Periodically grown quantum nanostructures with arbitrary geometries : periodicity effects on the induced electro-elastic fields

Quantum nanostructures ( QNSs), due to their widespread and attractive physical, optical, and electronic properties, have been at the center of attention of many nanoscience and nanotechnology researches. In order to predict the electro-mechanical behavior of QNSs, accurate determination of the electro-elastic fields induced by quantum wells ( QWs), quantum wires ( QWRs), and quantum dots ( QDs) in such nanostructures would be of great importance and particular interest. In this study, by utilization of the electro-mechanical eigenfield concept in conjunction with the Fourier series technique, an analytical solution is presented which gives the electro-elastic fields induced by one-, two-, and three-dimensional periodic distribution of QWs, QWRs, and QDs, respectively. This methodology takes into account the electro-mechanical couplings of elastic and electric fields within the piezoelectric barrier as well as the interaction between periodically grown QWRs and QDs. The latter would be so important since the density of the periodically grown QNSs will have significant effects on the induced electro-elastic fields within both the QNSs and the surrounding barrier; this issue is addressed precisely in the present study by measuring the induced electro-elastic fields due to different periodicities of pyramidal QDs. Furthermore, the current formulation is capable of treating arbitrary geometries of QWRs and QDs which makes the solution more interesting and powerful. (C) 2015 Published by Elsevier Ltd

Interacting functionally graded quantum wires/quantum dots with arbitrary shapes and general anisotropy within a distinct piezoelectric matrix

An accurate determination of the two- and three-dimensional electro-elastic fields of periodically as well as arbitrarily distributed interacting quantum wires (QWRs) and interacting quantum dots (QDs) of arbitrary shapes within a piezoelectric matrix is of particular interest. Both the QWR/QD and the barrier may be made of materials with distinct general rectilinear anisotropy in elastic, piezoelectric, and dielectric constants. The lattice mismatch between the QWR/QD and the barrier is accounted by prescribing an initial misfit strain field within the QWR/QD. Previous analytical treatments have neglected the distinction between the electro-mechanical properties of the QWR/QD and those of the barrier. This simplifying assumption is circumvented in the present work by using a novel electro-mechanical equivalent inclusion method in Fourier space (FEMEIM). Moreover, the theory can readily treat cases where the QWRs/QDs are multiphase or functionally graded (FG). It was proven that for two-dimensional problems of either a periodic or an arbitrary distribution of FG QWRs in a transversely isotropic piezoelectric barrier, the elastic and electric fields are electrically and elastically impotent, respectively, and no electric field would be induced in the medium provided that the rotational symmetry and polarization axes coincide. Some numerical examples of more frequent shapes and different distributions of indium nitride QDs/QWRs within transversely isotropic aluminum nitride barrier are solved

On the exact nature of the coupled-fields of magneto-electro-elastic ellipsoidal inclusions with non-uniform eigenfields and general anisotropy

The current work reveals the exact nature of the induced interior and exterior coupled-fields of magneto-electro-elastic ellipsoidal inclusions with non-uniform generalized eigenfields, consisting of eigenstrain, eigenelectric, and eigenmagnetic fields. The medium has general rectilinear anisotropic elastic moduli, piezoelectric, piezomagnetic, dielectric, magneto-electric, and magnetic permeability tensors. The non-uniform eigenfields are assumed to be representable as the product of any arbitrary functions whose arguments are the equation of the boundary of the ellipsoidal inclusion with homogeneous polynomials. As a special case, it has been proved that the homogeneous polynomial eigenstrain, eigenelectric, and eigenmagnetic fields simultaneously induce in homogeneous polynomial strain, electric, magnetic, stress, electric displacement, and magnetic induction fields of the same degree at the interior points of the inclusion. Certain series forms of the eigenfields in cylindrical coordinates are also treated. A special class of impotent eigenstrain, eigenelectric, and eigenmagnetic fields which give rise to vanishing strain, electric, and magnetic fields within the ellipsoidal domain is introduced and proved. Furthermore, the energies pertinent to the magneto-electro-elastic inclusions with arbitrary geometries and eigenfields are formulated. Also, the exact analytical expressions of the magneto-electro-elastic jump conditions of the generalized stress and the gradient of the generalized displacement fields are obtained. A number of theorems, lemmas, and corollaries in connection with the exact nature of the solution are stated and proved for the first time. The presented formulations and theoretical developments are of great value in the determination of the exact induced interior and exterior coupled-fields of anisotropic quantum wire/quantum dot structures as well as anisotropic piezoelectric/piezomagnetic composites

Novel theories on magneto-electro-elastic ellipsoidal multi-inclusions and inhomogeneities and associated impotent fields

The exact nature of the induced coupled-fields of anisotropic magneto-electro-elastic ellipsoidal inclusions, multi-inclusions, and inhomogeneities with non-uniform eigenfields under polynomial magneto-electro-elastic far-field loadings is of particular interest. For the sake of prediction of the induced coupled-fields of magnetoelectro-elastic multi-inclusions due to piecewise polynomial generalized eigenfields several theorems and corollaries are stated and proved. Some classes of impotent generalized eigenfields associated with encapsulated ellipsoidal multi-inclusion result in vanishing generalized disturbance strains within the innermost ellipsoidal domain. On the other hand, it is found that there are certain classes of impotent generalized eigenfields for which the generalized disturbance stresses vanish everywhere. Furthermore, it is proved that there exists a unique equivalent magneto-electro-elastic inclusion associated with an anisotropic magneto-electro-elastic ellipsoidal inhomogeneity subjected to polynomial far-field loadings. It is shown that associated with every anisotropic magneto-electro-elastic ellipsoidal inhomogeneity, there exists a set of infinite numbers of far-field loadings for which the inhomogeneity does not induce any disturbance generalized stresses anywhere within the entire medium. In other words, under certain far-field loadings the inhomogeneity is not sensed by the surrounding magneto-electro-elastic medium

Analytical solutions for electro-elastic fields of periodic quantum nanostructures within transversely isotropic piezoelectric media : studying the geometry effects

Accurate determination of the electro-elastic fields of quantum nanostructures within piezoelectric media is an important issue for realizing the electro-mechanical behavior of these nanostructures. In this paper, the governing partial differential equations corresponding to piezoelectric media containing quantum nanostructures are presented and subsequently, generalized analytical solutions based on Fourier series technique are developed for determination of the coupled electro-elastic fields in transversely isotropic piezoelectric barrier due to periodically distributed quantum nanostructures. The electro-elastic couplings of the piezoelectric barrier as well as the interactions between the quantum nanostructures are exhibited within the framework of the presented analytical solution. It is observed that no electric field and no electric potential will be induced anywhere in the medium for periodic distribution of quantum wires. The presented analytical solution is capable of treating different shapes and geometries of quantum wires/quantum dots. The electro-elastic fields of various shapes of sections of quantum wires and different geometries of quantum dots are studied and the effects of the geometry of periodically distributed quantum nanostructures are demonstrated. The results show that geometry of quantum nanostructures may highly affect the induced electro-elastic fields and therefore, accurate determination of the geometry of quantum nanostructures as well as the induced electro-elastic fields would be essential for employment of these nanostructures in different fields of research and technology

Analytical study of electro-elastic fields in quantum nanostructure solar cells : the inter-nanostructure couplings and geometrical effects

Recent investigations on multifunctional piezoelectric semiconductors have shown their excellent potential as photovoltaic components in high-efficiency third-generation quantum nanostructure (QNS) solar cells. The current work is devoted to studying the electro-elastic behavior of high-density QNS photovoltaic semiconductors within which initial mismatch strains of arrays of quantum dots (QDs) or quantum wires (QWRs) induce coupled electro-mechanical fields. The inter-nanostructure couplings which are of great importance in high-density QNS arrays are incorporated in the presented analytical framework. In practice, QNSs with different geometries such as spherical, cuboidal, or pyramidal QDs and circular or rectangular QWRs can be grown. The present solutions take into consideration any arbitrary geometry of grown QNSs as well. In addition, the current methodology treats functional variations of electro-mechanical properties of anisotropic QNSs and their difference with electro-elastic constants of the anisotropic barrier. Furthermore, nonuniform initial misfit strains within high-density QDs have been incorporated and revealed that change the induced strains by as much as 52 percent in comparison with the case of uniform misfit strains in InAs/GaAs pyramidal QDs. When different material properties of QNSs and barrier have shown to make small effects on the induced fields, it has been observed that both inter-QD couplings and QD geometry significantly affect the coupled induced electro-elastic fields either within QNSs or in the piezoelectric barrier

Closed-form analytical solutions for predicting stress transfers and thermo-elastic properties of short fiber composites

Novel analytical solutions with closed-form expressions for the stress and displacement fields of short fiber reinforced composites (SFRCs) and analytical prediction of their effective thermo-elastic properties are presented. The cylindrical SFRC unit-cells with periodic boundary conditions are subjected to axial and transverse stresses as well as thermally induced residual stresses. By comparison with available numerical and analytical solutions, it is revealed that the present closed-form solutions provide accurate stress field variations as well as accurate predictions for the effective thermo-elastic properties of SFRCs in a split second, and thus, the developed model is much more computationally efficient than numerical methods