Strain influence on optical absorption of giant semiconductor colloidal quantum dots

Abstract

Abstract. The lattice mismatch strain field of core/multishell structures with spherical symmetry is modeled by a linear continuum elasticity approach. The effect of the strain on the energy structure and linear optical absorption in large core/shell/shell spherical semiconductor quantum dots is analyzed. Localization of the photoexcited carriers induced by coating is found to play an important role in explaining the optical stability of large CdSe/CdS/ZnS and ZnTe/ZnSe/ZnS quantum dots. IntroductionAs 'The Next Big Thing' in photovoltaics [1], the colloidal multishell semiconductor quantum dots (QDs) have led to the development of high-efficiency solar cells. To overcome the crystal irregularities induced by the lattice mismatch in the synthesis of these colloidal nanocrystals, the use of a strain-adapting intermediate shell in core/shell (CS) QDs has been proposed. Thus, 'giant' core/shell/shell (CSS) QDs of 18-19 monolayers shell thickness of are synthesized [2,3]. There are several theoretical studies of multi-component nanocrystals, in which the role of the strain is considered by first-principle calculations, by using, for example, the density-functional tight-binding method [4] or local density approximation [5] or densityfunctional theory [6]. Unfortunately, limitations of these ab-initio calculations (e.g., bandgap underestimation) make difficult comparison of their results with the experiment. More important, the main problem of the first-principle calculations, the computational cost, can make the method inadequate for larger structures, such as the large CSS QDs. On the other hand, the widely used for analyzing the linear elasticity of epitaxial strained heterointerfaces, the valence force field method (see, e.g., Ref. [7]) is dependent on a priori information regarding the interface structure and surface passivation. 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 * E-mail: cheche@gate.sinica.edu.twTel.: +40 724 536 908 2 for semiconductor QDs of spherical shape and cubic symmetry (see, e.g., Ref. [8]). In this context, we propose a continuum elasticity model for the lattice mismatch strain field in such nanocrystals. Keeping justified simplicity, based on our strain field model, we consider a twoband model within the effective mass approximation to theoretically investigate the energy structure and light absorption of a CSS QD with thick shells. In our model, we consider ideal multilayer structures. We assume the defects and impurities with low concentration are located at the interfaces, as reported by experiment, (see, e.g., Ref.[9]), and consequently, do not significantly influence the lattice mismatch strain field. Theoretical model Strain field and the band lineup in the presence of strainFirst, we describe our method for calculus of the lattice mismatch strain field. For spherical core/shell nanocrystals the displacement ( u ) has radial symmetry, that is the field is irrotation...

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Efficient Modeling of Optical Excitations of Colloidal Core–Shell Semiconductor Quantum Dots by Using Symmetrized Orbitals

“…In the continuous model the shear strain for spherical core is zero; consequently, no shear deformation potential enters in the core strain Hamiltonian, (there is no entering for core d v in Table ). Canceling of the shear strain in the spherical core justifies the widely accepted approximation of negligible piezoelectric potential for thin shells …”

“…To take into account the shape and size of the heterostructures in modeling the strain field we adopt the continuum elasticity theory for the strain of an inclusion in a finite elastic body. 31 The isotropic continuum elastic strain tensor for spherical core/shell heterostructure from Pahomi and Cheche 24 (see Supporting Information, section B) is implemented in the numerical code.…”

“…The linear absorption coefficient of CSQD is calculated by using Fermi’s golden rule, which, at low temperatures, is given by , where n is the refractive index, e is the electron charge, c is the speed of light in vacuum, ε 0 is the vacuum permittivity, Ω = 4 πR 3 /3, and E vc ( R ) = E c ( R ) – E v ( R ). N v and N c denote the numbers of SPSs for VB and CB states included in the calculation.…”

“…Related to the strain field it is important to mention that our method is applicable to core/multishell structures. Analytical expression of the strain tensor of such structures exists in the literature, 24 and it can be implemented in the electronic structure computation of the multiband k•p Hamiltonian including strain. In this work, we only consider core/shell nanostructures.…”