Determining the Concentration of CuInS2 Quantum Dots from the Size

May 8, 2012 - Phase dependent visible to near-infrared photoluminescence of CuInS 2 nanocrystals. A. D. P. Leach , L. G. Mast , E. A. Hernández-Pagá...
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Determining the Concentration of CuInS2 Quantum Dots from the Size-Dependent Molar Extinction Coefficient Matthew Booth,† Andrew P. Brown,‡ Stephen D. Evans,† and Kevin Critchley*,† †

School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, United Kingdom Institute for Materials Research, SPEME, University of Leeds, Leeds, LS2 9JT, United Kingdom

‡

S Supporting Information *

ABSTRACT: The size-dependent nature of the molar extinction coefficient of highly photoluminescent copper indium sulfide (CuInS2) quantum dots (CIS-QDs) is presented. We determined the extinction coefficients at both high photon energy (3.1 eV) and at the first excitonic transition band for CIS-QDs, ranging in size from 2.5 nm to 5.1 nm. Both coefficient trends displayed a power-law size dependence for the QDs. These data allow the in situ assessment of the CIS-QD concentration via routine optical absorption measurements, which is an important parameter for many applications. The formation of ZnS on the surface of CIS-QDs dramatically increases the photoluminescence quantum yield, while also blue-shifting the photoluminescent emission. Importantly, we conclude that the concentration of core/shell CIS/ZnS-QD dispersions can be determined using the molar extinction coefficient data of core CIS-QDs. The experimental uncertainties in the solution concentrations determined from the molar extinction coefficient data are in the range of 10%−15%.

KEYWORDS: bionanotechnology, biomedical applications, quantum dots, core/shell nanoparticles, molar extinction coefficient, CuInS2, NIR

1. INTRODUCTION Quantum dots (QDs) have been intensely studied since their discovery,1 and they have many applications: QD-based lasers,2 QD light-emitting diodes,3 light-harvesting systems,4 and biomedical labeling.5,6 QDs can be implemented as fluorescent labels in biological assays and have many advantages over organic dyes. For example, they have a broad excitation band, a narrow emission band, good chemical and optical stability, and they have tunable photoluminescence (PL).7,8 Furthermore, QDs can be doped to provide multimodal properties.9 QDs could be implemented as diagnostic biomedical imaging agents and this potential has been demonstrated by in vivo small animal studies.10 Importantly, QDs can have PL emission in the near infrared (NIR), which provides a method of imaging through tissue using the so-called biological window.11 The most common QDs studied thus far contain toxic heavymetal elements, such as cadmium and lead, raising concerns over potential environmental and health risks and delaying progress toward implementation for biomedical imaging.12−14 To minimize this risk, the growth of ZnS15 and SiO216 shells has been developed as a means to encapsulate the core and © 2012 American Chemical Society

prevent the leakage of toxic elements into the cellular environment. However, a shell cannot completely eliminate the risk and therefore alternative QD materials with similar or better optical properties which also show a reduced potential for toxicity are being sought. Several semiconductors have been investigated as alternatives to CdX (where X = Te, Se, or S), such as Si,17,18 Ge,19,20 InP,21,22 and CuInS2 (CIS).23−27 CIS is emerging as a candidate material for Cd-free QDs, because the dots have a relatively small size, good optical stability, the capacity for dispersion as a stable colloid, and tunable PL emission from the visible to the near infrared (NIR) regions.24 Until recently, CIS-QDs were mostly explored for use in photovoltaic devices, because of a direct band gap (≳1.5 eV)28 ideally suited for optical absorption. As is expected, CIS-QDs have relatively low toxicity, compared to Cd-based QDs,23,24,26 and are therefore strong candidates for biological imaging Received: January 20, 2012 Revised: April 19, 2012 Published: May 8, 2012 2064

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stirring to 120 °C over 20 min. The solution was held at 120 °C for an additional 10 min, until a clear yellow solution was formed. The solution was then heated to 230 °C and the solution gradually changed color from yellow to dark red. After refluxing for a set time (0−90 min), the reaction was quenched by rapidly cooling the flask in a water bath. 2.3. Synthesis of CuInS2/ZnS QDs. CIS-QDs were synthesized as above. Then, 158 mg (0.25 mmol) of zinc stearate was dissolved in 4 mL of ODE and heated to 60 °C until a clear solution was formed. This solution was added to the cooled CIS-QDs (without purification) and was subsequently heated to 220 °C and refluxed for 1 h, after which the reaction was quenched by rapidly cooling the flask in a water bath. 2.4. Purification of QDs. The QD dispersions were diluted by the addition of hexane. The solutions were added to a 1equiv solution of 1:1 chloroform:methanol. The QDs were precipitated via the addition of 10-equiv solutions of acetone, followed by centrifugation (4000 rpm) and decantation. This process was repeated three times. The resulting precipitate was resuspended in hexane. 2.5. Optical Characterization. The absorption spectra were recorded with a Perkin−Elmer Model Lambda35 spectrophotometer. The solution was diluted with hexane until the absorption at the first excitation was ∼0.1. PL spectra were recorded with a Perkin−Elmer Model LS55 spectrofluorometer fitted with a red-sensitive detector calibrated to the manufacturer’s standard. The excitation wavelength was set to 400 nm, and identical slit widths and scan rates (500 nm/min) were used for each solution. 2.6. Atomic Absorption Spectroscopy (AAS). The QD dispersions were dried under vacuum. The residual was digested with aqua regia and then diluted with deionized water to form an aqueous solution for AAS measurements. The AAS measurements were performed using a Perkin−Elmer Model Analyst 100 system. 2.7. Transmission Electron Microscopy (TEM) and Energy-Dispersive X-ray Spectroscopy (EDX). TEM and EDX data were obtained using a FEI/Philips Model CM200 field-emission gun, operated at 197 keV and fitted with a Gatan Imaging Filter (GIF 200) and an Oxford Instruments ultrathinwindow energy-dispersive X-ray spectrometer running ISIS software. QDs in hexane were dried onto holey carbon films on copper support grids (Agar Scientific, Ltd.). Silicon nitride grids were used to perform EDX measurements to determine the composition. 2.8. X-ray Photoelectron Spectroscopy (XPS). QD solutions were dropcast onto gold-coated silicon substrates. Spectra were obtained using a Thermo VG ESCA Lab 250 system with a chamber pressure maintained below 5 × 10−9 mbar during acquisition. A monochromated Al Kα X-ray source (15 kV, 150 W) irradiated the solutions, with a spot diameter of ∼0.5 mm. The spectrometer was operated in Large Area XL magnetic lens mode, using pass energies of 20 eV for highresolution spectra. 2.9. Powder X-ray Diffraction (XRD). QD solutions for XRD analysis were purified and subsequently dried in a glovebox until all solvent was removed. The remaining solid pellet was crushed and the XRD pattern was obtained using a Panalytical Model X’Pert Pro MPD X-ray diffractometer with Cu Kα source and a X’cellerator detector. A continuous scan over a 2θ range from 15° to 90° was performed with an acquisition time of 45 min per sample.

agents. In early studies, the photoluminescence quantum yield (PLQY) of CIS-QDs was comparatively low; however, recent reports have demonstrated that an order-of-magnitude increase in the efficiency can be achieved via the formation of a CdS or ZnS shell, resulting in CIS/ZnS core/shell QDs with up to 80% PLQY.27 For the majority of applications, it is essential that the concentration of QD dispersions can be determined. The most appropriate and widely used method of doing so is by using the Beer−Lambert law.29 This method requires that the molar extinction coefficient (ε) of the QDs be known, and, although the size dependency of the band gap of QDs is wellunderstood, the size dependency of ε is less well-established. A relationship between ε and the oscillator strength of transitions has been postulated; however, few experimental results show a correlation with theoretical predictions, arguably because of the wide variety of methodologies employed. At the first excitonic transition, E1, the molar extinction coefficient for QDs has been shown to follow a power-law size dependence for many materials, including CdTe,29,30 CdS,29,31 CdSe,29,32−34 PbS,35 and PbSe,36 and at short wavelengths, it has been observed that the extinction coefficient is not size-dependent and coincides with the bulk value.34,37,38 Measuring the concentration of a QD solution from the absorption spectrum is generally considered to be more sensitive when performed at photon energies well above the first excitonic transition band edge, E1, since the extinction coefficient at such high energies is larger than that at the band edge.39 In addition, at high energies, the absorption spectrum displays no significant features and can be considered to be size-independent. For CIS-QDs, we choose to consider the extinction coefficient at a photon energy of 3.1 eV (corresponding to a wavelength of 400 nm), so that interference from the organic solvent and the surfactant is low, and absorption by higher-energy transitions can be ignored. Furthermore, a ZnS layer with a band gap of ∼3.5 eV would introduce nonlinearity to the absorption at 350 nm and below. In this study, we focus on obtaining the size dependency of ε for CIS-QDs at E1 as well as at E = 3.1 eV. These data will enable the concentrations of CIS-QD dispersions to be easily determined and will thus facilitate precise bioconjugation techniques to be performed on CIS-QD surfaces. Furthermore, the effect of ZnS shell formation on the optical properties of CIS-QDs is identified and discussed. Finally, we demonstrate that the concentrations of CIS/ZnS-QD dispersions can be determined using the size dependence of ε for “core” CIS-QDs.

2. EXPERIMENTAL SECTION 2.1. Materials. Indium acetate (99.99%), copper iodide (99.999%), dodecanethiol (DDT, >98%), zinc stearate (90%), hexane, and octadecene (ODE, 90%) were purchased from Sigma−Aldrich. High-performance liquid chromatography (HPLC)-grade methanol, chloroform, acetone, nitric acid (70%), hydrochloric acid (32%), and hexane (>97%) were purchased from Fisher Scientific (U.K.). All chemicals were used as received. 2.2. Synthesis of CuInS2 QDs. High-quality CIS-QDs were synthesized based on recently reported methods.27 First, 73 mg (0.25 mmol) of indium acetate, 47.5 mg (0.25 mmol) of copper iodide, and 4 mL DDT were added to a three-necked roundbottom flask fitted with a condenser column. The flask was purged with argon for 30 min and subsequently heated while 2065

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3. RESULTS AND DISCUSSION 3.1. Nanoparticle Characterization. Following synthesis, well-dispersed nanoparticles (NPs) of tetrahedral morphology were visible in the TEM images (see Figure 1a). The identification of 0.195 and 0.320 nm lattice fringes by TEM is consistent with the (220) and (112) planes of the CIS chalcopyrite phase respectively (Figure 1b).

Figure 2. CIS-QD size, as determined from TEM analysis, plotted as a function of the PL maxima. The data are fitted to eq 1 (solid line).

and the PL spectral peak position λPL can be related to the QD size d, through an empirical polynomial function: d = 68.952 − 0.2136λPL + 1.717 × 10−4λPL 2

(1)

Omata et al. compared a more-sophisticated model to experimental data, this model is (also) in good agreement with our data.42 A large, weakly size-dependent Stokes shift was observed for all CIS-QD solutions analyzed (see the Supporting Information), consistent with trap state emission.27 Because of the broad nature of the first excitation feature in the absorption spectrum (Figure 3) of CIS-QDs, the most Figure 1. (a) Low-magnification transmission electron microscopy (TEM) image demonstrating the dispersivity and the uniform size distribution of CuInS2 nanoparticles (NPs) (scale bar = 10 nm). (b) High-magnification TEM image showing the tetrahedral CIS NPs with lattice spacings labeled. The definition of QD size (d (nm)), within this study, is shown (scale bar = 5 nm). (c) X-ray diffraction (XRD) patterns for CIS (solid line) and CIS/ZnS (dashed line); a good correlation with reference data for CIS chalcopyrite (shown as vertical lines on the x-axis (JPCDS File Card No. 75-0106)) is observed with peaks indexed to the Miller indices of this phase.

Powder X-ray diffraction (XRD) confirmed the formation of the tetragonal crystal structure of CIS chalcopyrite, in good agreement with previous reports (see Figure 1c).26,27 Elemental analysis using energy-dispersive X-ray spectroscopy (EDX) in the TEM and X-ray photoelectron spectroscopy (XPS) equipment confirmed the presence of stoichiometric CIS NPs (Table 1). In this study, the reported size of a NP (d) was defined as the length of the triangular projection of the NP in the TEM image (Figure 1b).

Figure 3. The absorption spectrum (solid line) and the corresponding second derivative (dashed line) of a range of CIS-QD dispersions. Bottom to top correspond to QD sizes of 3.0 nm, 3.2 nm, 3.4 nm, 3.6 nm, and 3.8 nm, respectively.

Table 1. Atomic Ratio of Cu:In:S Found in the CIS NPs Determined by EDX and XPS method

Cu

In

S

EDX XPS

1.0 1.1

1.0 1.0

2.1 2.3

reliable method of locating the excitation position is through determining the local minimum of the second derivative of the absorption spectrum (Figure 3). The difficulty in locating the position of E1 from the absorption spectra is obvious. However, when using the second derivatives, the location of E1 is clearer and a size-dependent red shift in the location of E1 is observed. 3.2. Surface Passivation with ZnS. Time-resolved PL studies by Li et al. have reported two separate exciton recombination pathways in CIS-QDs originating from internal and surface defects.27 Surface trap states result in a high proportion of nonradiative recombination events and explain the comparatively low PLQY observed for CIS-QDs. A considerable increase in PL intensity is evident upon surface passivation with ZnS (Figure 4), and this improved PLQY is

Ten (10) samples of CIS NPs were produced by varying the reflux time (see the Experimental Section), and the size distribution of each was determined by TEM analysis of at least 100 NPs per solution; the wavelength of the PL maxima was measured as a function of NP size (see Figure 2). The size dependency of the band gap Eg is well-understood for QDs that display band edge emission, and many QD materials show experimental agreement with theoretical predictions.7 However, CIS-QDs are known to be dominated by trap state emission 2066

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determined from the absorption at 3.1 eV or E1, respectively (see Figure 5).

associated with a reduction in the nonradiative recombination dynamics due to the elimination of surface trap states by the ZnS layer.26,27

Figure 5. The molar extinction coefficient at 3.1 eV (hollow circles) and at E1 (filled circles) plotted against size for CIS-QDs. The data for ε(E1) are fitted empirically to a power law (dashed line, eq 3) and to a semiempirical model (solid line, eq 5). The data for ε(3.1 eV) are also fitted empirically to a power law (dot-dashed line, eq 3). A fit based on the theory presented in refs 39 and 52 (dotted line) displays good correlation with the data for ε(3.1 eV). Note that, for CIS/ZnSQDs, “size” refers to the apparent core size, which is determined by the corresponding PL maxima using eq 1.

Figure 4. Photoluminescence (PL) emission spectra of CIS QDs, before passivation with ZnS (solid line) and after passivation with ZnS (dashed line). The CIS/ZnS-QDs display a significant increase in PL intensity and a blue shift (Δλ).

In addition to this significant increase in PLQY, the formation of a ZnS shell on CIS-QDs caused a blue shift (Δλ) of ∼25 nm for both the PL maxima and the first excitation absorption band (Figure 4), which is consistent with previous reports.25,27 The degree of the shift is dependent on the initial size of the CIS cores and the choice of Zn precursor,25 and this has been postulated to be caused by a cationic exchange of Zn2+ ions with either In3+ or Cu+ ions during ZnS shell formation.25 The XRD patterns for the CIS and CIS/ZnS-QDs provide support for the cationic exchange theory (Figure 1c); the CIS XRD pattern is fitted well by standard data for CIS (JPCDS File Card No. 75-0106), while the CIS/ZnS XRD pattern is fitted better to Cu0.66In0.66Zn0.66S2 (Zn-CIS) than to a combination of CIS and ZnS (not shown). This suggests that there is not a clear interface between the CIS and ZnS layers, more likely a gradated boundary consistent with that expected for core/shell QDs formed by cationic exchange. The Type I band alignment results in confinement of the charge carriers to the CIS cores; the wide band gap of ZnS, relative to CIS, renders the effect on the absorbance at the band gap negligible.43 3.3. Molar Extinction Coefficient. If the molar extinction coefficient at a given photon energy E (ε(E)) is known, then the concentration of QDs in solution can be deduced from the optical absorption of the solution at that wavelength. According to the Beer−Lambert law, the absorbance is the product of the molar extinction coefficient, the concentration of absorbent, and the optical path length. We take two approaches to this method: (i) the determination of ε at a photon energy above the first transition band (E = 3.1 eV) for a range of CIS-QD sizes, ε(3.1 eV); and (ii) the determination of ε at the wavelength corresponding to the first excitonic transition, ε(E1). The location of E1 for a CIS-QD solution was determined from the second derivative of the UV/visible spectra (see the Supporting Information). The solution was then dried and digested in aqua regia, so that the concentration of Cu could be determined using atomic absorption spectroscopy (AAS). Once this and the QD size distribution are established, the original NP concentration can be calculated (assuming stoichiometry of the CIS phase) and, thus, ε(3.1 eV) and ε(E1) can be

Recent studies into the size dependency of ε at the first excitonic transition for various materials have accounted for the size distribution of the QDs in the solution by either calculating the oscillator strength of the transition34 or working with calibrated29 or integrated32 absorbance values. By fitting Gaussian curves to the first excitation feature and measuring the polydispersity Δd via TEM, we have found a linear correlation between the relative standard deviation in QD size distribution (Δd/d) and the standard deviation of the first excitation feature (σm) for five samples, spanning the entire size range considered in this study. We then extrapolated this linear fit to determine the expected standard deviation of the first excitation feature for a monodisperse sample (σ0) where Δd = 0 (see the Supporting Information). We account for the sample size distribution by multiplying the measured absorption Am by the ratio of the sample standard deviation to the projected standard deviation for a monodisperse sample: ⎛σ ⎞ A = A m⎜ m ⎟ ⎝ σ0 ⎠

(2)

where A is the calibrated absorption value to be used in the Beer−Lambert law. The value of σ0 determined for the QD samples in this study is 0.146 ± 0.006 eV. The molar extinction coefficient (in units of cm−1 M−1) of these CIS-QD solutions can be related to the mean size d (nm) of the QDs within the solution by the empirical fitting function ε = xd y

(3)

Similar power law dependencies for other QD materials have been reported.29,32−35 3.3.1. Molar Extinction Coefficient at the First Excitation Transition Energy. The size dependence of the molar extinction coefficient at E1 can be fitted to eq 3 with coefficient x equal to 830 ± 660 and exponent y equal to 3.7 ± 0.6 (see Figure 5): ε(E1) = 830d3.7 2067

(4)

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ε(3.1 eV) = 2123d3.8

The exponent y at E1 is larger than that reported for other QD materials reported (Table 2) and the coefficient x is an order of

As is expected, the value of ε is larger at 3.1 eV than at E1 for a given QD size. The result of this observation is that the determination of solution concentration of CIS-QDs using ε(3.1 eV), as opposed to ε(E1), will provide greater sensitivity and enable lower concentrations to be detected. It is also important to note that the exponent at 3.1 eV should be closer to 3 than the exponent at E1, since the absorption at high energies is less dependent on size and, according to the theory presented in refs 39 and 52 (Figure 5, dotted line), should be proportional to the QD volume. The fact that this is not the case is likely to be caused by the contribution of the broad first excitation band for large QDs at 3.1 eV. 3.3.3. The Effect of ZnS Shell Formation on the Molar Extinction Coefficient. The formation of ZnS shells caused (i) the PLQY to be enhanced and (ii) the PL maxima to be blueshifted, indicating reduced core size (Figure 4). Thus, given the size dependency of the extinction coefficient, the reduction in core size must be taken into account when calculating ε for CIS/ZnS-QDs. The effective core size was determined from the PL maxima position using eq 1 (Figure 2). This method was validated by preparing two CIS samples of different sizes (A:CIS and B:CIS) and passivating them with ZnS until their PL maxima occurred at the same wavelength (Figure 6). The PL spectral peaks of solutions A:CIS/ZnS and B:CIS/ZnS are both centered at 638 ± 1 nm, corresponding to an effective core size of D = 2.6 ± 0.2 nm for both solutions (Figure 6b). Even though both solutions had the same final mean effective core size, there was a difference in initial size and, therefore, they must have different shell thicknesses (Figure 6a, inset).

Table 2. List of Physical Constants and Reported Exponent Relating to the Size Dependency of the Molar Extinction Coefficient for Various QD Materialsa

a

material

μ[me]

aB [nm]

Eg,bulk [eV]

exponent, y

CuInS2 CdTe CdS CdSe PbS

0.1440 0.0943 0.1643 0.1043 0.1343

4.141 7.330 2.448 5.449 1850

1.5328 1.4447 2.4210 1.7447 0.3751

3.7 ± 0.6 2.1229 2.329 2.65;29 332,33 2.3235

Reference sources are shown as superscripts to the values given.

magnitude smaller,29 suggesting a fundamental difference between CIS and other QD materials such as CdTe and CdSe. As the QD size increases, the absorbance of CIS-QDs increases at a faster rate than for both CdSe and CdTe QDs; this is consistent with the fact that the absorption coefficient for bulk CIS (∼5 × 105 cm−1) is an order of magnitude higher than that for bulk CdSe.44 In addition to an empirical fit, the experimentally observed size dependence of ε(E1) can be modeled using a more recently reported size-dependent function:45,46 ε(E1) =

E1

B 2π ΔE1

⎡ ⎢ B =⎢ ⎢ 2π Eg,bulk + ⎣

(

π 2ℏ2 2μR2

)

⎤ ⎥ μR2 ⎥ 2 2 ⎥ π ℏ δR ⎦

(6)

(5)

where δR is the standard deviation of QD radius divided by R. The material-specific constant B is dependent on the momentum matrix element Ep, the average light polarization ap, and the QD refractive index nCIS and, here, was determined to be 1.9 ± 0.1 × 105 eV2 M−1 cm−1 by fitting eq 5 to the molar extinction coefficient data for CIS-QDs in Figure 5. This semiempirical approach has a satisfactory fit to the data at E1; however, it does produce a size-dependent trend that can be fitted to eq 3 with an exponent of 3.2 ± 0.1, which is lower than that determined by the simple empirical fit (eq 4) (i.e., the two fits diverge as the QD size increases). This is due to the fact that the contribution of higher-energy transitions is ignored in eq 5. As the size of the QD increases, the energy levels become less discrete and the energy gap between the first and subsequent transitions decreases, making the approximation less valid and producing the discrepancy between our data (the empirical fit) and the semiempirical model. According to eq 5, the size dependence of the molar extinction coefficient at E1 is related to the magnitude of the QD radius, with respect to the Bohr exciton radius aB. For weak confinement (R > aB), ε will have an R2 dependence on QD size, whereas for QDs in the strong confinement regime (R < aB), ε is expected to have an R4 dependence. This explains why empirical fits of eq 3 to all QD materials give an exponent between 2 and 4 (see Table 2). 3.3.2. Molar Extinction Coefficient at 3.1 eV. The size dependence of the molar extinction coefficient at 3.1 eV can be fitted to eq 3 with coefficient x equal to 2123 ± 1090 and exponent y equal to 3.8 ± 0.3 (see Figure 4).

Figure 6. (a) The absorption spectra of two identically emissive CIS/ ZnS QD solutions with different ZnS shell thicknesses (A: solid line and B: dotted line); the absorption spectrum of B:CIS/ZnS is multiplied by a factor of 1.9 (dashed line) to correct for the difference in concentration from A:CIS/ZnS. (b) PL emission spectra of solutions A:CIS/ZnS (solid line) and B:CIS/ZnS (dotted line); the dashed vertical line depicts the common PL spectral maxima for both samples. 2068

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The effect of surface passivation with ZnS by cationic exchange has been shown to increase the photoluminescence quantum yield (PLQY), while also blue-shifting the PL emission. We have shown that, for the CIS/ZnS-QDs, an effective CIS core size can be extracted from the PL sizing curve and used to determine the concentration of dots in solution in identical fashion to the core CIS-QD methodology. These molar extinction coefficient data determined in this work will enable the concentration of QDs dispersed in solution to be routinely determined prior to bioconjugation or prior to being introduced to the biological environment in cellular uptake media.

The overall CIS/ZnS-QD size (from TEM) and the volumetric ratio of CIS to ZnS (from AAS) were combined to estimate the apparent shell thickness and the “effective” core diameter D. For both solutions, the estimated core sizes were the same as the core sizes predicted from the PL sizing curve for CIS-QDs within experimental error (see the Supporting Information). There is little difference between the absorption profiles of solutions A:CIS/ZnS and B:CIS/ZnS when B:CIS/ ZnS is normalized to A:CIS/ZnS. This supports the assumption that the thickness of the ZnS shell has little effect on the absorption properties of the CIS-QDs or, therefore, on the extinction coefficient. The concentration of QDs in solutions A:CIS/ZnS and B:CIS/ZnS were determined using the Beer− Lambert law in an identical manner to the CIS-QDs but using the effective core size (D), the molar extinction coefficients of the equivalent effective core size CIS-QDs, and the measured absorbance values of the CIS/ZnS solutions (corrected for size distribution). The ratio of concentration between solutions A:CIS/ZnS and B:CIS/ZnS is 1:1.8 (see Table 3), which is close to the factor of 1.9 used to normalize the two absorption profiles (see Figure 6a).

■

S Supporting Information *

Purification techniques, nanoparticle sizing methods, the location of the first excitonic transition, the absorption calibration method, and shell thickness determination have been provided as Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.

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Table 3. Concentration of Solutions A:CIS/ZnS and B:CIS/ ZnS Determined from Absorption Measurements and the Effective Core Diameter Obtained from eq 1 solution

concentration [μM]

A:CIS/ZnS B:CIS/ZnS

11.0 ± 0.8 6.0 ± 0.4

ASSOCIATED CONTENT

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was financially supported by the BHRC (University of Leeds), ESPRC, and the Royal Society. We thank Prof. R. Brydson and Dr. M. Califano for useful discussions.

The main sources of error in the determination of ε at E1 can be ascribed to the sizing methods used and the uncertainty in the location of the first excitonic absorption peak. The nonunity reaction yield of the synthesis requires compositional analysis to be carried out on digested solutions in order to determine the QD concentration in solution independently. Therefore, the purification procedure prior to digestion is vital, because any unreacted Cu precursor remaining in solution during AAS measurements will affect the accuracy of the determined concentration (see the Supporting Information for evidence of effective purification).

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4. CONCLUSIONS For the first time, the size dependency of the molar extinction coefficient of copper indium sulfide (CuInS2) quantum dots (CIS-QDs) has been measured, enabling the concentration of a dispersion of CIS-QDs to be determined through routine optical spectroscopy. At the first excitation transition, the molar extinction coefficient data were fitted to a power function with an exponent (y) of 3.7 ± 0.6. This is higher than the exponents that have been reported for other QD materials. These data were fit to existing theory with good agreement. The size dependency of the molar extinction coefficient at photon energy (3.1 eV) above the first excitation band was also investigated. The exponent varied little as the photon energy was increased from E1 to 3.1 eV (remaining the same, within experimental error) and the value for the extinction coefficient increased for the entire QD size range investigated. Both sets of data enable the concentration of a dispersion of CIS-QDs to be determined through UV/visible spectroscopy once the solution size distribution has been determined by photoluminescence (PL) spectroscopy (or TEM), with the extinction coefficient at 3.1 eV providing greater sensitivity to low concentrations. 2069

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Chemistry of Materials

Article

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