J. Semicond. > Volume 37 > Issue 9 > Article Number: 092001

Scaling relation of domain competition on (2+1)-dimensional ballistic deposition model with surface diffusion

Kenyu Osada 1, , Hiroyasu Katsuno 2, 3, , Toshiharu Irisawa 2, and Yukio Saito 4,

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Abstract: During heteroepitaxial overlayer growth multiple crystal domains nucleated on a substrate surface compete with each other in such a manner that a domain covered by neighboring ones stops growing. The number density of active domains ρ decreases as the height h increases. A simple scaling argument leads to a scaling law of ρ~h-γ with a coarsening exponent γ=d/z, where d is the dimension of the substrate surface and z the dynamic exponent of a growth front. This scaling relation is confirmed by performing kinetic Monte Carlo simulations of the ballistic deposition model on a two-dimensional (d=2) surface, even when an isolated deposited particle diffuses on a crystal surface.

Key words: domain competitionballistic deposition modelKardar-Parisi-Zhang universality classsurface diffusion

Abstract: During heteroepitaxial overlayer growth multiple crystal domains nucleated on a substrate surface compete with each other in such a manner that a domain covered by neighboring ones stops growing. The number density of active domains ρ decreases as the height h increases. A simple scaling argument leads to a scaling law of ρ~h-γ with a coarsening exponent γ=d/z, where d is the dimension of the substrate surface and z the dynamic exponent of a growth front. This scaling relation is confirmed by performing kinetic Monte Carlo simulations of the ballistic deposition model on a two-dimensional (d=2) surface, even when an isolated deposited particle diffuses on a crystal surface.

Key words: domain competitionballistic deposition modelKardar-Parisi-Zhang universality classsurface diffusion



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Hersee S D, Sun X Y, Wang X. Nanoheteroepitaxial growth of GaN on Si nanopillar arrays[J]. J Appl Phys, 2005, 97: 124308. doi: 10.1063/1.1937468

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Saito Y, Omura S. Domain competition during ballistic deposition: effect of surface diffusion and surface patterning[J]. Phys Rev E, 2011, 84: 021601.

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Alves S G, Oliveira T J, Ferreira S C. Origins of scaling corrections in ballistic growth models[J]. Phys Rev E, 2014, 90: 052405. doi: 10.1103/PhysRevE.90.052405

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Ballestad A, Ruck B J, Admcyk M. Evidence from the surface morphology for nonlinear growth of epitaxial GaAs films[J]. Phys Rev Lett, 2001, 86: 2377. doi: 10.1103/PhysRevLett.86.2377

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Halpin-Healy T, Palasantzas G. Universal correlators and distributions as experimental signatures of (2+1)-dimensional Kardar-Parisi-Zhang growth[J]. Euro Phys Lett, 2014, 105: 50001. doi: 10.1209/0295-5075/105/50001

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Schwoebel R L, Shipsey E J. Step motion on crystal surfaces[J]. J Appl Phys, 1966, 37: 3682. doi: 10.1063/1.1707904

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Saberi A A, Dashti-Naserabadi H, Rouhani S. Classification of (2+1)-dimensional growing surfaces using Schramm-Loewner evolution[J]. Phys Rev E, 2010, 82: 020101.

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Oliveira T J, Alves S G, Ferreira S C. Kardar-Parisi-Zhang universality class in (2+1) dimensions: universal geometry-dependent distributions and finite-time corrections[J]. Phys Rev E, 2013, 87: 040102.

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Moser K, Wolf D E. Numerical solution of the Kardar-Parisi-Zhang equation in one, two and three dimensions[J]. Physica A, 1991, 178: 215. doi: 10.1016/0378-4371(91)90017-7

[21]

Tamborenea P, Das Sarma S. Surface-diffusion-driven kinetic growth on one-dimensinoal substrate[J]. Phys Rev E, 1993, 48: 2575. doi: 10.1103/PhysRevE.48.2575

[1]

Hayes W, Stoneham A M. Defects and defect processes in nonmetallic solids. New York: John Wiley & Sons, 1985

[2]

Amano H, Sawai N, Akasaki I. Metalorganic vapor phase epitaxial growth of a high quality GaN film using an AlN buffer layer[J]. Appl Phys Lett, 1986, 48: 353. doi: 10.1063/1.96549

[3]

Nakamura S. GaN growth using GaN buffer layer[J]. Jpn J Appl Phys, 1991, 30: L1705. doi: 10.1143/JJAP.30.L1705

[4]

Zheleva T S, Nam O H, Bremser M D. Dislocation density reduction via lateral epitaxy in selectively grown GaN structures[J]. Appl Phys Lett, 1997, 71: 2472. doi: 10.1063/1.120091

[5]

Hersee S D, Sun X Y, Wang X. Nanoheteroepitaxial growth of GaN on Si nanopillar arrays[J]. J Appl Phys, 2005, 97: 124308. doi: 10.1063/1.1937468

[6]

Saito Y, Omura S. Domain competition during ballistic deposition: effect of surface diffusion and surface patterning[J]. Phys Rev E, 2011, 84: 021601.

[7]

Family F, Vicsek T. Scaling of the active zone in the Eden process on percolation networks and the ballistic deposition model[J]. J Phys A, 1985, 18(2): L75. doi: 10.1088/0305-4470/18/2/005

[8]

Barabási A L, Stanley H E. Fractal concepts in surface growth. Cambridge: Cambridge University Press, 1995

[9]

Kardar M, Parisi G, Zhang Y C. Dynamic scaling of growing interfaces[J]. Phys Rev Lett, 1986, 56: 889. doi: 10.1103/PhysRevLett.56.889

[10]

Farnudi B, Vvdensky D D. Large-scale simulations of ballistic deposition: the approach to asymptotic scaling[J]. Phys Rev E, 2011, 83: 020103.

[11]

Alves S G, Oliveira T J, Ferreira S C. Origins of scaling corrections in ballistic growth models[J]. Phys Rev E, 2014, 90: 052405. doi: 10.1103/PhysRevE.90.052405

[12]

Ballestad A, Ruck B J, Admcyk M. Evidence from the surface morphology for nonlinear growth of epitaxial GaAs films[J]. Phys Rev Lett, 2001, 86: 2377. doi: 10.1103/PhysRevLett.86.2377

[13]

Halpin-Healy T, Palasantzas G. Universal correlators and distributions as experimental signatures of (2+1)-dimensional Kardar-Parisi-Zhang growth[J]. Euro Phys Lett, 2014, 105: 50001. doi: 10.1209/0295-5075/105/50001

[14]

Michely T, Krug J. Island, mounds and atoms: patterns and processes in crystal growth far from equilibrium. Berlin: Springer-Verlag, 2004

[15]

Ehrlich G, Hudda F G. Atomic view of surface self-diffusion: tungsten on tungsten[J]. J Chem Phys, 1966, 44: 1039. doi: 10.1063/1.1726787

[16]

Schwoebel R L, Shipsey E J. Step motion on crystal surfaces[J]. J Appl Phys, 1966, 37: 3682. doi: 10.1063/1.1707904

[17]

Bortz A B, Kalos M H, Lebowitz J L. A new algorithm for Monte Carlo simulation of Ising spin system[J]. J Comput Phys, 1975, 17: 10. doi: 10.1016/0021-9991(75)90060-1

[18]

Saberi A A, Dashti-Naserabadi H, Rouhani S. Classification of (2+1)-dimensional growing surfaces using Schramm-Loewner evolution[J]. Phys Rev E, 2010, 82: 020101.

[19]

Oliveira T J, Alves S G, Ferreira S C. Kardar-Parisi-Zhang universality class in (2+1) dimensions: universal geometry-dependent distributions and finite-time corrections[J]. Phys Rev E, 2013, 87: 040102.

[20]

Moser K, Wolf D E. Numerical solution of the Kardar-Parisi-Zhang equation in one, two and three dimensions[J]. Physica A, 1991, 178: 215. doi: 10.1016/0378-4371(91)90017-7

[21]

Tamborenea P, Das Sarma S. Surface-diffusion-driven kinetic growth on one-dimensinoal substrate[J]. Phys Rev E, 1993, 48: 2575. doi: 10.1103/PhysRevE.48.2575

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K. Osada, H Katsuno, T Irisawa, Y Saito. Scaling relation of domain competition on (2+1)-dimensional ballistic deposition model with surface diffusion[J]. J. Semicond., 2016, 37(9): 092001. doi: 10.1088/1674-4926/37/9/092001.

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Manuscript received: 16 March 2016 Manuscript revised: 19 April 2016 Online: Published: 01 September 2016

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