Shallow donor inside core/shell spherical nanodot: Effect of nanostructure size and dielectric environment on energy spectrum

doi:10.1016/j.spmi.2017.07.063

Superlattices and Microstructures

Volume 111, November 2017, Pages 976-982

https://doi.org/10.1016/j.spmi.2017.07.063 Get rights and content

Highlights

•
Theoretical model of a centered donor in core/shell nanodots.
•
Comparison between CdSe/ZnTe and ZnTe/CdSe structures.
•
Influence of the core/shell sizes and of the external dielectric constant on the binding energy.

Abstract

We have reported the impact of the core and shell radii on the energy spectrum of centered shallow donor confined inside CdSe/ZnTe core/shell quantum dot and ZnTe/CdSe inverted core/shell quantum dot. The dielectric discontinuity between the nanosystems and their surrounding medium was considered. In order to examine the behavior of the donor binding energy as a function of the spatial parameters a variational approach within the framework of the effective-mass approximation was deployed. Our model shows that for a fixed shell radius the increase of the core radius value blue-shifts the binding energy of the donor inside inverted core/shell quantum dot only if the value of the core to shell radii ratio is between 0.9 and 1, otherwise it is red-shifted. By contrast, for core/shell quantum dot system the binding energy is red-shifted by increasing the core radius for a fixed nanostructure size and for all values of the core to shell radii ratio. We have also found that the donor binding energy values are more important in a core/shell nanodot than in an inverted core/shell quantum dot.

Introduction

The intense challenges which electronic and optoelectronic device applications present have stimulated an important number of fundamental and experimental research works [1]. Indeed, present-day electronic and optoelectronic devices build on a long history of invention, discovery, and basic scientific research. We can cite, for example, the quantum confinement effect (QCE) which is one of the notorious fundamental behavior of matter very useful in order to manufacture a new generation of electronic and optoelectronic devices less expensive and more performing. Nowadays, due to the development of the techniques for synthesis of nanomaterials, the use of the ultimate dependence of electronic structure on the shape and size of nanomaterials enables nanomaterials with desired electronic and optical properties [2].

Another important factor which drastically modifies the properties of materials and has a great implication in making a material useful or not for fabricating a device is the capacity to control the defects in semiconductor materials [3]. To this end, a growing number of papers were published this lasts decades. A variational approach was performed by Bastard [4] in order to examine the impact of the well thickness and of the position of a shallow donor impurity inside a symmetric quantum well. It was found that the donor binding energy decreases when the impurity moves from the center to the border of the quantum well or when the quantum well thickness increases. The effect of the dielectric-constant mismatch on the donor binding energy was treated by Bassani and coworkers [5]. Their results, obtained using a variational computation, showed that the impact of the dielectric constant mismatch is much larger than previously anticipated and such effect is more remarkable when the impurity moves away from the center of the quantum well. By deploying a diffusion quantum Monte Carlo method the negative-donor center under a magnetic field inside bulk semiconductor and quantum well is studied in Ref. [6]. Compared with the magneto-optical experiments the obtained results at zero magnetic field are in good agreement in the case of bulk system. It is also found that a sevenfold increase in binding energy over that of the bulk case is estimated. More recently, the dependence of the shallow donor binding energies of the ground and excited states, and the optical absorption between the related states on the electric and intense laser fields was investigated by Kasapoglu et al. [7]. The problem of shallow donor impurities in quantum well wires was extensively investigated by various authors for more details see Refs. [8], [9], [10], [11], [12], [13].

Due to the important electronic and optical properties revealed by zero dimensional semiconductors, diverse papers were aimed on the study of shallow donors inside quantum dot systems. For example, PorrasMontenegro et al. [14] have examined the effect of the donor localization and the nanodot size on the behavior of the binding energy of a donor confined in a spherical quantum dot. It was shown that due to the higher geometrical electronic confinement in such systems the binding energy undergoes a great enhancement compared to that in quantum well and quantum wire. One year later, using a linear variational method, Zhu [15] computes the energy levels and binding energies of an off-center donor in a GaAs-Ga_1-xAl_xAs spherical nanodot. His paper shows that the splitting and ordering of quantum levels is dependent on the quantum dot diameter, the donor ion localization, and the barrier height of the confinement potential. Using a variational approach the density of impurity states and donor binding energies of a shallow impurity inside a quantum dot are presented in Ref. [16]. The authors of this comparative study have shown that the values of the binding energy of a quantum wire and a quantum well can be deducted from those of the quantum dot by applying the appropriate limits. Furthermore, it was demonstrated that the values of the donor binding energy for spherical and cubic quantum dots are very close if the dots have similar volumes. Assuming a parabolic confinement, Jayam et al. [17] have studied the dependence of the binding energy on external electric field and hydrostatic pressure of donor inside spherical quantum dot. Their results show a great dependence of the binding energy on the nanostructure size, the hydrostatic pressure, and the electric field strength. On the other hand, the behavior of the donor binding energy in a rectangular parallelepiped-shaped quantum dot was the subject of the paper of Xia et al. [18]. Their model has shown that if the impurity is located in the interior of the nanodot the finite potential gives a smaller binding energy than infinite potential model, and that the binding energy is more dependent on the applied electric field in the finite potential model. For the same reasons as before the behavior of the binding energy of donors inside quantum ring systems was also extensively studied whether without any external perturbation [19], [20], [21] or with external perturbation [22].

If one quantum dot is encapsulated by a layer of another semiconductor, then the resulting system is called core/shell quantum dot which is expected to have electric and optical properties much enhanced as compared with classic quantum dot [23]. Deploying a variational method, the donor binding energy as well as the inter-particle distance of shallow donor confined inside the well region of a core/shell spherical quantum dot were calculated by Ibral et al. [24]. Their theoretical model showed a remarkable dependence of the binding energy on the core and shell radii, and for core/shell structure with layer neighboring 1 nm they have demonstrated the producing of a giant electron-hole Coulomb correlation which improve the off-center donor binding energy. Following the same approach as in Ref. [24], Talbi et al. [25] have investigated the behavior of the donor binding energy as a function of the spatial parameters (core and shell radii) and the magnetic field strength. Their study reveal the possibility to accurately control the donor binding energy by tuning the magnetic field strength and the nanostructure size. A detailed study of the energy of a donor in core/shell/well/shell multilayered spherical quantum dot was performed by Hatice et al. [26]. Their paper provides the opportunity to improve the donor binding energy of the ground and excited states by controlling the sizes of the barrier, well, and core layers. Using respectively a variational calculation and the density matrix approach the electronic and the optical properties of shallow donor impurity inside a core/shell/shell nanosystem were investigated by Jasmine et al. [27]. The main result of their investigation is that the optical absorption wavelength is size controlled.

In the present paper, we deal with the spatial control of the binding energy of on-center donor inside CdSe/ZnTe core shell quantum dot and ZnTe/CdSe inverted core/shell quantum dot. For this end, and considering the effect of the surrounding medium, we have carried out a variational approach in order to study the variation of the donor binding energy with respect to the systems size. The next section is devoted to introduce the theoretical background, while in section 3 we propose to present and analyze our numerical results.

Section snippets

Model and the applied theory

Let us consider a shallow donor positioned at the center of a CdSe/ZnTe core shell quantum dot and ZnTe/CdSe inverted core/shell quantum dot. The two systems are submerged in a SiO₂ dielectric matrix. The schematic description of our nanoheterostructures are displayed in Fig. 1, where $R_{C}$ and $R_{S}$ are, respectively, the inner and outer radii, while $Δ E_{c} = U_{e} = 1.27 e V$ is the confinement potential of electrons.

Within the framework of the effective-mass approximation, applying the isotropic and non

Numerical results

In this section, we present our investigation about the impact of the nanodot size on the donor binding energy as well as we compare the two systems under study which are CdSe/ZnTe and ZnTe/CdSe core/shell nanodots. The influence of the dielectric environment on the energy is considered via the self-energy term introduced previously in Eq. (6). The used parameters are as follows [31]: for CdSe, $E_{g} = 1.75 e V$ , $ε_{r c} = 10.6$ , $m_{e c}^{*} = 0.13 m_{0}$ and for ZnTe, $E_{g} = 2.2 e V$ , $ε_{r z} = 9.7$ , $m_{e z}^{*} = 0.15 m_{0}$ . The dielectric

Conclusion

To summarize, the binding energy of a shallow donor was investigated using a variational approach and taking into account the impact of the dielectric environment on the energy spectrum. In this study, we have considered two different systems, CdSe/ZnTe core shell quantum dot and ZnTe/CdSe inverted core/shell quantum dot. Our numerical results show that tailoring the nanodot geometry leads us to accurately control the electronic properties of the nanostructures such as electron energy, total

Acknowledgements

This work has been initiated with the support of URAC: 08, the project PPR: (MESRSFC-CNRST) and the Swedish Research Links programme dnr-348-2011-7264. The authors would like to thank all the organizations.

References (31)

E. Kasapoglu et al.
Opt. Mater
(2016)
E. Kasapoglu et al.
Phys. E
(2003)
R. Khordad
Superlattices Microstruct.
(2010)
S.G. Jayam et al.
Solid State Commun.
(2003)
F.J. Betancur et al.
Phys. B
(2007)
M.G. Barseghyan et al.
Superlattices Microstruct.
(2012)
A. Talbi et al.
Superlattices Microstruct.
(2015)
A. Chafai et al.
Superlattices Microstruct.
(2017)
R. Angus
The Materials Science of Semiconductors
(2007)
I. Fedin et al.
J. Am. Chem. Soc.
(2016)

Y. Peter et al.

Cardona, Fundamentals of Semiconductors Physics and Materials Properties

(2010)

G. Bastard

Phys. Rev. B

(1981)

S. Fraizzoli et al.

Phys. Rev. B

(1990)

T. Pang et al.

Phys. Rev. Lett.

(1990)

Z.Y. Deng et al.

J. Appl. Phys.

(1994)

Cited by (20)

Exploring the microscopic effects of surrounding matrices (HfO<inf>2</inf> and SiO<inf>2</inf>) on CdSe/ZnS and ZnS/CdSe cylindrical core/shell quantum dot for microelectronic transport applications
2024, Materials Science and Engineering: B
The primary goal of this study is to comprehensively describe the physical impact of surrounding dielectrix oxides on the electronic and optical properties of a confined electron within CdSe/ZnS and ZnS/CdSe cylindrical core/shell quantum dot (CCSQD). The effective mass approximation and the compact density matrix approach have been employed to compute the energy eigenvalues as well as the optical absorption coefficients (OACs) and the refractive index changes (RICs). Our calculations revealed that the presence of enveloping oxides acts as an additional confinement tool altering the electron energy spectrum. The ZnS/CdSe CCSQD exhibited more pronounced response and the exploitation of the local electric factor can effectively enhance the optical nonlinearity of OACs and RICs. We demonstrated that confined electrons within the ZnS/CdSe CCSQD are subjected to an intense interaction at the microscopic scale with the host medium. In addition, saturation effects in the nonlinear computed coefficients have been meticulously analyzed in terms of size and dielectric surroundings. Our findings demonstrated that electronic band edge states are heavily impacted by the sharp dielectric mismatch occurring at QD/matrix interface which could be exploited for the creation of novel optoelectronic devices in the future.
Theoretical modeling of nonlinear optical properties in spheroidal CdTe/ZnTe core/shell quantum dot embedded in various dielectric matrices
2024, Results in Physics
The theoretical investigation of the electronic and nonlinear optical properties in spheroid-shaped CdTe/ZnTe core/shell quantum dots (CSQDs) embedded into two commonly adopted dielectric matrices (PVA, SiO₂) is done in the framework of the Effective Mass Approximation (EMA). The discrete intra-band confined energy levels and their matching wave functions were calculated by solving the stationary Schrödinger equation taking into account the Compact Density Matrix (CDM) approach. The effect of the dielectric mismatch between the system and the capped matrix has been studied and discussed. Our numerical results revealed that the third-order nonlinear (TON) optical susceptibility $χ^{(3)}$ is strongly influenced by the geometrical parameters and the dielectric environment.
Role of surrounding dielectric matrices on the nonlinear properties of group II-VI core/shell dot in the presence of electric field
2024, Micro and Nanostructures
The effects of geometrical parameters, relaxation time, impurity distance, incident optical intensity and electric strength on binding energy of an impurity situated in CdSe/ZnS CSQD embedded into three commonly used dielectric environments (SiO₂, CFM and 2M2P) are reported in the present paper. By means of effective mass approximation, density matrix approach and variationnal technique, electronic states and corresponding wavefunctions are employed in order to investigate the impact of mentioned parameters on the real and imaginary parts of both third order (nonlinear) optical suscepetibility as well as the complex dielectric function. The results show the effect of impact of dielectric environment surrounded by the core/shell dot, the third order (nonlinear) coefficients of dot embedded with SiO₂ is found to be largest, the peak amplitude of third order susceptibility is blue shifted with the enhancement of electric field, the peak value not only increases but also suffers red shift as the optical intensity is increased, the single peak is doubled as the optical intensity is enhanced and it is broadened and the reduction of peak values of real and imaginary parts of dielectric function is observed with the surrounding of dielectric matrices. The dielectric environment, external perturbation, optical intensity in addition to the geometrical confinement can improve the performance of the optical properties.
Electronic and optical properties of CdSe/ZnSe core/shell QDs within centered hydrogenic impurity and their tunability when subjected to an external electric field
2024, Physica B: Condensed Matter
The electronic and optical properties of CdSe/ZnSe semiconductor core/shell quantum dots with hydrogenic donor impurity were investigated theoretically. The perturbation approach and variational method were used in calculations under Effective Mass Approximation. The considered structure is embedded in a variable polymer matrix. The binding energy (BE), photoionization cross-section, polarizability, and diamagnetic susceptibility of the excited impurity were calculated first according to the core/shell radius ratio and then under a significant external electric field and in the absence of an external electric field. A significant stark shift was observed in the BE relative to the embedded matrix element.
Tuning of binding energy, polarizability and photoionization cross-section of a hydrogenic impurity in CdTe/ZnTe core-shell nanostructure by the electric field and capped matrix
2023, Physics Letters, Section A: General, Atomic and Solid State Physics
The current work describes in detail the effect of polarization charges on the electronic properties of core/shell spherical quantum dots (CSQDs) structures composed of CdTe/ZnTe semiconductors. In the calculations, energy levels and wave functions matching these levels were calculated by using the effective mass approach (EMA). Furthermore, the binding energy of a hydrogenic impurity was calculated under the variational approach. The matrix effects surrounding the CSQDs structure, the quantum dot size, the impurity, and how the applied external electric field affects the impurity binding energy ( $E_{b}$ ), polarizability (P_a) and photoionization cross-section (PICS) are calculated and discussed in detail. The obtained results revealed that the $E_{b}$ , the PICS and P_a are not only affected by the quantum parameter size but also by the capped matrix, the impurity and external electric field EF actions.
Photoionization cross-section and polarizability of impurity in CdS/ZnS core/shell quantum dots capped in a dielectric matrix
2023, Solid State Communications
Using the effective mass approximation (E.M.A), we have performed theoretically the influence of the capped matrix, the geometrical parameters and the applied electric intensity on the Polarizability and photoionization cross-section (PCS) of CdS/ZnS core/shell quantum dots CSQDs. The energy states of the binding energy (BE) and their corresponding wave functions are computed by solving Schrödinger equation in three-dimensional based on the variational approach. Our numerical results show that the EF and the nature of dielectric medium have an obvious influence on the BE, PCS and Polarizability of the structure. The present study suggests that the c/s nanostructure dispersed in a dielectric matrix may improve the performance of optoelectronic and photonic devices.

View all citing articles on Scopus

View full text

Shallow donor inside core/shell spherical nanodot: Effect of nanostructure size and dielectric environment on energy spectrum

Highlights

Abstract

Introduction

Section snippets

Model and the applied theory

Numerical results

Conclusion

Acknowledgements

Opt. Mater

Phys. E

Superlattices Microstruct.

Solid State Commun.

Phys. B

Superlattices Microstruct.

Superlattices Microstruct.

Superlattices Microstruct.

The Materials Science of Semiconductors

J. Am. Chem. Soc.

Cardona, Fundamentals of Semiconductors Physics and Materials Properties

Phys. Rev. B

Phys. Rev. B

Phys. Rev. Lett.

J. Appl. Phys.