Equations of motion for epitaxial growth

Zangwill, Andrew; Luse, C. N.; Vvedensky, Dimitri D.; Wilby, Mark Richard

doi:10.1016/0039-6028(92)90517-a

Cited by 31 publications

(27 citation statements)

References 17 publications

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“…The faceting on CdTe(100) has many of the characteristics identified in the discussions of "coarsening" of high-symmetry surfaces during MBE growth. [14][15][16][17][18][19] The facets are pyramidal and have a low angle (10°) which is greater than the critical angle (4°) at which faceting vanishes. The facets are epitaxial, single crystalline, and they vanish when a critical misorientation of the substrate is used.…”

Section: Discussionmentioning

confidence: 99%

“…13 Experimental and theoretical contributions to the general area of coarsening of singular surfaces provide a foundation for understanding facet formation in systems as diverse as GaAs epitaxy and Fe epit- The Morphology of CdTe Deposited by Organometallic Vapor Phase Epitaxy: The Effect of Substrate Misorientation axy. [14][15][16][17][18][19] Schwoebel barriers 20,21 at the step edges prevent downward diffusion of adatoms to the next lower terrace on stepped surfaces, which leads to instabilities on high-symmetry surfaces with low step densities. Two-dimensional nucleation occurs when steps are too far apart; Johnson et al 16 demonstrated by simulations that "mounds" appear when many stable nuclei form on terraces.…”

Section: Introductionmentioning

confidence: 99%

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The morphology of CdTe deposited by organometallic vapor phase epitaxy: The effect of substrate misorientation

Yong

Sides

Gellman

1997

Journal of Elec Materi

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Substrate misorientation and growth temperature influence the morphology of CdTe epilayers grown by organometallic vapor phase homoepitaxy. These effects were investigated by using CdTe{100} and CdTe{100} misoriented by 2, 4, 6, and 8° toward <111> Te as substrates for growth in the temperature range from 337 to 425°C. Low angle pyramidal facets appeared on films grown on the CdTe (100) surface. The number density of these pyramidal facets decreased to zero as the substrate misorientation angle increased to 4°. At higher misorientation angles, low angle protrusions, resembling fish scales, appeared on the surface. When the temperature was increased, facet size decreased but facet density increased. The film morphology at the high misorientations, however, improved remarkably with increasing temperature. Cross-sectional transmission electron microscopy provided evidence that both the faceted CdTe films and films with a mirror-like finish were epitaxial single crystals with no planar defects. Schwoebel barriers are suggested as the reason for the faceting of the surface grown on CdTe{100}.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The morphology of CdTe deposited by organometallic vapor phase epitaxy: The effect of substrate misorientation

Yong

Sides

Gellman

1997

Journal of Elec Materi

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“…In the following, we use Eq. (17) in order to express the step velocity, the right-hand side of Eq. (15), as the sum of adatom fluxes toward the step edge.…”

Section: Scaling Limit As a -*•mentioning

confidence: 99%

“…Notably, in Ref. [ 17] the authors start with a 2D master equation and reduce it to a Langevin-type description for continuous-in-time height columns by retaining discreteness in the lateral directions. We believe that a direct comparison of this last approach to the BCF theory is not compelling.…”

Section: Introductionmentioning

confidence: 99%

Emergence of step flow from an atomistic scheme of epitaxial growth in1+1dimensions

Liu

Margetis

2015

Phys. Rev. E

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The Burton-Cabrera-Frank (BCF) model for the flow of line defects (steps) on crystal surfaces has offered useful insights into nanostructure evolution. This model has rested on phenomenological grounds. Our goal is to show via scaling arguments the emergence of the BCF theory for noninteracting steps from a stochastic atomistic scheme of a kinetic restricted solid-on-solid model in one spatial dimension. Our main assumptions are: adsorbed atoms (adatoms) form a dilute system, and elastic effects of the crystal lattice are absent. The step edge is treated as a front that propagates via probabilistic rules for atom attachment and detachment at the step. We formally derive a quasistatic step flow description by averaging out the stochastic scheme when terrace diffusion, adatom desorption, and deposition from above are present.

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“…Using these assumptions, performing a growth simulation requires us to find the sequence of configurations starting from an initial one ͑which corresponds to the initial surface͒. Mathematically, this is described by a master equation: [11][12][13][14][15][16] …”

Section: ͑1͒mentioning

confidence: 99%

Adatom density kinetic Monte Carlo: A hybrid approach to perform epitaxial growth simulations

et al. 2003

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We describe an alternative approach to perform growth simulations that combines the kinetic Monte Carlo ͑KMC͒ method with elements from continuum and rate equations. Similar to the KMC method it takes the atomistic structure of the growing surface fully into account but is based on the adatom density rather than on explicit trajectories of the adatoms. As will be demonstrated, this approach decouples the fast time scale of adatom motion from the much slower time scale of changes in growth morphology. This decoupling allows a reduction of the number of simulation time steps by several orders of magnitude. Based on a comparison with the KMC calculation performance, reliability and limits of this approach are discussed.

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Equations of motion for epitaxial growth

Cited by 31 publications

References 17 publications

The morphology of CdTe deposited by organometallic vapor phase epitaxy: The effect of substrate misorientation

The morphology of CdTe deposited by organometallic vapor phase epitaxy: The effect of substrate misorientation

Emergence of step flow from an atomistic scheme of epitaxial growth in1+1dimensions

Adatom density kinetic Monte Carlo: A hybrid approach to perform epitaxial growth simulations

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