Lateral motion of SiGe islands driven by surface-mediated alloying

Kinetic Monte Carlo simulations of self-organization of Ge islands on Si(001)

The self-organization of germanium islands on a silicon(001) substrate is studied using lattice-based kinetic Monte Carlo simulations. These islands form spontaneously via the Stranski-Krastanov mode during growth. The interplay of deposition flux and competing surface diffusion leads to a size and shape distribution of islands that varies with temperature and coverage. For the simulation parameters chosen, a kinetic regime of irreversible growth is observed at 500 K, and this changes to quasi-equilibrium growth at 600 K. At 550 K, we see that the surface roughness increases abruptly from a low value and crosses the roughness curve at 600 K. This behavior is explained on the basis of a change in the island formation mechanism. At 500 K, the island formation involves a nucleation barrier; whereas at 600 K this barrier is almost nonexistent. At an intermediate temperature, the stochastic effects due to the incoming flux initially slow down island growth, but the subsequent island nucleation rapidly increases the roughness. These results illustrate how island self-assembly is affected by mechanistic in addition to kinetic and energetic effects. Our results are discussed in the context of experiments on a Si-Ge system and show how the kMC models can be used to understand the processes in heteroepitaxial growth.

Topics in the mathematical design of materials

We present a perspective on several current research directions relevant to the mathematical design of new materials. We discuss: (i) design problems for phase-transforming and shape-morphing materials, (ii) epitaxy as an approach of central importance in the design of advanced semiconductor materials, (iii) selected design problems in soft matter, (iv) mathematical problems in magnetic materials, (v) some open problems in liquid crystals and soft materials and (vi) mathematical problems on liquid crystal colloids. The presentation combines topics from soft and hard condensed matter, with specific focus on those design themes where mathematical approaches could possibly lead to exciting progress. This article is part of the theme issue 'Topics in mathematical design of complex materials'.

Film Thickness of Pb Islands on the Si(111) Surface

We analyze topographic scanning force microscopy images together with Kelvin probe images obtained on Pb islands and on the wetting layer on Si(111) for variable annealing times. Within the wetting layer we observe negatively charged Si-rich areas. We show evidence that these Si-rich areas result from islands that have disappeared by coarsening. We argue that the islands are located on Si-rich areas inside the wetting layer such that the Pb/Si interface of the islands is in line with the top of the wetting layer rather than with its interface to the substrate. We propose that the Pb island heights are one atomic layer smaller than previously believed. For the quantum size effect bilayer oscillations of the work function observed in this system, we conclude that for film thicknesses below 9 atomic layers large values of the work function correspond to even numbers of monolayers instead of odd ones. The atomically precise island height is important to understand ultrafast "explosive" island growth in this system.

Asymmetric shape transitions of epitaxial quantum dots

We construct a two-dimensional continuum model to describe the energetics of shape transitions in fully faceted epitaxial quantum dots (strained islands) via minimization of elastic energy and surface energy at fixed volume. The elastic energy of the island is based on a third-order approximation, enabling us to consider shape transitions between pyramids, domes, multifaceted domes and asymmetric intermediate states. The energetics of the shape transitions are determined by numerically calculating the facet lengths that minimize the energy of a given island type of prescribed island volume. By comparing the energy of different island types with the same volume and analysing the energy surface as a function of the island shape parameters, we determine the bifurcation diagram of equilibrium solutions and their stability, as well as the lowest barrier transition pathway for the island shape as a function of increasing volume. The main result is that the shape transition from pyramid to dome to multifaceted dome occurs through sequential nucleation of facets and involves asymmetric metastable transition shapes. We also explicitly determine the effect of corner energy (facet edge energy) on shape transitions and interpret the results in terms of the relative stability of asymmetric island shapes as observed in experiment.

Designer Ge/Si composite quantum dots with enhanced thermoelectric properties

An otherwise random, self-assembly of Ge/Si composite quantum dots (CQDs) on Si was controlled by inserting a layer of Si, sub-dot stacks, and post-annealing to produce micron-scale-thick QD layers with desired QD morphology, interface density, and composition distribution. A heterostructure consisting of a deliberate insertion of Si between Ge sub-dots is shown to improve the epitaxial coherence of the Ge QDs by suppression of the Ge surface interdiffusion and coarsening. As compared to regular-QD materials, the thin-film-like multifold-CQD materials are found to exhibit both reduced cross-plane thermal conductivity and enhanced electrical conductivity, and 1.5 times higher ZT value by calculation, providing a promising building block for practical thermoelectric applications in micro- or nanoelectronics.

Composition and conductance distributions of single GeSi quantum rings studied by conductive atomic force microscopy combined with selective chemical etching

Atomic force microscopy imaging combined with selective chemical etching is employed to quantitatively investigate three-dimensional (3D) composition distributions of single GeSi quantum rings (QRs). In addition, the 3D quantitative composition distributions and the corresponding conductance distributions are simultaneously obtained on the same single GeSi QRs by conductive atomic force microscopy combined with selective chemical etching, allowing us to investigate the correlations between the conductance and composition distributions of single QRs. The results show that the QRs' central holes have higher Ge content, but exhibit lower conductance, indicating that the QRs' conductance distribution is not consistent with their composition distribution. By comparing the topography, composition and conductance profiles of the same single QRs before and after different etching processes, it is found that the conductance distributions of GeSi QRs do not vary with the change of composition distribution. Instead, the QRs' conductance distributions are found to be consistent with their topographic shapes, which can be supposed to be due to the shape determined electronic structures.

Anomalous smoothing preceding island formation during growth on patterned substrates

We show that on suitably pit-patterned Si(001), deposition of just a few atomic layers of Ge can trigger a far larger flow of Si into the pits. This surprising effect results in anomalous smoothing of the substrate preceding island formation in the pits. We show that the effect naturally arises in continuum simulations of growth, and we identify its physical origin in the composition dependence of the surface diffusivity. Our interpretation suggests that anomalous smoothing is likely to also occur in other technologically relevant heteroepitaxial systems.

Ordering of epitaxial quantum dots on nanomembranes

Semiconductor nanomembranes (NMs) provide fascinating opportunities to create unique structures and electronic devices owing to their mechanical flexibility. A fascinating question is whether the growth mediated by such flexibility can lead to the formation of ordered epitaxial surface nanostructures. By using computational modeling, we investigate the energetics of ordering of SiGe quantum dots (QDs) on both Si(001) and Si(111) NMs. We calculate the interaction energies for quantum dots grown on one side and on both sides of the NM and assembled in a square lattice for the Si(001) surface and in a hexagonal lattice for the Si(111) surface. Our calculations show that for QDs grown on the Si(001) NM the interaction energy possesses a minimum at a well-defined spacing only when the QDs are positioned on both sides in a square array and aligned along the [110] direction. The predicted QD ordering, spacing, and other features are in excellent agreement with recent experimental results. For QDs grown on the Si(111) NM, our calculations predict that ordered QDs can be achieved for both one-side and both-side growth, albeit with different QD spacings. The present work suggests that semiconductor NMs are a fascinating template for the self-assembled growth of ordered QDs.

Effects of pulsed laser radiation on epitaxial self-assembled Ge quantum dots grown on Si substrates

Laser irradiation of Ge quantum dots (QDs) grown on Si(100) substrates by solid-source molecular beam epitaxy has been performed using a Nd:YAG laser (532 nm wavelength, 5 ns pulse duration) in a vacuum. The evolution of the Ge QD morphology, strain and composition with the number of laser pulses incident on the same part of the surface, have been studied using atomic force microscopy, scanning electron microscopy and Raman spectroscopy. The observed changes in the topographical and structural properties of the QDs are discussed in terms of Ge-Si diffusion processes. Numerical simulations have been developed for the investigation of the temperature evolution of the QDs during laser irradiation. The obtained results indicate that the thermal behaviour and structural variation of the nanostructures differ from conventional thermal annealing treatments and can be controlled by the laser parameters. Moreover, an unusual island motion has been observed under the action of subsequent laser pulses.

Self-organized Ce(1-x)Gd(x)O(2-y) nanowire networks with very fast coarsening driven by attractive elastic interactions

Assembling arrays of ordered nanowires is a key objective for many of their potential applications. However, a lack of understanding and control of the nanowires' growth mechanisms limits their thorough development. In this work, an appealing new path towards self-organized epitaxial nanowire networks produced by high-throughput solution methods is reported. Two requisites are identified to generate the nanowires: a thermodynamic driving force for an unrestricted elongated equilibrium island shape, and a very fast effective coarsening rate. These requirements are met in anisotropically strained Ce(1-x)Gd(x)O(2-y) nanowires with the (011) orientation grown on the (001) surface of LaAlO(3) substrates. Nanowires with aspect ratios above ≈100 oriented along two mutually orthogonal axes are obtained leading to labyrinthine networks. A very fast effective nanowire growth rate (≈60 nm min(-1)) for ex-situ thermally annealed nanostructures derives from simultaneous kinetic processes occurring in a branched network. Ostwald ripening and anisotropic dynamic coalescence, both promoted by strain-driven attractive nanowire interaction, and rapid recrystallization, enabled by fast atomic diffusion associated with a high concentration of oxygen vacancies, contribute to such an effective growth rate. This bottom-up approach to self-organized nanowire growth has a wide potential for many materials and functionalities.

Morphological evolution of InAs/InP quantum wires through aberration-corrected scanning transmission electron microscopy

Evolution of the size, shape and composition of self-assembled InAs/InP quantum wires through the Stranski-Krastanov transition has been determined by aberration-corrected Z-contrast imaging. High resolution compositional maps of the wires in the initial, intermediate and final formation stages are presented. (001) is the main facet at their very initial stage of formation, which is gradually reduced in favour of [114] or [118], ending with the formation of mature quantum wires with {114} facets. Significant changes in wire dimensions are measured when varying slightly the amount of InAs deposited. These results are used as input parameters to build three-dimensional models that allow calculation of the strain energy during the quantum wire formation process. The observed morphological evolution is explained in terms of the calculated elastic energy changes at the growth front. Regions of the wetting layer close to the nanostructure perimeters have higher strain energy, causing migration of As atoms towards the quantum wire terraces, where the structure is partially relaxed; the thickness of the wetting layer is reduced in these zones and the island height increases until the (001) facet is removed.

Morphology Analysis of Si Island Arrays on Si(001)

The formation of nanometer-scale islands is an important issue for bottom-up-based schemes in novel electronic, optoelectronic and magnetoelectronic devices technology. In this work, we present a detailed atomic force microscopy analysis of Si island arrays grown by molecular beam epitaxy. Recent reports have shown that self-assembled distributions of fourfold pyramid-like islands develop in 5-nm thick Si layers grown at substrate temperatures of 650 and 750°C on HF-prepared Si(001) substrates. Looking for wielding control and understanding the phenomena involved in this surface nanostructuring, we develop and apply a formalism that allows for processing large area AFM topographic images in a shot, obtaining surface orientation maps with specific information on facets population. The procedure reveals some noticeable features of these Si island arrays, e.g. a clear anisotropy of the in-plane local slope distributions. Total island volume analysis also indicates mass transport from the substrate surface to the 3D islands, a process presumably related to the presence of trenches around some of the pyramids. Results are discussed within the framework of similar island arrays in homoepitaxial and heteroepitaxial semiconductor systems.

Phase-field-crystal dynamics for binary systems: Derivation from dynamical density functional theory, amplitude equation formalism, and applications to alloy heterostructures

The dynamics of phase field crystal (PFC) modeling is derived from dynamical density functional theory (DDFT), for both single-component and binary systems. The derivation is based on a truncation up to the three-point direct correlation functions in DDFT, and the lowest order approximation using scale analysis. The complete amplitude equation formalism for binary PFC is developed to describe the coupled dynamics of slowly varying complex amplitudes of structural profile, zeroth-mode average atomic density, and system concentration field. Effects of noise (corresponding to stochastic amplitude equations) and species-dependent atomic mobilities are also incorporated in this formalism. Results of a sample application to the study of surface segregation and interface intermixing in alloy heterostructures and strained layer growth are presented, showing the effects of different atomic sizes and mobilities of alloy components. A phenomenon of composition overshooting at the interface is found, which can be connected to the surface segregation and enrichment of one of the atomic components observed in recent experiments of alloying heterostructures.

Transport of deposited atoms throughout strain-mediated self-assembly

Using enriched isotopes, we developed a method to elucidate the long-standing issue of Ge transport governing the strain-driven self-assembly. Here 76Ge was employed to form the 2D metastable layer on a Si(001) surface, while the 3D transition and growth were completed by additional evaporation of 70Ge. This isotope tracing combined with the analysis of the Ge-Ge LO phonon enables the tracking of the origin of Ge atoms and their flow towards the growing islands. This atomic transport was quantified based on the quasiharmonic approximation of Ge-Ge vibrations and described using a rate equation model.

Ge diffusion at the Si(100) surface

Using scanning tunneling microscopy movies, we directly observe individual embedded Ge atoms to be mobile within the Si(100)-(2x1)-Ge surface at temperatures as low as 90 degrees C. We demonstrate that Ge atoms move by exchange diffusion with (1) adsorbed monomers and (2) individual constituent atoms of adsorbed dimers. Our observations are consistent with recent density-functional theory calculations, which give the atomistic pathways and energetic barriers for both exchange mechanisms. We find that neither adsorbed monomers nor dimers can diffuse more than a few nanometers between exchange events, illustrating how Ge diffusion and intermixing are intimately coupled at the nanoscale on the Si(100) surface.

Nanoscale pit formation at 2D Ge layers on Si: influence of energy and entropy

The structural stability of two-dimensional (2D) SiGe nanostructures is studied by scanning tunneling microscopy. The formation of pits with a diameter of 2-30 nm in one atomic layer thick Ge stripes is observed. The unanticipated pit formation occurs due to an energetically driven motion of the Ge atoms out of the Ge stripe towards the Si terminated step edge followed by an entropy driven GeSi intermixing at the step edge. Using conditions where the pits coalesce results in the formation of freestanding 8 nm wide GeSi wires on Si(111).

Three-dimensional composition profiles of single quantum dots determined by scanning-probe-microscopy-based nanotomography

Scanning probe microscopy combined with selective wet chemical etching is employed to quantitatively determine the full three-dimensional (3D) composition profiles of single strained SiGe/Si(001) islands. The technique allows us to simultaneously obtain 3D profiles for both coherent and dislocated islands and to collect data with large statistics. Lateral and vertical composition gradients are observed, and their origin is discussed. X-ray scattering measurements performed on a large sample area are used to validate the results.

Alloying mechanisms for epitaxial nanocrystals

The different mechanisms involved in the alloying of epitaxial nanocrystals are reported in this Letter. Intermixing during growth, surface diffusion, and intraisland diffusion were investigated by varying the growth conditions and annealing environments during chemical vapor deposition. The relative importance of each mechanism was evaluated in determining a particular composition profile for dome-shaped Ge:Si (001) islands. For samples grown at a faster rate, intermixing during growth was reduced. Si surface diffusion dominates during H2 annealing, whereas Ge surface diffusion and intraisland diffusion prevail during annealing in a PH3 environment.

Coarsening, mixing, and motion: the complex evolution of epitaxial islands

During heteroepitaxy, misfit strain causes nanoscale islands to form spontaneously, as "self-assembled quantum dots." The growth and evolution of these islands are remarkably complex. We show that continuum modeling reproduces and explains many of the surprising phenomena observed experimentally. The free energy is reduced by both morphological change and alloy intermixing. However, because diffusion occurs only at the surface, the morphological and compositional evolution are strongly coupled. This leads to a complex dynamical response to the rather simple thermodynamic driving forces.

Dendrochronology of strain-relaxed islands

We report on the observation and study of tree-ring structures below dislocated SiGe islands (superdomes) grown on Si(001) substrates. Analogous to the study of tree rings (dendrochronology), these footprints enable us to gain unambiguous information on the growth and evolution of superdomes and their neighboring islands. The temperature dependence of the critical volume for dislocation introduction is measured and related to the composition of the islands. We show clearly that island coalescence is the dominant pathway towards dislocation nucleation at low temperatures, while at higher temperatures anomalous coarsening is effective and leads to the formation of a depletion region around superdomes.

Interplay between thermodynamics and kinetics in the capping of InAs/GaAs(001) quantum dots

A microscopic picture for the GaAs overgrowth of self-organized quantum dots is developed. Scanning tunneling microscopy measurements reveal two capping regimes: the first being characterized by a dot shrinking and a backward pyramid-to-dome shape transition. This regime is governed by fast dynamics resulting in island morphologies close to thermodynamic equilibrium. The second regime is marked by a true overgrowth and is controlled by kinetically limited surface diffusion processes. A simple model is developed to describe the observed structural changes which are rationalized in terms of energetic minimization driven by lattice mismatch and alloying.

Self-ordering of a Ge island single layer induced by Si overgrowth

We provide a direct experimental proof and the related modeling of the role played by Si overgrowth in promoting the lateral ordering of Ge islands grown by chemical vapor deposition on Si(001). The deposition of silicon induces a shape transformation, from domes to truncated pyramids with a larger base, generating an array of closely spaced interacting islands. By modeling, we show that the resulting gradient in the chemical potential across the island should be the driving force for a selective flow of both Ge and Si atoms at the surface and, in turn, to a real motion of the dots, favoring the lateral order.

Polarized fine structure in the photoluminescence excitation spectrum of a negatively charged quantum dot

We report polarized photoluminescence excitation spectroscopy of the negative trion in single charge-tunable quantum dots. The spectrum exhibits a p-shell resonance with polarized fine structure arising from the direct excitation of the electron spin triplet states. The energy splitting arises from the axially symmetric electron-hole exchange interaction. The magnitude and sign of the polarization are understood from the spin character of the triplet states and a small amount of quantum dot asymmetry, which mixes the wave functions through asymmetric e-e and e-h exchange interactions.