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shell quantum dots
Physica E 85 (2017) 334–339
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The effects of strain and spacer layer in CdSe/CdS/ZnS and CdSe/ZnS/CdS core/shell quantum dots Hadi S. Pisheha, Negar Gheshlaghia, Hilmi Ünlüa,b, a b
⁎
Nanoscience and Nanoengineering Programme, Institute of Science and Technology, İstanbul Technical University, Maslak, Istanbul 34469, Turkey Department of Physics, Faculty of Science and Letters, İstanbul Technical University, Maslak, Istanbul 34469, Turkey
A R T I C L E I N F O
A BS T RAC T
Keywords: CdSe/ZnSCdS and CdSe/CdSZnS heterostructures Core/shell Quantum dots Exciton energy Interface strain
The effects of lattice mismatch induced interface strain on the structural, optical and dielectric properties of CdSe based Cd(Zn)S shell and Cd(Zn)S/Zn(Cd)S multishell quantum dots (QDs) is studied. Introducing Zn(Cd) S spacer layer to the CdSe/Cd(Zn)S core/shell structure is found to influence induced interfacial strain through changing the lattice parameter, band gap and band offset of core/shell nanostructure. Lattice parameter of spacer layer affected by outer shell, changes the interface strain in the core region. Theoretically obtained strain in the core/shell(multishell) is used in the effective mass approximation (EMA) to determine the capped core diameter. We show that introducing ZnS spacer layer to the CdSe/CdS core/shell QDs rises the amount of strain and cause more decrease in the core size in CdSe/ZnS/CdS. Furthermore, CdS sandwiched between CdSe/ZnS decreases the amount of strain in crystal and suppresses the size decrease of the core in the CdSe/ZnS. Good agreement is found between the strain included EMA core size predictions in core/shell and multishell and observed size image from transmission electron microscopy (TEM) measurements of bare CdSe core nanocrystals.
1. Introduction The possibility of tuning the electrical and optical properties with adjustment of size and composition of quantum dots (QDs) offers great prospects in photoactive applications [1,2]. CdSe based nanostructures are one of the best characterized semiconductor QD systems to date, with optical characterization around the visible region of the spectrum [3]. In particular, CdSe nanocrystal (NC) covered either with ZnS [3,4] or CdS [5,6] results in core/shell system where the band gap of the core lies energetically within the band gap of the shell material. In these nanocrystals the photogenerated exciton pairs (electrons and holes) are mainly confined inside the CdSe core. Capping such a compressive shell material (ZnS and CdS) on nano size core crystal changes optical and structural properties of core and shell [7,8]. 12% of lattice mismatch in CdSe and ZnS accumulate strain at interfacial layer of core and shell. On the other hand, relatively lower lattice mismatch (about 4%) in CdSe and CdS leads in lower induced strain in crystal structure of core and shell. Lattice mismatch induced strain in core/shell(multishell) nanocrystals, affect the structural, electronic and optical properties in the core and shell regions of quantum dots [9–12]. Therefore, investigating the effects of lattice mismatch strain of shelled quantum dots have been one of the main topics among scientists.
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In this work, we investigated the effects of spacer layer and interfacial strain on structural, optical and dielectric properties of CdSe based Cd(Zn)S shell and Cd(Zn)S/Zn(Cd)S multishell QDs. The article is organized as follows: Synthesis of the CdSe based Cd(Zn)S shell and Cd(Zn)S/Zn(Cd)S multishell nanocrystals will be summarized in Section 2; Structural and optical characterization of as produced nanocrystals will be discussed in Section 3; The detailed discussion of the results about the effect of lattice mismatch induced interface strain on the size and energy bandgap of CdSe core region of the CdSe/Cd(Zn) S core/shell and CdSe/Cd(Zn)S/Zn(Cd)S core/multishell quantum dots will be discussed in Section 4; The summary and conclusion will be given in Section 5. 2. Synthesis of CdSe based core/shell (multishell) QDs 2.1. Chemicals Cadmium oxide (CdO, 99.5%), Selenium powder (Se, 99.99%), Sulfur powder (S, purum, 99.5%) and Tributylphosphine (TBP) were purchased from Aldrich. Paraffin liquid (chemical pure), Stearic acid (analytical grade), Zinc acetate dehydrate (Zn(OAc)2·2H2O, analytical grade), were obtained from Sinopharm chemical. Rhodamine B,
Corresponding author at: Department of Physics Engineering, Faculty of Science and Letters, İstanbul Technical University, Maslak, Istanbul 34469, Turkey. E-mail address: [email protected] (H. Ünlü).
http://dx.doi.org/10.1016/j.physe.2016.07.007 Received 5 June 2016; Received in revised form 6 July 2016; Accepted 8 July 2016 Available online 09 July 2016 1386-9477/ © 2016 Elsevier B.V. All rights reserved.
Physica E 85 (2017) 334–339
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Methanol (analytical reagent), n-Hexane (analytical reagent) and Acetone (analytical grade) were also purchased from Merck Chemicals. Chemical elements were used without any refinement in our synthesis.
peaks of type I core/shell QDs, shows band exciton energy and size changes of core influenced with the shell layer deposition since electron–hole pairs are excited inside the core region. The following empirical expression is used to determine the size dependent excitation energy of the colloidal nanoparticles [12]
2.2. Synthesis of CdSe Core QDs
Egnc (d ) = hc / λ max ,
(1)
Egnc (d )
The synthesis of CdSe QDs was carried out according to Zhu et al. method [13]. Briefly, Cadmium stearate was prepared by heating the mixture of CdO and Stearic acid as Cd precursor. Then Se powder added to Cd precursor mixture and heated for CdSe QDs growth.
is the nanoparticle band gap measured at wavelength λ max where which the absorption of the nanoparticles is maximum. Later, obtained values of Egnc (d ) for the CdSe/Cd(Zn)S core/shell and CdSe/Cd(Zn)S/ Zn(Cd)S core/multishell nanoparticles are used in effective mass approximation to estimate core size of the QDs capped with shell (multishell) in discussion section.
2.3. Synthesis of CdSe/ZnS and CdSe/CdS Core/Shell NCs
3.2. Transmission electron microscopy (TEM) Characterization
CdSe capping process with ZnS were prepared according to Zhu et al. method [13]. Shortly, the resulting core solution (CdSe of 50 min grown), Zn(OAc)2·2H2O (0.01866 g) and S powder (0.00272 g) were mixed together in the reaction vessel. Under flow of N2 and heat, ZnS shell starts capping CdSe. Synthesizing CdSe/CdS core/shell took place by applying method of Yordanov et al. [14]. Briefly, TBP-S was injected to the solution of CdSe QDs dispersed in cadmium stearate and paraffin with increasing temperature of mixture. Monitoring the reaction, aliquots were taken at different time intervals.
Structural characterization of the bare CdSe core and CdSe/Cd(Zn) S core/shell and CdSe/Cd(Zn)S/Zn(Cd)Score/multi shell nanocrystals were carried out using high resolution transmission electron microscopy JEM-ARM200F at an acceleration voltage of 200 kV, cold FEG emitter and 0.27 eV energy spread. A drop of dispersed QDs diluted in n-Hexane dropped over an amorphous carbon substrate supported on a copper grid of 400 mesh for taking images. TEM Images are phase contrast images without aperture. Fig. 2(a) and (b) shows TEM image and size distribution of bare CdSe, respectively. Capping CdSe core with CdS and ZnS increases size of QD as shown in Fig. 2(c) and (d), respectively. Bare CdSe QD Size is approximately 3.8 nm while size of a single crystal CdSe/CdS or CdSe/ ZnS demonstrated in Fig. 2(c) and (d) is about 4.14 and 4.22 nm, respectively. STEM image of produced CdSe/CdS NC in spherical shape with fast Fourier Transform (FFT) analysis confirms the single CdS crystal of cubic ZB phase, illustrated in Fig. 3(a) [18]. Fig. 3(b) shows magnification of single crystal CdSe/ZnS and related FFT pattern of ZB phase ZnS QD [19]. The FFT patterns also show bright spots confirming the highly crystalline nature of the QDs heterostructures. In many reports, shell thickness of core/shell QDs obtained via subtracting core/shell crystal size from initial non-strained core size [20,21]. Since, TEM and HRTEM images illustrate bare core and core/ shell size, it would be inaccurate to predict shell thickness neglecting the induced interfacial strain effect on core region after shell deposition. Precise estimation of shell thickness can be pursued through strain effect consideration on capped core. In discussion section, we will calculate interfacial strain in core region and substitute it in EMA method in order to estimate strain effected capped core size.
2.4. Synthesis of core/multiShell NCs Synthesized CdSe/ZnS core/shell nanocrystals, covered with CdS using Yordanov et al. [14] method and CdSe/CdS capped with ZnS through Zhu et al. [13] methods as described in previous section. Further growth of QDs stopped with adding n-Hexane to the reaction mixture and the mixtures were cooled down to room temperature after the preferred size of QDs obtained. Washing away paraffin from NCs is crucial in order to have precise characterization. Methanol and acetone, in multiple sequences, added to mixture and centrifuged. Quantum dots were separated by decantation of the solution waste and applied in characterization analysis. 3. Characterization of nanocrystals 3.1. Absorption and fluorescence measurements The absorption and photoluminescence (PL) spectra of synthesized QDs were measured using the Schimadzu UV-3600 UV–vis NIR Spectrometer and Varian Cary eclipse fluorescence spectrometer. The synthesized samples were diluted with n-Hexane directly for characterization without any size sorting. Quartz cuvettes used in absorbance and emission measurements of samples in air at room temperature. UV–vis spectra of pure n-Hexane as base line of experiment, were obtained under emission of light in visible spectrum. Addition of ZnS and CdS mid-layer to CdSe/CdS and CdSe/ZnS cause change in band offset energy and Fermi level of heterostructure. Fig. 1(a) and (b) demonstrates absorption and PL of produced core/ shell (multishell) QDs, respectively. Capping CdSe with ZnS and CdS shows 26 nm and 7 nm red shift of exciton transition in UV spectra, respectively. Red shift in exciton transition of CdSe/CdS/ZnS is more than CdSe/ZnS/CdS due to stepwise increase in confinement potential and extension of the electronic wave function leakage from core [15,16] along with weak barrier potential created by cadmium sulfide spacer layer [17] (Fig. 1(a) and (b)). Capping CdSe/ZnS with CdS shows low red shift in UV and Pl spectra due to rise of barrier potential energy created by ZnS which suppress excitons leakage (electron–hole pairs) from CdSe core. Observed distinct absorption peak and moderate red shift in absorption and Pl spectra of the CdSe after being capped with shell (multishell), represents type I semiconductors, in which exciton pairs are generated in core. Therefore, red shift in absorption and PL spectra
3.3. X-ray diffraction measurements XRD patterns of as produced QDs carried out using a X’Pert³ MRD (XL) X-ray diffractometer operating at 45 kV/40 mA using Copper Kα line (λ=1.5406 Å). Fig. 4(a) and (b) shows XRD patterns of bare CdSe, CdSe/Cd(Zn)S core/shell and CdSe/Cd(Zn)S/Zn(Cd)S core/multishell nanocrystals. The XRD pattern of CdSe exhibits broad peaks at 2θ values of 25° related to 〈111〉, 42° to 〈220〉 and 49° to 〈311〉 crystalline plane for low temperature synthesized zinc-blende CdSe (Joint Committee on Powder Diffraction Standards file No. 77-2100). Growth of CdS and ZnS shell on CdSe led in slight shift (broader shift in ZnS shell) of XRD pattern toward larger degrees (crystalline plans of CdS and ZnS) shown in Fig. 4(a) and (b), respectively. This phenomena is lattice disorder effect on NC structure which manifest itself as compressive or tensile strain. If the uniform compressive strain is applied to a grain at right angles to the reflecting planes, their spacing becomes smaller and the corresponding diffraction line shifts to higher angles [22]. Hence, capping CdSe with larger lattice parameter (6.07 A°) shell like CdS or ZnS (5.8 and 5.41 A°, respectively) led to a compressive strain on CdSe lattice structure and shift of XRD pattern 335
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4 1.4
CdSe CdSe/CdS CdSe/ZnS
1.2
CdSe/ZnS/CdS
CdSe/ZnS/CdS
CdSe/CdS/ZnS
CdSe
CdSe/CdS/ZnS
1.0
PL (a.u.)
Absorbance (a.u.)
3
CdSe/ZnS CdSe/CdS
2
1
0.8 0.6 0.4 0.2
0 0.0 400
500
600
700
800
500
550
Wavelength (nm)
600
650
Wavelength (nm)
Fig. 1. Normalized UV spectrum (a) and PL intensity (b) comparison of bare CdSe core and CdSe/Cd(Zn)S core/shell and CdSe/Cd(Zn)S/Zn(Cd)S core/multishell.
optical devices. The uniaxial component of biaxial strain tensor splits the heavy-hole, light-hole and split-off valence band edges relative to the average valence band edge [23]. Meanwhile, the hydrostatic component of biaxial strain tensor causes a volume change of the nanocrystal. Considering the spherical core/shell nanostructure, the continuous elasticity theory (CET) allows one to write the interface strain in the core semiconductor as [24]
toward larger 2θ. 4. Discussion Reliable and precise determination of the interface strain in the CdSe/Cd(Zn)S and CdSe/Cd(Zn)S/Zn(Cd)S heterostructures is important in order to predict their potential in nanoscale electronic and
22 20 18 16
Count
14 12 10 8 6 4 2 0
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
CdSe Size Distribution
Fig. 2. TEM image and size distribution of bare CdSe core NCs (a,b), STEM image of CdSe/CdS and CdSe/ZnS core–shell crystal with diameter measured of a single crystal QD (c) and (d).
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Fig. 3. STEM images of CdSe/CdS and CdSe/ZnS with ZB FFT (right) of CdS and ZnS Single crystal (a) and (b), respectively.
εrr = εθθ = εϕϕ = ε = 3B∘c εm /(3B∘c + 4μs ),
in which nanoparticle diameter is smaller than sum of the exciton Bohr radius for free electron and hole aB = (ℏ2ε / e 2 )((me* + mh*)/ me* mh*) (6.0 nm for bulk CdSe), the solution of Schrödinger equation for a particle in a spherical box gives the (1s–1s) excited state energy (or also called the band gap energy) of the nanoparticle given by
(2)
where εrr ,εθθ and εϕϕ are the strain components in spherical coordinates. εm is defined as the average lattice percent difference at the core/ shell interface:ϵm = Δa / a = 2(as − ac )/(as + ac ) [25]. ac and as are the lattice constants of CdSe core and shell semiconductors in bulk forms, respectively. B∘c is elastic bulk modulus of CdSe core and μs is the shear modulus of shell semiconductor in bulk. a (εm ) = a 0 (1 − εm ) used to calculate strained spacer layer lattice parameter affected by outer shell and then substituted it in Eq. (2) to calculate the strain in the core region. Considering the spherical core/shell nanostructure, CET gives about 7.9% and 3.3% compressive strain in the core region of the CdSe/ ZnS and CdSe/CdS core/shell interface due to the 12% and 4% lattice mismatch, respectively. Compressive strain increases to 3.9% (18% increase) after introducing ZnS spacer layer to CdSe/CdS due to sudden increase in lattice mismatch and accumulation of stain in ZnS. Whereas, addition of CdS space layer in CdSe/ZnS cause stepwise decrease in lattice parameter to 7.5% (5% decrease). In the next section, obtained interfacial strain (Eq. (2)) in capped core region, will be substituted in EMA formula to find core size changes under compressive strain from shell (multishell). Obtained theoretical results will be compared with core size from TEM images, showing accuracy of used method in calculation.
Egnc (d ) = Egb +
2ℏ2π 2 ⎡ 1 1 ⎤ 3.572e 2 0.124e 4 ⎡ me* mh* ⎤ + − ⎥, ⎢ ⎥− ⎢ d 2 ⎣ me* mh* ⎦ ε∞ d ℏ2ε∞2 ⎣ me* + mh* ⎦ (3)
where Egb is the band gap energy obtained from Eq. (1), me* and mh* effective masses of electrons and holes and ε∞ is the optical dielectric constant of core semiconductor in its bulk form (Egb = 1.68eV , me* = 0.13m∘ , mh* = 0.43m∘ and ε∞ = 6.2ε∘ [27]). Strain effects on energy levels can be determined by using the so called statistical thermodynamic model [28], in which the free electrons and holes are treated as charged chemical particles, one expresses the conduction and valence band edges as a function of pressure at any temperature
Egi (T , P ) = Egi (0) + ΔCiP0 T (1 − ln T ) −
agi ⎡ P2 (1 + B′) P 3 ⎤ − ⎥, ⎢P − ⎦ B ⎣ 2B 3B2 (4)
The logarithmic term represents the contributions due to the lattice vibration. The third term represents the volume expansion contribution when P = BΔV /V = −3Bαth (T − T0 ). Here, αth is the linear thermal expansion coefficient. T and T0 are the growth and measurement temperatures, respectively. agi = −B (∂Egi /∂P ) is the bandgap deformation potential and ΔCiP0 is standard state heat capacity of reaction for the formation of electron–hole pair due to the transition from top of
4.1. Strain effects on exciton energy and particle size The diameter (d) of bare CdSe QD can be calculated using the effective mass approximation (EMA) proposed by Brus [26]. In this approximation, the excitons are considered to be confined to a spherical volume of the nanocrystal. Assuming strong confinement, ZnS
ZnS
CdS
CdS
(311)
(220)
(111)
(220)
(111)
(311)
Intensity (a.u.)
Intensity (a.u.)
CdSe/CdS/ZnS
CdSe/CdS
CdSe/ZnS/CdS
CdSe/ZnS
CdSe
CdSe
CdSe
CdSe
20
30
40
50
60
70
20
2θ
(111)
(220)
30
40
(311)
50
60
2θ
Fig. 4. X-ray Diffraction of (a); CdSe, CdSe/CdS and CdSe/CdS/ZnS structure and (b); CdSe, CdSe/ZnS and CdSe/ZnS/CdS.
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* = (me* mh*/(me* + mh*) is the reduced between electrons and holes. mcv effective mass of electron–hole pair. Eq. (5) can be converted in quadratic form to calculate the diameter of the CdSe core of the core/shell(multi-shell) nanocrystals as: Ad 2 + Bd + C = 0 , where A, B and C are constant coefficients involving material parameters. We should keep in mind that the lattice mismatch induced strain can also influence the electron and hole masses and dielectric constant of bare CdSe core nanocrystal, which can be neglected to first order approximation. Tables 1 and 2 are illustrating core diameter of 3.74, 3.54, 3.86 and 3.66 nm obtained for CdSe/CdS, CdSe/ZnS, CdSe/ZnS/CdS and CdSe/CdS/ZnS, with (Eq. (5)) and without (Eq. (3)) strain contribution, respectively. These results are in good agreement with initial core size of CdSe (3.70 nm) from TEM image (Fig. 2(b)). Our suggested model can be used in finding capped core size and deposited shell thickness on the core. Contribution of strain amount in EMA method gives an accurate estimation of capped core size and shell thickness. Fig. 5 shows effect of compressive strain on capped core size reduction (Tables 1 and 2). Interfacial strain cause 10% decrease in core size of CdSe/CdS and this amount rises to 13.5% after introducing ZnS space layer. This is due to increase of lattice mismatch induced strain in CdSe/ZnS/CdS (18% more strain). Meanwhile, the interfacial strain cause 20.5% decrease in core size of CdSe/ZnS and 21.4% in CdSe/CdS/ZnS. Stepwise decrease in lattice parameter from core (CdSe) to CdS spacer layer and finally ZnS (outern shell), suppress momentum of core size decrease from CdSe/ZnS core/shell to CdSe/ CdS/ZnS.
Table 1 Core diameter calculation of CdSe/CdS and CdSe/ZnS/CdS with (Eq. (5)) and without (Eq. (3)) strain contribution, exciton energy calculated with Eq. (1). Growth time (Min)
10 20 30 40 50
CdSe/CdS
CdSe/ZnS/CdS
Without stain
With strain
Without stain
With strain
4.09 4.15 4.17 4.19 4.21
3.66 3.70 3.72 3.73 3.74
4.35 4.40 4.43 4.44 4.47
3.78 3.81 3.83 3.84 3.86
Table 2 Core diameter calculation of CdSe/ZnS and CdSe/CdS/ZnS with (Eq. (5)) and without (Eq. (3)) strain contribution, exciton energy calculated with Eq. (1). Growth time (Min)
10 20 30 40 50
CdSe/ZnS
CdSe/CdS/ZnS
Without stain
With strain
Without stain
With strain
4.38 4.40 4.43 4.44 4.46
3.50 3.52 3.53 3.54 3.54
4.60 4.61 4.63 4.64 4.66
3.63 3.64 3.65 3.66 3.66
5.0
CdSe/CdS/ZnS Unstrained CdSe/CdS/ZnS Strained CdSe/ZnS/CdS Unstrained CdSe/ZnS/CdS Strained
Core Diameter (nm)
4.5
5. Conclusions We presented a comparative theoretical and experimental study for the determination of the core diameter of CdSe/Cd(Zn)S core/shell and CdSe/Cd(Zn)S/Zn(Cd)S core/multi shell nanocrystals as a function of exciton energy with and without the interface strain effects. Agreement between the caped core (CdSe) size predictions and TEM measurements of bare core has been reached. The decrease in the core diameter of CdSe/ZnS core/shell nanocrystal with strain is larger than that in the CdSe/CdS core/shell nanocrystal. This is attributed to the fact that the lattice mismatch at the CdSe/ZnS interface is greater than that at the CdSe/CdS interface. Introducing ZnS spacer layer in CdSe/CdS increases induced strain amount to 18% more, leding much more CdSe core size decrease compared with CdSe/CdS. Sandwitched CdS layer between CdSe/ZnS decreases the induced strain amount to 5% less. Core size decrease momentum in CdSe/ZnS supressed with introducing CdS spacer layer.
4.0
3.5
3.0 2.15
CdSe/ZnS Unstrained CdSe/ZnS Strained CdSe/CdS Unstrained CdSe/CdS Strained 2.20
2.25
2.30
2.35
2.40
Exciton Energy (eV) Fig. 5. Exciton peak versus core diameter for CdSe/Cd(Zn)S and CdSe/Cd(Zn)S/Zn(Cd) S NCs. Core diameter calculated via Eqs. (3) and (5) in order to demonstrate strain effect on capped core size.
the valence band maximum to the conduction band minimums at i = Γ , L , X symmetry points of the core semiconductor in bulk form. B is bulk modulus and B′ = ∂B /∂P . ΔCiP0 is obtained by fitting Eq. (4) to the measured bandgap of bulk semiconductor at any temperature (e.g., 300 K) and constant pressure, with lattice thermal expansion taken into account. Substituting P = BΔV / V = −3Bc ϵc in Eq. (4), one can obtain the strain effect (Eq. (2)) on the capped CdSe core bandgap energy Egnc (d ) = E1s,1s (d )) of CdSe/Cd(Zn)S core/shell and CdSe/Cd(Zn)S/ Zn(Cd)S core/multishell nanocrystals at any temperature:
Egnc (d )
=
Egb (T ) −
Acknowledgment The authors would like to greatly acknowledge the financial support by İstanbul Technical University Research Foundation (ITU-BAP Project no. 38857). Technical assistance of Prof. Dr. M. Ali Gülgün for TEM measurements is appreciated. References [1] Young Pyo Jeon, Sung June Park, Tae Whan Kim, Opt. Mater. Express 2 (2012). [2] Atef Y. Shenouda, El Sayed, M. El Sayed, Ain Shams Eng. J. 6 (2015) 341. [3] G.Q. Liu, Z.Q. Liu, K. Huang, Y.H. Chen, L. Li, F.L. Tang, L.X. Gong, Mater. Lett. 167 (2016) 134. [4] S.K. Davidowski, C.E. Lisowski, J.L. Yarger, Magn. Reson. Chem. 54 (2016) 234. [5] K.M. Goodfellow, C. Chakraborty, K. Sowers, P. Waduge, M. Wanunu, T. Krauss, K. Driscoll, A.N. Vamivakas, Appl. Phys. Lett. 108 (2016). [6] Raja Angeloni, W. Brescia, R. Polovitsyn, F. A; De Donato, M. Canepa, G. Bertoni, R.P. Zaccaria, Moreels,, ACS Photonics 3 (2016) 58. [7] V. Kocevski, J. Rusz, O. Eriksson, D.D. Sarma, Sci. Rep. 5 (2015). [8] Worasak Sukkabot, J. Nanomater. (2016). [9] Andrew M. Smith, Aaron M. Mohs, Shuming Nie, Nat. Nanotechnol. 4 (2008) 56. [10] R. Diaz, J.M. Merino, T. Martin, F. Rueda, M. Leon, J. Appl. Phys. 83 (1998) 616. [11] J. Sun, E.M. Goldys, J. Phys. Chem. C 112 (2008) 9261. [12] S. Suresh, Appl. Nanosci. 4 (2014) 325.
9 2ℏ2π 2 + 3agcΓ ε + agcΓ ε 2 − 9agcΓ (1 + B′) ε 3 + * d2 mcv 2
3.572e 2 0.124e 4 − 2 , * ε∞2 ε∞ d ℏ mcv
(5)
Egb (T )
is the temperature dependent part of the unstrained direct where bandgap energy of bulk CdSe, second, third and fourth terms are the strain contribution to the bulk CdSe direct bandgap with deformation potential agΓ = acΓ − a v at i = Γ symmetry point. The fifth term gives the kinetic energy of electron–hole pair, sixth term belongs to Coulomb interaction and the last term determines the correlation energy 338
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The effects of strain and spacer layer in CdSe/CdS/ZnS and CdSe/ZnS/CdS core/shell quantum dots Hadi S. Pisheha, Negar Gheshlaghia, Hilmi Ünlüa,b, a b
⁎
Nanoscience and Nanoengineering Programme, Institute of Science and Technology, İstanbul Technical University, Maslak, Istanbul 34469, Turkey Department of Physics, Faculty of Science and Letters, İstanbul Technical University, Maslak, Istanbul 34469, Turkey
A R T I C L E I N F O
A BS T RAC T
Keywords: CdSe/ZnSCdS and CdSe/CdSZnS heterostructures Core/shell Quantum dots Exciton energy Interface strain
The effects of lattice mismatch induced interface strain on the structural, optical and dielectric properties of CdSe based Cd(Zn)S shell and Cd(Zn)S/Zn(Cd)S multishell quantum dots (QDs) is studied. Introducing Zn(Cd) S spacer layer to the CdSe/Cd(Zn)S core/shell structure is found to influence induced interfacial strain through changing the lattice parameter, band gap and band offset of core/shell nanostructure. Lattice parameter of spacer layer affected by outer shell, changes the interface strain in the core region. Theoretically obtained strain in the core/shell(multishell) is used in the effective mass approximation (EMA) to determine the capped core diameter. We show that introducing ZnS spacer layer to the CdSe/CdS core/shell QDs rises the amount of strain and cause more decrease in the core size in CdSe/ZnS/CdS. Furthermore, CdS sandwiched between CdSe/ZnS decreases the amount of strain in crystal and suppresses the size decrease of the core in the CdSe/ZnS. Good agreement is found between the strain included EMA core size predictions in core/shell and multishell and observed size image from transmission electron microscopy (TEM) measurements of bare CdSe core nanocrystals.
1. Introduction The possibility of tuning the electrical and optical properties with adjustment of size and composition of quantum dots (QDs) offers great prospects in photoactive applications [1,2]. CdSe based nanostructures are one of the best characterized semiconductor QD systems to date, with optical characterization around the visible region of the spectrum [3]. In particular, CdSe nanocrystal (NC) covered either with ZnS [3,4] or CdS [5,6] results in core/shell system where the band gap of the core lies energetically within the band gap of the shell material. In these nanocrystals the photogenerated exciton pairs (electrons and holes) are mainly confined inside the CdSe core. Capping such a compressive shell material (ZnS and CdS) on nano size core crystal changes optical and structural properties of core and shell [7,8]. 12% of lattice mismatch in CdSe and ZnS accumulate strain at interfacial layer of core and shell. On the other hand, relatively lower lattice mismatch (about 4%) in CdSe and CdS leads in lower induced strain in crystal structure of core and shell. Lattice mismatch induced strain in core/shell(multishell) nanocrystals, affect the structural, electronic and optical properties in the core and shell regions of quantum dots [9–12]. Therefore, investigating the effects of lattice mismatch strain of shelled quantum dots have been one of the main topics among scientists.
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In this work, we investigated the effects of spacer layer and interfacial strain on structural, optical and dielectric properties of CdSe based Cd(Zn)S shell and Cd(Zn)S/Zn(Cd)S multishell QDs. The article is organized as follows: Synthesis of the CdSe based Cd(Zn)S shell and Cd(Zn)S/Zn(Cd)S multishell nanocrystals will be summarized in Section 2; Structural and optical characterization of as produced nanocrystals will be discussed in Section 3; The detailed discussion of the results about the effect of lattice mismatch induced interface strain on the size and energy bandgap of CdSe core region of the CdSe/Cd(Zn) S core/shell and CdSe/Cd(Zn)S/Zn(Cd)S core/multishell quantum dots will be discussed in Section 4; The summary and conclusion will be given in Section 5. 2. Synthesis of CdSe based core/shell (multishell) QDs 2.1. Chemicals Cadmium oxide (CdO, 99.5%), Selenium powder (Se, 99.99%), Sulfur powder (S, purum, 99.5%) and Tributylphosphine (TBP) were purchased from Aldrich. Paraffin liquid (chemical pure), Stearic acid (analytical grade), Zinc acetate dehydrate (Zn(OAc)2·2H2O, analytical grade), were obtained from Sinopharm chemical. Rhodamine B,
Corresponding author at: Department of Physics Engineering, Faculty of Science and Letters, İstanbul Technical University, Maslak, Istanbul 34469, Turkey. E-mail address: [email protected] (H. Ünlü).
http://dx.doi.org/10.1016/j.physe.2016.07.007 Received 5 June 2016; Received in revised form 6 July 2016; Accepted 8 July 2016 Available online 09 July 2016 1386-9477/ © 2016 Elsevier B.V. All rights reserved.
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Methanol (analytical reagent), n-Hexane (analytical reagent) and Acetone (analytical grade) were also purchased from Merck Chemicals. Chemical elements were used without any refinement in our synthesis.
peaks of type I core/shell QDs, shows band exciton energy and size changes of core influenced with the shell layer deposition since electron–hole pairs are excited inside the core region. The following empirical expression is used to determine the size dependent excitation energy of the colloidal nanoparticles [12]
2.2. Synthesis of CdSe Core QDs
Egnc (d ) = hc / λ max ,
(1)
Egnc (d )
The synthesis of CdSe QDs was carried out according to Zhu et al. method [13]. Briefly, Cadmium stearate was prepared by heating the mixture of CdO and Stearic acid as Cd precursor. Then Se powder added to Cd precursor mixture and heated for CdSe QDs growth.
is the nanoparticle band gap measured at wavelength λ max where which the absorption of the nanoparticles is maximum. Later, obtained values of Egnc (d ) for the CdSe/Cd(Zn)S core/shell and CdSe/Cd(Zn)S/ Zn(Cd)S core/multishell nanoparticles are used in effective mass approximation to estimate core size of the QDs capped with shell (multishell) in discussion section.
2.3. Synthesis of CdSe/ZnS and CdSe/CdS Core/Shell NCs
3.2. Transmission electron microscopy (TEM) Characterization
CdSe capping process with ZnS were prepared according to Zhu et al. method [13]. Shortly, the resulting core solution (CdSe of 50 min grown), Zn(OAc)2·2H2O (0.01866 g) and S powder (0.00272 g) were mixed together in the reaction vessel. Under flow of N2 and heat, ZnS shell starts capping CdSe. Synthesizing CdSe/CdS core/shell took place by applying method of Yordanov et al. [14]. Briefly, TBP-S was injected to the solution of CdSe QDs dispersed in cadmium stearate and paraffin with increasing temperature of mixture. Monitoring the reaction, aliquots were taken at different time intervals.
Structural characterization of the bare CdSe core and CdSe/Cd(Zn) S core/shell and CdSe/Cd(Zn)S/Zn(Cd)Score/multi shell nanocrystals were carried out using high resolution transmission electron microscopy JEM-ARM200F at an acceleration voltage of 200 kV, cold FEG emitter and 0.27 eV energy spread. A drop of dispersed QDs diluted in n-Hexane dropped over an amorphous carbon substrate supported on a copper grid of 400 mesh for taking images. TEM Images are phase contrast images without aperture. Fig. 2(a) and (b) shows TEM image and size distribution of bare CdSe, respectively. Capping CdSe core with CdS and ZnS increases size of QD as shown in Fig. 2(c) and (d), respectively. Bare CdSe QD Size is approximately 3.8 nm while size of a single crystal CdSe/CdS or CdSe/ ZnS demonstrated in Fig. 2(c) and (d) is about 4.14 and 4.22 nm, respectively. STEM image of produced CdSe/CdS NC in spherical shape with fast Fourier Transform (FFT) analysis confirms the single CdS crystal of cubic ZB phase, illustrated in Fig. 3(a) [18]. Fig. 3(b) shows magnification of single crystal CdSe/ZnS and related FFT pattern of ZB phase ZnS QD [19]. The FFT patterns also show bright spots confirming the highly crystalline nature of the QDs heterostructures. In many reports, shell thickness of core/shell QDs obtained via subtracting core/shell crystal size from initial non-strained core size [20,21]. Since, TEM and HRTEM images illustrate bare core and core/ shell size, it would be inaccurate to predict shell thickness neglecting the induced interfacial strain effect on core region after shell deposition. Precise estimation of shell thickness can be pursued through strain effect consideration on capped core. In discussion section, we will calculate interfacial strain in core region and substitute it in EMA method in order to estimate strain effected capped core size.
2.4. Synthesis of core/multiShell NCs Synthesized CdSe/ZnS core/shell nanocrystals, covered with CdS using Yordanov et al. [14] method and CdSe/CdS capped with ZnS through Zhu et al. [13] methods as described in previous section. Further growth of QDs stopped with adding n-Hexane to the reaction mixture and the mixtures were cooled down to room temperature after the preferred size of QDs obtained. Washing away paraffin from NCs is crucial in order to have precise characterization. Methanol and acetone, in multiple sequences, added to mixture and centrifuged. Quantum dots were separated by decantation of the solution waste and applied in characterization analysis. 3. Characterization of nanocrystals 3.1. Absorption and fluorescence measurements The absorption and photoluminescence (PL) spectra of synthesized QDs were measured using the Schimadzu UV-3600 UV–vis NIR Spectrometer and Varian Cary eclipse fluorescence spectrometer. The synthesized samples were diluted with n-Hexane directly for characterization without any size sorting. Quartz cuvettes used in absorbance and emission measurements of samples in air at room temperature. UV–vis spectra of pure n-Hexane as base line of experiment, were obtained under emission of light in visible spectrum. Addition of ZnS and CdS mid-layer to CdSe/CdS and CdSe/ZnS cause change in band offset energy and Fermi level of heterostructure. Fig. 1(a) and (b) demonstrates absorption and PL of produced core/ shell (multishell) QDs, respectively. Capping CdSe with ZnS and CdS shows 26 nm and 7 nm red shift of exciton transition in UV spectra, respectively. Red shift in exciton transition of CdSe/CdS/ZnS is more than CdSe/ZnS/CdS due to stepwise increase in confinement potential and extension of the electronic wave function leakage from core [15,16] along with weak barrier potential created by cadmium sulfide spacer layer [17] (Fig. 1(a) and (b)). Capping CdSe/ZnS with CdS shows low red shift in UV and Pl spectra due to rise of barrier potential energy created by ZnS which suppress excitons leakage (electron–hole pairs) from CdSe core. Observed distinct absorption peak and moderate red shift in absorption and Pl spectra of the CdSe after being capped with shell (multishell), represents type I semiconductors, in which exciton pairs are generated in core. Therefore, red shift in absorption and PL spectra
3.3. X-ray diffraction measurements XRD patterns of as produced QDs carried out using a X’Pert³ MRD (XL) X-ray diffractometer operating at 45 kV/40 mA using Copper Kα line (λ=1.5406 Å). Fig. 4(a) and (b) shows XRD patterns of bare CdSe, CdSe/Cd(Zn)S core/shell and CdSe/Cd(Zn)S/Zn(Cd)S core/multishell nanocrystals. The XRD pattern of CdSe exhibits broad peaks at 2θ values of 25° related to 〈111〉, 42° to 〈220〉 and 49° to 〈311〉 crystalline plane for low temperature synthesized zinc-blende CdSe (Joint Committee on Powder Diffraction Standards file No. 77-2100). Growth of CdS and ZnS shell on CdSe led in slight shift (broader shift in ZnS shell) of XRD pattern toward larger degrees (crystalline plans of CdS and ZnS) shown in Fig. 4(a) and (b), respectively. This phenomena is lattice disorder effect on NC structure which manifest itself as compressive or tensile strain. If the uniform compressive strain is applied to a grain at right angles to the reflecting planes, their spacing becomes smaller and the corresponding diffraction line shifts to higher angles [22]. Hence, capping CdSe with larger lattice parameter (6.07 A°) shell like CdS or ZnS (5.8 and 5.41 A°, respectively) led to a compressive strain on CdSe lattice structure and shift of XRD pattern 335
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4 1.4
CdSe CdSe/CdS CdSe/ZnS
1.2
CdSe/ZnS/CdS
CdSe/ZnS/CdS
CdSe/CdS/ZnS
CdSe
CdSe/CdS/ZnS
1.0
PL (a.u.)
Absorbance (a.u.)
3
CdSe/ZnS CdSe/CdS
2
1
0.8 0.6 0.4 0.2
0 0.0 400
500
600
700
800
500
550
Wavelength (nm)
600
650
Wavelength (nm)
Fig. 1. Normalized UV spectrum (a) and PL intensity (b) comparison of bare CdSe core and CdSe/Cd(Zn)S core/shell and CdSe/Cd(Zn)S/Zn(Cd)S core/multishell.
optical devices. The uniaxial component of biaxial strain tensor splits the heavy-hole, light-hole and split-off valence band edges relative to the average valence band edge [23]. Meanwhile, the hydrostatic component of biaxial strain tensor causes a volume change of the nanocrystal. Considering the spherical core/shell nanostructure, the continuous elasticity theory (CET) allows one to write the interface strain in the core semiconductor as [24]
toward larger 2θ. 4. Discussion Reliable and precise determination of the interface strain in the CdSe/Cd(Zn)S and CdSe/Cd(Zn)S/Zn(Cd)S heterostructures is important in order to predict their potential in nanoscale electronic and
22 20 18 16
Count
14 12 10 8 6 4 2 0
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
CdSe Size Distribution
Fig. 2. TEM image and size distribution of bare CdSe core NCs (a,b), STEM image of CdSe/CdS and CdSe/ZnS core–shell crystal with diameter measured of a single crystal QD (c) and (d).
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Fig. 3. STEM images of CdSe/CdS and CdSe/ZnS with ZB FFT (right) of CdS and ZnS Single crystal (a) and (b), respectively.
εrr = εθθ = εϕϕ = ε = 3B∘c εm /(3B∘c + 4μs ),
in which nanoparticle diameter is smaller than sum of the exciton Bohr radius for free electron and hole aB = (ℏ2ε / e 2 )((me* + mh*)/ me* mh*) (6.0 nm for bulk CdSe), the solution of Schrödinger equation for a particle in a spherical box gives the (1s–1s) excited state energy (or also called the band gap energy) of the nanoparticle given by
(2)
where εrr ,εθθ and εϕϕ are the strain components in spherical coordinates. εm is defined as the average lattice percent difference at the core/ shell interface:ϵm = Δa / a = 2(as − ac )/(as + ac ) [25]. ac and as are the lattice constants of CdSe core and shell semiconductors in bulk forms, respectively. B∘c is elastic bulk modulus of CdSe core and μs is the shear modulus of shell semiconductor in bulk. a (εm ) = a 0 (1 − εm ) used to calculate strained spacer layer lattice parameter affected by outer shell and then substituted it in Eq. (2) to calculate the strain in the core region. Considering the spherical core/shell nanostructure, CET gives about 7.9% and 3.3% compressive strain in the core region of the CdSe/ ZnS and CdSe/CdS core/shell interface due to the 12% and 4% lattice mismatch, respectively. Compressive strain increases to 3.9% (18% increase) after introducing ZnS spacer layer to CdSe/CdS due to sudden increase in lattice mismatch and accumulation of stain in ZnS. Whereas, addition of CdS space layer in CdSe/ZnS cause stepwise decrease in lattice parameter to 7.5% (5% decrease). In the next section, obtained interfacial strain (Eq. (2)) in capped core region, will be substituted in EMA formula to find core size changes under compressive strain from shell (multishell). Obtained theoretical results will be compared with core size from TEM images, showing accuracy of used method in calculation.
Egnc (d ) = Egb +
2ℏ2π 2 ⎡ 1 1 ⎤ 3.572e 2 0.124e 4 ⎡ me* mh* ⎤ + − ⎥, ⎢ ⎥− ⎢ d 2 ⎣ me* mh* ⎦ ε∞ d ℏ2ε∞2 ⎣ me* + mh* ⎦ (3)
where Egb is the band gap energy obtained from Eq. (1), me* and mh* effective masses of electrons and holes and ε∞ is the optical dielectric constant of core semiconductor in its bulk form (Egb = 1.68eV , me* = 0.13m∘ , mh* = 0.43m∘ and ε∞ = 6.2ε∘ [27]). Strain effects on energy levels can be determined by using the so called statistical thermodynamic model [28], in which the free electrons and holes are treated as charged chemical particles, one expresses the conduction and valence band edges as a function of pressure at any temperature
Egi (T , P ) = Egi (0) + ΔCiP0 T (1 − ln T ) −
agi ⎡ P2 (1 + B′) P 3 ⎤ − ⎥, ⎢P − ⎦ B ⎣ 2B 3B2 (4)
The logarithmic term represents the contributions due to the lattice vibration. The third term represents the volume expansion contribution when P = BΔV /V = −3Bαth (T − T0 ). Here, αth is the linear thermal expansion coefficient. T and T0 are the growth and measurement temperatures, respectively. agi = −B (∂Egi /∂P ) is the bandgap deformation potential and ΔCiP0 is standard state heat capacity of reaction for the formation of electron–hole pair due to the transition from top of
4.1. Strain effects on exciton energy and particle size The diameter (d) of bare CdSe QD can be calculated using the effective mass approximation (EMA) proposed by Brus [26]. In this approximation, the excitons are considered to be confined to a spherical volume of the nanocrystal. Assuming strong confinement, ZnS
ZnS
CdS
CdS
(311)
(220)
(111)
(220)
(111)
(311)
Intensity (a.u.)
Intensity (a.u.)
CdSe/CdS/ZnS
CdSe/CdS
CdSe/ZnS/CdS
CdSe/ZnS
CdSe
CdSe
CdSe
CdSe
20
30
40
50
60
70
20
2θ
(111)
(220)
30
40
(311)
50
60
2θ
Fig. 4. X-ray Diffraction of (a); CdSe, CdSe/CdS and CdSe/CdS/ZnS structure and (b); CdSe, CdSe/ZnS and CdSe/ZnS/CdS.
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* = (me* mh*/(me* + mh*) is the reduced between electrons and holes. mcv effective mass of electron–hole pair. Eq. (5) can be converted in quadratic form to calculate the diameter of the CdSe core of the core/shell(multi-shell) nanocrystals as: Ad 2 + Bd + C = 0 , where A, B and C are constant coefficients involving material parameters. We should keep in mind that the lattice mismatch induced strain can also influence the electron and hole masses and dielectric constant of bare CdSe core nanocrystal, which can be neglected to first order approximation. Tables 1 and 2 are illustrating core diameter of 3.74, 3.54, 3.86 and 3.66 nm obtained for CdSe/CdS, CdSe/ZnS, CdSe/ZnS/CdS and CdSe/CdS/ZnS, with (Eq. (5)) and without (Eq. (3)) strain contribution, respectively. These results are in good agreement with initial core size of CdSe (3.70 nm) from TEM image (Fig. 2(b)). Our suggested model can be used in finding capped core size and deposited shell thickness on the core. Contribution of strain amount in EMA method gives an accurate estimation of capped core size and shell thickness. Fig. 5 shows effect of compressive strain on capped core size reduction (Tables 1 and 2). Interfacial strain cause 10% decrease in core size of CdSe/CdS and this amount rises to 13.5% after introducing ZnS space layer. This is due to increase of lattice mismatch induced strain in CdSe/ZnS/CdS (18% more strain). Meanwhile, the interfacial strain cause 20.5% decrease in core size of CdSe/ZnS and 21.4% in CdSe/CdS/ZnS. Stepwise decrease in lattice parameter from core (CdSe) to CdS spacer layer and finally ZnS (outern shell), suppress momentum of core size decrease from CdSe/ZnS core/shell to CdSe/ CdS/ZnS.
Table 1 Core diameter calculation of CdSe/CdS and CdSe/ZnS/CdS with (Eq. (5)) and without (Eq. (3)) strain contribution, exciton energy calculated with Eq. (1). Growth time (Min)
10 20 30 40 50
CdSe/CdS
CdSe/ZnS/CdS
Without stain
With strain
Without stain
With strain
4.09 4.15 4.17 4.19 4.21
3.66 3.70 3.72 3.73 3.74
4.35 4.40 4.43 4.44 4.47
3.78 3.81 3.83 3.84 3.86
Table 2 Core diameter calculation of CdSe/ZnS and CdSe/CdS/ZnS with (Eq. (5)) and without (Eq. (3)) strain contribution, exciton energy calculated with Eq. (1). Growth time (Min)
10 20 30 40 50
CdSe/ZnS
CdSe/CdS/ZnS
Without stain
With strain
Without stain
With strain
4.38 4.40 4.43 4.44 4.46
3.50 3.52 3.53 3.54 3.54
4.60 4.61 4.63 4.64 4.66
3.63 3.64 3.65 3.66 3.66
5.0
CdSe/CdS/ZnS Unstrained CdSe/CdS/ZnS Strained CdSe/ZnS/CdS Unstrained CdSe/ZnS/CdS Strained
Core Diameter (nm)
4.5
5. Conclusions We presented a comparative theoretical and experimental study for the determination of the core diameter of CdSe/Cd(Zn)S core/shell and CdSe/Cd(Zn)S/Zn(Cd)S core/multi shell nanocrystals as a function of exciton energy with and without the interface strain effects. Agreement between the caped core (CdSe) size predictions and TEM measurements of bare core has been reached. The decrease in the core diameter of CdSe/ZnS core/shell nanocrystal with strain is larger than that in the CdSe/CdS core/shell nanocrystal. This is attributed to the fact that the lattice mismatch at the CdSe/ZnS interface is greater than that at the CdSe/CdS interface. Introducing ZnS spacer layer in CdSe/CdS increases induced strain amount to 18% more, leding much more CdSe core size decrease compared with CdSe/CdS. Sandwitched CdS layer between CdSe/ZnS decreases the induced strain amount to 5% less. Core size decrease momentum in CdSe/ZnS supressed with introducing CdS spacer layer.
4.0
3.5
3.0 2.15
CdSe/ZnS Unstrained CdSe/ZnS Strained CdSe/CdS Unstrained CdSe/CdS Strained 2.20
2.25
2.30
2.35
2.40
Exciton Energy (eV) Fig. 5. Exciton peak versus core diameter for CdSe/Cd(Zn)S and CdSe/Cd(Zn)S/Zn(Cd) S NCs. Core diameter calculated via Eqs. (3) and (5) in order to demonstrate strain effect on capped core size.
the valence band maximum to the conduction band minimums at i = Γ , L , X symmetry points of the core semiconductor in bulk form. B is bulk modulus and B′ = ∂B /∂P . ΔCiP0 is obtained by fitting Eq. (4) to the measured bandgap of bulk semiconductor at any temperature (e.g., 300 K) and constant pressure, with lattice thermal expansion taken into account. Substituting P = BΔV / V = −3Bc ϵc in Eq. (4), one can obtain the strain effect (Eq. (2)) on the capped CdSe core bandgap energy Egnc (d ) = E1s,1s (d )) of CdSe/Cd(Zn)S core/shell and CdSe/Cd(Zn)S/ Zn(Cd)S core/multishell nanocrystals at any temperature:
Egnc (d )
=
Egb (T ) −
Acknowledgment The authors would like to greatly acknowledge the financial support by İstanbul Technical University Research Foundation (ITU-BAP Project no. 38857). Technical assistance of Prof. Dr. M. Ali Gülgün for TEM measurements is appreciated. References [1] Young Pyo Jeon, Sung June Park, Tae Whan Kim, Opt. Mater. Express 2 (2012). [2] Atef Y. Shenouda, El Sayed, M. El Sayed, Ain Shams Eng. J. 6 (2015) 341. [3] G.Q. Liu, Z.Q. Liu, K. Huang, Y.H. Chen, L. Li, F.L. Tang, L.X. Gong, Mater. Lett. 167 (2016) 134. [4] S.K. Davidowski, C.E. Lisowski, J.L. Yarger, Magn. Reson. Chem. 54 (2016) 234. [5] K.M. Goodfellow, C. Chakraborty, K. Sowers, P. Waduge, M. Wanunu, T. Krauss, K. Driscoll, A.N. Vamivakas, Appl. Phys. Lett. 108 (2016). [6] Raja Angeloni, W. Brescia, R. Polovitsyn, F. A; De Donato, M. Canepa, G. Bertoni, R.P. Zaccaria, Moreels,, ACS Photonics 3 (2016) 58. [7] V. Kocevski, J. Rusz, O. Eriksson, D.D. Sarma, Sci. Rep. 5 (2015). [8] Worasak Sukkabot, J. Nanomater. (2016). [9] Andrew M. Smith, Aaron M. Mohs, Shuming Nie, Nat. Nanotechnol. 4 (2008) 56. [10] R. Diaz, J.M. Merino, T. Martin, F. Rueda, M. Leon, J. Appl. Phys. 83 (1998) 616. [11] J. Sun, E.M. Goldys, J. Phys. Chem. C 112 (2008) 9261. [12] S. Suresh, Appl. Nanosci. 4 (2014) 325.
9 2ℏ2π 2 + 3agcΓ ε + agcΓ ε 2 − 9agcΓ (1 + B′) ε 3 + * d2 mcv 2
3.572e 2 0.124e 4 − 2 , * ε∞2 ε∞ d ℏ mcv
(5)
Egb (T )
is the temperature dependent part of the unstrained direct where bandgap energy of bulk CdSe, second, third and fourth terms are the strain contribution to the bulk CdSe direct bandgap with deformation potential agΓ = acΓ − a v at i = Γ symmetry point. The fifth term gives the kinetic energy of electron–hole pair, sixth term belongs to Coulomb interaction and the last term determines the correlation energy 338
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