Composition maps in self-assembled alloy quantum dots

Nanoscale variations in composition arising from the competition between chemical mixing effects and elastic relaxation can substantially influence the electronic and optical properties of self-assembled alloy quantum dots. Using a combination of finite element and quadratic programming optimization methods, we have developed an efficient technique to compute the equilibrium composition profiles in strained quantum dots. We find that the composition profiles depend strongly on the morphological features such as the slopes and curvatures of their surfaces and the presence of corners and edges as well as the ratio of the strain and chemical mixing energy densities. More generally, our approach provides a means to quantitatively model the interplay among the composition variations, the temperature, the strain, and the shapes of small-scale lattice-mismatched structures.     

Theory of strain relaxation for epitaxial layers grown on substrate of a finite dimension

We present an equilibrium theory for strain relaxation in epitaxial layers grown on substrates of a finite dimension. The conventional dislocation model is refined to take account of the multiple reflection of image dislocations. The effect of strain transfer and dilution due to finite vertical and lateral dimensions of the substrate is also considered. The critical thickness has been obtained based on an energy balance approach. Detailed numerical analysis with primary experiments for the SiGe alloy system is also provided.     

Dislocation-induced composition profile in alloy semiconductors

We present a novel computational method by combining the finite element method and the method of moving asymptotes to study the dislocation-induced composition profile in alloy semiconductors. Segregated cylindrical nanoscale regions appear around the dislocation core. We find that the dominant driving force of non-uniform composition is strain contribution. Moreover, the method can be applied to the dislocated nanoscale heterostructures which are inaccessible by atomic treatment.     

Strain relaxation in epitaxial GaAs/Si (0 0 1) nanostructures

Abstract

Crystal defects, present in ~100 nm GaAs nanocrystals grown by metal organic vapour phase epitaxy on top of (0 0 1)-oriented Si nanotips (with a tip opening 50–90 nm), have been studied by means of high-resolution aberration-corrected high-angle annular dark-field scanning transmission electron microscopy. The role of 60° perfect, 30° and 90° Shockley partial misfit dislocations (MDs) in the plastic strain relaxation of GaAs on Si is discussed. Formation conditions of stair-rod dislocations and coherent twin boundaries in the GaAs nanocrystals are explained. Also, although stacking faults are commonly observed, we show here that synthesis of GaAs nanocrystals with a minimum number of these defects is possible. On the other hand, from the number of MDs, we have to conclude that the GaAs nanoparticles are fully relaxed plastically, such that for the present tip sizes no substrate compliance can be observed.     

Novel silica stabilization method for the analysis of fine nanocrystals using coherent X‐ray diffraction imaging

High‐energy X‐ray Bragg coherent diffraction imaging (BCDI) is a well established synchrotron‐based technique used to quantitatively reconstruct the three‐dimensional morphology and strain distribution in nanocrystals. The BCDI technique has become a powerful analytical tool for quantitative investigations of nanocrystals, nanotubes, nanorods and more recently biological systems. BCDI has however typically failed for fine nanocrystals in sub‐100 nm size regimes – a size routinely achievable by chemical synthesis – despite the spatial resolution of the BCDI technique being 20–30 nm. The limitations of this technique arise from the movement of nanocrystals under illumination by the highly coherent beam, which prevents full diffraction data sets from being acquired. A solution is provided here to overcome this problem and extend the size limit of the BCDI technique, through the design of a novel stabilization method by embedding the fine nanocrystals into a silica matrix. Chemically synthesized FePt nanocrystals of maximum dimension 20 nm and AuPd nanocrystals in the size range 60–65 nm were investigated with BCDI measurement at beamline 34‐ID‐C of the APS, Argonne National Laboratory. Novel experimental methodologies to elucidate the presence of strain in fine nanocrystals are a necessary pre‐requisite in order to better understand strain profiles in engineered nanocrystals for novel device development.     

The theory of equilibrium antiphase boundaries in ordered solid solutions of the AuCu3 type

The Gorsky-Bragg-Williams approximation gives expressions which determine the equilibrium values of the long-range-order parameter and the concentrations of components in the vicinity of the antiphase boundary 1/2 (110) {111} in an L1₂ super-structure of stoichiometric composition AB₃. On the assumption that the changes in the alloy due to the presence of an antiphase boundary are distributed over a great number of planes on both sides of the boundary, the long-range-order parameter and the concentration of components in these planes have been calculated. It is found that the long-range-order parameter at the antiphase boundary is considerably lower than it is in the matrix over a wide temperature range. The concentration of the components at the antiphase boundary under conditions of thermodynamic equilibrium is somewhat lower than the mean concentration in the alloy.Estimates are made of the critical stress for the start of superdislocations with equilibrium antiphase boundaries, the equilibrium width of the superdislocations, and the defect in the elastic modulus due to the reversible movement of the superparticle dislocations.     

Elliptic nanopores in deformed nanocrystalline and nanocomposite materials

A theoretical model is suggested which describes the nucleation of nanoscale pores (nanopores) of elliptic shape in deformed nanocrystalline and nanocomposite materials. In the framework of the model, elliptic nanopores in nanocrystalline and nanocomposite materials nucleate at interfaces in the stress fields of interfacial edge dislocations with large Burgers vectors. When elliptic nanopores nucleate, they remove the cores of interfacial dislocations. The stress field and energy of such dislocated elliptic nanopores are calculated, and their equilibrium sizes and shape parameters are revealed. It is theoretically shown that the elliptic shape of nanopores is due to the effects of interfaces (grain and interphase boundaries) on fracture processes at the nanoscale level.     

Vibronic Sidebands of Coherent Phonon States

Recently experiments have been reported about phonon sidebands in doped crystals, which may originate from coherent phonon states. The corresponding modes are either confined phonon modes in nanocrystals or localized phonon modes in bulk materials, both showing small damping due to phonon-phonon interaction. We present a theory of the lineshape of vibronic sideband spectra due to coherent phonon states using the conventional model of linear electron-phonon coupling and displaced equilibrium positions of the oscillators in the initial and final electronic states. Unlike in the conventional theory, the initial state of the oscillator is taken as a coherent phonon state and not as a thermalized one. Under these conditions we got an exact analytical solution for the lineshape of the vibronic sideband. The lineshape is determined by two parameters, the Huang-Rhys parameter S and the coherence parameter α of the phonon state. For α = 0 the lineshape converts into the standard Pekarian form for T = 0.     

The fine structure of FCC nanocrystals in Al-and Ni-based alloys

The structural perfection of nanocrystals in alloys of different chemical composition is studied by x-ray diffraction and high-resolution electron microscopy. In all the alloys studied, crystallization of the amorphous phase produces a nanocrystalline structure. The nanocrystal size depends on the chemical composition of the alloy and varies in aluminum-based alloys from 5 nm in Al₈₉Ni₅Y₆ to 12 nm in Al₈₂Ni₁₁Ce₃Si₄. Nanocrystals in nickel-based alloys vary in size from 15 to 25 nm. Al nanocrystals are predominantly defect-free, with microtwins observed only in some nanocrystals. The halfwidth of the diffraction lines is proportional to sec θ, which implies the small grain size provides the major contribution to the broadening. Nanocrystals in nickel alloys contain numerous twins, stacking faults, and dislocations.     

Electronic states at dislocations and metal silicide precipitates in?crystalline silicon and their role in?solar cell materials

Predominant dislocation types in solar silicon are dissociated into 30°- and 90°-partials with reconstructed cores. Besides shallow 1D-band localized in their strain field and a quasi-2D band at the stacking fault connecting the two partials, the existence of several intrinsic core defects with deep lying levels has been demonstrated by electron spin resonance. The majority of core defects occur in nonequilibrium situations and, with the exception of a small EPR-signal assigned to a reconstruction defect, vanish after careful annealing above 800°C. There is good evidence now that part of deep levels observed in dislocated silicon is associated with impurities, especially with transition metal impurities. Electron-hole-pair recombination at a dislocation mainly runs via its shallow bands and is strongly increased by impurities bound to its core or in the strain field. The concentration of these impurities can be reduced by gettering processes to such a low level that radiative recombination at dislocations yields a luminescence efficiency of 0.1% at room temperature. A quite coherent picture has emerged for metal impurity precipitation in silicon. Early stages of precipitation in defect-free silicon are characterised by kinetically selected metastable defects forming as a result of large chemical driving forces for precipitation. Such defects are associated with deep level spectra which show the properties of extended multielectron defects. The evolution of the system to energetically more favourable configurations proceeds via ordinary particle coarsening but also via internal ripening, a process reminiscent of the above-mentioned metastable defects. Electronically, the defects evolve into metal-like inclusions which in general seem to act as strong recombination centers for minority carriers. In the presence of dislocations metastable defects quickly transform into equilibrium structures in the course of precipitation or do not form at all. In the presence of several metal impurities silicide precipitates which can be described as solid solutions of the respective metal atoms are observed, which is at least qualitatively in accord with ternary phase diagrams. Like single-metal silicide precipitates, strong minority carrier recombination is also typical for those multi-metal silicide particles.     

Electronic structures of alloy quantum dots with nonuniform composition

In this study, the significant effect of the nonuniform composition in alloy quantum dots (QDs) on electronic structure is analyzed in depth. The equilibrium composition profiles in experimentally observed dome and barn shaped GeSi/Si QDs are determined by combining the finite element method and the method of moving asymptotes. Due to the composition variation, the total band edge of heavy hole is dominated by the band offset and spin-orbit coupling rather than the strain effect. The numerical results reveal that the wave function of heavy hole trends to be localized in the Ge-rich region at the top of the large QD. Moreover, the size effect gradually compensates the composition effect as the size of QD decreases.     

Magnetic nanostructures by adaptive twinning in strained epitaxial films

We exploit the intrinsic structural instability of the Fe(70)Pd(30) magnetic shape memory alloy to obtain functional epitaxial films exhibiting a self-organized nanostructure. We demonstrate that coherent epitaxial straining by 54% is possible. The combination of thin film experiments and large-scale first-principles calculations enables us to establish a lattice relaxation mechanism, which is not expected for stable materials. We identify a low twin boundary energy compared to a high elastic energy as key prerequisite for the adaptive nanotwinning. Our approach is versatile as it allows to control both, nanostructure and intrinsic properties for ferromagnetic, ferroelastic, and ferroelectric materials.     

Formation and structure of nanocrystals in an Al86Ni11Yb3 alloy

The formation and structure of the nanocrystalline phase in the Al₈₆Ni₁₁Yb₃ alloy are investigated using differential scanning calorimetry (DSC), transmission electron and high-resolution electron microscopy, and x-ray diffraction. The nanocrystalline phase is formed upon controlled crystallization of the amorphous alloy prepared by quenching of the melt on a rapidly moving substrate. It is revealed that the nanocrystalline alloy consists of aluminum nanocrystals (5–12 nm in size) randomly distributed in the amorphous matrix. The maximum fraction of the nanocrystalline phase does not exceed 25%. The nanocrystal size substantially increases at the initial stage of isothermal treatment (at 473 K) and then changes insignificantly. It is found that nanocrystals are usually free of defects. However, some nanocrystals have a more complex microstructure with twins and dislocations. The size distributions of nanocrystals are determined at several durations of isothermal treatment. It is demonstrated that the nucleation of nanocrystals predominantly occurs through the heterogeneous mechanism. The experimental distributions are compared with those obtained from a computer simulation. The activation energy of crystallization, the time-lag, and the coefficient of ytterbium diffusion in the alloy are estimated     

Transition from coherence to bistability in a model of financial markets

We present a model describing the competition between information transmission and decision making in financial markets. The solution of this simple model is recalled, and possible variations discussed. It is shown numerically that despite its simplicity, it can mimic a size effect comparable to a crash localized in time. Two extensions of this model are presented that allow to simulate the demand process. One of these extensions has a coherent stable equilibrium and is self-organized, while the other has a bistable equilibrium, with a spontaneous segregation of the population of agents. A new model is introduced to generate a transition between those two equilibriums. We show that the coherent state is dominant up to an equal mixing of the two extensions. We focus our attention on the microscopic structure of the investment rate, which is the main parameter of the original model. A constant investment rate seems to be a very good approximation. Received 7 August 2000 and Received in final form 10 September 2000     

Self-assembled superlattice by spinodal decomposition during growth

We examine the dynamics of alloy growth by vapor deposition and bulk diffusion, predicting a new type of self-organized growth. When material is deposited at a composition unstable against spinodal decomposition, we find three distinct regimes depending on growth rate. Intermediate growth rates lead to spontaneous formation of a superlattice with layers parallel to the surface. Slow growth leads to more complex three-dimensional decomposition. For fast growth, the alloy composition remains uniform near the surface, with a composition wave propagating up from the interface.     

On the isotropy of continuized dislocated crystals. I. The isotropic lattice distortion

The geometrical theory of continuous distributions of dislocations traditionally neglects the dependence of a distribution of dislocations on the existence of point defects created by this distribution (e.g., due to intersections of dislocation lines). In this paper the influence of such point defects on metric properties of the continuized dislocated Bravais crystalline structure is assumed to be isotropic. The influence of the point defects on the distribution of dislocations is then modeled by treating dislocations as those located in a conformally flat space. This approach leads (among others) to new results concerning the geometry of glide surfaces.     

Regularities of Al layer structure formation near phase equilibrium in plasma-condensate system

A fundamentally new technological approach to creating porous metal structures on isotropic substrates during condensation of a reverse diffusion flow in a planar dc magnetron is proposed. The physical foundations of the operation of self-organized sputtering systems are analyzed. Conditions of the formation of main varieties of porous structures, such as weakly coupled micro-and nanocrystals, and three-dimensional labyrinth structures, are found using scanning electron microscopy. It is established that the main prerequisites for the formation of pores are the stationarity of the process and proximity to the phase equilibrium in the plasma-condensate system.     

Spontaneous symmetry breaking at the fluctuating level

Phase transitions not allowed in equilibrium steady states may happen, however, at the fluctuating level. We observe for the first time this striking and general phenomenon measuring current fluctuations in an isolated diffusive system. While small fluctuations result from the sum of weakly correlated local events, for currents above a critical threshold the system self-organizes into a coherent traveling wave which facilitates the current deviation by gathering energy in a localized packet, thus breaking translation invariance. This results in Gaussian statistics for small fluctuations but non-Gaussian tails above the critical current. Our observations, which agree with predictions derived from hydrodynamic fluctuation theory, strongly suggest that rare events are generically associated with coherent, self-organized patterns which enhance their probability.     

A phase-field model for elastically anisotropic polycrystalline binary solid solutions

A phase-field model for modeling the diffusional processes in an elastically anisotropic polycrystalline binary solid solution is described. The elastic interactions due to coherency elastic strain are incorporated by solving the mechanical equilibrium equation using an iterative-perturbation scheme taking into account elastic modulus inhomogeneity stemming from different grain orientations. We studied the precipitate interactions among precipitates across a grain boundary and grain boundary segregation–precipitate interactions. It was shown that the local pressure field from one coherent precipitate influences the shape of precipitates in other grains. The local pressure distribution due to primary coherent precipitates near the grain boundary leads to inhomogeneous solute distribution along the grain boundary, resulting in non-uniform distribution of secondary nuclei at the grain boundary.