Atomistic tight-binding calculations of CdSe/CdS core/shell dot-in-hexagonal platelet nanocrystals with interesting electronic structures and optical properties

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Abstract

I theoretically determine the electronic and optical signatures of CdSe/CdS core/shell dot-in-hexagonal platelet nanocrystals with experimentally synthesized dimensions exploiting the atomistic tight-binding theory. With the increasing lateral sizes and thicknesses of the CdS hexagonal platelets, the reduction of excitonic band gaps is ascribed to the quantum confinement consequence. The excitonic band gaps emitting the visible spectra are carried out by CdS shell sizes. The optical characteristic of CdSe/CdS dot-in-hexagonal platelet nanocrystals is advanced when comparing with bare CdSe nanocrystal. The reduction of oscillator strengths, excitonic binding energies and stokes shift with the increasing sizes of CdSe shell is ascribed to the electron-hole wave function overlaps. The key findings from the tight-binding analysis agree well with the experimental observation. Finally, this theoretical study delivers the essential direction to predesign of core/shell dot-in-hexagonal platelet nanocrystals with specific characteristics for various optoelectronic technologies.

Introduction

Colloidal semiconductor nanoparticles convey an extensive assortment of applications in biologics, optics and optoelectronics [[1], [2], [3], [4], [5]]. Recently, the natural properties of semiconductor nanocrystals are outstandingly tuned by the alternatives of material composition, dimension, geometric structure and shape. The shape is of importance for significant fundamental and applied research because of the highly shape dependence on the physical and chemical properties [[6], [7], [8]]. The study of 2D material leads to the discovery of an emerging class of low-dimensional materials with the great applications in the next generation of optoelectronic devices [9,10]. The encapsulation over the core by the shell to yield type-I or type-II core/shell nanocrystal delivers the manipulation of the electronic structures and optical properties. With the combination of the core/shell nanocrystal with the quantum-mechanical behavior of 2D system, core/shell dot-in-platelet or dot-in-plate nanocrystal, dot-shaped nanocrystal surrounded by 2D nanoplatelet or nanoplate, is materialized. In the available literature, only few reports are found by the authors on the synthesis and characterization of 2D core/shell system. For instance, Elsa Cassette et al. [11] informed the synthesis and natural properties of a CdSe/CdS dot-in-plate core/shell nanostructures. The optical spectra determined by in-plane [110] polarization were emitted in these nanocrystals. A new synthesis scheme CdSe/CdS core/shell dot-in-hexagonal platelet nanocrystals was demonstrated by Himani Chauhan et al. [12] The oleylamine was accountable for determining 2D core/shell nanocrystals by hindering the CdS growth shell in z direction. Kali R. Williams et al. [13] reported the synthesis of PbSe quantum dots encapsulated by two-dimensional CdSe nanoplatelets. PbSe/CdSe core/shell nanocrystals with type-I band gap demonstrated the high optical properties with near-infrared emission. CdSe/CdS dot/platelet nanocrystals with well controlled size and shape distribution were synthesized by Yonghong Wang et al. [14] The optical properties of the 2D nanocrystals were improved when comparing to the spherical core/shell nanocrystals.

According to the literature described in the above paragraph, CdSe/CdS core/shell dot-in-hexagonal platelet nanocrystals lack of the theoretical study. Consequently, this work is to theoretically debate and analyze the previous work in the detail of the electronic structures and optical properties. The simulation of CdSe/CdS core/shell dot-in-hexagonal platelet nanocrystals in the atomistic methods is complicated because of the relatively complex systems. For the description of the electronic and optical properties of the nanostructures, the methodologies are classified into three classes: (i) continuous empirical methods (effective mass and k. p method [15,16]); (ii) density functional theory [[17], [18], [19]] and (iii) atomistic empirical methods [[20], [21], [22], [23]]. Each method has its own advantage and drawback. To fill the gap between density functional theory and continuous empirical methods, the concession between precision and computational resource may be sorted out by the atomistic empirical methods. To obtain the results with precision of density functional theory with the optimized computational cost, the empirical tight-binding model is considered. To this persistence, the atomistic tight-binding theory is theoretically implemented to analyze the electronic structures and optical properties of CdSe/CdS core/shell dot-in-hexagonal platelet nanocrystals with the experimentally synthesized dimensions. The scientific manuscript is structured as follows. In the first part of the paper, the theoretical method is briefly presented. I then discuss the natural properties of CdSe/CdS core/shell dot-in-platelet nanocrystals with the experimentally synthesized sizes. In the last part, the resulting calculations with interesting electronic structures and optical signatures are concluded.

The atomistic tight binding theory for the modelling of electronic structures and optical signatures of CdSe dot embedded in CdS hexagonal platelet is developed. Briefly, I start by building the 3D geometry of CdSe/CdS core/shell dot-in-platelet nanocrystals. According to the available experiment [11], these nanostructures have the wurtzite crystal. The geometry comprises of different domains: the spherical CdSe core and the hexagonal CdS shell. Each domain has its own material parameters, the electron and hole effective mass, the conduction and valence band potential and lattice constants. Owing to the different lattice constants between CdSe dot and CdS platelet, these structures are optimized within the framework of the atomistic valence force field approach [24,25]. Subsequently the minimized atomic positions are attained, the energy levels and the wave functions are computed by empirical tight-binding model with the assistance of the nearest-neighbouring interaction, strain field, spin-orbit coupling and sp3s orbital hybridization [26]. The tight-binding Hamiltonian (HTB) [27] is identified by the creation ciα (annihilation ciα) operator of a carrier on the α orbital with the spin component localized on site i in the N-atom system as given by:HTB=i=1Nα=1mεiαciαciα+i=1Nα=1mα=1mλiααciαciα+i=1Ni=1Nα=1mα=1mtiα,iαciαciα

Here, εiα, tiα,iα and λiαα are symbolized as on-site empirical parameters, overlaps between the orbitals of the nearest-neighbouring atoms and spin-orbit couplings, respectively. The spin-orbit interaction is only contributed by the atomic p orbitals [28]. Owing to the different domains between CdSe and CdS semiconductor, the valence-band offset of +0.55 eV [29] is incorporated into the Hamiltonian of tight-binding theory. The tight-binding parameterization of CdSe and CdS is exploited from P. E. Lippens et al. [30] and O. Akinci et al. [31], respectively. Within these fitting parameters, bulk CdSe and CdS band gaps are in a good consensus with the data in the literatures [[32], [33], [34], [35]]. To eliminate the appearance of the gap states, I apply the surface dangling by the energy shift to CdSe/CdS core/shell dot-in-platelet nanocrystals [36]. To gain the single-particle spectra, this matrix is diagonalized.

From view of the second quantization, the single excitonic Hamiltonian (Hex) is equalized as:Hex=iEieiei+jEjhjhjijklVijkleh,coulhiejekhl+ijklVijkleh,exchhiejekhl

Here, Eie, Eih, Vijkleh and Vijkleh,exch are the electron energies, hole energies, electron-hole coulomb matrix elements and electron-hole exchange matrix elements, respectively. To obtain the excitonic spectra, the matrix of excitonic Hamiltonian is solved from an electron-hole pair generated from 12 lowest electron wave functions and 12 highest hole wave functions concerning on the spin components. The excitonic energies and states are obtained by diagonalizing this matrix. For the evaluation of the stimulatingly atomistic characteristics, the analysis containing single-particle spectra, orbital character, band gap, overlap between electron and hole wave function, oscillation strength, binding energy of exciton and stokes shift is finally exposed.

Section snippets

Results and discussions

CdSe/CdS dot-in-hexagonal platelet nanocrystals, dot-shaped CdSe nanocrystals embedded in CdS hexagonal nanoplatelets, afford synthetically tunable paths to control the electronic structures and optical properties and have been the concentration of substantial fundamental and applied research determination. The objective of this work is to examine the potential influence of the experimentally structural dimensions on the electronic structures and optical properties through the atomistic

Conclusions

On the basis of the scientific investigations above, I successfully determine the electronic structures and optical signatures of CdSe/CdS dot-in-hexagonal platelet nanocrystals with experimentally synthesized sizes by the atomistic tight-binding model. The computations on the distinct schemes of CdSe/CdS dot-in-hexagonal platelet nanocrystals are indispensable in numerous respects. The atomistic characteristics is significantly sensitive with the lateral sizes and thicknesses in the CdS

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

This project is funded by National Research Council of Thailand (NRCT): NRCT5-RSA63023-04.

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      The accurate computational models in the electronic structures and optical properties of the semiconductor nanostructures still encounter the serious challenge for methods exploiting the continuum-media approximation and atomistic methods. In the present work, I use the amalgamation of tight-binding and configuration-interaction methods which prove its capability to determine the electronic structures and optical properties in a good agreement with experiments [44–47]. The focus manuscript aims to underline the potential influence of the quantum-confined layers on the electronic structures and optical properties of these semiconductor nanoshells.

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