Elastic Interaction of Surface Steps: Effect of Atomic-Scale Roughness

Rv, Kukta; Peralta, Alonso; Kouris, Demitris

doi:10.1103/physrevlett.88.186102

Cited by 38 publications

(26 citation statements)

References 15 publications

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“…The effect of such steps on the growth process, the morphology, the stress and strain distributions, and the functionality of the materials has been extensively investigated. [1][2][3][4][5][6][7][8][9][10][11] In particular, these steps are thought to constitute a heterogeneous source of nucleation for the formation of nano-objects and structural defects at the initial stages of the growth of many semiconductor nanostructures. 12,13 It is critically important to identify the nucleation sources for individual nano-objects such as quantum dots and wires because they constitute the fundamental blocks of future nanoelectronics and nanophotonics devices.…”

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confidence: 99%

Direct imaging of quantum wires nucleated at diatomic steps

Molina

Varela

Sales

et al. 2007

Applied Physics Letters

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Atomic steps at growth surfaces are important heterogeneous sources for nucleation of epitaxial nano-objects. In the presence of misfit strain, we show that the nucleation process takes place preferentially at the upper terrace of the step as a result of the local stress relaxation. Evidence for strain-induced nucleation comes from the direct observation by postgrowth, atomic resolution, Z-contrast imaging of an InAs-rich region in a nanowire located on the upper terrace surface of an interfacial diatomic step. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2790483͔Atomic steps located at the surfaces of substrates play a central role in controlling the growth mechanism of a wide range of materials. The effect of such steps on the growth process, the morphology, the stress and strain distributions, and the functionality of the materials has been extensively investigated. [1][2][3][4][5][6][7][8][9][10][11] In particular, these steps are thought to constitute a heterogeneous source of nucleation for the formation of nano-objects and structural defects at the initial stages of the growth of many semiconductor nanostructures. 12,13 It is critically important to identify the nucleation sources for individual nano-objects such as quantum dots and wires because they constitute the fundamental blocks of future nanoelectronics and nanophotonics devices. 14 The ability to control the nucleation of these nano-objects will contribute significantly to the development of reliable single-photon sources for applications in quantum information technology. [15][16][17] Nanowires constitute a special case of self-assembled nano-objects. 18 Self-assembled nano-objects can be formed spontaneously via the Stranski-Krastanov growth mode for certain semiconductor materials when a few monolayers are epitaxially deposited on a lattice-mismatched substrate. 19,20 Strain is widely accepted to be the driving force for the nucleation of these nano-objects, but as yet there has been no direct experimental evidence for the role of steps, and their associated stress enhancement, in the self-organized growth of nanowire arrays. 21,22 In this letter we show the direct imaging, by aberrationcorrected Z-contrast scanning transmission electron microscopy ͑STEM͒ and atomic force microscopy, that, in the presence of misfit strain, nanowires preferentially nucleate on the upper terrace of a diatomic step. With finite element elasticity calculations, we demonstrate that the driving force is the stress relaxation at the upper terrace of a diatomic step, which explains the observed nucleation site of semiconductor nanowires.The nanowires investigated consist of InAs͑P͒ selfassembled quantum wires grown by solid source molecular beam epitaxy ͑MBE͒ on InP ͑001͒ substrates. The lattice mismatch between InAs and InP is 3.2%. The control of the relaxation process of these nanostructures has recently been followed with high precision by in situ accumulated stress measurements from the initial phases of the self-assembly process. 23 The process of format...

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mentioning

confidence: 99%

Direct imaging of quantum wires nucleated at diatomic steps

Molina

Varela

Sales

et al. 2007

Applied Physics Letters

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“…The nature of the elastic force dipole interaction implies that steps of the same sign (i.e., steps either descending or ascending) exert repulsive forces on each other. The situation is different, and more delicate, with steps of opposite sign [6].…”

Section: Force Dipole Step Interaction: a Reviewmentioning

confidence: 99%

“…Accordingly, these authors were able to make predictions in close agreement with observed relaxations of atomistic simulations. 6 Recall that the interaction energy of two electric dipoles with moments p A and p B at distance r AB is [31] …”

Section: Force Dipole Step Interaction: a Reviewmentioning

confidence: 99%

“…This behavior is contrasted to the elastic interaction energy arising in heteroepitaxy, where steps amount to force monopoles [4,5]. Effects such as atomicscale roughness [6], elastic anisotropy [7], and surface elasticity under concentrated normal and shear loads [8] have enriched the MP model. Germane computations address mainly interactions between straight steps.…”

Section: Introductionmentioning

confidence: 99%

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Formulas for the force dipole interaction of surface line defects in homoepitaxy

Quah¹,

Liang²,

Margetis³

2010

J. Phys. A: Math. Theor.

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Abstract. By use of asymptotics, we derive explicit, simplified formulas for integrals representing the force dipole interaction energy per unit length between curved line defects (steps) of the same sign in homoepitaxy. Our starting point is continuum linear elasticity in accordance with the classic model by Marchenko and Parshin (1981 Soviet Phys. JETP 52 129). We consider geometries that stem from perturbations of concentric circular steps (radial case). In the radial case, we define a small geometric parameter, δ 2 , expressing the smallness of interstep distance relative to the circle radii. We invoke the Mellin transform with respect to δ 2 and derive systematically an approximation for the requisite integral. This technique offers an alternative to an exact evaluation in terms of elliptic integrals. We then demonstrate the use of the Mellin transform when calculating the force dipole interaction energy between smoothly, slowly varying steps that form perturbations of circles. We discuss conditions by which the force dipole interaction may favor the modulation of closed step profiles.

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“…The most important assumption is that we neglect the effect of stress caused by the lattice mismatch between the supported crystal and the substrate, 21 considering this to be sufficiently small. In the straight-step model ͓Fig.…”

Section: Step Equations Of Motionmentioning

confidence: 99%

Facet evolution on supported nanostructures: Effect of finite height

2008

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The surface of a nanostructure relaxing on a substrate consists of a finite number of interacting steps and often involves the expansion of facets. Prior theoretical studies of facet evolution have focused on models with an infinite number of steps, which neglect edge effects caused by the presence of the substrate. By considering diffusion of adsorbed atoms ͑adatoms͒ on terraces and attachment-detachment of atoms at steps, we show that these edge or finite height effects play an important role in the structure's macroscopic evolution. We assume diffusion-limited kinetics for adatoms and a homoepitaxial substrate. Specifically, using data from step simulations and a continuum theory, we demonstrate a switch in the time behavior of geometric quantities associated with facets: the facet edge position in a straight-step system and the facet radius of an axisymmetric structure. Our analysis and numerical simulations focus on two corresponding model systems where steps repel each other through entropic and elastic dipolar interactions. The first model is a vicinal surface consisting of a finite number of straight steps; for an initially uniform step train, the slope of the surface evolves symmetrically about the centerline, i.e., the middle step when the number of steps is odd. The second model is an axisymmetric structure consisting of a finite number of circular steps; in this case, we include curvature effects which cause steps to collapse under the effect of line tension. In the first case, we show that the position of the facet edge, measured from the centerline, switches from O͑t 1/4 ͒ behavior to O͑t 1/5 ͒ ͑where t is time͒. In the second case, the facet radius switches from O͑t 1/4 ͒ to O͑t͒. For the axisymmetric case, we also predict analytically through a continuum shock wave theory how the individual collapse times are modified by the effects of finite height under the assumption that step interactions are weak compared to the step line tension.

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Elastic Interaction of Surface Steps: Effect of Atomic-Scale Roughness

Cited by 38 publications

References 15 publications

Direct imaging of quantum wires nucleated at diatomic steps

Direct imaging of quantum wires nucleated at diatomic steps

Formulas for the force dipole interaction of surface line defects in homoepitaxy

Facet evolution on supported nanostructures: Effect of finite height

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