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1.
Phys Rev E ; 109(4-1): 044131, 2024 Apr.
Article in English | MEDLINE | ID: mdl-38755851

ABSTRACT

Many manifestations of natural processes give rise to interesting morphologies; it is all too easy to cite the corrugation of the Earth's surface or of planets in general. However, limiting ourselves to 2D cases, the morphology to which crystal growth gives rise is also intriguing. In particular, it is interesting to study some characteristics of the cluster projection in 2D, namely the study of the shapes of the speckles (fractal dimension of their rims) or the distribution of their areas. Recently, for instance, it has been shown that the size cumulative distribution function (cdf) of "voids" in a corrole film on Au(111) is well described by the well known Weibull distribution. The present article focuses on the cdf of cluster areas generated by numerical simulations: the clumps (clusters) are generated by overlapping grains (disks) whose germs (disk centers) are chosen randomly in a 2000×2000 square lattice. The obtained cdf of their areas is excellently fitted to the Weibull function in a given range of surface coverage. The same type of analysis is also performed for a fixed-time clump distribution in the case of Kolmogorov-Johnson-Mehl-Avrami (KJMA) kinetics. Again, a very good agreement with the Weibull function is obtained.

2.
J Phys Condens Matter ; 30(46): 465502, 2018 Nov 21.
Article in English | MEDLINE | ID: mdl-30359332

ABSTRACT

We present a joint experimental and theoretical study of the electronic properties of the rebonded-step reconstructed Ge/Si(1 0 5) surface which is the main strained face found on Ge/Si(0 0 1) quantum dots and is considered a prototypical model system for surface strain relaxation in heteroepitaxial growth. Using a vicinal surface as a model system for obtaining a stable single-domain film structure with large terraces and rebonded-step surface termination, we realized an extended and ordered Ge/Si planar hetero-junction suitable for direct study with angle-resolved photoemission spectroscopy. At the coverage of four Ge monolayers photoemission spectroscopy reveals the presence of 2D surface and film bands displaying energy-momentum dispersion compatible with the 5 × 4 periodicity of the system. The good agreement between experiment and first-principles electronic structure calculations confirms the validity of the rebonded-step structural model. The direct observation of surface features within 1 eV below the valence band maximum corroborates previously reported analysis of the electronic and optical behavior of the Ge/Si hetero-interface.

3.
J Phys Condens Matter ; 27(43): 435001, 2015 Nov 04.
Article in English | MEDLINE | ID: mdl-26416776

ABSTRACT

We investigate the surface structure of Ge(0 0 1) during the (2 × 1)-(1 × 1) phase transition occurring at T > 1130 K by high-resolution scanning tunnelling microscopy. We find a drastic size reduction of dimerized domains in line with substantial dimer breakup accompanied by surface roughening. Completing the picture provided by previous spectroscopic observations, probing with high spatial resolution reveals the nucleation of several nanodomains with distinct vicinal orientations and reconstructions. The structural transformation is irreversible and is not observed for other singular faces of Ge.

4.
J Phys Condens Matter ; 27(25): 253001, 2015 Jul 01.
Article in English | MEDLINE | ID: mdl-26021279

ABSTRACT

Starting with the basic definition, a short description of a few relevant physical quantities playing a role in the growth process of heteroepitaxial strained systems, is provided. As such, the paper is not meant to be a comprehensive survey but to present a connection between the Stranski-Krastanov mechanism of nanostructure formation and the basic principles of nucleation and growth. The elastic field is described in the context of continuum elasticity theory, using either analytical models or numerical simulations. The results are compared with selected experimental results obtained on GeSi nanostructures. In particular, by tuning the value of quantities such as vicinality, substrate orientation and symmetry of the diffusion field, we elucidate how anisotropic elastic interactions determine shape, size, lateral distribution and composition of quantum dots.

5.
J Phys Condens Matter ; 25(39): 395801, 2013 Oct 02.
Article in English | MEDLINE | ID: mdl-23999271

ABSTRACT

We investigate the interdependent processes of strain and diffusion in the formation of holes and atolls obtained by rapid annealing of Ge/Si(111) islands at T ≈ 970 °C. We show that the shape evolution from islands to atolls and holes is closely captured by an analytical model including strain-driven diffusion. In the model, strain profiles obtained by finite element solutions of continuum elasticity equations are introduced in the diffusion equation as the source of a diffusion flux driven by the strain gradient. When the shape of the elastic field in Ge/Si(111) islands is coupled to diffusion, the morphology of the SiGe nanostructures observed after annealing is reproduced.

6.
J Phys Condens Matter ; 25(7): 075802, 2013 Feb 20.
Article in English | MEDLINE | ID: mdl-23327904

ABSTRACT

By exploiting a fully three-dimensional finite-element modeling of strain fields, we investigate the spatial dependence of the elastic interaction energy between misfitting nanostructures beyond the point-dipole approximation. When interacting islands are finite in size, the detailed shape of the elastic strain field around and under the islands may convert the repulsive interactions, usually experienced between equal-sized islands, into an attractive basin between a large island and a population of neighboring clusters smaller than a critical size. The results of the simulations applied to large Ge islands grown on a Si(111) substrate have significant implications for the understanding of the strain-mediated coarsening of quantum dots around the islands.


Subject(s)
Germanium/chemistry , Models, Chemical , Models, Molecular , Nanostructures/chemistry , Nanostructures/ultrastructure , Silicon/chemistry , Computer Simulation , Crystallization/methods , Elastic Modulus , Energy Transfer , Molecular Conformation
7.
J Phys Condens Matter ; 24(35): 355002, 2012 Sep 05.
Article in English | MEDLINE | ID: mdl-22854199

ABSTRACT

The distribution of points on a 2D domain influences the kinetics of its coverage when a growth law is attached at each point. This implies that the kinetics of space filling can be adopted as a descriptor of the degree of order of the initial point distribution. In this paper, the degree of order of an initial array of points has been changed following two paths: (i) from a regular square lattice, through increasing displacement assigned to each point, towards Poissonian disorder; (ii) from a Poissonian distribution, by introducing a hard core potential with increasing correlation lengths, towards a more ordered lattice. A linear growth law has been attached to the points of the initial array and the kinetics X(X(e)), where X(e) is the extended coverage as defined in the Kolmogorov-Johnson-Mehl-Avrami model, has been monitored. The quantitative analysis has been performed by fitting the kinetics to an equation which we propose for the first time and which has proved to be, in fact, highly suitable for the purpose. The results demonstrate that the gross of variation from order to disorder is obtained for point displacements, u, of the order of a, the latter being the constant of a square lattice. Vice versa, the introduction of a correlation distance in a random distribution provokes at most an order limited to the first neighbors and no real order can ever be reached. Others descriptors have been investigated, all confirming our results. We also developed an analytical description based on the use of the f-functions, as have been defined by Van Kampen, up to the second order terms. Such a description has been shown to work well for u/a < 1 within an interval ΔX(e) which depends on the ϵ value.

8.
Phys Rev E Stat Nonlin Soft Matter Phys ; 85(2 Pt 1): 021606, 2012 Feb.
Article in English | MEDLINE | ID: mdl-22463222

ABSTRACT

The theory of Kolmogorov-Johnson-Mehl-Avrami for phase transition kinetics is subjected to severe limitations concerning the functional form of the growth law. This paper is devoted to sidestepping this drawback through the use of the correlation function approach. Moreover, we put forward an easy-to-handle formula, written in terms of the experimentally accessible actual extended volume fraction, which is found to match several types of growths. Computer simulations have been performed for corroborating the theoretical approach.


Subject(s)
Growth/physiology , Models, Biological , Models, Statistical , Animals , Computer Simulation , Humans
9.
Phys Rev E Stat Nonlin Soft Matter Phys ; 86(6 Pt 1): 061605, 2012 Dec.
Article in English | MEDLINE | ID: mdl-23367962

ABSTRACT

The distributions of the size of islands and of the capture zones are discussed comparatively, both experimentally and numerically, for the case of a sudden nucleation process with and without coarsening. The experiments were performed by growing InAs islands on GaAs(001) and the coarsening was altered by varying the temperature. In the two-dimensional kinetic Monte Carlo simulations a single-species diffusing adatom was taken into account, and the coarsening was altered in this case by modifying the binding energy between adatoms and islands. The results show that size and capture zone distributions overlap only when coarsening can be disregarded.

10.
Phys Rev Lett ; 106(5): 055503, 2011 Feb 04.
Article in English | MEDLINE | ID: mdl-21405409

ABSTRACT

We present a novel approach to engineer the growth of strained epitaxial films based on tailoring the elastic-interaction potential between nanostructures with substrate vicinality. By modeling the island-island interaction energy surface within continuum elasticity theory, we find that its fourfold symmetry is broken at high miscuts, producing directions of reduced elastic-interaction energy. As a consequence, it is possible to direct the Ge island growth on highly misoriented Si(001) substrates towards desired pathways.

11.
Nanotechnology ; 22(19): 195602, 2011 May 13.
Article in English | MEDLINE | ID: mdl-21430313

ABSTRACT

The evolution of InAs and In(0.85)Mn(0.15)As quantum dots grown at 270 °C is studied as a function of coverage. We show that, in contrast to what occurs at high temperature, the two-dimensional to three-dimensional transition is not abrupt but rather slow. This is due to the finding that part of the deposited material also contributes to the wetting layer growth after quantum dot formation. This aspect is particularly accentuated in In(0.85)Mn(0.15)As deposition. The Voronoi area analysis reveals a significant spatial correlation between islands.


Subject(s)
Arsenic/chemistry , Arsenicals/chemistry , Indium/chemistry , Manganese/chemistry , Nanotechnology/methods , Quantum Dots , Cold Temperature , Diffusion , Kinetics , Microscopy, Atomic Force/methods
12.
J Nanosci Nanotechnol ; 11(10): 9185-9, 2011 Oct.
Article in English | MEDLINE | ID: mdl-22400321

ABSTRACT

A complete description of Ge growth on vicinal Si(001) surfaces is provided. The distinctive mechanisms of the epitaxial growth process on vicinal surfaces are clarified from the very early stages of Ge deposition to the nucleation of 3D islands. By interpolating high-resolution scanning tunneling microscopy measurements with continuum elasticity modeling, we assess the dependence of island's shape and elastic interaction on the substrate misorientation. Our results confirm that vicinal surfaces offer an additional degree of control over the shape and symmetry of self-assembled nanostructures.

13.
Phys Rev Lett ; 104(3): 036104, 2010 Jan 22.
Article in English | MEDLINE | ID: mdl-20366663

ABSTRACT

A complete description of Ge growth on vicinal Si(001) surfaces in the angular miscut range 0 degrees -8 degrees is presented. The key role of substrate vicinality is clarified from the very early stages of Ge deposition up to the nucleation of 3D islands. By a systematic scanning tunneling microscopy investigation we are able to explain the competition between step-flow growth and 2D nucleation and the progressive elongation of the 3D islands along the miscut direction [110]. Using finite element calculations, we find a strict correlation between the morphological evolution and the energetic factors which govern the {105} faceting at atomic scale.

14.
J Phys Condens Matter ; 18(17): 4219-30, 2006 May 03.
Article in English | MEDLINE | ID: mdl-21690776

ABSTRACT

A mean field approach is employed for determining the kinetics of two main quantities for film morphology, namely the number of islands and the film perimeter. These two quantities have been computed for both coalescence and impingement growth regimes. For each case the growth of two- and three-dimensional islands has been considered. In addition, the effect of the spatial correlation among nuclei has been taken into account on the grounds of the hard core interaction. Analytic formulae have been derived for each case.

18.
Phys Rev B Condens Matter ; 52(15): 10721-10724, 1995 Oct 15.
Article in English | MEDLINE | ID: mdl-9980153
19.
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