, which describes the dependence of the saturation island density N_{sat}∼(D_{h}/F)^{-χ} on the ratio D_{h}/F of the monomer hopping rate D_{h} to the deposition rate F. While standard rate equation (RE) theory predicts that χ=i/(i+2) (where i is the critical island size), more recently it has been predicted that in the presence of a strong barrier to the attachment of monomers to islands, a significantly larger value χ=2i/(i+3) may be observed. While this prediction has recently been tested using kinetic Monte Carlo simulations for the case of irreversible growth corresponding to i=1, it has not been tested for the case of reversible island growth corresponding to i>1. Here we present a mean-field self-consistent RE method which we have used to study the dependence of the effective value of χ on D_{h}/F and barrier-strength for i=1,2,3, and 6. Both the no-nucleation-barrier case in which there exists a barrier for monomers to attach to islands larger than the critical island size (but not to smaller islands) and the nucleation-barrier case in which there is a barrier for monomers to attach to islands of all sizes are studied. In all cases, we find that the existence of attachment barriers significantly increases the effective value of χ for a given barrier strength. In addition, for i=1 we find good agreement between our extrapolated asymptotic value of χ and the theoretical strong-barrier prediction both with and without a nucleation barrier. In contrast, for i>1 the value of χ is significantly larger in the presence of a nucleation barrier than in its absence. In particular, while an asymptotic analysis of our results for i>1 also leads to excellent agreement with the strong barrier prediction in the presence of a nucleation barrier, in the absence of a nucleation barrier the asymptotic values are significantly lower.
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Affiliation(s)
- Oliver Smirnov
- Department of Physics & Astronomy, University of Toledo, Toledo, Ohio 43606, USA
- Department of Physics, Columbia University, New York, New York 10027, USA
| | - Jacques G Amar
- Department of Physics & Astronomy, University of Toledo, Toledo, Ohio 43606, USA
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4
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Marguet B, Reis FDAA, Pierre-Louis O. Interface collisions with diffusive mass transport. Phys Rev E 2022; 106:014802. [PMID: 35974503 DOI: 10.1103/physreve.106.014802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2022] [Accepted: 06/23/2022] [Indexed: 06/15/2023]
Abstract
We report on a linear Langevin model that describes the evolution of the roughness of two interfaces that move towards each other and are coupled by a diffusion field. This model aims at describing the closing of the gap between two 2D material domains during growth, and the subsequent formation of a rough grain boundary. We assume that deposition occurs in the gap between the two domains and that the growth units diffuse and may attach to the edges of the domains. These units can also detach from edges, diffuse, and reattach elsewhere. For slow growth, the edge roughness increases monotonously and then saturates at some equilibrium value. For fast growth, the roughness exhibits a maximum just before the collision between the two interfaces, which is followed by a minimum. The peak of the roughness can be dominated by statistical fluctuations or by edge instabilities. A phase diagram with three regimes is obtained: Slow growth without peak, peak dominated by statistical fluctuations, and peak dominated by instabilities. These results reproduce the main features observed in kinetic Monte Carlo simulations.
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Affiliation(s)
- Bastien Marguet
- Institut Lumière Matière, UMR5306 Université Lyon 1-CNRS, Université de Lyon, 69622 Villeurbanne, France
| | - F D A Aarão Reis
- Instituto de Física, Universidade Federal Fluminense, Avenida Litorânea s/n, 24210-340 Niterói RJ, Brazil
| | - Olivier Pierre-Louis
- Institut Lumière Matière, UMR5306 Université Lyon 1-CNRS, Université de Lyon, 69622 Villeurbanne, France
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5
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Shi H, Zhu X, Zhang S, Wen G, Zheng M, Duan H. Plasmonic metal nanostructures with extremely small features: new effects, fabrication and applications. NANOSCALE ADVANCES 2021; 3:4349-4369. [PMID: 36133477 PMCID: PMC9417648 DOI: 10.1039/d1na00237f] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2021] [Accepted: 06/14/2021] [Indexed: 06/14/2023]
Abstract
Surface plasmons in metals promise many fascinating properties and applications in optics, sensing, photonics and nonlinear fields. Plasmonic nanostructures with extremely small features especially demonstrate amazing new effects as the feature sizes scale down to the sub-nanometer scale, such as quantum size effects, quantum tunneling, spill-out of electrons and nonlocal states etc. The unusual physical, optical and photo-electronic properties observed in metallic structures with extreme feature sizes enable their unique applications in electromagnetic field focusing, spectra enhancing, imaging, quantum photonics, etc. In this review, we focus on the new effects, fabrication and applications of plasmonic metal nanostructures with extremely small features. For simplicity and consistency, we will focus our topic on the plasmonic metal nanostructures with feature sizes of sub-nanometers. Subsequently, we discussed four main and typical plasmonic metal nanostructures with extremely small features, including: (1) ultra-sharp plasmonic metal nanotips; (2) ultra-thin plasmonic metal films; (3) ultra-small plasmonic metal particles and (4) ultra-small plasmonic metal nanogaps. Additionally, the corresponding fascinating new effects (quantum nonlinear, non-locality, quantum size effect and quantum tunneling), applications (spectral enhancement, high-order harmonic wave generation, sensing and terahertz wave detection) and reliable fabrication methods will also be discussed. We end the discussion with a brief summary and outlook of the main challenges and possible breakthroughs in the field. We hope our discussion can inspire the broader design, fabrication and application of plasmonic metal nanostructures with extremely small feature sizes in the future.
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Affiliation(s)
- Huimin Shi
- Center for Research on Leading Technology of Special Equipment, School of Mechanical and Electrical Engineering, Guangzhou University Guangzhou 510006 China
| | - Xupeng Zhu
- School of Physics Science and Technology, Lingnan Normal University Zhanjiang 524048 China
| | - Shi Zhang
- College of Mechanical and Vehicle Engineering, Hunan University Changsha 410082 China
| | - Guilin Wen
- Center for Research on Leading Technology of Special Equipment, School of Mechanical and Electrical Engineering, Guangzhou University Guangzhou 510006 China
| | | | - Huigao Duan
- College of Mechanical and Vehicle Engineering, Hunan University Changsha 410082 China
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6
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Sánchez JA, González DL, Einstein TL. Two-step unconventional protocol for epitaxial growth in one dimension with hindered reactions. Phys Rev E 2019; 100:052805. [PMID: 31869889 DOI: 10.1103/physreve.100.052805] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2019] [Indexed: 11/07/2022]
Abstract
We study the effect of hindered aggregation and/or nucleation on the island formation process in a two-step growth protocol. In the proposed model, the attachment of monomers to islands and/or other monomers is hindered by additional energy barriers which decrease the hopping rate of the monomers to the occupied sites of the lattice. For zero and weak barriers, the attachment is limited by diffusion while for strong barriers it is limited by reaction. We describe the time evolution of the system in terms of the monomer and island densities, N_{1} and N. We also calculate the gap length, the capture zone and the island distributions. For all the sets of barriers considered, the results given by the proposed analytical model are compared with those from kinetic Monte Carlo simulations. We found that the behavior of the system depends on the ratio of the nucleation barrier to the aggregation barrier. The two-step growth protocol allows more control and understanding on the island formation mechanism because it intrinsically separates the nucleation and aggregation processes in different time regimes.
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Affiliation(s)
- Julián A Sánchez
- Departamento de Física, Universidad del Valle, A.A. 25360, Cali, Colombia
| | | | - T L Einstein
- Department of Physics and Condensed Matter Theory Center, University of Maryland, College Park, Maryland 20742-4111, USA
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7
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Headrick RL, Ulbrandt JG, Myint P, Wan J, Li Y, Fluerasu A, Zhang Y, Wiegart L, Ludwig KF. Coherent X-ray measurement of step-flow propagation during growth on polycrystalline thin film surfaces. Nat Commun 2019; 10:2638. [PMID: 31201329 PMCID: PMC6570654 DOI: 10.1038/s41467-019-10629-8] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2018] [Accepted: 05/14/2019] [Indexed: 11/09/2022] Open
Abstract
The properties of artificially grown thin films are strongly affected by surface processes during growth. Coherent X-rays provide an approach to better understand such processes and fluctuations far from equilibrium. Here we report results for vacuum deposition of C60 on a graphene-coated surface investigated with X-ray Photon Correlation Spectroscopy in surface-sensitive conditions. Step-flow is observed through measurement of the step-edge velocity in the late stages of growth after crystalline mounds have formed. We show that the step-edge velocity is coupled to the terrace length, and that there is a variation in the velocity from larger step spacing at the center of crystalline mounds to closely-spaced, more slowly propagating steps at their edges. The results extend theories of surface growth, since the behavior is consistent with surface evolution driven by processes that include surface diffusion, the motion of step-edges, and attachment at step edges with significant step-edge barriers.
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Affiliation(s)
- Randall L Headrick
- Department of Physics and Materials Science Program, University of Vermont, Burlington, VT, 05405, USA.
| | - Jeffrey G Ulbrandt
- Department of Physics and Materials Science Program, University of Vermont, Burlington, VT, 05405, USA
| | - Peco Myint
- Division of Materials Science and Engineering, Boston University, Boston, MA, 02215, USA
| | - Jing Wan
- Department of Physics and Materials Science Program, University of Vermont, Burlington, VT, 05405, USA
| | - Yang Li
- Department of Physics and Materials Science Program, University of Vermont, Burlington, VT, 05405, USA
| | | | - Yugang Zhang
- National Synchrotron Light Source II, Upton, NY, 11967, USA
| | - Lutz Wiegart
- National Synchrotron Light Source II, Upton, NY, 11967, USA
| | - Karl F Ludwig
- Division of Materials Science and Engineering, Boston University, Boston, MA, 02215, USA.,Department of Physics, Boston University, Boston, MA, 02215, USA
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8
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Civantos A, Barnwell A, Shetty AR, Pavón JJ, El-Atwani O, Arias SL, Lang E, Reece LM, Chen M, Allain JP. Designing Nanostructured Ti 6Al 4V Bioactive Interfaces with Directed Irradiation Synthesis toward Cell Stimulation to Promote Host-Tissue-Implant Integration. ACS Biomater Sci Eng 2019; 5:3325-3339. [PMID: 33405575 DOI: 10.1021/acsbiomaterials.9b00469] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A new generation of biomaterials are evolving from being biologically inert toward bioactive surfaces, which can further interact with biological components at the nanoscale. Here, we present directed irradiation synthesis (DIS) as a novel technology to selectively apply plasma ions to bombard any type of biomaterial and tailor the nanofeatures needed for in vitro growth stimulation. In this work, we demonstrate for the first time, the influence of physiochemical cues (e.g., self-organized topography at nanoscale) of medical grade Ti6Al4V results in control of cell shape, adhesion, and proliferation of human aortic smooth muscle stem cells. The control of surface nanostructures was found to be correlated to ion-beam incidence angle linked to a surface diffusive regime during irradiation synthesis with argon ions at energies below 1 keV and a fluence of 2.5 × 1017 cm-2. Cell viability and cytoskeleton morphology were evaluated at 24 h, observing an advance cell attachment state on post-DIS surfaces. These modified surfaces showed 84% of cell biocompatibility and an increase in cytoplasmatic protusions ensuring a higher cell adhesion state. Filopodia density was promoted by a 3-fold change for oblique incidence angle DIS treatment compared to controls (e.g., no patterning) and lamellipodia structures were increased more than a factor of 2, which are indicators of cell attachment stimulation due to DIS modification. In addition, the morphology of the nanofeatures were tailored, with high fidelity control of the main DIS parameters that control diffusive and erosive regimes of self-organization. We have correlated the morphology and the influence in cell behavior, where nanoripple formation is the most active morphology for cell stimulation.
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Affiliation(s)
- Ana Civantos
- Department of Nuclear, Plasma and Radiological Engineering, College of Engineering, University of Illinois at Urbana-Champaign, 104 S Wright St, Urbana, Illinois 61801, United States.,Micro and Nanotechnology Laboratory, University of Illinois at Urbana-Champaign, 208 N Wright St, Urbana, Illinois 61801, United States
| | - Alethia Barnwell
- Department of Nuclear, Plasma and Radiological Engineering, College of Engineering, University of Illinois at Urbana-Champaign, 104 S Wright St, Urbana, Illinois 61801, United States
| | - Akshath R Shetty
- Department of Nuclear, Plasma and Radiological Engineering, College of Engineering, University of Illinois at Urbana-Champaign, 104 S Wright St, Urbana, Illinois 61801, United States.,Micro and Nanotechnology Laboratory, University of Illinois at Urbana-Champaign, 208 N Wright St, Urbana, Illinois 61801, United States
| | - Juan Jose Pavón
- Department of Nuclear, Plasma and Radiological Engineering, College of Engineering, University of Illinois at Urbana-Champaign, 104 S Wright St, Urbana, Illinois 61801, United States.,Micro and Nanotechnology Laboratory, University of Illinois at Urbana-Champaign, 208 N Wright St, Urbana, Illinois 61801, United States.,Group of Advanced Biomaterials and Regenerative Medicine, Bioengineering Program, University of Antioquia, Cl. 67, 53-108 Medellín, Antioquia, Colombia
| | - Osman El-Atwani
- Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, New México 87545, United States
| | - Sandra L Arias
- Micro and Nanotechnology Laboratory, University of Illinois at Urbana-Champaign, 208 N Wright St, Urbana, Illinois 61801, United States.,Department of Bioengineering, University of Illinois at Urbana-Champaign, 1406 W Green St, Urbana, Illinois 61801, United States
| | - Eric Lang
- Department of Nuclear, Plasma and Radiological Engineering, College of Engineering, University of Illinois at Urbana-Champaign, 104 S Wright St, Urbana, Illinois 61801, United States
| | - Lisa M Reece
- University of Texas Medical Branch at Galveston Sealy Center for Vaccine Development, 301 University Blvd, Galveston, Texas 77555, United States
| | - Michael Chen
- City of Hope National Research Medical Center, 1500 E Duarte Road, Duarte, California 91010-3012, United States
| | - Jean Paul Allain
- Department of Nuclear, Plasma and Radiological Engineering, College of Engineering, University of Illinois at Urbana-Champaign, 104 S Wright St, Urbana, Illinois 61801, United States.,Micro and Nanotechnology Laboratory, University of Illinois at Urbana-Champaign, 208 N Wright St, Urbana, Illinois 61801, United States.,Department of Bioengineering, University of Illinois at Urbana-Champaign, 1406 W Green St, Urbana, Illinois 61801, United States
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9
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Lai KC, Han Y, Spurgeon P, Huang W, Thiel PA, Liu DJ, Evans JW. Reshaping, Intermixing, and Coarsening for Metallic Nanocrystals: Nonequilibrium Statistical Mechanical and Coarse-Grained Modeling. Chem Rev 2019; 119:6670-6768. [DOI: 10.1021/acs.chemrev.8b00582] [Citation(s) in RCA: 38] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Affiliation(s)
- King C. Lai
- Department of Physics & Astronomy, Iowa State University, Ames, Iowa 50011, United States
- Division of Chemical & Biological Sciences, Ames Laboratory − USDOE, Iowa State University, Ames, Iowa 50011, United States
| | - Yong Han
- Department of Physics & Astronomy, Iowa State University, Ames, Iowa 50011, United States
- Division of Chemical & Biological Sciences, Ames Laboratory − USDOE, Iowa State University, Ames, Iowa 50011, United States
| | - Peter Spurgeon
- Department of Chemistry, Iowa State University, Ames, Iowa 50011, United States
| | - Wenyu Huang
- Department of Chemistry, Iowa State University, Ames, Iowa 50011, United States
| | - Patricia A. Thiel
- Department of Chemistry, Iowa State University, Ames, Iowa 50011, United States
- Department of Materials Science & Engineering, Iowa State University, Ames, Iowa 50011, United States
| | - Da-Jiang Liu
- Division of Chemical & Biological Sciences, Ames Laboratory − USDOE, Iowa State University, Ames, Iowa 50011, United States
| | - James W. Evans
- Department of Physics & Astronomy, Iowa State University, Ames, Iowa 50011, United States
- Division of Chemical & Biological Sciences, Ames Laboratory − USDOE, Iowa State University, Ames, Iowa 50011, United States
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10
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González DL, Pimpinelli A, Einstein TL. Fragmentation approach to the point-island model with hindered aggregation: Accessing the barrier energy. Phys Rev E 2018; 96:012804. [PMID: 29347254 DOI: 10.1103/physreve.96.012804] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2017] [Indexed: 11/07/2022]
Abstract
We study the effect of hindered aggregation on the island formation process in a one- (1D) and two-dimensional (2D) point-island model for epitaxial growth with arbitrary critical nucleus size i. In our model, the attachment of monomers to preexisting islands is hindered by an additional attachment barrier, characterized by length l_{a}. For l_{a}=0 the islands behave as perfect sinks while for l_{a}→∞ they behave as reflecting boundaries. For intermediate values of l_{a}, the system exhibits a crossover between two different kinds of processes, diffusion-limited aggregation and attachment-limited aggregation. We calculate the growth exponents of the density of islands and monomers for the low coverage and aggregation regimes. The capture-zone (CZ) distributions are also calculated for different values of i and l_{a}. In order to obtain a good spatial description of the nucleation process, we propose a fragmentation model, which is based on an approximate description of nucleation inside of the gaps for 1D and the CZs for 2D. In both cases, the nucleation is described by using two different physically rooted probabilities, which are related with the microscopic parameters of the model (i and l_{a}). We test our analytical model with extensive numerical simulations and previously established results. The proposed model describes excellently the statistical behavior of the system for arbitrary values of l_{a} and i=1, 2, and 3.
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Affiliation(s)
- Diego Luis González
- Departamento de Física, Universidad del Valle, A.A. 25360, Cali, Colombia.,Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA
| | - Alberto Pimpinelli
- Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA.,Smalley-Curl Institute & Materials Science and Nanoengineering Department, Rice University, Houston, Texas 77005, USA
| | - T L Einstein
- Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA.,CMTC, University of Maryland, College Park, Maryland 20742-4111, USA
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11
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Nie Y, Liang C, Cha PR, Colombo L, Wallace RM, Cho K. A kinetic Monte Carlo simulation method of van der Waals epitaxy for atomistic nucleation-growth processes of transition metal dichalcogenides. Sci Rep 2017; 7:2977. [PMID: 28592802 PMCID: PMC5462835 DOI: 10.1038/s41598-017-02919-2] [Citation(s) in RCA: 38] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2017] [Accepted: 04/20/2017] [Indexed: 11/25/2022] Open
Abstract
Controlled growth of crystalline solids is critical for device applications, and atomistic modeling methods have been developed for bulk crystalline solids. Kinetic Monte Carlo (KMC) simulation method provides detailed atomic scale processes during a solid growth over realistic time scales, but its application to the growth modeling of van der Waals (vdW) heterostructures has not yet been developed. Specifically, the growth of single-layered transition metal dichalcogenides (TMDs) is currently facing tremendous challenges, and a detailed understanding based on KMC simulations would provide critical guidance to enable controlled growth of vdW heterostructures. In this work, a KMC simulation method is developed for the growth modeling on the vdW epitaxy of TMDs. The KMC method has introduced full material parameters for TMDs in bottom-up synthesis: metal and chalcogen adsorption/desorption/diffusion on substrate and grown TMD surface, TMD stacking sequence, chalcogen/metal ratio, flake edge diffusion and vacancy diffusion. The KMC processes result in multiple kinetic behaviors associated with various growth behaviors observed in experiments. Different phenomena observed during vdW epitaxy process are analysed in terms of complex competitions among multiple kinetic processes. The KMC method is used in the investigation and prediction of growth mechanisms, which provide qualitative suggestions to guide experimental study.
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Affiliation(s)
- Yifan Nie
- Department of Materials Science and Engineering, The University of Texas at Dallas, Richardson, Texas, 75080, United States
| | - Chaoping Liang
- Department of Materials Science and Engineering, The University of Texas at Dallas, Richardson, Texas, 75080, United States
| | - Pil-Ryung Cha
- School of Advanced Materials, Kookmin University, Jeongneung-gil 77, Seongbuk-gu, Seoul, 136-702, Korea
| | - Luigi Colombo
- Texas Instruments Incorporated, 13121 TI Boulevard, Dallas, Texas, 75243, United States
| | - Robert M Wallace
- Department of Materials Science and Engineering, The University of Texas at Dallas, Richardson, Texas, 75080, United States
| | - Kyeongjae Cho
- Department of Materials Science and Engineering, The University of Texas at Dallas, Richardson, Texas, 75080, United States.
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12
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Thomas SR, Chen CW, Date M, Wang YC, Tsai HW, Wang ZM, Chueh YL. Recent developments in the synthesis of nanostructured chalcopyrite materials and their applications: a review. RSC Adv 2016. [DOI: 10.1039/c6ra05502h] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
Abstract
Nanostructured chalcopyrites: synthesis and applications.
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Affiliation(s)
- Stuart R. Thomas
- Institute of Fundamental and Frontier Sciences
- University of Electronic Science and Technology of China
- People's Republic of China
- Department of Materials Science and Engineering
- National Tsing Hua University
| | - Chia-Wei Chen
- Department of Materials Science and Engineering
- National Tsing Hua University
- Hsinchu 30013
- Taiwan
| | - Manisha Date
- Department of Materials Science and Engineering
- National Tsing Hua University
- Hsinchu 30013
- Taiwan
| | - Yi-Chung Wang
- Department of Materials Science and Engineering
- National Tsing Hua University
- Hsinchu 30013
- Taiwan
| | - Hung-Wei Tsai
- Department of Materials Science and Engineering
- National Tsing Hua University
- Hsinchu 30013
- Taiwan
| | - Zhiming M. Wang
- Institute of Fundamental and Frontier Sciences
- University of Electronic Science and Technology of China
- People's Republic of China
| | - Yu-Lun Chueh
- Department of Materials Science and Engineering
- National Tsing Hua University
- Hsinchu 30013
- Taiwan
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13
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Gianfrancesco AG, Tselev A, Baddorf AP, Kalinin SV, Vasudevan RK. The Ehrlich-Schwoebel barrier on an oxide surface: a combined Monte-Carlo and in situ scanning tunneling microscopy approach. NANOTECHNOLOGY 2015; 26:455705. [PMID: 26489518 DOI: 10.1088/0957-4484/26/45/455705] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The controlled growth of epitaxial films of complex oxides requires an atomistic understanding of key parameters determining final film morphology, such as termination dependence on adatom diffusion, and height of the Ehrlich-Schwoebel (ES) barrier. Here, through an in situ scanning tunneling microscopy study of mixed-terminated La5/8Ca3/8MnO3 (LCMO) films, we image adatoms and observe pile-up at island edges. Image analysis allows determination of the population of adatoms at the edge of islands and fractions on A-site and B-site terminations. A simple Monte-Carlo model, simulating the random walk of adatoms on a sinusoidal potential landscape using Boltzmann statistics is used to reproduce the experimental data, and provides an estimate of the ES barrier as ∼0.18 ± 0.04 eV at T = 1023 K, similar to those of metal adatoms on metallic surfaces. These studies highlight the utility of in situ imaging, in combination with basic Monte-Carlo methods, in elucidating the factors which control the final film growth in complex oxides.
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Affiliation(s)
- Anthony G Gianfrancesco
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge TN 37831, USA. ORNL Institute for Functional Imaging of Materials, Oak Ridge National Laboratory, Oak Ridge TN 37831, USA. UT/ORNL Bredesen Center, University of Tennessee, Knoxville, TN, USA
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14
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Directed Kinetic Self-Assembly of Mounds on Patterned GaAs (001): Tunable Arrangement, Pattern Amplification and Self-Limiting Growth. NANOMATERIALS 2014; 4:344-354. [PMID: 28344227 PMCID: PMC5304676 DOI: 10.3390/nano4020344] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/18/2014] [Revised: 04/05/2014] [Accepted: 04/23/2014] [Indexed: 11/17/2022]
Abstract
We present results demonstrating directed self-assembly of nanometer-scale mounds during molecular beam epitaxial growth on patterned GaAs (001) surfaces. The mound arrangement is tunable via the growth temperature, with an inverse spacing or spatial frequency which can exceed that of the features of the template. We find that the range of film thickness over which particular mound arrangements persist is finite, due to an evolution of the shape of the mounds which causes their growth to self-limit. A difference in the film thickness at which mounds at different sites self-limit provides a means by which different arrangements can be produced.
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15
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Beausoleil A, Desjardins P, Rochefort A. Impact of nucleation on step-meandering instabilities during step-flow growth on vicinal surfaces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032406. [PMID: 24730851 DOI: 10.1103/physreve.89.032406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2014] [Indexed: 06/03/2023]
Abstract
Step-meandering instabilities can manifest during step-flow growth on vicinal surfaces [Bales and Zangwill, Phys. Rev. B 41, 5500 (1990); Pierre-Louis, D'Orsogna, and Einstein, Phys. Rev. Lett. 82, 3661 (1999)]. A phase diagram based on the various growth regimes of a vicinal surface allows us to study the impact of nucleation on these meanders and to predict a meandering instability caused by the nucleation and the coalescence of both islands and steps. Using an accelerated kinetic Monte Carlo method, we find that the coalescence of islands with steps produces large protrusions and deep ripples and that the resulting meandering instability is reinforced by the growth of the islands at almost the same positions from one monolayer to the other. A coarsening phenomenon occurs for the instability wavelength until mounds appear, favored by a large Ehrlich-Schwoebel barrier. Such a meandering instability could be exploited for periodic self-assembly.
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Affiliation(s)
- A Beausoleil
- Regroupement Québécois sur les Matériaux de Pointe and Département de Génie Physique, École Polytechnique de Montréal, Montréal, Québec, Canada H3C 3A7
| | - P Desjardins
- Regroupement Québécois sur les Matériaux de Pointe and Département de Génie Physique, École Polytechnique de Montréal, Montréal, Québec, Canada H3C 3A7
| | - A Rochefort
- Regroupement Québécois sur les Matériaux de Pointe and Département de Génie Physique, École Polytechnique de Montréal, Montréal, Québec, Canada H3C 3A7
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16
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Nicoli M, Misbah C, Politi P. Coarsening dynamics in one dimension: the phase diffusion equation and its numerical implementation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:063302. [PMID: 23848801 DOI: 10.1103/physreve.87.063302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2013] [Indexed: 06/02/2023]
Abstract
Many nonlinear partial differential equations (PDEs) display a coarsening dynamics, i.e., an emerging pattern whose typical length scale L increases with time. The so-called coarsening exponent n characterizes the time dependence of the scale of the pattern, L(t)≈t(n), and coarsening dynamics can be described by a diffusion equation for the phase of the pattern. By means of a multiscale analysis we are able to find the analytical expression of such diffusion equations. Here, we propose a recipe to implement numerically the determination of D(λ), the phase diffusion coefficient, as a function of the wavelength λ of the base steady state u(0)(x). D carries all information about coarsening dynamics and, through the relation |D(L)|=/~L(2)/t, it allows us to determine the coarsening exponent. The main conceptual message is that the coarsening exponent is determined without solving a time-dependent equation, but only by inspecting the periodic steady-state solutions. This provides a much faster strategy than a orward time-dependent calculation. We discuss our method for several different PDEs, both conserved and not conserved.
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Affiliation(s)
- Matteo Nicoli
- Physique de la Matière Condensée, École Polytechnique, CNRS, Palaiseau, F-91128, France
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17
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Barakat F, Martens K, Pierre-Louis O. Nonlinear wavelength selection in surface faceting under electromigration. PHYSICAL REVIEW LETTERS 2012; 109:056101. [PMID: 23006189 DOI: 10.1103/physrevlett.109.056101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2012] [Indexed: 06/01/2023]
Abstract
We report on the control of the faceting of crystal surfaces by means of surface electromigration. When electromigration reinforces the faceting instability, we find perpetual coarsening with a wavelength increasing as t(1/2). For strongly stabilizing electromigration, the surface is stable. For weakly stabilizing electromigration, a cellular pattern is obtained, with a nonlinearly selected wavelength. The selection mechanism is not caused by an instability of steady states, as suggested by previous works in the literature. Instead, the dynamics is found to exhibit coarsening before reaching a continuous family of stable nonequilibrium steady states.
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Affiliation(s)
- Fatima Barakat
- Laboratoire de Physique de la Matière Condensée et Nanostructures, Université Lyon, Villeurbane, France
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18
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Ograin C, Lowengrub J. Geometric evolution law for modeling strongly anisotropic thin-film morphology. Phys Rev E 2012; 84:061606. [PMID: 22304101 DOI: 10.1103/physreve.84.061606] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2011] [Indexed: 11/07/2022]
Abstract
The morphology of the solid-vapor interface of a nanoscale thin crystalline film is influenced by many factors including surface diffusion, attachment-detachment, deposition, and interface kinetics. Using a high-order accurate and efficient numerical method, we investigate the dynamics of two dimensional thin films when all of these effects are considered. The observed morphologies consist of facets of constant slope separated by narrow transition intervals: kinks (valleys) and antikinks (hills). The number of kinks and antikinks decreases as the system coarsens in time. Our numerical results confirm that when deposition is present, the only possible coarsening event is the kink-ternary where two kinks meet and annihilate an antikink. We characterize the total amount of coarsening, the time over which the coarsening occurs and the associated coarsening scaling laws when all effects are considered. As found in previous work that considered only attachment-detachment, or surface diffusion, there are three distinct coarsening regimes associated with increasing magnitudes of the deposition flux-fast coarsening, a regime in which periodic structures form with little or no subsequent coarsening, and a regime in which the film surface evolves chaotically. We find that the inclusion of attachment-detachment leads to additional coarsening compared to the dynamics that result from driven surface diffusion alone. When deposition and interface kinetics are both considered, the slowdown of evolution caused by the kinetic effects necessitates a decrease in the deposition flux in order to produce a nonchaotic coarsening regime. Together, these provide testable predictions for experiments of thin-film dynamics.
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Abstract
AbstractWe examine a class of step ow models of epitaxial growth obtained from a Burton-Cabrera-Frank (BCF) type approach in one space dimension. ur goal is to derive a consistent contin uummodel for the ev olutionof the lm surface. Away from peaks and valleys, the surface height solves a Hamilton- acobi equation (H E). he peaks are free boundaries for this H E. heir evolution must be speci ed by boundary conditions re ecting the microscopic physics of nucleation. e investigate this boundary condition by numerical simulation of the step ow dynamics using a simple n ucleationlaw. ur results rev ealthe presence of sp ecial structures in the pro le near a peak; we discuss the relationship between these structures and the contin uumequation. e further address the importance of ev aporationfor matching the local behavior near the peak to the solution of the contin uum equation.
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Kanjanaput W, Limkumnerd S, Chatraphorn P. Growth instability due to lattice-induced topological currents in limited-mobility epitaxial growth models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:041607. [PMID: 21230287 DOI: 10.1103/physreve.82.041607] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2010] [Revised: 06/25/2010] [Indexed: 05/30/2023]
Abstract
The energetically driven Ehrlich-Schwoebel barrier had been generally accepted as the primary cause of the growth instability in the form of quasiregular moundlike structures observed on the surface of thin film grown via molecular-beam epitaxy (MBE) technique. Recently the second mechanism of mound formation was proposed in terms of a topologically induced flux of particles originating from the line tension of the step edges which form the contour lines around a mound. Through large-scale simulations of MBE growth on a variety of crystalline lattice planes using limited-mobility, solid-on-solid models introduced by Wolf-Villain and Das Sarma-Tamborenea in 2+1 dimensions, we show that there exists a topological uphill particle current with strong dependence on specific lattice crystalline structure. Without any energetically induced barriers, our simulations produce spectacular mounds very similar, in some cases, to what have been observed in many recent MBE experiments. On a lattice where these currents cease to exist, the surface appears to be scale invariant, statistically rough as predicted by the conventional continuum growth equation.
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Affiliation(s)
- Wittawat Kanjanaput
- Department of Physics, Faculty of Science, Chulalongkorn University, Phayathai Road, Patumwan, Bangkok 10330, Thailand.
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21
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Dumont J, Sporken R, Verstraete MJ, Ghijsen J, Gonze X. Demixing processes in AgPd superlattices. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:315002. [PMID: 21828587 DOI: 10.1088/0953-8984/21/31/315002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The present scanning tunneling microscopy (STM) study describes the growth of silver-palladium heterostructures at room temperature, with ab initio simulations of ordered AgPd phases supporting the interpretation of STM images. First, the growth of Pd on an Ag(111) surface proceeds in a multilayer mode, leading to the formation of a columnar structure. Then, upon Ag deposition on this structure, Ag and Pd partially mix and form a two-dimensional AgPd alloy on top of the columns. Finally, an atomically flat Ag(111) surface is restored, and two-dimensional growth continues. An interpretation of this peculiar growth mode including interfacial alloying is proposed based on thermodynamic and kinetic arguments.
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Affiliation(s)
- J Dumont
- Laboratoire de Physique des Matériaux Electroniques (LPME), Facultés Universitaires Notre-Dame de la Paix, Namur, B-5000, Belgium
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22
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Li M, Han Y, Thiel PA, Evans JW. Formation of complex wedding-cake morphologies during homoepitaxial film growth of Ag on Ag(111): atomistic, step-dynamics, and continuum modeling. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:084216. [PMID: 21817368 DOI: 10.1088/0953-8984/21/8/084216] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
An atomistic lattice-gas model is developed which successfully describes all key features of the complex mounded morphologies which develop during deposition of Ag films on Ag(111) surfaces. We focus on this homoepitaxial thin film growth process below 200 K. The unstable multilayer growth mode derives from the presence of a large Ehrlich-Schwoebel step-edge barrier, for which we characterize both the step-orientation dependence and the magnitude. Step-dynamics modeling is applied to further characterize and elucidate the evolution of the vertical profiles of these wedding-cake-like mounds. Suitable coarse-graining of these step-dynamics equations leads to instructive continuum formulations for mound evolution.
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Affiliation(s)
- Maozhi Li
- Department of Physics, Renmin University of China, Beijing 100872, People's Republic of China
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23
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Moktadir Z. Scale decomposition of molecular beam epitaxy. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2008; 20:235240. [PMID: 21694330 DOI: 10.1088/0953-8984/20/23/235240] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
In this work, a study of epitaxial growth was carried out by means of the wavelets formalism. We showed the existence of a dynamic scaling form in a wavelet discriminated linear molecular beam epitaxy (MBE) equation where diffusion and noise are the dominant effects. We determined simple and exact scaling functions involving the scale of the wavelets when the system size is set to infinity. Exponents were determined for both correlated and uncorrelated noise. The wavelet methodology was applied to a computer model simulating linear epitaxial growth; the results showed very good agreement with analytical formulation. We also considered epitaxial growth with the additional Ehrlich-Schwoebel effect. We characterized the coarsening of mounds formed on the surface during the nonlinear phase using the wavelet power spectrum. The latter has an advantage over other methods, in the sense that one can track the coarsening in both frequency (or scale) space and real space simultaneously. Wavelets analysis also provides a quantitative tool for the characterization of the mounded surfaces through its concise scale discrimination. We showed that the averaged wavelet power spectrum (also called scalegram) over all the positions on the surface profile identified the existence of a dominant scale a(*), which increases with time following a power law relation of the form a(*)∼t(n), where [Formula: see text].
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Affiliation(s)
- Z Moktadir
- School of Electronics and Computer Science, Southampton University, UK
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24
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Li M, Evans JW. Theoretical analysis of mound slope selection during unstable multilayer growth. PHYSICAL REVIEW LETTERS 2005; 95:256101. [PMID: 16384474 DOI: 10.1103/physrevlett.95.256101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2005] [Indexed: 05/05/2023]
Abstract
A "step dynamics" model is developed for mound formation during multilayer homoepitaxy. Downward funneling of atoms deposited at step edges is incorporated and controls mound slope selection. Behavior of the selected slope differs from that predicted by phenomenological continuum treatments where the lateral mass current vanishes identically. Instead, this current is shown to vary periodically and vanish only on average. An exact coarse-grained continuum formulation with appropriate boundary conditions is derived and recovers step dynamics results.
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Affiliation(s)
- Maozhi Li
- Institute of Physical Research and Technology, and Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA
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25
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Slanina F, Krug J, Kotrla M. Kinetics of step bunching during growth: a minimal model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:041605. [PMID: 15903680 DOI: 10.1103/physreve.71.041605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2004] [Indexed: 05/02/2023]
Abstract
We study a minimal stochastic model of step bunching during growth on a one-dimensional vicinal surface. The formation of bunches is controlled by the preferential attachment of atoms to descending steps (inverse Ehrlich-Schwoebel effect) and the ratio d of the attachment rate to the terrace diffusion coefficient. For generic parameters (d>0) the model exhibits a very slow crossover to a nontrivial asymptotic coarsening exponent beta approximately 0.38 . In the limit of infinitely fast terrace diffusion (d=0) linear coarsening (beta=1) is observed instead. The different coarsening behaviors are related to the fact that bunches attain a finite speed in the limit of large size when d=0 , whereas the speed vanishes with increasing size when d>0 . For d=0 an analytic description of the speed and profile of stationary bunches is developed, and a connection to the problem of front propagation into an unstable state is pointed out.
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Affiliation(s)
- Frantisek Slanina
- Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic.
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26
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Chakrabarti B, Dasgupta C. Interplay of instabilities in mounded surface growth. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:020601. [PMID: 15783307 DOI: 10.1103/physreve.71.020601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2004] [Indexed: 05/24/2023]
Abstract
We numerically study a one-dimensional conserved growth equation with competing linear (Ehrlich-Schwoebel) and nonlinear instabilities. As a control parameter is varied, this model exhibits a nonequilibrium phase transition between two mounded states, one of which exhibits slope selection and the other does not. The coarsening behavior of the mounds in these two phases is studied in detail. In the absence of noise, the steady-state configuration depends crucially on which of the two instabilities dominates the early time behavior.
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Affiliation(s)
- Buddhapriya Chakrabarti
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.
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27
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Kim TC, Ghim CM, Kim HJ, Kim DH, Noh DY, Kim ND, Chung JW, Yang JS, Chang YJ, Noh TW, Kahng B, Kim JS. Kinetic roughening of ion-sputtered Pd(001) surface: beyond the Kuramoto-Sivashinsky model. PHYSICAL REVIEW LETTERS 2004; 92:246104. [PMID: 15245109 DOI: 10.1103/physrevlett.92.246104] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2003] [Revised: 02/10/2004] [Indexed: 05/24/2023]
Abstract
We investigate the kinetic roughening of Ar+ ion-sputtered Pd(001) surface both experimentally and theoretically. In situ real-time x-ray reflectivity and in situ scanning tunneling microscopy show that nanoscale adatom islands form and grow with increasing sputter time t. Surface roughness W(t) and lateral correlation length xi(t) follow the scaling laws W(t) approximately t(beta) and xi(t) approximately t(1/z) with the exponents beta approximately 0.20 and 1/z approximately 0.20, for an ion beam energy epsilon=0.5 keV, which is inconsistent with the prediction of the Kuramoto-Sivashinsky (KS) model. We thereby extend the KS model by applying the coarse-grained continuum approach of the Sigmund theory to the order of O(inverted Delta(4),h(2)), where h is the surface height, and derive a new term of the form inverted Delta(2)(inverted Delta h)(2) which plays a decisive role in describing the observed morphological evolution of the sputtered surface.
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Affiliation(s)
- T C Kim
- Department of Materials Science and Engineering, Gwangju Institute of Science and Technology, Gwangju, 500-712, Korea
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28
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Politi P, Misbah C. When does coarsening occur in the dynamics of one-dimensional fronts? PHYSICAL REVIEW LETTERS 2004; 92:090601. [PMID: 15089457 DOI: 10.1103/physrevlett.92.090601] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2003] [Indexed: 05/24/2023]
Abstract
Dynamics of a one-dimensional growing front with an unstable straight profile are analyzed. We argue that a coarsening process occurs if and only if the period lambda of the steady-state solution is an increasing function of its amplitude A. This statement is rigorously proved for two important classes of conserved and nonconserved models by investigating the phase diffusion equation of the steady pattern. We further provide clear numerical evidence for the growth equation of a stepped crystal surface.
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Affiliation(s)
- Paolo Politi
- Istituto di Fisica Applicata N. Carrara, Consiglio Nazionale delle Ricerche, Via Madonna del Piano, 50019 Sesto Fiorentino, Italy.
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29
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Chakrabarti B, Dasgupta C. Mound formation and coarsening from a nonlinear instability in surface growth. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:011601. [PMID: 14995627 DOI: 10.1103/physreve.69.011601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2003] [Indexed: 05/24/2023]
Abstract
We study spatially discretized versions of a class of one-dimensional, nonequilibrium, conserved growth equations for both nonconserved and conserved noise using numerical integration. An atomistic version of these growth equations is also studied using stochastic simulation. The models with nonconserved noise are found to exhibit mound formation and power-law coarsening with slope selection for a range of values of the model parameters. Unlike previously proposed models of mound formation, the Ehrlich-Schwoebel step-edge barrier, usually modeled as a linear instability in growth equations, is absent in our models. Mound formation in our models occurs due to a nonlinear instability in which the height (depth) of spontaneously generated pillars (grooves) increases rapidly if the initial height (depth) is sufficiently large. When this instability is controlled by the introduction of a nonlinear control function, the system exhibits a first-order dynamical phase transition from a rough self-affine phase to a mounded one as the value of the parameter that measures the effectiveness of control is decreased. We define an "order parameter" that may be used to distinguish between these two phases. In the mounded phase, the system exhibits power-law coarsening of the mounds in which a selected slope is retained at all times. The coarsening exponents for the spatially discretized continuum equation and the atomistic model are found to be different. An explanation of this difference is proposed and verified by simulations. In the spatially discretized growth equation with conserved noise, we find the curious result that the kinetically rough and mounded phases are both locally stable in a region of parameter space. In this region, the initial configuration of the system determines its steady-state behavior.
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Affiliation(s)
- Buddhapriya Chakrabarti
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
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30
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Ghaisas SV. Surface kinetics and generation of different terms in a conservative growth equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:011605. [PMID: 12935155 DOI: 10.1103/physreve.68.011605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2003] [Indexed: 05/24/2023]
Abstract
A method based on the kinetics of adatoms on a growing surface under epitaxial growth at low temperature in (1+1) dimensions is proposed to obtain a closed form of the local growth equation. It can be generalized to any growth problem where surface morphology is governed by adatom diffusion. The method can be easily extended to higher dimensions. The kinetic processes contributing to various terms in the growth equation are identified from the analysis of in-plane and downward hops. In particular, processes corresponding to the term that breaks h-->-h symmetry and the curvature dependent term are discussed. Effects of these terms on the stable to unstable transition in (1+1) dimension are analyzed. In (2+1) dimensions, it is shown that an additional asymmetric term is generated due to the in-plane curvature associated with mound-like structures. This term is independent of any diffusion barrier differences between in-plane and out-of-plane migration. It is shown that terms generated in the presence of downward hops are the relevant terms in a growth equation. A growth equation in closed form is obtained for various growth models introduced to capture most of the processes in experimental molecular beam epitaxial growth. The effect of dissociation is also considered and is seen to have a stabilizing effect on growth. It is shown that for uphill current the growth equation approach fails to describe the growth since a given single equation does not apply over the entire substrate.
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Affiliation(s)
- S V Ghaisas
- Department of Electronic Science, University of Pune, Pune 411007, India
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31
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Nanostructuring by ion beam. MATERIALS SCIENCE & ENGINEERING. C, MATERIALS FOR BIOLOGICAL APPLICATIONS 2003. [DOI: 10.1016/s0928-4931(02)00268-0] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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32
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Ghaisas SV. Mounding instability and incoherent surface kinetics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:010601. [PMID: 12636480 DOI: 10.1103/physreve.67.010601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2002] [Indexed: 05/24/2023]
Abstract
Mounding instability in a conserved growth from vapor is analyzed within the framework of adatom kinetics on the growing surface. The analysis shows that depending on the local structure of the surface, kinetics of adatoms may vary, leading to disjoint regions in the sense of a continuum description. This is manifested particularly under the conditions of instability. Mounds grow on these disjoint regions and their lateral growth is governed by the flux of adatoms hopping across the steps in the downward direction. Asymptotically ln t dependence is expected in (1+1) dimensions. Simulation results confirm the prediction. Growth in (2+1) dimensions is also discussed.
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Affiliation(s)
- S V Ghaisas
- Department of Electronic Science, University of Pune, Pune 411007, India
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33
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Chatraphorn PP, Sarma SD. Layer-by-layer epitaxy in limited mobility nonequilibrium models of surface growth. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:041601. [PMID: 12443210 DOI: 10.1103/physreve.66.041601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2002] [Indexed: 05/24/2023]
Abstract
We study, using noise-reduction techniques, layer-by-layer epitaxial growth in limited mobility solid-on-solid nonequilibrium surface growth models, which have been introduced in the context of kinetic surface roughening in ideal molecular beam epitaxy. Multiple hit noise reduction and long surface diffusion length lead to qualitatively similar layer-by-layer epitaxy in (1+1)- and (2+1)-dimensional limited mobility growth simulations. We discuss the dynamic scaling characteristics connecting the transient layer-by-layer growth regime with the asymptotic kinetically rough growth regime.
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Affiliation(s)
- P Punyindu Chatraphorn
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, MD 20742-4111, USA
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34
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Politi P, Castellano C. Process of irreversible nucleation in multilayer growth. II. Exact results in one and two dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:031606. [PMID: 12366129 DOI: 10.1103/physreve.66.031606] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2001] [Indexed: 05/23/2023]
Abstract
We study irreversible dimer nucleation on top of terraces during epitaxial growth in one and two dimensions, for all values of the step-edge barrier. The problem is solved exactly by transforming it into a first passage problem for a random walker in a higher-dimensional space. The spatial distribution of nucleation events is shown to differ markedly from the mean-field estimate except in the limit of very weak step-edge barriers. The nucleation rate is computed exactly, including numerical prefactors.
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Affiliation(s)
- Paolo Politi
- Istituto Nazionale per la Fisica della Materia, Unità di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy.
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35
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Politi P, Castellano C. Process of irreversible nucleation in multilayer growth. I. Failure of the mean-field approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:031605. [PMID: 12366128 DOI: 10.1103/physreve.66.031605] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2001] [Indexed: 05/23/2023]
Abstract
The formation of stable dimers on top of terraces during epitaxial growth is investigated in detail. In this paper we focus on mean-field theory, the standard approach to study nucleation. Such theory is shown to be unsuitable for the present problem, because it is equivalent to considering adatoms as independent diffusing particles. This leads to an overestimate of the correct nucleation rate by a factor N, which has a direct physical meaning: on average, a visited lattice site is visited N times by a diffusing adatom. The dependence of N on the size of the terrace and on the strength of step-edge barriers is derived from well-known results for random walks. The spatial distribution of nucleation events is shown to be different from the mean-field prediction, for the same physical reason. In the following paper we develop an exact treatment of the problem.
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Affiliation(s)
- Paolo Politi
- Istituto Nazionale per la Fisica della Materia, Unità di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy.
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Pierre-Louis O, Haftel MI. Oscillatory driving of crystal surfaces: a route to controlled pattern formation. PHYSICAL REVIEW LETTERS 2001; 87:048701. [PMID: 11461651 DOI: 10.1103/physrevlett.87.048701] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2000] [Revised: 03/28/2001] [Indexed: 05/23/2023]
Abstract
We show that the oscillatory driving of crystal surfaces can induce pattern formation or smoothening. Depending on driving conditions, step bunching and meandering, mound formation, or surface smoothening may be seen in the presence of a kinetic asymmetry at the steps or kinks. We employ a step model to calculate the induced mass flux along misoriented surfaces, which accounts for surface dynamics and stability. Slope selection, surface metastability, and frequency-dependent surface stability are found. Quantitative predictions for pattern formation on metal surfaces in an electrolyte are provided.
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Affiliation(s)
- O Pierre-Louis
- LSP-GREPHE, CNRS, UJF-Grenoble 1, BP 87, F38402 Saint Martin d'Hères, France
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Rusanen M, Koponen IT, Heinonen J, Ala-Nissila T. Instability and wavelength selection during step flow growth of metal surfaces vicinal to fcc(001). PHYSICAL REVIEW LETTERS 2001; 86:5317-5320. [PMID: 11384487 DOI: 10.1103/physrevlett.86.5317] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2000] [Indexed: 05/23/2023]
Abstract
We study the onset and development of ledge instabilities during growth of vicinal metal surfaces using kinetic Monte Carlo simulations. We observe the formation of periodic patterns at [110] close packed step edges on surfaces vicinal to fcc(001) under realistic molecular beam epitaxy conditions. The corresponding wavelength and its temperature dependence are studied in detail. Simulations suggest that the ledge instability on fcc(1,1,m) vicinal surfaces is controlled by the strong kink Ehrlich-Schwoebel barrier, with the wavelength determined by dimer nucleation at the step edge. Our results are in agreement with recent continuum theoretical predictions, and experiments on Cu(1,1,17) vicinal surfaces.
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Affiliation(s)
- M Rusanen
- Helsinki Institute of Physics and Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 HUT, Espoo, Finland
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Ghaisas SV. (2+1)-dimensional stochastic growth model and its application to some experimental observations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:062601. [PMID: 11415151 DOI: 10.1103/physreve.63.062601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2000] [Revised: 01/25/2001] [Indexed: 05/23/2023]
Abstract
A (2+1)-dimensional stochastic growth model is proposed in order to understand various experimental observations at low temperature growth. The model includes step attached adatom hopping in the upward direction to provide a source of additional particle current. The flexibility obtained due to additional current control allows one to express most of the experimental observations within the framework of this model. It is argued that the time evolution exponent beta for surface roughness is >0.5 only if upward hops are included. Simulations using this model are shown to be qualitatively consistent with the observations for homoepitaxial growth on Cu(100) and Ge(100) at different temperatures.
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Affiliation(s)
- S V Ghaisas
- Department of Electronic Science, University of Pune, Pune 411007, India
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Thiel PA, Evans JW. Nucleation, Growth, and Relaxation of Thin Films: Metal(100) Homoepitaxial Systems. J Phys Chem B 2000. [DOI: 10.1021/jp9933471] [Citation(s) in RCA: 38] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- P. A. Thiel
- Departments of Chemistry and Mathematics, and Ames Laboratory, Iowa State University, Ames, Iowa 50011
| | - J. W. Evans
- Departments of Chemistry and Mathematics, and Ames Laboratory, Iowa State University, Ames, Iowa 50011
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Chapter 1 Surface processes in epitaxial growth. ACTA ACUST UNITED AC 1997. [DOI: 10.1016/s1571-0785(97)80004-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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