To obtain the strain field, the linear stress‐strain tensor ( σ i j − ε i j) relation is used. Within the continuum elasticity approach, the equilibrium equation is grad div u = 0. We start by observing that for an elastic spherical core/shell structure, the displacement field, u, has radial symmetry and consequently the field is irrotational. In what follows, we introduce an efficient simple method to obtain the strain field in concentric spherical domains of different elastic parameters, which satisfies the necessary accuracy level for our problem. Elaborate solutions for such a problem are obtained in few particular cases for Eshelby‐type inclusion of a finite elastic body (see Ref. In the elasticity theory, description of the strain field in finite‐domain elastic bodies is a difficult problem. Strain field and the band lineup in the presence of the strain Conclusions are presented in Section 4.Ģ.1. In Section 3, we apply the theory presented in the previous section to several types of semiconductor CSQDs with heterostructures of type I and II. In Section 2.5, the optical absorption coefficient is obtained by taking into account the excitonic effect. In Section 2.4, we discuss the excitonic effect in QDs. In Sections 2.2 and 2.3, we describe the electronic structures and obtain the single‐particle states (SPSs) by an effective two‐band model and by an eight‐band model within the k In Section 2.1, we describe the lattice‐mismatch strain field in core/multi‐shell nanostructures by a continuum elasticity approach. In Section 2, we introduce the theoretical modelling. In this context, in this chapter, we discuss optical properties of CSQDs. The continuum elasticity approach in the limits of homogeneous and isotropic materials has been shown to be in good agreement with the valence force field models for semiconductor QDs of spherical shape and cubic symmetry (see, e.g. band gap underestimation) and also more important, the computational cost for larger QDs, make difficult comparison between theoretical predictions and the experiment. Structural limitations of these first‐principle calculations (e.g. There are several theoretical studies of multi‐component nanocrystals, in which the role of the strain is considered by ab‐initio calculations. ) has some limitations as the predictions are dependent of a priori information regarding the interface structure and surface passivation. Widely used for analysing the linear elasticity of epitaxial‐strained heterointerfaces, the valence force field method (see, e.g. Modelling of the lattice‐mismatch strain is a key factor in obtaining an accurate physical description of CSQDs. The theoretical predictions of electronic structures and optical properties are important in the core/shell quantum dots (CSQDs) engineering. ‘Giant’ core/multi‐shell of 18–19 monolayers (MLs) shell thickness can be prepared with low cost by chemical synthesis. The main factors used in tuning the physical properties of QDs are the shape and size confinement, and the lattice‐mismatch‐induced strain. At theoretical level, the study of magnetism or photon entanglement is an example in which the theoretical studies emerge in promising new properties of electronic devices for spintronics or computer microchips. For example, the colloidal multi‐shell QDs have led to the development of high‐efficiency solar cells or laser applications, and probably the most important in the immediate future, to molecular diagnostics and pathology. The large interest for these materials comes from their technical applications and theoretical openings. Semiconductor quantum dots (QDs) are nanometre‐scale objects that are different to the usual optical materials, have size‐tuneable and narrow fluorescence and broad absorption spectra.
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