Strain Induced Vertical and Lateral Correlations in Quantum Dot Superlattices

Holý, V.; Springholz, G.; Pinczolits, M.; Bauer, G.

doi:10.1103/physrevlett.83.356

Cited by 252 publications

(148 citation statements)

References 15 publications

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“…This situation is dramatically changed, however, when the substrate surface orientation is different from (100). Indeed, for a (311) substrate orientation the 3D array is laterally aligned in a square-like lattice while (as predicted [15]) the vertical alignment of the 3D QDs forms an inclination angle of α = 10° to the surface normal, towards the [2-3-3]-direction. In fact, our observations show that α varies systematically changed from (100) in the direction towards (111)B and is in good agreement with theoretical simulations based on linear elasticity theory.…”

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confidence: 99%

Controlling Planar and Vertical Ordering in Three-Dimensional (In,Ga)As Quantum Dot Lattices by GaAs Surface Orientation

et al. 2006

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Anisotropic surface diffusion and strain are used to explain the formation of three-dimensional (In,Ga)As quantum dot lattices. The diffusion characteristics of the surface coupled with the elastic anisotropy of the matrix, provides an excellent opportunity to influence the dot positions. In particular, quantum dots that are laterally organized into long chains or chessboard two-dimensional arrays vertically organized with strict vertical ordering or vertical ordering that is inclined to the sample surface normal are accurately predicted and observed.PACS 68.35.Fx,81.15.Hi During the last decade semiconductor quantum dots (QDs) have attracted increasing attention because of potential applications as novel semiconductor devices [1,2]. Besides time consuming techniques using electron beam lithography and subsequent etching to fabricate QDs, selforganized growth techniques have captured research interest [2][3][4][5][6]. In the Stranski-Krastanow growth mode, while the growth conditions can be optimized to produce nanostructures of near identical size and shape, often only a random spatial distribution of the QD is observed for a single layer of QDs [7]. However, for multiple layers a range of different results, from near perfect QD chains to threedimensional (3D) lattices, have been reported and discussed [8][9][10][11]. In this case, it has been suggested that the anisotropy in surface diffusion for (In,Ga)As QDs on GaAs (100), which is mainly caused by the (2x4) surface reconstruction with dimer rows running along [0][1][2][3][4][5][6][7][8][9][10][11], is responsible for the formation of QD chains along the [0-11]-direction [9,12]. In particular, the surface diffusion length along [0-11] is larger than along [011]. This leads to greater strain relaxation along the [0-11]-direction, producing an elliptical strain relief that is transferred to succeeding layers. This, eventually causes an asymmetric separation between neighboring dots and consequently leads to QD chain structures. Another example of the outcome of multiple layers of QD growth is the PbSe/PbEuTe system where a nearly perfect 3D lattice is reported along with the suggestion that the self-organized result is caused by anisotropic strain transfer from QD layerto-QD layer [10,11]. In each case the explanation is qualitative and a quantitative understanding of the role of diffusion and strain and the corresponding ability to design 3D QD structures is still lacking.In this letter, we report on experiments that use natural surface steps on high index substrates to further uncover the role of both surface diffusion and strain in producing 3D ordering of QDs. In particular we examine the formation and development of 3D square-like lattices of (In,Ga)As QDs in a GaAs matrix. The square lattices are created by vertically stacking QD layers while simultaneously introducing surface steps in each layer in order to vary and control the symmetry of the diffusion and strain pattern in each layer. Our findings show that by using different high index substrates...

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Controlling Planar and Vertical Ordering in Three-Dimensional (In,Ga)As Quantum Dot Lattices by GaAs Surface Orientation

et al. 2006

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“…Apart from the site, the size of the buried islands, elastic anisotropy of the spacer material, the growth direction, corrugated surface morphologies, and the modulation of the chemical composition of the spacer material influence the subsequent nucleation. [11][12][13][14][15] However, despite the fact that elastic interactions favor lateral ordering of islands as well, they turned out to be rather weak 16 and only rather short-range ordering was observed in the above mentioned systems by atomic force microscopy, transmission electron microscopy, and x-ray diffraction ͑XRD͒. [16][17][18][19][20][21] Apart from vertical island ordering in columnar form, in III-V, 22,23 II-VI, [24][25][26] and IV-VI compounds 27 also oblique ordering was observed, 28 typically for larger spacer layer thicknesses, before for sufficiently wide spacers the ordering finally vanishes.…”

Section: Introductionmentioning

confidence: 99%

X-ray diffraction investigation of a three-dimensional Si/SiGe quantum dot crystal

et al. 2009

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High-resolution x-ray diffraction was employed to study the structural properties of a three-dimensional periodic arrangement of SiGe quantum dots in a Si matrix. Using extreme ultraviolet lithography at a synchrotron source a two-dimensional array of pits ͑period 90ϫ 100 nm 2 ͒ was defined and transferred into a ͑001͒ Si wafer by reactive ion etching. By molecular-beam epitaxy SiGe islands of about 30 nm diameter and 3 nm height were grown into the pits. Subsequent deposition of Si spacer layers of 10 nm thickness and SiGe island layers results in a three-dimensionally periodic arrangement of quantum dots, mediated by the strain fields of the buried dots. Their so far unmatched structural perfection is assessed by coplanar x-ray diffractometry using synchrotron radiation. Reciprocal-space maps around the ͑004͒ and ͑224͒ reciprocal-lattice maps were recorded and analyzed to get quantitative information on the disorder of the dot positions and to obtain the mean Ge content of the dots. In addition, information on the strain fields was deduced from the analysis of the diffraction data. Together with atomic force microscopy data on the island shape and size distribution, a complete structural characterization is achieved.

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“…It was also found that only anisotropic models give rise to dispersion relations with discrete peaks, thus explaining why elastic anisotropy contributes to SAQD order as previously reported. 30,[32][33][34] The dispersion relation was then used to generate a spectrum function in the linear approximation, and the spectrum function in turn could be used to define and predict two correlation lengths that grow as the square root of time. These correlation lengths were identified as the key quantities describing SAQD order.…”

Section: Introductionmentioning

confidence: 99%

Predicting and Understanding Order of Heteroepitaxial Quantum Dots

Friedman

2007

Journal of Elec Materi

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Heteroepitaxial self-assembled quantum dots (SAQDs) will allow breakthroughs in electronics and optoelectronics. SAQDs are a result of Stranski-Krastanow growth, whereby a growing planar film becomes unstable after an initial wetting layer is formed. Common systems are Ge x Si 1Àx =Si and In x Ga 1Àx As/GaAs: For applications, SAQD arrays need to be ordered. The roles of crystal anisotropy, random initial conditions and thermal fluctuations in influencing SAQD order during early stages of SAQD formation are studied through a simple stochastic model of surface diffusion. Surface diffusion is analyzed through a linear and perturbatively non-linear analysis. The role of crystal anisotropy in enhancing SAQD order is elucidated. It is also found that SAQD order is enhanced when the deposited film is allowed to evolve at heights near the critical wetting surface height that marks the onset of non-planar film growth.

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Strain Induced Vertical and Lateral Correlations in Quantum Dot Superlattices

Cited by 252 publications

References 15 publications

Controlling Planar and Vertical Ordering in Three-Dimensional (In,Ga)As Quantum Dot Lattices by GaAs Surface Orientation

Controlling Planar and Vertical Ordering in Three-Dimensional (In,Ga)As Quantum Dot Lattices by GaAs Surface Orientation

X-ray diffraction investigation of a three-dimensional Si/SiGe quantum dot crystal

Predicting and Understanding Order of Heteroepitaxial Quantum Dots

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