Band Gap Bowing at Nanoscale - American Chemical Society

Mar 19, 2013 - Centre for Modeling and Simulation, University of Pune, Pune 411 007, India. §. Department of Physics, University of Pune, Pune 411007...
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Band Gap Bowing at Nanoscale: Investigation of CdSxSe1−x Alloy Quantum Dots through Cyclic Voltammetry and Density Functional Theory Pravin P. Ingole,†,∥ Ganesh B. Markad,† Deepashri Saraf,‡,§ Laxman Tatikondewar,§ Omkar Nene,§,⊥ Anjali Kshirsagar,*,‡,§ and Santosh K. Haram*,† †

Department of Chemistry, University of Pune, Pune 411007, India Centre for Modeling and Simulation, University of Pune, Pune 411 007, India § Department of Physics, University of Pune, Pune 411007, India ‡

S Supporting Information *

ABSTRACT: The band gap bowing effect in oleic acid-stabilized CdSxSe1−x alloy quantum dots (Q-dots) with varying composition has been studied experimentally by means of cyclic voltammetry and theoretically using density functional theory based calculations. Distinct cathodic and anodic peaks observed in the cyclic voltammograms of diffusing quantum dots alloy are attributed to the respective conduction and valence band edges. The quasi-particle gap values determined from voltammetric measurements are compared with interband transition peaks in UV−vis and PL spectra. Electronic structure for alloy Q-dots is determined computationally with projector augmented wave method for a particular size of dots. The band gap bowing is observed predominantly in the conduction band states. The bowing parameter determined experimentally (0.45 eV) has been found to be in good agreement with the one estimated from DFT (0.43 eV).

1. INTRODUCTION Alloy semiconductor quantum dots are important class of composite materials due to their immense applications in photovoltaics,1,2 in vivo imaging,3 quantum dot sensitized solar cells,4 plasmon wave guides,5 coherent emitter,6 and magnetooptical devices.7 Semiconductor quantum dots (Q-dots) in their strong confined regime display size dependent band structure parameter governed by size quantization effect (SQE). In case of alloy Q-dots, besides SQE, the control over composition provides an additional handle in tailoring their electronic properties.8,9 Thus, a thorough knowledge about the band structure parameters as a function of composition is very advantageous in development of nanotechnology, based on alloy Q-dots. In this regard, studies related to the determination of band edge positions and lattice mismatch in heterostructure, viz. ABxC1−x ternary nanocomposites are presently a subject of immense interest.9−11 The composition-dependent physicochemical properties of such alloys are governed by Vegard’s law, which states that lattice constant of the alloy changes linearly with composition, while band gap often varies nonlinearly.9,12,13 This phenomenon of nonlinearity is termed as band gap bowing effect. The extent of bowing is expressed in terms of bowing constant b. The band gap bowing effect is readily realized by noting composition-dependent band gaps of alloy Q-dots by UV− visible (UV−vis) and photoluminescence (PL) spectroscopy.10,14,15 However, for many applications the information on © 2013 American Chemical Society

absolute values of band edge positions with respect to vacuum are desirable which cannot be obtained by UV−vis and PL spectroscopy techniques. Recently, we demonstrated the use of cyclic voltammetry to study the size-dependent band structure parameters, viz. conduction band edge, valence band edge, and the quasiparticle gap in case of CdSe and CdTe Q-dots (Q-CdSe and QCdTe).16 In the case of CdTe, the voltammetry results were corroborated using density functional theory (DFT).17 The voltammetric analysis has provided better insight about the electronic structure of semiconductor Q-dots compared to the UV−vis and PL methods.16−21 For example, the band gap values obtained by UV−vis and PL measurements have contribution from the Coulombic interaction between electron and hole (Je1,h1), which becomes significant in the strong confinement regime. On the contrary, the electrochemical measurements yield pure quasi-particle gap.16 Cyclic voltammetry is therefore expected to give a more realistic picture of the bowing effect. To the best of our knowledge, a detailed investigation and related data regarding the composition-dependent band gap bowing effect in semiconductor alloy Q-dots and their comparison with a known theoretical model are lacking in Received: January 2, 2013 Revised: March 18, 2013 Published: March 19, 2013 7376

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(XRD) were recorded on the dried samples using a Bruker, D8Advance, X-ray diffractometer (Cu Kα, 40 kV and 40 mA) for 2θ values between 20° and 80°. For the estimation of average size of Q-CdSxSe1−x, transmission electron micrographs (TEM) were recorded using a Philips CM200 transmission electron microscope (200 kV). The samples for TEM measurements were prepared by drop-casting the dispersion of Q-CdSxSe1−x in toluene onto a carbon precoated copper grid. Elemental analysis (EDAX) was carried out using an EOL JSM-6360 electron microscope. 2.1.4. Voltammetric Characterization. The voltammetry was carried out at room temperature in an inert atmosphere. The measurements are performed with the help of Metrohm Autolab PGSTAT 100 electrochemical workstation having a three-electrode system consisting of glassy carbon (3 mm diameter), Ag wire, and Pt wire as working, quasi-reference, and counter electrodes, respectively. An indigenous vacuum electrochemical cell having water circulation jacket was used.16 Weighed amounts of TBAP crystals were first added (net concentration 100 mM) into the cell, and the system was evacuated using rotary pump at 0.1 Torr. The temperature of the cell was raised to ∼80 °C by using circulating bath and TBAP was dried in situ for about 2 h. The cell was then brought down to room temperature, and the pressure of the cell was restored by dry Ar gas. Into it, a mixture of DMSO (4 mL) and toluene (1 mL) was injected through silicone septum, and the solution was stirred with a magnetic stirrer under an inert atmosphere. The background voltammograms were recorded in such a solution. For CV measurements on Q-dots, QCdSxSe1−x premixed with a small quantity of DMSO/toluene mixture was injected into the cell through silicone septum. The net concentration of the Q-dots was maintained to be 1 mg/ mL. The cyclic voltammograms were recorded on such solutions. All the potentials were calibrated to the reference potential of normal hydrogen electrode (NHE) or vacuum level. For that, a ferrocene/ferrocenium couple was used as an internal standard.22 2.2. Theoretical Section. Bulk CdS and CdSe semiconductors occur in nature, in two crystallographic forms, viz. wurtzite and zinc blend (ZB), of which the ZB geometry is lower in energy. Both forms have direct band gaps at Γ point of the Brillouin zone (BZ). Moreover, it has been reported that these structures in their nanoform possess an identical geometry as that of their bulk counterparts, with slight variation in the lattice parameters.17,23,24 Experiments carried out in the present work also support these findings. Hence, in the present theoretical work, Q-CdSxSe1−x are considered as atom-centered ZB fragments. The algorithm used to generate the Q-dots having experimental sizes and varying compositions is explained in the Supporting Information. 2.2.1. Computational Details. Electronic structure calculations based on density functional theory (DFT) were carried out using accurate frozen-core plane augmented wave (PAW) method as implemented in Vienna Ab-initio Simulations Package (VASP).25 The exchange-correlation energy functional as given by Perdew, Burke, and Ernzerhof (PBE) was used, as it provides descent estimates for electronic properties. The valence electronic configurations used for Cd, Se, and S are 5s24d10, 4s24p4, and 3s23p4, respectively. Cut-off energy for the plane wave expansion is set to 280 eV with self-consistent convergence threshold of 10−4 eV. Occupation numbers are treated according to the Gaussian scheme with a broadening of 0.001 eV. A sufficiently large unit cell, periodically repeated in

the literature. For this purpose, oleic acid stabilized CdSxSe1−x alloy Q-dots (Q-CdSxSe1−x) having fixed size but with varying composition have been chosen for this study. These samples were characterized by UV−vis, PL, and cyclic voltammetry measurements to provide band structure parameters, quasiopt particle gap (εqp gap), and optical band gap (εgap) as a function of composition (x). To understand the experimental results, density functional theory (DFT) based calculations have been performed for nonstoichiometric clusters using projector augmented wave (PAW) method. To render the surface inert, the surface sites have been passivated with fictitious hydrogen atom (H*) as terminating ligands. The computed HOMO and LUMO positions and the energy gap (εDFT gap ) as a function of composition have been found to be in good agreement with the one obtained from CV measurements. In building the theoretical model for computation, we have used the observational data about the geometric structures (phase and lattice constants) of Q-dots. For direct comparison of theoretical results with experimental data, certain calibration runs are carried out for bulk structures of CdSxSe1−x for varying values of x. These are later applied to nano sizes.

2. METHODOLOGY 2.1. Experimental Section. 2.1.1. Materials and Solutions. Cadmium oxide (99.50%, s.d. Fine Chemical Ltd.), oleic acid (OA, min. 65%, s. d. Fine Chemical Ltd.), tri-noctylphosphine (TOP, 90%, Aldrich), octadecene (ODE, 90%, Acros Organics), selenium powder (99.50%, Laba Chemie), sulfur powder (99.99%, Merck), and dimethyl sulfoxide (DMSO, Spectrochem, dry solvent) were used as received. Toluene (Merck, 99.99%) was dried over calcium hydride (CaH2), distilled twice, and stored over 4 Å molecular sieves. Tetrabutylammonium perchlorate (Acros Organics, 99%) was recrystallized from dry methanol and stored in a vacuum desiccator. 0.1 M sulfur stock solution was prepared by stirring 0.16 g of sulfur in 50 mL of ODE at 80−100 °C, for several hours, until complete dissolution. 0.1 M selenium stock solution was prepared by dissolving 0.395 g of Se powder in 1.25 mL of TOP with the help of sonication. This solution was further diluted to 50 mL in ODE. 2.1.2. Preparation of Alloy Q-Dots. Oleic acid capped CdSxSe1−x Q-dots with varied compositions are prepared by the following method suggested by Swafford et al.9 Typically, 64 mg of CdO, 0.6 mL of OA, and 2.0 mL of ODE were mixed with constant stirring at 315 °C under an Ar atmosphere, until the solution turned colorless, suggesting the formation of cadmium oleate. To prepare varied composition of Q-dots of CdSxSe1−x (x = 0.0, 0.15, 0.36, 0.63, 0.79, and 1.0), the mixture of 2x mL of 0.1 M sulfur stock solution and 2(1 − x) mL of 0.1 M selenium stock solution was swiftly injected into the reaction vessel together at 315 °C with a constant vigorous stirring. After a while, the temperature of the vessel was maintained at 290 °C, and the nanoparticles were allowed to grow to the desired size. The products were flocculated by adding 1:1 mixture of 1-butanol and ethanol as an antisolvent. The floc was centrifuged, washed several times with dry methanol, and dried under vacuum. 2.1.3. Material Characterization. For the routine characterization, UV−vis spectra were recorded using a Shimadzu UV1650PC spectrophotometer. Steady state photoluminescence (PL) spectra were recorded at room temperature with the help of a Shimadzu RF-5301PC spectrophotometer, within a wavelength range of 200−800 nm. Powder X-ray diffractograms 7377

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alloys with concentration at the nanoscale. DFT is known to underestimate the band gaps due to the underneath approximations used for the exchange-correlation energy functional. To facilitate the comparison of DFT results with experiments performed at room temperature, we employed scissor operator method. For this, we performed calculations for bulk CdSxSe1−x counterparts with corresponding x values for the Q-dots. Scissor operator is used to match the theoretical band gap with the experimental value for the bulk material by rigidly shifting the conduction band maximum. This shift is then used to correct the HOMO−LUMO gap for the Q-dots as described in eq 3.

all three directions, is chosen so that the minimum distance from the cluster boundary to the unit cell boundary is 0.6 nm in each direction. Thus, two cluster edges are separated by 1.2 nm, and the interaction between two neighboring clusters is found to be negligible (as indicated by the charge density of the cluster which dies down at the cell boundaries). This observation allows us to assume that our computationally generated model system represents a free-standing Q-dot. The small Brillouin zone (BZ) resulting due to a large unit cell is sampled using only the Γ point, thereby reducing the cost of computation. Dangling bonds at the surface of bare clusters make them highly reactive and therefore susceptible to growth and coalescence. In actual system, dangling bonds on the Q-dot surface are passivated by organic ligands as capping agents. To mimic these conditions with effective and computationally economic modeling, surface of the Q-dots is passivated using the scheme suggested by Chelikowsky et al.26 The simplistic and computationally inexpensive model potentials make this passivation technique more efficient for II−VI semiconductor Q-dots as compared to other alternative methods.27−29 In this method, two types of fictitious hydrogen atoms (H*) having nonintegral atomic number (Z) are used to complete the requisite coordination of surface atoms. H* species, having Z > 1, are attached to the cations, and those having Z < 1 are attached to the anions maintaining the charge neutrality of the system. Chelikowsky et al. have also shown that for II−VI semiconductors the specific values of Z = 1.5 (for H* attached to the cation) and Z = 0.5 (for H* attached to the anion) open up maximum HOMO−LUMO gap.26 We have shown in our earlier work that passivation locks the symmetry for threedimensionally confined structures.30 Hence, no structural minimizations are carried out for these passivated ZB fragments having experimental diameter (∼4.4 nm). The lattice constants used to generate the ZB fragments for theoretical calculations on Q-dots are the ones obtained from our experimental XRD data. We have also calculated the total energy for a Q-dot of radius 1.6 nm by varying the lattice constant. The value of lattice constant obtained for minimum value of the total energy, matches with the experimentally observed lattice constant for each value of x. Ternary semiconductor alloys, in bulk, are characterized by Vegard’s law, which states that the lattice constant changes linearly with composition:13 aCdSxSe1−x = xaCdS + (1 − x)aCdSe

εgcorrected(QD) = εgDFT(QD) + εgexp(bulk) − εgDFT(bulk) (3)

Here, εcorrected (QD) is the corrected DFT-band gap for a Q-dot g which can be directly compared with experiments and εDFT g (QD) is the band gap obtained from DFT calculations DFT for a Q-dot for same x value. εexp g (bulk) and εg (bulk) are respective experimental and DFT calculated band gaps of the corresponding composition x in the bulk. Experimental band gap values for a composition x are obtained by applying Vegard’s law (see eq 2) using standard experimental band gap = 2.42 eV values for pure systems at room temperature (εCdS g = 1.74 eV)30 with the value of b = 0.29. To determine and εCdSe g εDFT g (bulk), we performed electronic structure calculations for bulk CdSxSe1−x (0 ≤ x ≤ 1.0). The lattice constants for ZB structures of pure CdSe and CdS (aCdSe = 6.050 Å and aCdS = 5.835 Å) are chosen from the standard experimental data.32 The BZ for these unit cells is sampled with a Monkhorst−Pack grid of regular k-mesh of 6 × 6 × 6. The lattice constants for the intermediate compositions, aCdSxSe1−x, are then calculated with the help of Vegard’s law (see eq 1) using the above values of aCdSe, aCdS, and b = 0.29. To generate compositional variance, 3 × 3 × 3 supercells are constructed from standard ZB unit cell and S atoms are randomly substituted at Se site. The BZ for these supercells is sampled by the Monkhorst−Pack grid of regular k-mesh of 2 × 2 × 2. The cutoff energy used in plane wave expansion for bulk structures is 315 eV, and the selfconsistent convergence criterion of energy is set to 10−5 eV.

3. RESULTS AND DISCUSSION 3.1. Characterization of CdSxSe1−x Q-Dots. As described in the Experimental Section, Q-CdSxSe1−x with varied x were prepared, extracted from the mother liquor, purified, and isolated in the form of solid products. From the EDAX analyses (refer to Supporting Information) on these samples, the values of x were estimated to be 0.0, 0.15, 0.36, 0.63, 0.79, and 1.0, which are close to the starting ratios of the precursors, viz. 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0, respectively. Figure 1 depicts the absorption and corresponding emission spectra recorded on these redispersed products in toluene. The overall narrow full width at half-maxima (fwhm) in absorption and emission spectra for all the samples suggests a narrow particle size distribution.8 A distinct shift in absorption maxima from x = 0.0 (CdSe, 564 nm) to x = 1.0 (CdS, 413 nm) is attributed to the variation of optical band gap energies with sulfur/selenium mole ratio. By fitting the values of absorption maxima in sizing curve suggested by Yu et al.,33 the average particle sizes for Q-CdS and Q-CdSe are found to be ca. 4.0 nm for both CdS and CdSe Q-dots.

(1)

where aCdSxSe1−x is the lattice constant for a particular composition of the alloy defined by x. aCdS and aCdSe are lattice constants for bulk CdS and CdSe, respectively. Further, other physical properties such as band gap often vary nonlinearly, and to a first approximation, the variation is quadratic, as described below: εgCdSxSe1−x = xεgCdS + (1 − x)εgCdSe − bx(1 − x)

(2)

xSe1−x εCdS g

Here, is the band gap of a particular composition of the bulk alloy defined by x, εCdS and εCdSe are the band gaps of g g pure bulk CdS and bulk CdSe, respectively, and b is known as bowing parameter which defines the extent of nonlinearity in the variation of band gaps with composition. The value of b for bulk CdSxSe1−x alloy systems is reported in the literature to be b = 0.29.9,31 Our experiments suggested that CdSxSe1−x Q-dots also follow Vegard’s law; i.e., even at nanoscale, a linear relation is observed for variations in nearest-neighbor distances. It is our aim to study the nonlinearity in the electronic properties of 7378

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neous alloy rather than a physical mixture of CdS and CdSe Qdots, which otherwise would have shown a superposition of the reflections from pure CdS and pure CdSe in the XRD.5 For the estimation of the size of these nanocomposites, low-resolution transmission electron micrographs are recorded on these samples (refer to Supporting Information). The formation of nearly spherical Q-dots with an average diameter of 4.5 ± 0.5 nm seen in the micrographs is in close agreement with the size estimated using the sizing curves suggested by Yu et al.29 3.2. Cyclic Voltammetric Investigations on CdSxSe1−x Q-Dots. In the case of both Q-CdS and Q-CdSe, use of cyclic voltammetry (CV) analysis has been successfully demonstrated in the determination of “electrochemical band gap” as a function of size.16,17,36 Herein, CV have been used to investigate the composition-dependent shift in the band structure parameters of Q-CdSxSe1−x Figure 3A shows a representative CV recorded on the dispersion of CdS0.79Se0.21 Q-dots at the scan rate of 100 mV/s. The controlled

Figure 1. UV−vis (solid line) and photoluminescence (PL) spectra (dotted line) recorded on dispersion of Q-CdSxSe1−x in toluene for varied compositions: (a) CdSe, (b) CdS0.15Se0.85, (c) CdS0.36Se0.64, (d) CdS0.63Se0.37, (e) CdS0.79Se0.21, and (f) CdS.

The PL spectra recorded on these samples are also included in Figure 1. A red-shift of ca. 5−20 nm with respect to the corresponding absorption maxima was observed. Increase in the sulfur percentage has been accompanied by large a Stokes shift as well as increase in the fwhm in the emission spectra. These observations were attributed to the deep-trap-state emission caused by trapping of the photoexcited hole to unpassivated surface anion states.34,35 During the formation of such alloy Qdots, the nucleation kinetics is different from growth kinetics. This leads to a sulfur-rich surface9 which is manifested as increase in the mole fraction of sulfur, resulting in broadening of peaks.9 Figures 2a and 2f depict the X-ray diffractograms (XRD) recorded for Q-CdSe and Q-CdS, respectively. The observed

Figure 2. Powder X-ray diffractograms recorded on Q-CdSxSe1−x for varied compositions: (a) CdSe, (b) CdS0.15Se0.85, (c) CdS0.36Se0.64, (d) CdS0.63Se0.37, (e) CdS0.79Se0.21, and (f) CdS. The dotted vertical lines are just eye guides. Inset shows a plot of lattice spacing for three peaks marked as (I), (II), and (III) in XRD vs mole fraction of sulfur.

reflections are fitted faithfully with the cubic phase (JCPDS-751546 and JCPDS-19-191) of bulk CdS and CdSe, respectively. Parts b, c, d, and e are the XRD recorded for x = 0.2, 0.4, 0.6, and 0.8, respectively. All these diffractograms are again fitted faithfully in the cubic phase with systematic shift in the 2θ as a function of composition. The inset of Figure 2 shows a plot of lattice spacing as a function of mole fraction S/(S + Se), depicting a linear change in lattice spacing as composition changes from CdSe to CdS. The observed trend is in accordance with the predictions of Vegard’s law.12 The linear change in lattice spacing suggests the formation of homoge-

Figure 3. (A) Cyclic voltammograms recorded on Q-CdS0.79Se0.21 dispersions in DMSO/toluene mixture (black line). The controlled run (without Q-dots) is shown as a red dotted line. The scan rate is 100 mV s−1. The electron transfers through band edges are marked as C1 and A1. (B) Cyclic voltammograms recorded on CdS0.79Se0.21 alloy Q-dots at different scan rates, ranging from 20 to 500 mV/s. (C) Cyclic voltammograms recorded on CdSxSe1−x alloy Q-dots for varied compositions: (a) CdSe, (b) CdS0.15Se0.85, (c) CdS0.36Se0.64, (d) CdS0.63Se0.37, (e) CdS0.79Se0.21, and (f) CdS. The scan rates are 50 mV/ s. 7379

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measurements on background electrolyte without Q-dots are superimposed for comparison. Prominent cathodic and anodic peaks, marked as A1 and C1, are observed at potentials −2.13 and 0.88 V, respectively. The potential difference of 3.01 V between these two peaks is found to be close to the one with the band gap of 3.04 eV obtained from the absorption maxima in the UV−vis spectrum (refer to Table S1 of Supporting Information). Irreversibility of the voltammogram, i.e., absence of complementary anodic and cathodic peaks, is attributed to the chemical reaction after electron transfer on the Q-dots surface.16,18 Besides these peaks, the interband cathodic and anodic peaks, in the potential range −0.5 to −1.0 V, are also legible. Perhaps, these could be the redox processes of the products formed after the charge transfer. However, the exact nature of the products could not be estimated.16,18 Figure 3B shows a CV recorded on the dispersion of CdS0.79Se0.21 Q-dots at the different scan rate; the corresponding inset shows plot of peak current values at C1 and A1 positions vs square root of the scan rates. The fitting of data in the linear regression suggests that the charge transfer is diffusion controlled.22 Figure 3C shows an overlay of CVs recorded on QCdSxSe1−x with x = 0.0 (CdSe) to x = 1.0 (CdS) at the scan rate of 50 mV/s. All the samples show similar features, i.e., irreversible, cathodic and anodic peaks separated by a gap, which increases with increase in sulfur mole fraction. From the separation between these two peaks electrochemical band gaps as a function of composition are obtained.18 These values are in good agreement with the optical band gap values, determined from UV−vis spectra (refer to Table S1). Since the electron transfer is mediated through the conduction and valence band states, the cathodic and anodic peaks seen in the voltammograms mark the respective band edge positions of Q-CdSxSe1−x. These values of band gap for varied composition of S and/or Se are enlisted in Table S1. To the best of our knowledge, there are no reports in the literature dealing with the estimation of the band offsets (i.e., band edge positions) for the CdSxSe1−x alloy Q-dots with varying composition through voltammetry. 3.3. DFT Calculations. DFT-based calculations are performed for H*-passivated CdSxSe1−x alloy Q-dots as explained in section 2.2.1. In order to estimate the effect of actual geometries of S atoms in the alloy Q-dots, we performed DFT calculations for smaller sizes (diameter ∼2 nm) of alloy Q-dots, with six different random geometries generated by randomly substituting S atoms at Se sites, for the same value of x = 0.15. The values of the HOMO−LUMO gaps and the total energy are found to be same within the numerical accuracy of the calculations, irrespective of the actual site occupation of the S atoms within the alloy cluster. We have therefore concluded that if the alloy nanostructure is really homogeneous, then the single particle levels and the total energy are not crucially dependent on the actual geometric positions of the S/Se atoms but depend on the value of x. For Q-dots of diameter ∼4.4 nm, we have carried out calculations for two different geometries of S atoms for each value of x (see Figure 4C). We observe that for the same composition the total energy and the band gap of the Q-dot are invariant, i.e., do not depend on the random positional changes (see Figure 4A,B) of S and Se atoms. 3.4. Band Gap Bowing. Vegard’s law has been applied to explain the nonlinear behavior of physical properties like optical band gap with change in composition for the semiconductor alloy nanomaterials.9,11,13 Since the optical band gap obtained from UV−vis spectroscopy is reported to agree with the electrochemical band gap determined from voltammetry,16−19

Figure 4. (A) and (B) are illustrations for two different random configurations of unpassivated Q-CdS0.15Se0.85, (diameter ∼4.4 nm). Blue, magenta, and yellow balls represent Cd, S, and Se atoms, respectively. The 3-fold symmetry of the structure with respect to the central Cd atom is legible in the illustration. (C) Comparison of theoretical band gaps vs composition for the configurations shown in (A) and (B).

in principle, Vegard’s law could also be applied to the voltammetrically estimated band structure parameters. The plot of electrochemical band gap of CdSxSe1−x Q-dots (x = 0.0−1.0) as a function of S/(S + Se) mole fraction is shown in Figure 5. The band gap continuously increases nonlinearly from one end member (CdSe) to the other (CdS), indicating band gap bowing. It can be observed that electrochemical band gap shows larger bowing effect as compared to the optical band gap. The bowing constant determined from electrochemical band gap values is 0.45 eV. Voltammetric measurements are much more sensitive to the surface electronic structure than the optical measurements which are mainly characterized by the bulk electronic structure, and as evidenced from PL measurements, the sulfur enrichment at the Q-CdSxSe1−x surface results in trap states. Thus, at higher surface sulfur concentration an interaction between localized A1 symmetry states from more electronegative sulfur atoms and extended states of semiconductor matrix is expected to dominate.12 It may result into the higher bowing observed in the case of voltammetry. Figure 5 shows the composition dependence of band offsets in QCdS x Se 1−x at ambient conditions. For the first time, voltammetric data have been used to study the band gap bowing in semiconductor alloy Q-dots. Further investigations on such alloy nanosystems may result in better understanding of the band gap bowing effect. For example, it may include changing the cations in order to monitor the trend in band edge positions and hence band gap bowing effect. The calculated band gaps (εDFT g (QD)) and HOMO−LUMO levels for six different compositions (chosen close to experimental values) are plotted in Figure 5A,B (the numerical values are enlisted in Tables S1 and S2). In Figure 5A, the optical band gaps obtained from UV−vis spectra, quasi-particle band gaps determined from CV measurements, and the corrected DFT band gaps (using eq 3) are plotted as a function of composition x. The band gaps obtained from DFT calculations show a trend similar to those obtained from CV 7380

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value of band gap obtained in CV measurements. Thus, the quadratic nature of electronic properties like band gap is wellestablished even for alloy Q-dots, in agreement with experiments for the measured size. Table 1 depicts comparison of theoretical values of bowing constants for Q-CdSxSe1−x with experimental results. The variations in the band gaps with respect to composition are reflections in the variation of HOMO and LUMO energy levels. In order to compare these variations in experimental and theoretical values, we shifted LUMO rigidly for each composition x of Q-CdSxSe1−x by the corresponding amount DFT (εexp g (bulk) − εg (bulk)). Figure 5B shows the plot of valence and conduction band edge positions of the alloy Q-dots, obtained from CV measurements and DFT calculations, as a function of composition (refer to Table S2 for numerical values). The graphs clearly show that the values of HOMO obtained from DFT calculations match reasonably well with those measured electrochemically. Although the values of LUMO from DFT and CV measurements do not match exactly, they follow a similar trend, as evident from Figure 5B and values in Table S2. Swafford et al.9 have performed experiments for various sizes of Q-CdSxSe1−x. They considered the bowing constant b to be dependent on the diameter d of the Q-dot and the band gap to be dependent on d and composition x of the alloy. The change in band gap due to quantum confinement has been separately dealt with, based on the effective mass approximation model proposed by Brus.37 This approach had led to the conclusion that bowing constant b for Q-dots is approximately the same as that for bulk. In the present work, no such attempt is made. We report b for a given size of alloy Q-dots, and we find that it is different from bulk. Earlier reports on band gap bowing in alloy structures have attributed the underlying nonlinearity to (i) change in lattice constant, (ii) difference in the electronegativity of the anions, and (iii) changes in the anion−cation bond lengths and bond angles in order to accommodate the differently sized constituents. Since the electronegativity mismatch for S and Se atoms is not large, the HOMO and LUMO levels change almost continuously with change in the composition. We have carried out calculations for Q-dots for varying lattice constants as observed in our synthesized samples. Thus, the effects expected from (i) and (iii) above have been indirectly taken care of in the calculations. We would like to point out that we have not relaxed the geometries; hence, the local changes in the anion−cation bond lengths/bond angles are not accounted for. However, within the given geometries generated based on experimental observations, complete electronic self-consistency has been achieved allowing for mixing of localized states of the impurity atoms with the comparatively extended states of the host Q-dots. Considering the proposed variation in the band gap as per Vegard’s law (eq 2) and using the band gap values for the

Figure 5. Comparison of experimental and theoretical results showing variation in (A) the band gaps and (B) HOMO and LUMO levels for Q-CdSxS1−x as a function of composition. Curve fittings in the secondorder polynomials in x are shown as dashed lines (by Vegard’s law, eq 2). Vegard’s law based band gap for the bulk CdSxS1−x (marked as “▽” in panel A) are also plotted for comparison. Using this data set, the bowing constant values for the Q-CdSxS1−x system are found out to be 0.45 eV (experimental) and 0.43 eV (theoretical).

measurements. However, UV−vis spectra yield a different trend in the band gap variation with respect to composition. Optical measurements take into account the excitonic binding effect, which may result in the observed deviation in bowing. The band gap values have been used to fit a quadratic polynomial in x, εg = bx2 + b′x + b″ (as required by Vegard’s law, eq 2). As expected, the intercept of this curve on Y-axis (b″ ∼ 2.14 eV) is close to the value of εCdSe (QD) for x = 0 for Q-dot of size ∼4.4 g nm. From the coefficient of x2 (b), the bowing constant is found to be 0.43, in excellent agreement with the experimental result, viz. b = 0.45. Bowing constants and other fitted parameters from CV measurements as well as theoretical calculations are listed in Table 1. It is clear that these bowing constants for Q-dots are higher than the bowing constant in bulk (b = 0.29), indicating higher nonlinearity between band gap and composition (see Figure 5A). From fitted coefficients, the value of εCdS g (QD) for the particular size of the Q-dot is estimated to be ∼2.65 eV, again in excellent agreement with the

Table 1. Comparison of Theoretical Values of the Coefficients of Fitted Quadratic Polynomial εg = bx2 + b′x + b″ for QCdSxSe1−x with the Experimental Resultsa CV measurements theoretical

b (eV)

b′ (eV)

εCdSe (QD) = b″ (eV) (for x = 0) g

εCdS g (QD) = b + b′ + b″(eV) (for x = 1)

0.45 0.43

0.08 0.08

2.55 (2.57 ± 0.02) 2.14 (2.13)

3.05 (3.00 ± 0.02) 2.65 (2.66)

Second column gives the values of the bowing constants while columns four and five respectively correspond to band gaps of pure CdSe(x = 0) and CdS(x = 1). The values of band gaps obtained from CV measurements and DFT calculations are shown in parentheses. a

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extreme cases namely, pure CdS and pure CdSe Q-dots, the band gap does not attain an extremum value in the range 0 ≤ x ≤ 1.0. This fact agrees with our experimental and theoretical results. As is evident from Figure 5, change in band gap with composition results mainly from the corresponding change in LUMO level with x. We do not observe any downward shift of LUMO/conduction band states and decrease in band gap for both Q-dots and bulk systems. Band gap continuously increases from CdSe to CdS. States near the HOMO in Q-dots mainly comprise of the anion p states while those near LUMO are hybrid states formed from Cd s states and anion p states. The hybridization inversely depends on the difference in energies of the Cd s and anion p states. Although S and Se are isovalent, there is appreciable difference in the atomic orbital energies of their p states, Cd s being closer to S p levels. The effect is more dominant for large x values. Wei et al.29 have calculated bowing coefficient b for bulk CdSxSe1−x and have studied the effect of cation d states on valence band offsets. In the present work, we find that Cd d states are quite deep and anion−cation coupling is weak. Thus, the HOMO levels are not significantly affected with changing x. However, in bulk, Wei et al.31 have found large valence band offsets and small conduction band offsets which is not observed by us for alloy Q-dots. LUMO levels are more affected indicating larger Cd s and anion p hybridization for Q-dots than in bulk. Moreover, the size difference for S and Se atoms is not large; hence, the changes are comparatively small and more significant for larger x values only.

∥

P.P.I.: School of Chemical Sciences and Pharmacy, Central University of Rajasthan, NH-8, Kishangarh, Dist. Ajmer, Rajasthan 305801, India. ⊥ O.N.: Department of Metallurgical Engineering and Materials Science, Indian Institute of Technology, Bombay, Powai, Mumbai 400076, India. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are thankful to the CNQS, University of Pune, for the XRD facility and financial assistance. G.B.M. thanks BARCPune University collaborative Ph.D. program. A.L.K. is thankful to C-DAC for HPC facility and BCUD, University of Pune, for the financial support.

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4. CONCLUSIONS We have successfully determined the band gap values and band edge positions in CdSxSe1−x alloy Q-dots for the varied composition through cyclic voltammetry and density functional calculations. It is observed that the valence band edge does not change appreciably for all the values of x, while the conduction band edge increase in energy from −2.38 to −2.81 eV, indicating that the bowing effect of band gap in anionsubstituted alloys is mainly contributed by the conduction band states. Voltammetric data show that the electrochemical band gap (Eg) values are sensitive to the S mole fraction. Optical band gap as determined from UV−vis is in fair agreement with that of the electrochemical band gap. DFT-based band gap values for bulk and Q-dots show continuous increase with the composition from CdSe to CdS, which is in agreement with eq 1. No downward shift is observed for LUMO with increasing x while HOMO shows a nominal rise and then a downward shift. The bowing coefficient b is found to be composition independent.

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ASSOCIATED CONTENT

S Supporting Information *

(I) TEM images, (II) elemental analysis, (III) details for generation of alloy quantum dot (Q-dot) geometry, and (IV) comparison of theoretical band gaps and HOMO, LUMO values of CdSxSe1−x Q-dots with experimental results. This material is available free of charge via the Internet at http:// pubs.acs.org.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*Ph +91 20 25691373; Fax +91 20 25691728; e-mail haram@ chem.unipune.ac.in (S.K.H.), [email protected] (A.K.). 7382

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