The Eshelby formalism for inclusion/inhomogeneity problems is extended to the nano-scale at which surface/interface effects become important. The interior and exterior Eshelby tensors for a spherical inhomogeneous inclusion with the interface stress effect subjected to an arbitrary uniform eigenstrain embedded in an infinite alien matrix, and the stress concentration tensors for a spherical inhomogeneity subjected to an arbitrary remote uniform stress field are obtained. Unlike their counterparts at the macro-scale, the Eshelby and stress concentration tensors are, in general, not uniform inside the inhomogeneity but are position-dependent. They have the property of radial transverse isotropy. It is also shown that the size-dependence of the Eshelby tensors and the stress concentration tensors follow very simple scaling laws. Finally, the Eshelby formula to calculate the strain energy in the presence of the interface effect is given.

Eshelby formalism for nano-inhomogeneities

A review of recent works on inclusions

Colloidal nanocrystals combine size- and facet-dependent properties with solution processing. They offer thus a compelling suite of materials for technological applications. Their size- and facet-tunable features are studied in synthesis; however, to exploit their features in optoelectronic devices, it will be essential to translate control over size and facets from the colloid all the way to the film. Larger-diameter colloidal quantum dots (CQDs) offer the attractive possibility of harvesting infrared (IR) solar energy beyond absorption of silicon photovoltaics. These CQDs exhibit facets (nonpolar (100)) undisplayed in small-diameter CQDs; and the materials chemistry of smaller nanocrystals fails consequently to translate to materials for the short-wavelength IR regime. A new colloidal management strategy targeting the passivation of both (100) and (111) facets is demonstrated using distinct choices of cations and anions. The approach leads to narrow-bandgap CQDs with impressive colloidal stability and photoluminescence quantum yield. Photophysical studies confirm a reduction both in Stokes shift (≈47 meV) and Urbach tail (≈29 meV). This approach provides a ≈50% increase in the power conversion efficiency of IR photovoltaics compared to controls, and a ≈70% external quantum efficiency at their excitonic peak.

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A Facet-Specific Quantum Dot Passivation Strategy for Colloid Management and Efficient Infrared Photovoltaics.

This paper presents a simple analytical method for calculating the strain distribution in and around self-assembled (In,Ga)As/GaAs quantum-dot nanostructures. The dots are assumed to be buried in an infinite medium so that the effects of free surfaces can be neglected. This assumption is based on the relative size of the dot, compared to that of the overlayer. The model—based on classical continuum elasticity—is capable of handling dots of arbitrary shapes; here, however, only dots with pyramidal and truncated-pyramidal shapes are considered. The approximate shape of the dots is extracted from high-resolution transmission electron microscope observations. The electronic energy levels in the dots are calculated by solving the three-dimensional effective mass Schrodinger equation. The carrier confinement potential in this equation is modified by the strain distribution. Because the dots are in a strong confinement regime, the effects of Coulomb interactions are neglected. The calculated confined eigen-energies agree with our experimental photoluminescence data. The calculations also support previous results reported by others.

Self-assembled (In,Ga)As/GaAs quantum-dot nanostructures: strain distribution and electronic structure

Highly aligned graphene-based nanocomposites are of great interest due to their excellent electrical properties along the aligned direction. Graphene fillers in these composites are not necessarily perfectly aligned, but their orientations are highly confined to a certain angle, [Formula: see text] with 90° giving rise to the randomly oriented state and 0° to the perfectly aligned one. Recent experiments have shown that electrical conductivity and dielectric permittivity of highly aligned graphene-polymer nanocomposites are strongly dependent on this distribution angle, but at present no theory seems to exist to address this issue. In this work we present a new effective-medium theory that is derived from the underlying physical process including the effects of graphene orientation, filler loading, aspect ratio, percolation threshold, interfacial tunneling, and Maxwell-Wagner-Sillars polarization, to determine these two properties. The theory is formulated in the context of preferred orientational average. We highlight this new theory with an application to rGO/epoxy nanocomposites, and demonstrate that the calculated in-plane and out-of-plane conductivity and permittivity are in agreement with the experimental data as the range of graphene orientations changes from the randomly oriented to the highly aligned state. We also show that the percolation thresholds of highly aligned graphene nanocomposites are in general different along the planar and the normal directions, but they converge into a single one when the statistical distribution of graphene fillers is spherically symmetric.

https://iopscience.iop.org/article/10.1088/1361-648X/aa68ec/pdf

Theory of electrical conductivity and dielectric permittivity of highly aligned graphene-based nanocomposites.

This paper presents a study of electronic carrier redistribution in doped (In, Ga)As/GaAs quantum dots due to size variation. The dots in our samples fall roughly into "large" and "small" size clusters. At low temperatures, the carriers predominantly occupy the large-size dots. As the sample temperature is raised, thermal energy redistributes the carriers so that some begin to occupy energy states in the small-size dots. At room-temperature, the photoluminescence emission spectrum exhibits two distinct peaks due to transitions from the large- and small-size dots. This carrier redistribution can also be followed by observing the integrated absorbance as a function of temperature. The transition energy levels extracted from photoluminescence data compare favorably with theoretically calculated values for dots with truncated pyramidal shapes.

https://iopscience.iop.org/article/10.1143/JJAP.41.482/pdf

Quantum Dot-Size Variation and Its Impact on Emission and Absorption Characteristics: An Experimental and Theoretical Modeling Investigation

Three sets of self-organized InAs quantum dots (QDs) embedded in an external InGaAs quantum well samples were grown by solid source molecular beam epitaxy (MBE). By modifying Indium composition profile within quantum well (QW) region, it’s found the photoluminescence emission from quantum dots can be greatly enhanced when employing a graded quantum well to surround QDs. This quantum dots in a graded quantum well structure also preserves the long wavelength (1.3 μm) spectrum requirement for the future use in optoelectronics devices.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S1946427400624144

Valeria-Gabriela Stoleru

Papers

Self-assembled (In,Ga)As/GaAs quantum-dot nanostructures: strain distribution and electronic structure

Quantum Dot-Size Variation and Its Impact on Emission and Absorption Characteristics: An Experimental and Theoretical Modeling Investigation

Enhanced Photoluminescence from Long Wavelength InAs Quantum Dots Embedded in a Graded (In,Ga)As Quantum Well