CdS

Article pubs.acs.org/JPCC

Modified Phonon Confinement Model and Its Application to CdSe/ CdS Core−Shell Magic-Sized Quantum Dots Synthesized in Aqueous Solution by a New Route Anielle Christine A. Silva,*,† Ernesto S. Freitas Neto,† Sebastiaõ W. da Silva,‡ Paulo C. Morais,‡,§ and Noelio O. Dantas*,† †

Laboratório de Novos Materiais Isolantes e Semicondutores (LNMIS), Instituto de Física, Universidade Federal de Uberlândia, CP 593, Uberlândia MG 38400-902, Brazil ‡ Universidade de Brasília, Instituto de Física, Núcleo de Física Aplicada, Brasília DF 70910-900, Brazil § Huazhong University of Science and Technology, Department of Control Science and Engineering, Wuhan 430074, People’s Republic of China ABSTRACT: In this study we present modifications in a phonon confinement model in order to obtain a better description for the Raman spectra of spherical nanocrystals, namely: bare-core, core−shell, and core−multishell. Our new interpretations allow investigating the influences of the interfacial alloying and strain effects on the vibrational spectra of core−shell nanocrystals. The robustness of the modified phonon confinement model was confirmed by precisely describing the Raman spectra of wurtzite CdSe/CdS core− shell magic-sized quantum dots (CS-MSQDs) synthesized directly in aqueous solution by a new route. The CdSe MSQD sample was used as template to growth CdSe/CdS CS-MSQDs with different shell thickness by setting the synthesis temperature. By using our modified model to fit the Raman spectra of samples, we have obtained the size dimensions of CSMSQDs (core-diameter and shell-thickness), in excellent agreement with the values obtained by the atomic force microscopy results, confirming that the change in the synthesis temperature is a simple and efficient way to control the CdS-shell thickness during the growth process. Furthermore, we have confirmed the formation of an alloy layer (CdSxSe1‑x) at the interface of these CdSe/CdS CS-MSQDs and that the strain effects can be neglected for the wurtzite structure.

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INTRODUCTION

Moreover, with respect to bulk materials, there is a strong change in the Raman spectrum of a nanostructure with large surface-to-volume ratio due to the phonon localization in the region limited by the size dimension which can be suitably described by a phenomenological Gaussian confinement model.11 Consequently, this Gaussian confinement model has been extensively used to fit Raman spectra in order to assess the size dimensions of low-dimensional systems,2,12−14 including core−shell nanocrystals where the shell thickness cannot be evaluated by X-ray diffraction, photoluminescence, and high resolution transmission electron microscopy (for unknown core sizes).15,16 Additionally, Raman spectrum is also altered by alloying formation at the core−shell interface,9,17,18 and the influence of this extra effect on the Gaussian confinement model was not considered yet. Therefore, in the present study, we introduce some modifications regarding the phenomenological Gaussian confinement model aiming to improve the description of the

Several properties of semiconductor materials can be comprehensively understood from the analysis of their vibrational spectrum by employing Raman spectroscopy. Thus, because of the simplicity and efficiency of this technique, in many cases, Raman spectroscopy is also worth using to investigate semiconductor nanostructures, such as nanowires,1,2 quantum dots,3−6 and nanosheets.7 In comparison with the bulk semiconductor crystal changes on the phonon spectrum induced by the quantum confinement effect observed in very small nanocrystals is not presently completely understood.8 For instance, a high-frequency shoulder (HFS) above the LO phonon frequency have been identified for CdSe8,9 and CdTe nanocrystals10 using Raman spectroscopy, whereas its origin was associated with the possible participation of acoustic phonons to the scattering process. Then, the Raman spectra of ultrasmall core−shell magic-sized quantum dots (CS-MSQDs) offer a great opportunity to test the consistence of phonon confinement models, with emphasis on the use of the size effect for modulating the vibrational properties of ultrasmall CSMSQDs. © 2013 American Chemical Society

Received: August 27, 2012 Revised: January 4, 2013 Published: January 4, 2013 1904

dx.doi.org/10.1021/jp308500r | J. Phys. Chem. C 2013, 117, 1904−1914

The Journal of Physical Chemistry C

Article

water was adjusted to pH 4 (using 1 M NaOH aqueous solution) at 0 °C. Under magnetic stirring and using a syringe the second solution (Cd2+-aqueous with thiol) was injected into the as-prepared NaHSe solution, immediately producing a bright-green transparent suspension. Afterward, the resulting suspension was refluxed for 30 min and a 30 mL aliquot was collected. This aliquot was precipitated under centrifugation using ethanol in three repeated cycles and the resultant precipitate was dispersed into 50 mL of ultrapure water. This suspension was labeled S0 sample. Synthesis of CdSe/CdS Core−shell Magic-Sized Quantum Dots. In the CdSe bare-core MSQDs solution, placed in the three-necked flask at 0 °C with Ar atmosphere, was added 4 mmol thioglycerol dissolved in 20 mL ultrapure water under magnetic stirring. Then, this mixture was refluxed for 30 min before collecting a 30 mL aliquot and labeling it as S1 sample. In the sequence, the temperature of the left-over suspension was increased to 80 °C and then refluxed for further 30 min, from which a 30 mL aliquot was collected and labeled sample S2. The two suspensions (samples S1 and S2) were then precipitated under centrifugation using ethanol in three repeated cycles and the resultant precipitates were dispersed in 50 mL ultrapure water. Sample Characterization. Room temperature absorption band edge of the as-produced colloidal samples (S0, S1, and S2) was assessed using a double beam UV−VIS−NIR spectrophotometer (Shimadzu, UV-3600) operating between 200 and 800 nm, with a spectral resolution of 1 nm. Atomic force microscopy (AFM) images of the nanocrystalline samples were recorded at room temperature with a scanning probe microscope (Shimadzu, SPM-9600). In order to perform the AFM measurements the colloidal aqueous solution was first diluted to avoid (or to reduce) formation of QD-based aggregates (or clusters), driven by the high surface energy of small nanocrystals.19,27,37 The diluted colloidal suspensions were deposited onto mica surface, which meets the substrate requirements to support our samples: (i) roughness smaller than 0.1 nm (atomically flat surface) and (ii) cleaved material highly stable for storage.38 It is important to note that an adsorption process starts immediately after dripping of the colloidal solution onto the substrate’s surface, meaning that some nanocrystals remain strongly adhered to the substrate’s surface while the solvent is being dried out. Actually, this adsorption process helps recording high quality AFM images. In order to perform X-ray diffraction (XRD) and Raman characterization the as-produced colloidal suspensions were precipitated under centrifugation using ethanol with a subsequent step for drying up the precipitates at room temperature using Ar atmosphere, resulting in nanocrystals’ powders. In order to identify the structural phase of the asprecipitated powders Room temperature XRD patterns were recorded using a XRD-6000 Shimadzu diffractometer, operating with monochromatic Cu−Kα1 radiation (λ = 1.54056 Å). Room temperature Stokes Raman scattering spectra of the asprecipitated powders were recorded with a JY-T64000 microRaman spectrometer excited with the low power Ar+ 488 nm laser line and detected in backscattering geometry. It was used an objective of 50× to focus the laser beam down to a spot of 1.5 μm in diameter. Thus, the laser power and the power density hitting the sample were 5 mW and 3 × 105 W/cm2, respectively. Thus, any heating effect on the vibrational spectra of the samples was neglected.

confined longitudinal optical (LO) phonon mode in spherical nanocrystals, namely bare-core, core−shell, and core−multishell structures. Among the modifications we included different Gaussian functions to confine phonons in the core and in the shell plus additional modifications regarding the interfacial alloying and strain effects. This modified phonon confinement model is tested in spherical CdSe/CdS CS-MSQDs with wurtzite phase which were directly grown in aqueous solution by the novel approach herein introduced. MSQDs are ultrasmall and extremely stable nanocrystals consisting of a well-defined number of atoms (fixed sizes) making them quite different from traditional quantum dots (QDs).19−22 For instance, CdSe QDs with size ranging between 1 and 2 nm are highly stable and then identified as MSQDs.23−25 Due to the unique MSQDs characteristics and driven by a wide diversity of potential technological applications considerable attention has been devoted to this exceptional material system.21,26−28 Particularly interesting are the CS-MSQDs which add even wider possibilities for properties modulation by simply varying the core−shell compositions and shell thickness, as for instance the CdTe/ CdS CS-MSQD whose light emission can be tuned from visible (480 nm) to near-infrared (820 nm) by changing the CdS shell thickness while overcoating the magic-sized CdTe core.29 Additionally, since MSQDs has a huge surface-to-volume ratio most of their atoms are located at or near to the QD-surface and thus under a strong influence of the surface-dressing molecules, which in turn can drastically affect their physicochemical properties.8,22,30 In this context, although a great variety of high-quality MSQDs have been synthesized by using organometallic precursor 31−34 and aqueous-based approach,22,35,36 the precisely controlled growth of CdSe/CdS CS-MSQD in colloidal aqueous solution is introduced in the present study. Thus, we herein introduce an important approach regarding the development of QD synthesis by describing a novel methodology to grow CdSe/CdS CSMSQDs directly within aqueous solution in which the CdSshell thickness could be controlled by tuning the synthesis temperature. This work is organized as follows. The details regarding the novel CdSe/CdS CS-MSQDs synthesis as well as the samples’ characterization are presented in the “Experimental Section”. Then, the theoretical background regarding the analysis of Raman data is given in the “Modified Phonon Confinement Model” section. The section entitled “Results and Discussions” is divided into several subsections: Optical Absorption; Atomic Force Microscopy; X-ray Diffraction; and Raman Spectroscopy. In the Raman Spectroscopy subsection, we detail how the modified phonon confinement model is used to describe the Raman spectra of the as-synthesized CdSe/CdS CS-MSQDs. Our findings are summarized in the “Conclusions” section.

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EXPERIMENTAL SECTION Synthesis of CdSe Bare-Core Magic-Sized Quantum Dots. Aqueous-based colloid consisting of CdSe bare-core MSQDs was fabricated through the addition of the Cd2+− aqueous solution using thiols as stabilizing agent into NaHSe aqueous solution. Shortly, a first NaHSe aqueous solution was prepared in a three-necked flask under Ar atmosphere by adding 1 mmol of Se plus 2 mmol of NaBH4 into 60 mL of ultrapure water at 0 °C under magnetic stirring. Additionally, a second aqueous solution containing 4 mmol of Cd(ClO4)2 plus 2 mmol of the stabilizer thioglycerol in 20 mL of ultrapure 1905



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MODIFIED PHONON CONFINEMENT MODEL Spherical Nanocrystals: Bare-Core, Core−Shell, And Core−Multishell. The Raman spectrum of a nanocrystal displays differences with respect to its corresponding bulk material, which are generally enhanced in intensity when the surface-to-volume ratio increases. In the longitudinal optical (LO) mode a characteristic broad shoulder contributes to the lower frequency tail and its origin can be ascribed to both: (i) the effect of optical phonon confinement25,26 and (ii) the surface optical (SO) phonons of spherical nanocrystal.39 The confined LO phonon mode in spherical nanocrystals has been extensively investigated by a phenomenological Gaussian confinement model,11,15 which was initially proposed by Richter et al.12 and subsequently extended to nonspherical shape nanostructures by Campbell and Fauchet.13 It is important to note that although there is a dependence between LO and SO modes in spherically shaped nanocrystals (barecore and core−shell)39,40 the phonon confinement model described by eq 2 is applied only to LO modes and cannot explain the origin of the SO modes. According to this model, a phonon weighting function W(r) is used to describe an optical phonon in a nanocrystal with finite size:14 W(r) = exp[−r2/ 2σ2], where the standard deviation σ is a constant related to a particular measurement setup and material in accordance to the sample’s dimensions. Thus, the wave function for a phonon of wave-vector q0 in the finite nanocrystal is given by: ψ(q0,r) = W(r) Φ(q0,r), where Φ(q0,r) is the phonon wave function while propagating in the corresponding infinite crystal (bulk material). In other words, the W(r) phonon weighting function actually works as a confinement function, localizing the phonon in the region limited by the nanocrystal size. Evidently, the choice of the σ parameter in the Gaussian-like weighting function defines the confined phonon amplitude at the material boundary. Two seminal examples are found for spherical nanocrystals with diameter d: (i) Richter et al. have chosen σ = d/2 resulting in a phonon amplitude of 1/e at the nanocrystal boundary12 whereas (ii) Campbell and Fauchet have obtained a phonon amplitude of exp (−4π2) at the boundary material by assuming σ = d/4π.13 For phonons confined within nanowires, it was shown that the Gaussian confinement model can fit to any results if the σ parameter is varied.2,14 Also, Roodenko et al. have intuitively proposed a square-wave function to be used as phonon weighting function in order to represent a nanowire in the Cartesian coordination system.14 Those authors have demonstrated that for the Gaussian function to match the square-wave function (especially after a Fourier transform), the standard deviation (σ) should be equals to the distance of all points in the square-wave from the center, normalized to the number of the points. Based on this approach and bearing in mind the spherically shaped nanocrystals, we suggest that the Gaussian function should be matched to a circumference with radius r described by y = (r2−x2)1/2, where the x−y plane is arbitrarily oriented in space but positioning through the sphere center, as depicted in Figure 1. Thus, the normalized σ parameter of the Gaussian function W(x) = exp[−x2/2σ2] (represented in the xdirection) was calculated as follows:14 σ=

⟨x 2⟩ − ⟨x⟩2 2r = = 20 ⟨N ⟩

d 20

Figure 1. The circumference function y = (r2 − x2)1/2 is represented by open circles in the top panel whereas the blue lines correspond to the phonon weighting function W(x) = exp[−x2/2σ2] (a) with σ = d/2 as proposed by Richter et al. (dashed line),12 (b) with σ = d/√20 as calculated in eq 1 (solid line), and (c) with σ = d/4π as proposed by Campbell and Fauchet (dashed-dotted line).13 The bottom panel represents the spherically shaped nanocrystal in which the optical phonon is confined.

with the standard deviation calculated by eq 1, σ = d/(20)1/2, and a comparison with other Gaussian functions proposed for spherical nanocrystals.12,13 It is interesting to note that the weighting function herein proposed (solid blue line) is quite reasonable, for it agrees better with the spherically shaped nanocrystal’s boundary than those previously proposed in the literature.12,13 Thus, at the boundary of spherical nanocrystals the Gaussian weighting function proposed here (σ = d/(20)1/2) provides the phonon amplitude of exp(−5), a value near to zero. Hence, in order to describe the phonon confinement in spherical nanocrystals a good agreement with experimental results can be expected while employing the Gaussian weighting function with σ = d/(20)1/2. The first-order LO-Raman spectrum is then obtained by the following expression11,13 (i) (ω) ILO

≈

d3q |C(i)(0, q)|2

∫ [ω − ω

2 (i)(q)]

+ (Γ(i)/2)2

(2)

where the Fourier coefficients for the Gaussian function are given by |C(i)(0,q)|2 ≈ exp(−q2(i)σ2(i)), and d3q ≈ q2dq due to the nanocrystals’ spherical symmetry. The i number is useful when applying this phonon confinement model to heteromaterials containing different bare nanocrystals. Thus, each i-th material can be represented by an integer value i. The present phonon confinement model is based on the assumption that LO phonon dispersion ω(i)(q) in nanostructures is the same as the corresponding bulk material. Since the size dimensions of spherical quantum dots are equivalent in all directions, an average ω(i)(q) is certainly a good approximation only for materials with almost isotropic LO phonon dispersions. The

(1)

The upper panel in Figure 1 shows the circumferencematched phonon weighting function W(x) = exp[−x2/2σ2] 1906



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which is the same value obtained by our Gaussian weighting function with σ = d/(20)1/2 for the spherical core nanocrystal. For instance, by labeling j = 2 for the first shell with thickness t, its phonon amplitude is evaluated by |W2(r)|2 = exp{−[r−((d + t)/2)]2/σ22}. Based on our assumption, the equality exp{−[r− ((d + t)/2)]2/σ22} = exp(−5) should be fulfilled at the internal boundary of the first shell where r = (d/2). Consequently, the value σ2 = t/(20)1/2 is obtained for the first shell, which can easily be generalized for any j-th shell with thickness t(j), namely σ(j) = t(j)/(20)1/2. Therefore, the Fourier coefficients related to the j-th shell material are given by:

CdSe/CdS CS-MSQDs investigated in this study fulfill this assumption, because the LO phonon dispersion of each corresponding bulk semiconductor (CdSe or CdS) is almost isotropic.41,42 In contrast, when different crystallographic planes contribute to the Raman signal in materials with anisotropic phonon dispersions, a 3D representation of the phonon function ω(q1,q2,q3) should be employed as recently demonstrated by Roodenko et al.14 Therefore, in isotropic materials, the average phonon dispersion ω(i)(q) in the bulk crystal can be taken as follows:11,15,43,44 ω(i)(q) = ω0(i) − Δω(i) q2(i), where ω0(i) and Δω(i) are respectively the LO phonon frequency at the Γ-point (q = 0) and the bandwidth related to the LO branch. The phonon wave-vector q(i) is represented in units of 2π/a(̅ i), i.e., q(i) ≡ [q(i)/(2π/a)], ̅ where a(̅ i) is taken as the mean lattice parameter of i-th bulk material. Γ(i) is the natural line width (fwhm) of the zone-center optical phonon in the corresponding bulk material. It is important to note that the line width Γ(i) can also suffer a further broadening when the Raman measurements are carried out for ensembles of nanocrystals because of their size dispersion. Even though the proper way is to choose a periodic function for the phonon dispersion and to carry out the integration over q in eq 2 from 0 to infinity,14 a good approximation is to use nonperiodic function and to carry the integration in the first Brillouin zone, as has been reported by several authors.11−13,15 The lower frequency tail of LO-mode has also contributions from the SO phonons, as previously mentioned, which can additionally be taken into account in the Raman spectrum using a Lorentzian function, as follows:15,16 (i) ISO (ω) =

C(j)(0, q)

≈

{2πσ ⎡⎣σ 2 (j)

2 (j)

+ r(2j)⎤⎦ −2σ(6j)q2 + 2σ(4j)r(2j)q2

} (

2

+ σ(8j)q 4 exp −σ(2j)q2

)

(4)

It is important to note that, by virtue the r(j) position, the Fourier coefficients (given by eq 4) for a specific m-th shell (j = m) dependent upon the diameter d of core as well as the sum of the internal shells’ thickness, as given by r(j=m) = [(d + ∑km= 1t(k))/2], where k is an integer number associate to every internal shell. Therefore, after replacing eq 3 into eq 2 a good description of the confined LO phonons in the shell is expected, even for very small core−shell or core−multishell QDs with large surface-to-volume ratio. Additional Effects on the Vibrations of a Core−Shell Nanocrystal: Interfacial Alloying and Strain. We present here a discussion related to the possible additional effects on the vibrational spectrum of a core−shell nanocrystal and their influences on the confined LO-modes described by eq 2 as well as on the SO-modes described by eq 3. This analysis is necessary in order to obtain a comprehensive understanding of the vibrational spectrum of a core−shell nanocrystal. The additional effects are mainly associated with both: (i) the interfacial alloying in a core−shell nanocrystal and (ii) the strain (compressive or tensile) on the core, on the shell, or even on the alloy material. Alloying formation at the interface of core−shell nanocrystals has been confirmed in recent studies.9,17,18 For instance, from the Raman spectra of CdSe/ ZnS core−shell nanocrystals Dzhagan et al. have confirmed the formation of a thin CdSxSe1‑x layer with an estimated intermixing of S with CdSe to be limited to the outer 1−2 monolayers of the CdSe core.17 Tschirner et al. have also detected alloy vibrations in Raman spectra of CdSe/CdS core− shell nanocrystals, confirming thus the presence of a mixed CdSxSe1‑x layer at the interface.9 Although an alloying layer at the interface of a core−shell nanocrystal can be limited to the surface between the two distinct materials (core and shell), with thickness of 1−2 monolayers depending on the growth mechanism (or synthesis approach), we can infer that the effect of this interfacial alloying can play an important role on the nanocrystal’s vibrational spectrum, especially in very small size dimensions. In other words, the vibrational spectrum of a core−shell nanoparticle should be actually defined by the interplay between the vibrations of the distinct materials (core or shell) and those of interfacial alloying. This conclusion is strongly supported by the study of Tschirner et al. on CdSe/CdS core−shell nanocrystals,9 where the alloy vibration from an interfacial CdSxSe1‑x layer appears at the low energy side of the pure LO phonon frequencies of both CdSe-core and CdS-shell. In addition, the lower frequency tail associated to each fundamental LO phonon has also contribution from the SO phonon, whose

B(i)ΓSO(i) 2 (ω − ωSO(i))2 + Γ SO( i)

2

(3)

where ΓSO(i) and ωSO(i) are respectively the fwhm and the SOphonon frequency and B(i) is an arbitrary constant. Thus, the intensity I(i)(ω) of a Raman peak associated with the optical phonons of spherically shaped nanocrystals can be adequately fitted by combining two line shapes by adding eqs 2 and 3, (i) namely I(i)(ω) = I(i) LO(ω) + ISO(ω). As previously mentioned, this phonon confinement model can be certainly extended to nonspherical shape structures such as nanowires,2,14 or even thin films as initially proposed by Campbell and Fauchet.13 This proposal has been used by many authors in order to describe phonons confined into the shell material in spherically shaped core−shell nanocrystals,15,16 assuming a similarity between the two-dimensional thin film and the spherical shape shell. However, we emphasize that the phonon confinement described by this approximation is more realistic for larger nanocrystals. In other words, the pronounced curvature of the shell surface in a small nanocrystal with large surface-to-volume ratio limits the use of this approximation. In order to avoid this limitation, we present in this study an alternative approximation, employing an additional Gaussian weighting function centered in the middle of the shell material. This approach can also be extended to core−multishell nanocrystals, by describing the phonon confinement in each j-th shell material by the Gaussian weighting function W(j)(r) = exp{−[r − r(j)]2/2σ2(j)}, where r(j) defines the center of the walls of every spherical shell. For instance, the center of the walls of the first shell (r(j)with j = 1) with thickness t on top of a core with diameter d is given by r(1) = ((d + t)/2). It is reasonable to assume that the phonon amplitude |W(j)(r)|2 at the boundary of each j-th shell with thickness t(j) should decay to exp(−5), 1907



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frequency can be slightly lower than the frequency of the CdSeor CdS-like LO modes of the alloy layer. We highlight that contribution to the SO phonons can also be originated from SO-modes of the alloy vibrations due to the finite size of the thin layer where the interfacial alloy is located. Within this model picture, there exists a neighboring proximity and even a partial overlapping between the LOmodes (or SO-modes) originated from both distinct materials (core or shell) and the interfacial alloying (mixed layer). Furthermore, these vibrations can be shifted due to strain effects that are mainly caused by the nanocrystal size dependence of the surface tension45 and the lattice mismatch between the core and the shell materials.16 Thus, it is interesting to note that the strain effects are dependent on the nanocrystal size as well as its structural phase, and possibly on the nanoparticle synthesis approach. Therefore, the above-mentioned additional effects (interfacial alloying and strain) in a core−shell nanocrystal should certainly cause alterations in the average LO-phonon dispersion curve of a bulk material, ω(i)(q) = ω0(i) − Δω(i) q2(i), and accordingly in the confinement of LO-modes which are described by eq 2. Thus, in order to take into account a gradual formation of alloy at the core−shell interface of a QD, or even possible strain effects, we propose in our modified phonon confinement model a new interpretation for the ω0(i) and Δω(i) parameters describing the phonon dispersion of bulk material. Instead of keeping LO-phonon dispersion curve fixed by the average values of the homogeneous bulk materials,11,15 we propose in this study that the ω0(i) and Δω(i) parameters will be found from the fitting procedure by employing eq 2 in order to describe the confined LO-phonons in core−shell QDs, or even core−multishell nanocrystals. Under this new interpretation, our modified phonon confinement model works as an important tool to evaluate changes in the average LO-phonon dispersion, induced by interfacial alloying or strain effects in core−shell nanocrystals, based on deviations of ω0(i) and Δω(i) parameters with respect to the homogeneous bulk materials. In connection with this understanding, we should emphasize that part of SO phonons described by eq 3 is also originated from the alloy vibrations at the interface of the core−shell nanocrystal. In the subsection Raman Spectroscopy presented below, our modified phonon confinement model is tested in spherical CdSe/CdS CS-MSQDs grown directly from aqueous solution.

Figure 2. Room temperature OA spectra of samples S0 (CdSe barecore MSQDs with mean radius R = 0.68 nm); S1 and S2 (CdSe/CdS CS-MSQDs where the corresponding CdS shell thickness (t) is indicated in each spectrum).

revealed a systematic increase in the CdS-shell thickness (t) from sample S0 to sample S2, as shown in Table 1 (first three Table 1. Mean Dimensions (all in nm) of MSQDs (S0, S1, and S2 Samples) Evaluated by the Raman and AFM Techniquesa sample or simulation S0 S1 S2 S3 S4

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RESULTS AND DISCUSSION Optical Absorption. Figure 2 presents the room temperature OA spectra of the as-prepared colloidal samples (S0, S1, and S2). The band gap energies of growing MSQDs were obtained from OA peaks, as indicated by the arrows in Figure 2, namely (i) 3.28 eV for sample S0; (ii) 3.26 eV for sample S1; and (iii) 3.11 eV for sample S2. The range of these band gap energies confirms that the as-grown nanostructures are actually very small and belong to a class of nanocrystals termed as “magic-sized nanocrystals”.19,26,28,46,47 From the band gap energy Eg = 3.28 eV of sample S0 (see Figure 2) and by employing a well-established relationship with dot size,48 we evaluated the mean radius around R ≈ 0.675 nm (or diameter D ≈ 1.35 nm) for the CdSe bare-core MSQD. Notice that we have obtained a very similar value D ≈ 1.39 nm by employing our modified phonon confinement model in order to describe the Raman spectra presented below. Our approach to evaluate the Raman spectra of MSQDs has also

raman

AFM

Dcore

t

DTotal

DTotal

t

ξ (%)

1.39 1.39 1.39 15.15 15.15

0.00 0.41 1.29 1.29 5.60

1.39 1.80 2.68 16.44 20.75

1.44 1.82 2.70

0 0.38 1.26

12 13 15

a

Core diameter (Dcore); shell thickness (t); and total diameter (DTotal = Dcore+ t). The last column shows the size dispersion (ξ) obtained from the AFM images. The dimensions shown for the S3 and S4 (simulations) were evaluated from the modified phonon confinement model.

rows). In addition, the same mean core diameter (D ≈ 1.39 nm) was also confirmed for the CdSe/CdS CS-MSQDs identified in samples S1 and S2, since the CdS-shell was grown by coating the CdSe bare-core MSQD. Thus, in Figure 2, the observed redshift in the OA peak in samples S0, S1, and S2, from 3.28 to 3.11 eV, can certainly be attributed to an increase of shell thickness in the CdSe/CdS CS-MSQDs as indicated in each spectrum. Similar redshifts in OA bands with increasing shell thickness have been reported for CdSe/CdS49 as well as CdS/ZnS nanocrystals,50 and this behavior is actually associated with a delocalization of the electron and hole wave functions over the entire core−shell nanostructure. Figure 2 1908



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spectra. All of these results have demonstrated that the shell thickness of CdSe-CdS CS-MSQDs can be effectively controlled by changing the synthesis temperature; in our case increasing from 0 °C (sample S1) to 80 °C (sample S2), with shell thicknesses values quoted in Table 1. In connection with the broadening in the OA spectra (Figure 2) when the CdS shell thickness increases, an increasing size dispersion of CS-MSQDs can also be observed from the height distribution shown in Figure 3. Indeed, this effect is related to the increase of the CdS-shell thickness dispersion in CdSe/CdS CS-MSQDs because the core size is equals for all samples (S0, S1, and S2). The height distributions shown in the AFM images were fitted by a log-normal function and thus we have confirmed the growing size dispersion (ξ) of MSQDs for increasing CdS-shell thickness. Similar behavior was also reported for zincblende CdSe/CdS core−shell nanocrystals synthesized via organometallic approach.54 X-ray Diffraction. Room temperature XRD patterns of the CdSe bare-core (sample S0) and CdSe/CdS CS-MSQDs (samples S1 and S2) are shown in Figure 4. These patterns

also shows that an increase in CdS-shell thickness causes a broadening in the OA band of CS-MSQDs. Evidently, this effect is attributed to an increase in size dispersion of MSQDs, which in turn is caused by the increase in the CdS-shell thickness dispersion. Atomic Force Microscopy. Figure 3 presents the (100 × 100 nm) AFM images of samples S0 (panel (a)); S1 (panel

Figure 3. Room temperature AFM images showing CdSe bare-core and CdSe/CdS CS-MSQDs deposited onto mica substrate: (a) sample S0; (b) sample S1; and (c) sample S2.

(b)); and S2 (panel (c)). The corresponding two-dimensional and three-dimensional images are displayed on the left and on the right-hand-side in each panel, respectively. Since any convolution effect does not influences the measurement in the vertical z direction of an AFM image,38,51−53 the coherent resource in order to evaluate the mean diameter of QDs is from their height distribution, which is shown on the right-hand-side of two-dimensional image in each panel (see Figure 3). Table 1 summarizes the mean values related to the total diameter of MSQDs for each sample (S0, S1, and S2), as obtained from this procedure. It is interesting to note in Table 1 that the mean diameters obtained from the AFM images agree well with those obtained by the fitting procedure of the Raman spectra using the modified phonon confinement model proposed here. The slight and negligible differences between these values can be attributed to the formation of MSQDs aggregates, as observed in the AFM images included in Figure 3, which are caused by high surface energy of very small nanocrystals.19,27,37 Table 1 shows the obtained values for the CdS-shell thickness (t) from AFM data when subtracting the diameter (D ≈ 1.44 nm) of the CdSe bare-core MSQDs (sample S0). It is interesting to note that for each CS-MSQD sample (S1 or S2) that there exist a close agreement between the values of the CdS-shell thickness obtained by AFM and from the evaluation of the Raman

Figure 4. Room temperature XRD patterns of nanocrystals present in samples: (S0) CdSe bare-core MSQDs; (S1) and (S2) CdSe/CdS CSMSQDs. Standard patterns of the CdS (top) and CdSe (bottom) with wurtzite (W) and zincblende (ZB) structures are also shown for comparison.

were compared with the values found in the standard cards of each cadmium chalcogenide, as given by the following: (i) CdSe (zincblende JCPDS no. 19−0191; wurtzite JCPDS no. 77−2307) and (ii) CdS (zincblende JCPDS no. 42−1411; wurtzite ICSD no. 620319). Although a percentage of MSQDs can present a mixed phase one can observe from Figure 4 that the CdSe bare-core MSQDs are predominantly structured in the hexagonal wurtzite phase. Similar results have been reported for CdSe nanocrystals synthesized by either the aqueous solution method15,55 or via the organometallic approach.16,56 For samples S1 and S2 the diffraction peaks of 1909



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the CdSe/CdS CS-MSQDs are slightly shifted to higher angles and are broader than those of CdSe bare-core MSQDs, giving evidence for the CdS shell growth and confirming that the wurtzite is the dominant phase. This result is also strongly supported by the (1 1 0) and (1 1 2) diffraction peaks attributed to the wurtzite CdS. In addition, the higher intensity of the hexagonal (1 0 1) diffraction peak in sample S2 with respect to sample S1 can certainly be attributed to the thicker CdS shell in the CdSe/CdS CS-MSQDs, in total agreement with the observed redshift in OA band shown in Figure 2. Raman Spectroscopy. The wurtzite phase of the CdSe bare-core and CdSe/CdS core−shell MSQDs plays an important role in the Raman selection rules, which are assumed to be the same as the bulk crystals. Thus, for the space group C46v of the wurtzite structure, we can conclude that the 2B1 mode is not Raman active, whereas A1, E1, and 2E2 modes are Raman active.57,58 Figure 5a shows the room temperature Raman spectrum of the as-synthesized CdSe bare-core MSQD, where the peak associated with the confined LO-phonon mode can be clearly observed. As previously mentioned (section “Modified Phonon Confinement Model”) the low frequency tail of this LO mode has contributions from confined LO phonon as well as SO phonon, as expected from spherical nanocrystals.12,13,39 Alongside these two characteristic frequencies (LO1 and SO1) of CdSe bare-core MSQDs, a high frequency shoulder (HFS) appearing around ≈ 226.8 cm−1 can also be observed in Figure 5a. The origin of this HFS is possibly related to the participation of acoustic phonons to the scattering process (i.e., LO + acoustic phonons) as it was initially proposed by Dzhagan et al., who have also observed a similar HFS in the LO-mode of small CdSe nanocrystals.8 In support to this explanation Tschirner et al. have also reported the presence of this HFS (around ≈ 234 cm−1) in the Raman spectrum of CdSe bare-core nanocrystals.9 It is worth mentioning that in another recent study we have confirmed that the presence of a HFS above the confined LO phonon frequency in semimagnetic Cd1‑xCoxS QDs is related to the acoustic-optical phonon coupling.59 However, after coating the CdSe bare-core MSQD (sample S0) with the CdS shell layer to produce the CdSe/CdS CS-MSQDs samples (samples S1 and S2), the HFS is ruled out from the Raman spectra, as can be observe in Figures 5b and 5c. This finding is also in agreement with the results reported by Tschirner et al.9 and Dzhagan et al.,8 who have argued that these changes in the phonon spectra reflect changes in the exciton−phonon coupling rather than elimination of certain surface bonds/defects. The modified phonon confinement model proposed here was employed to describe the Raman spectra (Figure 5) of samples S0, S1, and S2. Thus, the intensity I(ω) related to the experimental Raman spectrum of the CdSe bare-core (Figure 5a) was fitted by summing eqs 2 and 3, plus also an additional Lorentzian function to take into account the HFS around 226.8 (1) (1) cm−1, namely I(ω) = I(1) LO(ω) + ISO (ω) + IHFS(ω). For the (1) ILO(ω) intensity (see eq 2) we have used the values15 ω0(1) = 213 cm−1 and Δω(1) = 118 cm−1 in order to describe the average phonon dispersion in the CdSe bulk material, ω(1) (q) = ω0(1) − Δω(1) q2(1), since there is no formation of any interfacial alloying in the bare-core MSQDs. Here, the wavevector q(1) is represented in units of 2π/a(̅ 1), i.e., q(i) ≡ [q(i)/ (2π/a)], with mean lattice parameter of wurtzite structure ̅ given by Singha et al.15 Since the average phonon dispersion is described by a nonperiodic function, we have carried out the

Figure 5. Room temperature Raman spectra (circle symbols) of nanoparticles: (a) CdSe bare-core MSQDs; (b) and (c) CdSe/CdS CS-MSQDs. The frequency of each vibrational mode (SO1, LO1, HFS, SO2, or LO2) is indicated by numbers. The fitting of every Raman spectrum is shown by the red solid line, with subcomponents labeled by: the green line for vibrations related to the core; the blue line for vibrations related to the shell; the black line for the HFS only in S0 sample (panel (a)). S3 and S4 are Raman spectra simulated by the modified phonon confinement model.

integration in eq 2 for I(1) LO(ω) in the first Brillouin zone. In Figure 5a the quality of this theoretical fitting (red solid line) with the experimental data (circle symbols) is excellent, from which we have determined the mean diameter D ≈ 1.39 nm for the CdSe bare-core MSQD, in excellent agreement with the 1910



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Table 2. Parameters (All in cm−1) Obtained from the Fitting of the Raman Spectra of Samples S0, S1, and S2a sample or simulation S0 S1 S2 S3 S4 a

CdSe-core

CdS-shell

ω0(1)

Δω(1)

ωLO1

ΓLO1

ωSO1

ΓSO1

213 209.5 208 213 213

118 67 55 118 118

204 204 204 213 213

8.0 14.0 16.9 16.9 16.9

185.0 191.0 189.4

25 26 26

ω0(2)

Δω(2)

ωLO2

ΓLO2

ωSO2

ΓSO2

276.5 282.9 282.9 302

10 30 30 102

275.5 280.7 280.7 302

28 40 40 40

241.2 242.0 242.0

38 37 37

The parameters shown for S3 and S4 are simulations based on the modified phonon confinement model.

values obtained from OA spectra (D ≈ 1.35 nm) and AFM images (D ≈1.44 nm). Figure 5b,c shows the Raman spectra of the as-synthesized CdSe/CdS CS-MSQDs (samples S1 and S2). Besides the Raman peak at ∼204 cm−1 an additional peak appears for these CS-MSQDs, at ∼275.5 cm−1 for sample S1 (Figure 5b) and at ∼280.7 cm−1 for sample S2 (Figure 5c), confirming the CdSshell growth on top of the CdSe-core. The data presented in Figure 5b,c also display an excellent agreement between the experimental Raman spectra (open circles) and the fitting curves (red solid lines), obtained by adding eqs 2 and 3, I(i)(ω) (i) = I(i) LO(ω) + ISO(ω), for each one of the two Raman peaks. In this case we have defined the integer values as follows: (i) i = 1 for vibrations around the confined LO-mode of the CdSe-core and (ii) i = 2 for vibrations around the LO-mode of the CdSshell. The Fourier coefficient used to calculate the I(i) LO(ω) intensity (see eq 2) regarding confined-LO phonons of the CdSe-core was given by |C(1)(0,q)|2 ≈ exp(−q2(1)σ2(1)). However, calculation of the CdS-shell Fourier coefficient used eq 4 instead, with the defined value j = 2 for the shell material. Furthermore, in agreement with the new interpretation presented in Section “Modified Phonon Confinement Model”, the ω0(i) and Δω(i) parameters describing the average LO-phonon dispersion curve of bulk material (ω(i)(q) = ω0(i) − Δω(i) q2(i)) were obtained from the fitting procedure in order to assess the possible existence of interfacial alloying as well as strain effects in the CdSe/CdS CS-MSQDs. Here, the wavevector q(i) is represented in units of 2π/a(̅ i), i.e., q(i) ≡ [q(i)/(2π/ a)], ̅ with the mean lattice parameter of wurtzite structure given by:15 a(̅ 1) = 0.608 nm for the CdSe and a(̅ 2) = 0.582 nm for the CdS. Again, we have carried out the integration in eq 2 for I(i) LO(ω) in the first Brillouin zone because of the nonperiodicity of the average phonon dispersion. From the fitting procedures carried out on the Raman spectra of the as-synthesized MSQDs (samples S0, S1, and S2) we have evaluated the mean values associated with the core diameter and the shell thickness as displayed in Table 1 in comparison with the AFM data. The excellent agreement between these two sets of results (Raman and AFM) regarding the size of the as-synthesized QDs certainly confirms the robustness of the modified phonon confinement model proposed here. Finally, Table 2 (first three rows) collects the parameters (all in cm−1) obtained from the Raman data fittings. It is worthy of notice that we found the ωLO1 phonon frequency associated to the CdSe-core unchanged upon the shell growth in samples S1 and S2, demonstrating that any possible strain effect involving the core can be neglected. Similar behavior has been reported for CdSe/CdS core−shell nanocrystals,15,16 also structured in the wurtzite phase as in our samples, confirming that the strain effect related to the lattice mismatch between the CdSe-core and the CdS-shell is very small to be detected through Raman measurements. In

contrast, for CdSe/CdS core−shell nanocrystals with zincblende structure the strain effect induced by lattice mismatch has been clearly confirmed due to the blueshifts of the ωLO1 phonon frequency of the CdSe-core as the CdS-shell thickness increases.9,54 Additionaly, it is worth mentioning that in cubic CdSe/CdS core−shell nanocrystals, opposite strain effects for the core and the shell were reported by Tschirner et al.,9 namely: the difference in lattice constant leads to compressive and tensile strain in the core and in the shell, respectively. Therefore, we can conclude that the negligible lattice mismatch in the CdSe/CdS core−shell nanocrystals with wurtzite structure should be considered when these nanocrystals are structured in the zincblende-like phase. According to this finding, no strain-induced shift in the ωLO2 frequency of CdS-shell is also expected in the Raman spectra of the as-synthesized samples containing CdSe/CdS CS-MSQDs with hexagonal wurtzite phase. Thus, in Table 2, the observed blueshift of the ωLO2 frequency from 275.5 cm−1 (sample S1) to 280.7 cm−1 (sample S2) is a direct result of the weakening in the LO2-phonon confinement, which is caused by the increase in the CdS-shell thickness from 0.41 to 1.29 nm (as shown in Table 1). In eq 2, the ΓLO(i) fwhm is associated with the vibration around the confined LO-mode of the CdSe-core for i = 1, or CdS-shell for i = 2, and it is also influenced by alloy formation at the interface of CdSe/CdS CS-MSQDs. This effect is justified by the close proximity (and even a partial overlapping) between LO-modes from the homogeneous material (core or shell) and the interfacial alloying (mixed layer). In our samples, by estimating an interfacial alloying with thickness of about 1−2 monolayers,17 it is interesting to analyze the behavior of the CdSe- and CdS-like LO phonon frequencies in the bulk CdS0.5Se0.5 material based on a recent study,45 in which the frequencies of the optical phonons were calculated for bulk CdSxSe1‑x alloys with different x compositions. Thus, we have obtained the following values: (i) 191.91 cm−1 for CdSe-like LO frequency (x = 0.5) regarding the value of 210 cm−1 for pure CdSe LO frequency (x = 0.0) and (ii) 292.54 cm−1 for CdS-like LO frequency (x = 0.5) regarding the value of 302 cm−1 for pure CdS LO frequency (x = 1.0). These results confirm that the alloy vibration related to the CdSe-like LO frequency undergoes a bigger redshift with respect to the value of pure bulk material than the CdS-like LO one. Naturally, a similar behavior is expected for the alloy vibrations from the mixed layer of CdSxSe1‑x (with x ≈ 0.5), which is located at the CdSe/CdS CS-MSQDs interface. However, this thin interfacial alloy is also influenced by phonon confinement, which promotes an additional redshift in both CdSe- and CdSlike LO frequencies.45 The alloy effects can be used to explain the alteration of the ΓLO1 and ΓLO2 line widths induced by the CdS-shell growth. Explicitly, the ΓLO1 is increased from 8.0 cm−1 in the CdSe bare-core MSQDs (sample S0) to the following values in the 1911



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CdSe/CdS CS-MSQDs: 14.0 cm−1 and 16.9 cm−1 for samples S1 and S2, respectively. Nevertheless, for the CS-MSQDs ΓLO2 broadens from 28 cm−1 (sample S1) to 40 cm−1 (sample S2), in which there exist also a contribution attributed to the increase in size dispersion associated to the CdS-shell thickness, as confirmed by OA and AFM data. Furthermore, the onset of the mixed layer CdSxSe1‑x with x ≈ 0.5 (i.e., the interfacial alloy) in the CdSe/CdS CS-MSQDs certainly cause alterations in the average LO-phonon dispersion curve of the bulk material, clearly confirmed by deviations of the ω0(i) and Δω(i) parameters (as shown in Table 2) regarding the values related to the homogeneous bulk material, which are given by the following:15 (i) ω0(1) = 213 cm−1 and Δω(1) = 118 cm−1 for the bulk CdSe and (ii) ω0(2) = 302 cm−1 and Δω(2) = 102 cm−1for the bulk CdS. Even for the thinnest CdS-shell (sample S1) we have obtained the values of ω0(1) = 209 cm−1 and Δω(1) = 67 cm−1 for the core whereas we found ω0(2) = 276.5 cm−1 and Δω(2) = 10 cm−1 for the shell. These findings demonstrate the strong influence of interfacial alloy on the LOphonon dispersion which is more intensified in the shell due to its very tiny thickness (t = 0.41 nm). When the CdS-shell thickness is increased to t = 1.29 nm (sample S2) slight shifts in LO frequencies are observed for the core (ω0(1) = 208 cm−1 and shell (ω0(2) = 282.9 cm−1) materials. Furthermore, opposite behaviors between the Δω(i) band widths related to the core and shell materials were confirmed: Δω(1) decreases (Δω(1) = 55 cm−1) whereas Δω(2) increases (Δω(2) = 30 cm−1). In other words, the deviation of Δω(i) with respect to the value of homogeneous bulk material is slight increased for the core (i = 1) and considerably decreased for the shell (i = 2). Indeed, these results confirm a further influence on the core induced by a small growth of interfacial alloy, which is naturally being disregarded for shell due to the relative increasing in the fraction of homogeneous CdS material. From the parameters ω0(i) and Δω(i) obtained for samples S1 and S2 one can intuitively expect that the influence of the interfacial alloy on the core and shell phonon dispersions can be neglected for a nanocrystal with large dimensions (core diameter and shell thickness). Thus, in order to evaluate this effect we have employed the modified phonon confinement model to simulate two Raman spectra (S3 and S4) shown in Figure 5d,e. In Figure 5d, the simulation S3 was obtained by extrapolating the core diameter up to a certain value in which the ωLO1 frequency has matched the bulk CdSe frequency (ωLO1 = 213 cm−1) whereas the shell thickness was fixed to the value obtained for sample S2 (t = 1.29 nm), keeping the same phonon dispersion parameters (ω0(2) = 282.9 cm−1 and Δω(2) = 30 cm−1). Data regarding these simulations were collected on the last two rows of Tables 1 and 2. In the simulation S3, it is interesting to note the obtained core diameter (D = 15.15 nm), with no LO1 phonon confinement and yet the ωLO2 frequency matching the value obtained for sample S2 (ωLO2 = 280.7 cm−1). Figure 5e shows the simulation S4 in which the parameters regarding the core were the same as those of simulation S3 but with a shell thickness extrapolated to the value to which the ωLO2 frequency has leveled to that of bulk CdS (ωLO2 = 302 cm−1). Since the LO phonon dispersion of corresponding bulk material (CdSe or CdS) were recovered while extrapolating either the core diameter (simulation S3) or the core diameter and the shell thickness (simulation S4), we can conclude that for large size dimensions the influence of the interfacial alloy on the phonon dispersion is certainly neglected.

Our findings demonstrated that the modified phonon confinement model introduced in this report is quite useful in order to assess changes in the average phonon dispersion curves in a core−shell nanocrystal induced by the formation of an interfacial alloy. In particular, for the CdSxSe1‑x alloy located at the interface of the as-synthesized CdSe/CdS CS-MSQDs no data are available for the bulk phonon dispersion curves for CdSe- and CdS-like LO modes for comparison with our results. Thus, we shall use the analogy with the AlxGa1‑xAs alloy, which is very similar to the pseudobinary semiconductor CdSxSe1‑x alloy.45 On the basis of this correlation, it has been shown60,61 that besides the redshifts of LO phonon bands with respect to the pure phase their band widths (Δω(i)) are also narrowed due to the alloying effect. This picture is completely consistent with the results obtained for samples S1 and S2 (see Table 2) in which the parameters ω0(i) and Δω(i) are smaller than those related to the pure phases (CdSe or CdS), giving thus an additional support to the conclusions based on the modified phonon confinement model herein introduced. Additionally and in order to evaluate the fit quality, we have performed error estimation by calculating the mean squared error (MSE), which is defined by the following expression:14,62 MSE =

1 N−M

N

∑ (I jfit − I jexperimental)2 j=1

(5)

where N is the number of points in the Raman data, M is the number of varied fit parameters, and I is the Raman intensity at each wavenumber. Thus, in units of the Raman-signal, we have obtained the MSE values of 0.012, 0.011, and 0.011 for the samples S0, S1, and S2, respectively. Indeed, the small MSE values found confirm the excellent quality of the fittings, reinforcing the robustness of our findings. Figure 6 illustrates a small CdSe/CdS core−shell nanocrystal with hexagonal wurtzite structure, in which the CdSxSe1‑x alloy located at the interface is highlighted. In agreement with the modified phonon confinement model, this illustration depicts that each half of CdSxSe1‑x alloy layer contributes to the total

Figure 6. Schematic illustration of a spherical CdSe/CdS core−shell nanocrystal with hexagonal wurtzite structure. Red, yellow and blue spheres represent the Se2−, S2−, and Cd2+ ions, respectively. The CdSecore radius R and the CdS-shell thickness t are highlighted, besides the CdSxSe1‑x alloy at the interface of nanocrystal. 1912



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CONCLUSIONS In summary, an important step toward the production of semiconductor nanocrystals is reported in this study by describing a novel methodology to grow CdSe/CdS core− shell magic-sized quantum dots (CS-MSQDs) directly in aqueous medium, in which the change in the synthesis’ temperature can be successfully used to modulate the CdS-shell thickness. This approach allows one to fabricate different II−VI CS-MSQDs playing not only with the core-size and shellthickness, but also with alloying at the core−shell interface and strain effect, thus providing materials with a wide variety of physical properties. In addition to the successful growth of CdSe/CdS CSMSQDs, with different shell thicknesses, the Raman spectroscopy was deeply explored to provide key information regarding the sample’s dimensions, alloying at the core−shell interface, and strain effect. In order to provide a robust background for the use of the Raman spectroscopy while assessing the CSMSQD sample’s information, a phenomenological Gaussian confinement model was proposed, in which we have presented modifications regarding to the phonon weighting functions for spherical nanostructures aiming to improve the description of confined optical phonons. Our modified model has pointed out the differences between the phonon confinement in a core and in a shell material, so that it can be employed to study spherical bare-core, core−shell, or even core−multishell nanocrystals. Influences of the interfacial alloying and strain effects were also included as new interpretations within the model when describing the Raman spectra of core−shell nanocrystals (or core−multishell nanocrystals). Thus, the introduced modified phonon confinement model also works as an important tool to evaluating changes in the average LO-phonon dispersion induced by an interfacial alloying or strain effects in core− shell nanocrystals. We have tested this modified model in spherical CdSe/CdS CS-MSQDs, where the fitting procedure of Raman spectra allow us to evaluated the size dimensions of nanostructures (core diameter and shell thickness) in excellent agreement with those obtained by AFM images. As a practical conclusion of this study, we note that the strain effects are neglected for CdSe/CdS core−shell nanocrystals with wurtzite structure but should be considered when these nanocrystals are structured in the zincblende-like phase. However, the formation of a mixed CdSxSe1‑x layer at interface of the CdSe/CdS CSMSQDs with wurtzite phase was clearly confirmed by alloy vibrations in the Raman spectra resulting in characteristic signatures in the proposed modified phonon confinement model, namely changes on LO line widths, LO-phonon dispersion curves, and SO/LO intensity ratios. We believe that our modified model can also be successfully employed to investigate other spherical nanostructures.

length of either the CdSe-core radius R, or CdS-shell thickness t. In other words, core and shell are not formed only by the homogeneous materials (CdSe or CdS), but also by the interfacial alloy (CdSxSe1‑x). In this framework, we can clearly understand that the influence of the CdSxSe1‑x alloy on the average phonon dispersions of the CdSe-core and CdS-shell will be the stronger for the smaller dimensions (R or t) of the nanocrystal, in agreement with our previously presented analyses. Data in Table 2 regarding the samples S1 and S2 reveal that the decrease in the ωSO1 frequency is associated with changes in the surrounding dielectric environment induced by the shell thickness increase,39 an effect scaling with the increase in the difference between ωLO1 and ωSO1 phonon frequencies9,63 and certainly influenced by the interfacial alloy. In contrast, under the same condition, the increase in the ωSO2 frequency is also explained by the dielectric continuum approach.16,39 It is worth mentioning that in core−shell nanoparticles with large dimensions one can expect a reduction on the SO intensity induced by the decreasing surface-to-volume ratio. This effect is well represented in simulations S3 and S4 (Figure 5) by the absence of SO mode when the size dimension (diameter core or shell thickness) of core−shell nanocrystal is extrapolated up to a certain value in which the LO frequency equals that of the corresponding bulk material (CdSe or CdS). The SO1 intensity for sample S0 is actually originated only from the pure CdSe bare-core MSQD whereas in samples S1 and S2 both SO intensities (SO1 and SO2) have also contributions from vibrations of the CdSxSe1‑x alloy at the interface of the CS-MSQD. Although we have employed only a Lorentzian function (given by eq 3) to describe the SO intensity in every nanocrystal material (core or shell) a possible change in the SO mode relative intensity with respect to the LO mode can be expected. Hence, as shown in Table 3, we Table 3. Intensity Ratio of the SO Mode with Respect to the LO Mode (SO/LO) for the CdSe-Core and CdS-Shell Materials sample

[SO1/LO1] (±0.02) CdSe-core

[SO2/LO2] (±0.02) CdS-shell

S0 S1 S2

0.05 0.30 0.39

0.39 0.21

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have calculated this SO/LO intensity ratio for both the CdSecore (SO1/LO1) and CdS-shell (SO2/LO2), where the uncertainty was only ∼2% because the excellent accordance between the fitting and the experimental Raman spectra. After the CdS-shell (t = 0.41 nm) growth on sample S1 the SO1/ LO1 ratio enhances to 0.30 which is practically six times as larger than that for sample S0 (0.05), confirming therefore the strong contribution of CdSxSe1‑x alloy to the surface vibrations. The additional increase in the CdS-shell thickness (t = 1.29 nm) in sample S2 leads to a of the SO1/LO1 ratio down to 0.39, which can be explained by the small growth of interfacial alloy (already confirmed). The decreasing of the surface-tovolume ratio is used to clarify, though partially, the decrease on the SO2/LO2 ratio from 0.39 (sample S1) down to 0.21 (sample S2). However, the SO2/LO2 ratio reduction observed for sample S2 is also induced by the larger amount of pure CdS in the shell which in turn enhances the LO2 intensity.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (A.C.A.S.); [email protected] (N.O.D.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support of the Brazilian Agencies CAPES, FAPEMIG, and MCT/CNPq. We also thank the facilities for the AFM measurements at the 1913



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Institute of Physics (INFIS), Federal University of Uberlandia (UFU), supported by the grant “Pró-Equipamentos” from the Brazilian Agency CAPES.

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