Dislocations and morphological instabilities: Continuum modeling of misfitting heteroepitaxial films

Haataja, Mikko; Müller, Judith; Rutenberg, Andrew D.; Grant, Martin

doi:10.1103/physrevb.65.165414

Cited by 55 publications

(36 citation statements)

References 32 publications

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“…Here, two variables C 12 and C 44 are used, which correspond to λ iijj and λ ijij , respectively. (27) where δ ij is the Kronecher delta which is defined as 1 when i equals j and 0 otherwise. In Eq.…”

Section: Isotropic Elastic Surface Green Functionmentioning

confidence: 99%

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Phase field model for the dynamics of steps and islands on crystal surfaces

et al. 2003

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Surface stress and lattice strain are the essential factors on the self-organization of a surface, because they affect remarkably adatom diffusion on surfaces and at step edges and induce the elastic interaction between the surface steps. In spite of the importance, their kinetic role on the growth dynamics of the step and the islands in thin film deposition is not yet fully understood. Therefore, in this work, a continuum model is presented, which considers both elastic and entropic interactions between the steps or the islands on the crystal surface and growth dynamics of the steps or the islands. The present model is based on the Ginzburg-Landau approach on phase transition and reduces to the Gibbs-Thompson equation at the step edges. In addition, the elastic field, which is generated by the surface force, is calculated using elastic surface Green function under the assumption that the atomic displacement field decays exponentially from the surface. Using the resulting atomic displacement, the elastic interaction between the surface steps is incorporated into the model. Through numerical simulations, it is shown that the elastic interaction between the steps in our model is in good agreement with previous theories and that the phase field model has the ability to solve the various phenomena of the step dynamics.

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Section: Isotropic Elastic Surface Green Functionmentioning

confidence: 99%

“…The phase field model was extended to be applicable to the phenomena of adatom diffusion on the surface [11,24]. The phase field model has been used to analyze various elastic problems, for example, the growth of precipitates in matrix phases, instability of elastically stressed films, and so forth [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Phase field model for the dynamics of steps and islands on crystal surfaces

et al. 2003

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“…When applied at individual defect levels, the microscopic phase field model can predict the size, formation energy, saddle point configuration and activation energy of defect nuclei, and the micromechanisms of their mutual interactions [16]. Besides that, the microscopic phase field also has been applied to model dislocation [17][18][19], fracture [20][21][22][23] and voids [24][25][26]. According to Lu et al [27] and Hennig et al [28], the formation energy is a function of the defect concentration in a chemically non-uniform system caused by antisite atoms, thus, the antisite defect study by the microscopic phase field can be supplementary to the other physicists' work.…”

Section: Introductionmentioning

confidence: 99%

Microscopic phase field study of the antisite defect of Ni3Al in binary Ni-Al alloys

Zhang

Zheng

et al. 2010

Sci. China Phys. Mech. Astron.

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The temporal evolution feature of a microscopic phase field model is utilized to study the antisite defects of L1 2 -Ni 3 Al; this is quite different from other physicist' interests. There are mainly two points in brief. Firstly, antisite defects Ni Al and Al Ni , which are caused by the deviation from the stoichiometric Ni 3 Al, coexist in the Ni 3 Al phase. The surplus Ni atom in the Ni-rich side is prone to substitute Al thus producing the antisite defect Ni Al that maintains the stability of the L1 2 structure. In other case, the surplus Al atom in the Al-rich side is accommodated by a Ni sublattice consequently giving rise to antisite defect Al Ni . The calculated equilibrium occupancy probability of Ni Al is much higher than that of Al Ni . This point is generally in line with other theoretical and experimental works. Additionally, both Ni Al and Al Ni have a strong negative correlation to time step during the disorder-order transformation. Since the initial value of Ni Al and Al Ni on each site of the matrix is right at the concentration that we set, we can observe the decrease process of Ni Al and Al Ni from the initial disordered high anti-structure state to their respective equilibrium state, i.e. to the result of the ordering process further coarsening. antisite defect, L1 2 -Ni 3 Al, temporal evolution, microscopic phase field model PACS: 61.72.-, 61.50.Ah, 81.30.Mh

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“…In Refs. [122,247] a comprehensive phase-field model is proposed, mimicking the dislocation distribution by a dislocation-density field, eventually evolving in time. Therein, dislocations are observed to play a stabilizing role.…”

Section: Dislocationsmentioning

confidence: 99%

Continuum modelling of semiconductor heteroepitaxy: an applied perspective

Bergamaschini

Salvalaglio

Backofen

et al. 2016

Advances in Physics: X

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Semiconductor heteroepitaxy involves a wealth of qualitatively different, competing phenomena. Examples include threedimensional island formation, injection of dislocations, mixing between film and substrate atoms. Their relative importance depends on the specific growth conditions, giving rise to a very complex scenario. The need for an optimal control over heteroepitaxial films and/or nanostructures is widespread: semiconductor epitaxy by molecular beam epitaxy or chemical vapour deposition is nowadays exploited also in industrial environments. Simulation models can be precious in limiting the parameter space to be sampled while aiming at films/nanostructures with the desired properties. In order to be appealing (and useful) to an applied audience, such models must yield predictions directly comparable with experimental data. This implies matching typical time scales and sizes, while offering a satisfactory description of the main physical driving forces. It is the aim of the present review to show that continuum models of semiconductor heteroepitaxy evolved significantly, providing a promising tool (even a working tool, in some cases) to comply with the above requirements. Several examples, spanning from the nanometre to the micron scale, are illustrated. Current limitations and future research directions are also discussed.

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Dislocations and morphological instabilities: Continuum modeling of misfitting heteroepitaxial films

Cited by 55 publications

References 32 publications

Phase field model for the dynamics of steps and islands on crystal surfaces

Phase field model for the dynamics of steps and islands on crystal surfaces

Microscopic phase field study of the antisite defect of Ni3Al in binary Ni-Al alloys

Continuum modelling of semiconductor heteroepitaxy: an applied perspective

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