Size-Dependent Photovoltaic Performance of CuInS2 Quantum Dot

Nov 6, 2014 - The ratio of Cu/In in the crystallites is a major contributing factor in creating ... the emission quantum yield, emission band position...
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Size-Dependent Photovoltaic Performance of CuInS2 Quantum Dots Sensitized Solar Cells Danilo H Jara, Seogjoon Yoon, Kevin G. Stamplecoskie, and Prashant V. Kamat Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/cm5040886 • Publication Date (Web): 06 Nov 2014 Downloaded from http://pubs.acs.org on November 9, 2014

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Size-Dependent Photovoltaic Performance of CuInS2 Quantum Dots Sensitized Solar Cells. Danilo H. Jara, Seog Joon Yoon, Kevin G. Stamplecoskie, and Prashant V. Kamat1,*

Radiation Laboratory, Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556

*Address correspondence to this author [email protected] 1

Department of Chemical and Biomolecular Engineering

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ABSTRACT The optical and electronic properties of quantum dots (QDs) which are drastically affected by their size have major impact on their performance in devices like solar cells. We now report the size dependent solar cell performance for CuInS2 QDs capped with 1-dodecanethiol. Pyramidal shaped CuInS2 QDs with diameter between 2.9 nm and 5.3 nm have been synthesized and assembled on mesoscopic TiO2 films by electrophoretic deposition. Time resolved emission and transient absorption spectroscopy measurements have ascertained the role of internal and surface defects in determining the solar cell performance. An increase in power conversion efficiency (PCE) was observed with increasing size of QDs, with maximum values of 2.14 and 2.51% for 3.9 and 4.3 nm size particles, respectively. The drop in PCE observed for larger QDs (5.3 nm) is attributed to decreased charge separation following bandgap excitation. Since the origin of photocurrent generation in CuInS2 QDSC arises from the defect dominated charge carriers it offers the opportunity to further improve the efficiency by controlling these defect concentrations.

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KEYWORDS: Copper Indium Sulfide, Quantum Dots, Quantum Dots Solar Cells, Transient Absorption Spectroscopy, Size-Dependent Quantum Dots.

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INTRODUCTION Quantum dots solar cells (QDSCs) remain a promising candidate for the development of next generation photovoltaics due their unique properties such as tunability of the band gap,1 high absorption coefficient (105 cm2),2,3 multiple exciton generation (MEG),4 hot electron injection,5 facile synthesis and low cost of fabrication.6 Multinary quantum dots (QDs) have been the focus of recent investigations7 as an alternative to conventional CdSe, PbS and CdTe QDs. CuInS28–13 and CuInSSe14–16 have emerged as good candidate for the design of sensitizes in QDSCs achieving a certified photovoltaic performance of 6.66 % and 5.13 %, respectively.9, 16 CuInS2 has a bandgap of ~1.5 V (bulk material) that is well matched to harvest visible photons of the solar spectrum. The ability to tune the bandgap by changing the composition and size as well as a large absorption coefficients make them suitable as sensitizers in QDSC. Since CuInS2 nanocrystals (NCs) were first synthesized by Castro et al. through thermal decomposition of a molecular singlesource precursor,17 different synthetic strategies have been used to improve the quality and stability of CuInS2 NCs.18–22 Early studies by Li, T.-L. et al.10 reported photovoltaic conversion efficiency (PCE) using CuInS2 with sequential coatings of a CdS layer on top of CuInS2 reaching PCE up to 4.20 %. A similar approach was applied for CuInS2 QDSCs by using CdS doped with Mn2+ ions to increase the PCE to 5.38 %.23 Recently, a photovoltaic efficiency ~7 % was accomplished using type-I CuInS2/ZnS core-shell QDs and using mercapto propionic acid (MPA) as a capping ligand.9 Successive Ion Layer Adsorption and Reaction (SILAR) has also been used to make CuInS2 sensitizer solar cells, however the photovoltaic performance remains lower than those that use presynthesized QDs.13,24–30

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Despite the high efficiency obtained in QDSCs utilizing CuInS2 QDs, the effect of particle size on the photovoltaic performance is yet to be understood fully. An earlier work reported the photovoltaic performance of CuInS2 QDs of different sizes ranging from 2.6 to 7.7 nm where a decrease in the PCE was observed with increasing particle size.11 The size dependences was attributed to lower loading of larger CuInS2 QDs on mesoscopic TiO2 films and further speculated that the electron transfer from the CuInS2 QD to TiO2 was dependent on the quantization effects. Similar conclusions have been stated for CuInSe2 QDs.31 To better understand the effect of CuInS2 size and to determine the optimal size for solar cell efficiency a systematic study of the optical properties and photovoltaic performance of CuInS2 QDs of different sizes has now been performed. The defect controlled excited dynamics of different size QDs and its role in dictating solar cell efficiency is discussed. RESULTS/DISCUSSION Synthesis and Characterization of CuInS2 QDs. The synthesis of the CuInS2 QDs was performed using an earlier reported method.32 Briefly, the precursors CuI, In(Ac)3 and dodecanethiol (DDT) were mixed at 100°C under vacuum until the solution was clear and the temperature was raised to 200°C for the remainder of the reaction. The reaction was quenched at different times between 10 and 90 min to obtain different QD sizes and washed with toluene/methanol four times to remove excess ligands. The shape, structure and size of the QDs were determined by scanning (STEM) and high resolution transmission electron microscopy (HRTEM). STEM analysis revealed that all CIS QDs

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particles possess pyramidal shape but differ in size (Figure 1). As shown earlier, Ostwald ripening during particle growth is responsible for preferential evolution of the pyramidal shape.18,19

Figure 1. STEM image showing clearly the pyramidal shape of the CuInS2 (A) 2.9nm (B) 3.4nm (C) 3.9nm (D) 4.3 nm and (E) 5.3nm. (F) HRTEM image for 3.9 nm CuInS2 and measured 112 lattice spacing.

HRTEM analysis indicated a lattice spacing (Figure 1F inset) of 0.335 nm corresponding to the (112) plane of chalcopyrite phase.1 The size distribution of the pyramidal shaped QDs was determined by measuring the average edge length of the nanocrystals. Approximately 150 nanocrystals from TEM images were sampled to obtain the average size of the nanocrystal (see Figure S1 for the histogram of size distribution). The average size of the CuInS2 NCs are summarized in Table 1. X-ray diffraction (XRD) patterns (Figure S2, supporting information) show three diffraction peaks at 28, 46 and 54 degrees, which correspond to (112), (204/220) and (116/312) planes of the tetragonal phase.18, 33 No other secondary phases were evident from the XRD pattern.

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As the size of CuInS2 QD increases the peak width in the XRD spectrum becomes narrower, which is consistent with the inversely proportional size relationship of the Scherrer equation. The size of CuInS2 QDs estimated using the Scherrer equation18 match well with the values determined by STEM. The comparison of size of these nanocrystals obtained by two independent methods is presented in Table 1.

Figure 2. (A) Absorption spectra for the different sizes CuInS2 QDs in toluene (B) Emission spectra of the different sizes CuInS2 QDs in toluene at 450nm excitation.

Absorption spectra for the different sizes of CuInS2 QDs are shown in Figure 2A. These QDs fail to exhibit sharp excitonic peaks but display broad characteristic shoulder. As shown in previous studies20, 34 well-defined excitonic peak are not observed because of the dominance of internal and surface defects. This shoulder along with the absorption shifts to red with increasing particle size. This red-shift represents a quantum confinement effect of CuInS2 QDs. The photoluminescence (PL) spectra of the CuInS2 QDs shown in Figure 2B exhibit broad emission in the visible and near IR. The PL emission maximum peak shifts to the red and broadens with increasing CuInS2 QDs size (Table 1). The large stoke shift is indicative of the absence of band edge emission, and presence of defect induced emission in these QDs. In addition one can

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also see the appearance of a shoulder in the lower energy region of the emission spectra especially in the case of larger QDs. Such a spectral feature with broadened emission bands further supports the contribution of defect sites to the overall emission. The quantum yield (QY) of emission increases with size for particle below a diameter of 3.9 nm (Table 1). An optimal quantum yield of 6.9 % was measured for 3.9 nm QDs. Increased density of defect sites are likely to contribute to the decrease in emission quantum yield seen for larger particles.35 The ratio of Cu:In in the crystallites is a major contributing factor in creating internal or bulk defects while the surface-ligand interaction is likely to control surface defect sites. Based on the analysis of the emission decay Klimov and coworkers proposed that the charge recombination of conduction band electrons at the internal and surface defect sites were responsible for the observed emission in CuInS2 QDs.20 However, it has also been found that electrons are accumulated at the donor site lying below (~0.1 eV) the conduction band.36 The two possible defect induced charge recombination processes in CuInS2 QDs are illustrated as kr1 and kr2 in Scheme 1. Although these particles are quantized in terms of initial transition following the bandgap excitation, their emission is dictated by the internal and surface defects. The varying energy levels and density of these defect sites dictate the emission quantum yield, emission band position and radiative Scheme 1. Photoinduced processes in CuInS2 QD. (D: Donor site, Aint and Asurf: Acceptor sites for internal and surface defects, respectively)

and nonradiative decay processes. Varying density and energetics of the defect sites, thus determine the position and width of the emission bands.

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Table 1. Physical and photophysical properties of different size CuInS2 QDs. Size by STEM (nm)

Size by XRD (nm)

λem (nm)

QY (%)

PL fast decay (ns)*

PL slow decay (ns)*

PL decay average (ns)

S1 2.9 ± 0.4 2.8 661 0.8 3.84 [29] 26.7 [71] 20.1 S2 3.5 ± 0.4 3.7 678 3.3 4.43 [19] 32.2 [81] 26.9 S3 3.9 ± 0.5 3.9 689 6.9 5.12 [14] 39.5 [86] 34.7 S4 4.3 ± 0.7 4.9 714 2.2 4.93 [16] 37.9 [84] 32.6 --S5 5.3 ± 0.8 5.7 770 0.3 ----*The relative amplitude % for the slow and fast components of the emission are included in square brackets.

In order to further elucidate the emission decay of these QDs, we conducted time correlated single photon counting (TCSPC) measurements. The individual PL decay traces of CuInS2 QDs are shown in Figure S3 (supporting information). The multiexponential decay feature seen in these QDs further confirm the varying degree of the defect sites dictating the photoluminescence. Analysis of the decay traces using a biexponential fit provided an estimate of the lifetime of the fast component (3.84-5.12 ns) and slow component (26.7-39.5 ns). We attribute these processes to kr1 and kr2 in Scheme 1 respectively. The fast component arises mainly from the recombination through the surface defect states. As shown earlier, such faster decay component can be completely suppressed by growing a shell of CdS or ZnS around CuInS2 QDs.20 On the other hand, the slow component which arises from the recombination of charge carriers through internal defect states is mainly dependent on the Cu:In ratio and is not affected by the CdS or ZnS shell.20 The average lifetime of the emission ranges from 20.1-32.6 ns from 2.9-4.3 nm CuInS2 QD, respectively. It should be noted that Li et al. 20 reported a longer lifetime component as high as 190 ns. Since surface defects are dependent on the synthetic protocols we expect some variation in the observed emission lifetimes. Transient Absorption measurements. The PL decay measurements described above provide information on the overall radiative decay processes that extends into the nanoseconds

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time regime. In order to probe the subnanosecond charge separation/charge recombination processes, we employed femtosecond transient absorption spectroscopy measurements using 387 nm laser pulse (150 fs) with energy density of 27 μJ/cm2. The excited state behavior of CuInS2 QDs in deaerated CHCl3 solution was monitored by recording difference absorption spectra at varying probe times (Figure 3). Upon laser pulse excitation, the QDs undergo charge separation resulting in the bleaching of the absorption band. The bleaching maxima correspond to the shoulder absorption seen in the corresponding absorption spectra. With increasing QD size the bleaching maximum shifts to the red region in agreement with the size dependent optical properties of CuInS2. With increasing time the bleaching recovers as the charge carries become trapped and/or undergo charge recombination. The bleaching recovery thus provides insight into the fate

Figure 3. Difference absorption spectra of CuInS2 QDs different sizes with different delay time at 27μJ/cm2 for (A) 2.9 nm (B) 3.5 nm (C) 3.9 nm (D) 4.3 nm and (E) 5.3nm.

of the charge separated pair. Earlier studies have attempted to probe the excited state relaxation

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processes of semiconductors QDs, which usually are dominated by conduction band-valence band recombination.37–40 Since the surface and internal defect sites dominate in CuInS2 QDs, it is important to further analyze the transient bleach recovery. The absorption-time profiles monitored at 538, 568, 608, 638 and 680 nm for 2.9, 3.4, 3.9, 4.3 and 5.3 nm size QDs, respectively, are shown in Figure 4A. In each case the decay follows a multiexponential behavior, which is indicative of a various states involved in charge carrier recombination. Interestingly the decay profiles exhibited size dependent kinetic recovery indicating the varying nature of defect dominant recombination processes. Of particular interest is the initial part of the recovery which we attribute to the direct electron-hole recombination following laser pulse excitation. The longer lifetime component of the recovery correspond to the stabilization of charge carriers through various defect sites. We estimated the efficiency of charge stabilization (Φcs) by estimating the ratio of absorbance at 50 ps to maximum absorbance recorded immediately after laser pulse excitation (Φcs =∆A50ps/∆A0). The dependence of Φcs on the QD size is shown in Figure 4B. The QDs of ~4 nm size show maximum charge separation yield. The emission quantum yield also shows a similar dependence on the particle size. These parallel trends between the Φcs and emission yield confirms that the charge separation achieved through the trapping of charge carriers at defect sites dictates the excited state dynamics of CuInS2 QDs.

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Figure 4. (A) Normalized kinetic traces of the excited state of the CuInS2 QDs for each size monitored at 538, 568, 608, 638 and 680 nm. Samples were excited at 387 nm with same absorption at this wavelength (Figure S10). (B) Dependence of Charge separation yield (Φsc) and emission yield on the QD size. 3. Photovoltaic Performance of Different Sizes of CuInS2 QDs. To evaluate the photovoltaic performance of the different sizes of CIS QDs, liquid junction solar cells were fabricated. The photoanode was prepared by first depositing a TiO2 nanoparticle layer of an area of 0.20 cm2 on FTO followed by the deposition of CuInS2 QDs using electrophoretic deposition (EPD) method.12 A DC voltage of 150 V/cm was applied between the TiO2 film electrode and a FTO electrode immersed in QD suspensions. Loading of the CuInS2 QDs onto mesoscopic TiO2 film was optimized by tracking the absorption spectrum of the TiO2/CIS film versus the time of EPD (Figure S4 A and B, supporting information). A reduced graphene oxide (RGO)-Cu2S composite41 was used as the counter electrode and a 2M Na2S/S solution was used as the electrolyte. (Note that we have not included sacrificial electron donors such as methanol in the electrolyte.) Different size CuInS2 QDs loaded onto mesoscopic TiO2 film electrodes were used to fabricate the photoanodes for solar cells. These electrodes were subjected to two cycles of ZnS passivation layer using the SILAR method before assembling them in a solar cells. The absorption

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spectra of maximum loaded CuInS2 photoanodes shown in Figure S5B (supporting information) exhibit absorption features similar to that of solution spectra. Larger size particles show a red shifted absorption onset and also greater absorbance. CuInS2 QD of different size exhibited prompt photocurrent response with good stability. (Figure S5 in the supporting information). Figure 5A shows the J-V characteristics of the QDSCs for the different size CuInS2 QDs and the solar cell parameters are summarized in Table 2. The highest photocurrent and therefore photovoltaic performance was obtained for 3.9 nm and 4.3 nm CuInS2 with power conversion efficiency, PCE (η) of 2.16 and 2.51 %, respectively. Among the different size QDs tested, 4.3 nm CuInS2 QDs exhibit the maximum short-circuit current density (Jsc), 10.01± 0.30 mA/cm2, and open-circuit voltage (Voc), 0.501 ± 0.015 V. It should be noted that these efficiencies are about factor of 2 lower than the 5% efficiency reported with

CuInSexS2-x

QDs in a methanol-based

Figure 5. (A) J-V characteristics for the CuInS2 QDSCs with different sizes under 1 sun (AM 1.5) irradiation (B) IPCE spectra of different sizes CuInS2 QDSCs. (C) Picture of the TiO2/CuInS2 different sizes photoanodes with the maximum loading of CuInS2 QDs.

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polysulfide electrolyte.42 Both the type of QDs and electrolyte can make a difference in the observed efficiencies. Table 2. Photovoltaic parameters of CuInS2 QDSCs made with different sizes QDs.a 𝑺𝑺𝑺𝑺𝑺𝑺𝑺𝑺 𝒐𝒐𝒐𝒐 𝑸𝑸𝑸𝑸𝑸𝑸

𝐉𝐉𝐬𝐬𝐬𝐬 (𝐦𝐦𝐦𝐦/𝐜𝐜𝐜𝐜𝟐𝟐 )

2.9 nm 5.14 ± 0.20 3.5 nm 5.88 ± 0.57 3.9 nm 8.59 ± 0.45 4.3 nm 10.10 ± 0.30 5.3 nm 5.31 ± 0.40 a ( Average of four different cells. See solar cell characterization in each set)

𝐕𝐕𝐎𝐎𝐎𝐎 (𝐕𝐕)

𝑭𝑭𝑭𝑭

𝜼𝜼 (%)

0.460 ± 0.005 0.45 ± 0.01 1.05 ± 0.03 0.452 ± 0.018 0.47 ± 0.02 1.25 ± 0.13 0.487 ± 0.011 0.49 ± 0.01 2.05 ± 0.12 0.501 ± 0.015 0.47 ± 0.02 2.38 ± 0.13 0.462 ± 0.006 0.50 ± 0.02 1.23 ± 0.12 supporting information (Table S1) for individual

Incident photon-to carrier conversion efficiency (IPCE) or external quantum efficiency (EQE) represents the percentage of incident photons that are converted to charge carriers and collected at the electrode surface. The IPCE spectra shown in Figure 5B exhibit photoresponse that parallel the absorption onsets in Figure 2B. As anticipated from the size quantized particle absorption, we see a red shift in the photocurrent response with increasing particle size. Except for the electrode loaded with 5.3 nm CuInS2 QD, all other samples show a saturated IPCE around 35% at wavelengths below 525 nm. Figure 6 shows the trend of the individual photovoltaic parameters as a function of CuInS2 QDs size. As the particle size of QDs increases, the bandgap decreases due to size quantization effects. As a result of the size dependent optical absorption we expect increased light absorption with increasing particle size. Accordingly, all the photovoltaic parameters (Voc, Jsc, η and FF) increase with size except for the largest size QD. Despite the fact that the 5.3 nm QDs absorb a greater fraction of incident light we see poor performance from these QDs. Note that we have repeated these evaluations with several solar cells and in each case the largest QDs exhibit poor performance. This observation is also in agreement with lower efficiency of larger CuInS2 QDs reported in earlier studies.11, 31

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It should be noted that the experiments described above were carried out using maximum possible loading of QDs in the mesoscopic TiO2 film. Because of the presence of scattering layer, we could not directly estimate the loading accurately. Under these conditions difference in the absorbed photons can also introduce the variability in the photovoltaic performance. We also conducted another set of experiments without the scattering layer. In this set of experiment, we maintained a constant absorbance below 500 nm for all the films. This ensured similar absorbed photons at wavelengths below 500 nm. The photoelectrochemical parameters evaluated for all five QDs are presented in the supporting information (Figure S6 and S7 and Table S2). The trend observed in these experiments is similar to the one observed in Figure 6 and indicate that the ~4 nm QDs are best performing systems for CuInS2 based solar cells. Based on this set of experiment, we can rule out the loading effect as the major factor responsible for the observed variation in the photovoltaic performance of different size QDs. Factors influencing the Performance of Size Quantized CuInS2. The quantization effect arising from CuInS2 size variation is seen in both the IPCE spectra as well as absorption spectra. This observation supports the origin of the photocurrent generation to the size-quantized CuInS2 QDs. However, the five different CuInS2 QDs employed in this Figure 6. Dependence of the solar cell parameters on the different sizes of CuInS2 QDs: (A) short-circuit current (Jsc), (B) open-circuit voltage (Voc), and (C) overall power conversion efficiency (η) under global AM 1.5 illumination.

investigation exhibit properties that differ from other metal chalcogenide QDs such as CdSe

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and CdS.43, 44 The photoluminescence and transient absorption studies show that the internal and surface defect sites dictate the excited state dynamics of the CuInS2 QDs. Unlike CdS and CdSe QDs, we fail to observe any band edge emission in CuInS2 QDs. Despite the dominance of defect induced charge separation process, we are able to capture the photogenerated electrons to deliver photocurrent in CuInS2 QDSC with a reasonable external quantum efficiency. Earlier studies with quantized CdSe have shown size dependent electron injection process dictated by the energy gap between the conduction bands of CdSe and TiO2 as well as acceptor density of states.45, 46 However, our efforts to probe the charge injection process from excited CuInS2 and TiO2 using transient absorption spectroscopy fail to give conclusive results as they show little variance in the bleaching recovery rates. These observations as well as the conclusions drawn from our emission studies indicate that the electrons are injected from a trap site (Donor level) lying close to the conduction band of the semiconductor. The defect site controlled charge transfer between excited CuInS2 into TiO2 is expected to minimize the energy gap dependence of electron injection rate. Unlike CdSe QDs we do not see an increased IPCE at excitonic peaks with decreasing size, instead we see similar IPCE for all QDs smaller than 4.1 nm.47 The saturated IPCE at 35%, which is independent of QD size supports the argument that the charge injection into TiO2 must be occurring from a site (viz., a defect site near the conduction band) with minimal energy gap dependence. The increase seen in photocurrent and PCE with increasing CuInS2 QD size is expected from the increased fraction of the absorbed photons as the absorption spectrum shifts to the red region. Surprisingly, the largest size QD deviates from this trend as it shows poor performance. Despite the high loading and complete absorption of incident photons, the QDSC prepared with 5.3 nm QDs show significantly lower PCE. We have checked this behavior through repeat

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experiments, all of which confirm poor performance of 5.3 nm CuInS2 QDs. It is important to note that the excited state dynamics of these larger size QDs (Figure 4) show lower quantum yield of emission as well as lower extent of charge separation. Based on these observations we can conclude that 4-5 nm CuInS2 QDs are optimum for designing QDSC and the QDs of size greater than 5 nm are poor performers. We also conducted Electrochemical Impedance Spectroscopy (EIS) to check any internal impedance (e.g., charge recombination resistance) related issues in dictating the overall cell performance. The results are presented as Nyquist and Bode plots in the supporting information (Figure S8A and B). In the Nyquist plot one larger arc appeared in the region 105 ~ 100 Hz due to recombination of electron at TiO2/QDs/electrolyte interface.48–50 The overall shape of the arcs for CuInS2 QDs size remains the same (Figure S8A and B) and the frequency maximum domain of lowest phase appeared at similar frequency, 1 kHz. Based on these results we conclude that the recombination rate at TiO2/QDs/electrolyte is not a factor which affects the photovoltaic performance of CuInS2 QDs.

CONCLUSIONS CuInS2 QDs capped with 1-dodecanethiol exhibit size quantized photovoltaic performance. An increase in the photovoltaic performance with increasing QD size is observed as a result of increased absorption of incident photons. However, QDs of size greater than ~5 nm showed significant decrease in photoconversion efficiency. Based on controlled loading of quantum dots, we determined that variations in loading is not the reason for the size dependent photocurrents and PCE, as speculated previously.11,

31

Both emission and transient absorption spectroscopy

measurements point out the dominance of internal and surface defect sites dictating the excited

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state dynamics of CuInS2 QDs. As a result of this excited state behavior we observed participation of charge carriers in defect sites as the state involved in the charge injection into mesoscopic TiO2 films. Unlike, CdSe QDs, the participation of quantized conduction band electrons have little role to play in photocurrent generation in CuInS2. These studies point out that CuInS2 offers a unique opportunity to manipulate internal and surface defects through variation in Cu:In composition and/or surface ligand chemistry and thus control the excited state dynamics. Efforts are underway to understand and control such defect driven photodynamics to further enhance the efficiency of QDSC.

EXPERIMENTAL SECTIONS Materials: Copper (I) Iodide (Alfa Aesar, puratronic, 99.998%), indium (III) acetate (Alfa Aesar, 99.99%), 1-dodecanethiol (Aldrich, ≤ 98%), toluene (Fisher Scientific, certified ACS grade), methanol (Fisher Scientific, certified ACS grade), chloroform (AMRESCO, biotechnology grade), were used without purification. Synthesis of CuInS2 Quantum Dots: CIS QDs were synthesized using a previously reported thermolysis method2. In brief, 0.5 mmol of CuI and 0.5 mmol of In(Ac)3 were employed as precursors and an excess of dodecanethiol (DDT) was used as solvent, S donor and capping ligand. Under vacuum the reaction was heated for 30 min at 100oC and then raised to 200oC. To achieve different sizes, the temperature was kept constant and the time of the reaction was varied from 10 min to 90 min. The as-synthesized CIS QDs were then washed under N2 by dispersing and precipitating the QDs with toluene and methanol, respectively. CIS QDs were stored in N2purged toluene until further characterization. Optical Measurements. UV-Visible absorption spectra were collected using a Varian Cary50 Bio spectrometer. Steady state photoluminescence spectra were recorded using a Horiba Flurolog spectrometer with a 480 nm long pass filter to exclude scattering from the excitation source. Emission Life time measurement were recorded using a Jobin Yvon single photon counting

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system with a 452 nm LED excitation source incident on a 1cm quartz cuvette and using a 480nm long pass filter before the detector. Transient absorption measurements were performed using a Clark MXR-2010 laser system (775 nm fundamental, 1mJ/pulse, fwhm = 130 fs, 1 kHz repetition rate) using a Helios software provided by Ultrafast system. The pump beam, corresponding to 95% of the fundamental frequency doubled to 387 nm and the probe beam corresponding to the remaining 5% focused through a Ti:sapphire crystal to generate a white light continuum are incident on CuInS2 solution (CHCl3) purged with N2 contained in a 2 mm quartz cuvette. Material Characterization: Transmission electron microscope (TEM) images were collected using a TITAN 80-300 electron microscope at an accelerating voltage of 300 kV. The samples for TEM were prepared by dropping a diluted solution of CuInS2 QDs into a carbon coated copper grid and dried under vacuum at 40 oC overnight. X-ray diffraction (XRD) measurement were performed by using a Bruker D8 X-ray diffractometer with scan rate of 2o min-1 from 2Ɵ values of 20o to 70o employing Cu Kα radiation (λ = 1.5406 Å). Photoanode preparation. FTO (Fluorine-doped-tin oxide) glass plates from Pilkington (TEC-7) was cleaned in soap solution using ultrasonic bath for 30 min and washing in ethanol for 15 min. Three layers of TiO2 were deposited on FTO: blocking layer, active layer and scattering layer. The blocking layer was deposited by immersing the plates in 40 mM TiCl4 aqueous solution at 70 °C for 30 min and washed with DI water and ethanol. The active TiO2 layer (Solaronix Ti Nanoxide T/SP, particle size ~20 nm) was coated on top of the blocking layer by doctor blade printing TiO2 paste. The film was dried at 80 °C for 1 h followed by annealing at 500 °C for another 1 h. A scattering layer of TiO2 (CCIC, PST-400C, particle size ~ 400 nm) was deposited on top the active layer by the doctor blade printing. The TiO2 electrodes were further dried at 80°C and annealed at 500 °C for an hour. Finally, the electrodes were treated again with TiCl4 at 70 °C for 30 min and sintered at 500°C for 30 min. The counter electrodes were prepared by doctor blading Cu2S-RGO as reported earlier.41 The solar cells were fabricated by sandwiching the photoanode and counter electrodes using Parafilm as spacer and a drop of redox electrolyte (2M of S2-, 2M of S in water) for 40 min and washed with water. The typical electrode area was 0.20 cm2 for regular solar cells and 0.5 cm2 for no scattering layer solar cells. ImageJ 51 software was used to determine the precise area of the electrodes.

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Chemistry of Materials

Electrophoretic Deposition (EPD). EPD was used to sensitize the FTO/TiO2 photoanodes with CuInS2. A TiO2 photoanode and a blank FTO were immersed in a cuvette and kept at a distance of 0.4 cm. A dispersion of QDs in CHCl3 were added in the cuvette and a bias voltage of 150 V cm-1 was applied between the TiO2 photoanode and FTO for a different period of times time to deposit the QDs onto the mesoporous TiO2 electrode, which was connected to the positive terminal of the power supply unit. Successive Ionic Layer Adsorption and Reaction (SILAR). The deposition of ZnS onto TiO2 electrodes was performed by SILAR method. A Zn(NO3)2 (0.1 M) solution in methanol and Na2S (0.1 M) in a mixture of methanol and water (1:1) were used as cationic and anionic sources, respectively. Each cycle of SILAR consists of successive immersion of the TiO2 electrode in metal ion and sulfide anion solutions for 1 min and washing between each step. Two cycles were applied to the CuInS2/TiO2 photoanodes. Photoelectrochemical Measurements. Photoelectrochemical measurements were carried out with a sandwich cell configuration consisting of CuInS2 modified TiO2 photoanode, Cu2S/RGO deposited on ITO electrode as cathode (see reference 41 for preparation of the cathode) and sulfide/polysulfide electrolyte. The photovoltaic performances of QDSCs were evaluated using a PARStat 2273 (Princeton Applied Research) potentiostat. The illumination source was a 300 W Xe lamp (Oriel) with a global AM 1.5 filter. The solar cells were positioned to receive incident power energy of 1 sun intensity (100 mW/cm2). The incident photon to charge carrier generation efficiency (or external quantum efficiency) at different wavelengths was measured using Newport Oriel QE/IPCE Measurement Kit with Silicon Detector. EIS spectra of QDSCs were taken by using Gamry PCI4750 potentiostat with applying 0.4 V without illumination. Frequency range is between 300 kHz and 0.1 Hz with 10 mV rms purtubation.

Supporting Information. XRD spectrum, QD size histogram, photoluminescence decay and analysis, the absorption spectra showing the loading of QDs, individual photovoltaic performance of various QDSC are included in the supporting information. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Website: kamatlab.com. Notes The authors declare no competing financial interest. ACKNOWLEDGMENT The research described herein was supported by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences of the U.S. Department of Energy through Award DE-FC02-04ER15533. This is document no. NDRL 5042 from Notre Dame Radiation Laboratory. DHJ would like to thank “Becas Chile” Scholarship and Yong-Siou Chen for his assistance in TEM images. REFERENCES

(1)

Kongkanand, A.; Tvrdy, K.; Takechi, K.; Kuno, M.; Kamat, P. V. J. Am. Chem. Soc. 2008, 130, 4007.

(2)

Booth, M.; Brown, A. P.; Evans, S. D.; Critchley, K. Chem. Mater. 2012, 24, 2064−2070.

(3)

Qin, L.; Li, D.; Zhang, Z.; Wang, K.; Ding, H.; Xie, R.; Yang, W. Nanoscale 2012, 4, 6360.

(4)

Beard, M. C. J. Phys. Chem. Lett. 2011, 2, 1282.

(5)

Tisdale, W. A.; Williams, K. J.; Timp, B. A.; Norris, D. J.; Aydil, E. S.; Zhu, X. Y. Science 2010, 328, 1543.

(6)

Kamat, P. V. J. Phys. Chem. Lett. 2013, 4, 908.

(7)

Zhong, H. Z.; Bai, Z. L.; Zou, B. S. J. Phys. Chem. Lett. 2012, 3, 3167.

(8)

Kuo, K.-T.; Liu, D.-M.; Chen, S.-Y.; Lin, C.-C. J. Mater. Chem. 2009, 19, 6780.

(9)

Pan, Z.; Mora-Seró, I.; Shen, Q.; Zhang, H.; Li, Y.; Zhao, K.; Wang, J.; Zhong, X.; Bisquert, J. J. Am. Chem. Soc. 2014, 136, 9203.

(10)

Li, T.-L.; Lee, Y.-L.; Teng, H. Energy Environ. Sci. 2012, 5, 5315.

(11)

Peng, Z.; Liu, Y.; Shu, W.; Chen, K.; Chen, W. Eur. J. Inorg. Chem. 2012, 2012, 5239.

ACS Paragon Plus Environment

20

Page 21 of 23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemistry of Materials

(12)

Santra, P. K.; Nair, P. V.; Thomas, K. G.; Kamat, P. V. J. Phys. Chem. Lett. 2013, 4, 722.

(13)

Chang, C.-C.; Chen, J.-K.; Chen, C.-P.; Yang, C.-H.; Chang, J.-Y. ACS Appl. Mater. Interfaces 2013, 5, 11296.

(14)

Mcdaniel, H.; Koposov, A. Y.; Draguta, S.; Makarov, N. S.; Pietryga, M.; Klimov, V. I. J. Phys. Chem. C 2014, 118, 16987.

(15)

Mcdaniel, H.; Fuke, N.; Pietryga, M.; Klimov, V. I. J. Phys. Chem. Lett. 2013, 4, 355.

(16)

McDaniel, H.; Fuke, N.; Makarov, N. S.; Pietryga, J. M.; Klimov, V. I. Nat. Commun. 2013, 4, 2887.

(17)

Castro, S. L.; Bailey, S. G.; Raffaelle, R. P.; Banger, K. K.; Hepp, A. F. Chem. Mater. 2003, 15, 3142.

(18)

Zhong, H.; Lo, S. S.; Mirkovic, T.; Li, Y.; Ding, Y.; Li, Y.; Scholes, G. D. ACS Nano 2010, 4, 5253.

(19)

Zhong, H. Z.; Zhou, Y.; Ye, M. F.; He, Y. J.; Ye, J. P.; He, C.; Yang, C. H.; Li, Y. F. Chem. Mater. 2008, 20, 6434.

(20)

Li, L. A.; Pandey, A.; Werder, D. J.; Khanal, B. P.; Pietryga, J. M.; Klimov, V. I. J. Am. Chem. Soc. 2011, 133, 1176.

(21)

Pan, D. C.; An, L. J.; Sun, Z. M.; Hou, W.; Yang, Y.; Yang, Z. Z.; Lu, Y. F. J. Am. Chem. Soc. 2008, 130, 5620.

(22)

Xie, R. G.; Rutherford, M.; Peng, X. G. J. Am. Chem. Soc. 2009, 131, 5691.

(23)

Luo, J.; Wei, H.; Huang, Q.; Hu, X.; Zhao, H.; Yu, R.; Li, D.; Luo, Y.; Meng, Q. Chem. Commun. 2013, 49, 3881.

(24)

Hu, X.; Zhang, Q.; Huang, X.; Li, D.; Luo, Y.; Meng, Q. J. Mater. Chem. 2011, 21, 15903.

(25)

Zhou, Z.; Yuan, S.; Fan, J.; Hou, Z.; Zhou, W.; Du, Z.; Wu, S. Nanoscale Res. Lett. 2012, 7, 652.

(26)

Chang, J.-Y.; Su, L.-F.; Li, C.-H.; Chang, C.-C.; Lin, J.-M. Chem. Commun. 2012, 48, 4848.

(27)

Peng, Z.; Liu, Y.; Shu, W.; Chen, K.; Chen, W. Chem. Phys. Lett. 2013, 586, 85.

(28)

Xu, X.; Wan, Q.; Luan, C.; Mei, F.; Zhao, Q.; An, P.; Liang, Z.; Xu, G.; Zapien, J. A. ACS Appl. Mater. Interfaces 2013, 5, 10605.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 23

(29)

Wang, Y.-Q.; Rui, Y.-C.; Zhang, Q.-H.; Li, Y.-G.; Wang, H.-Z. ACS Appl. Mater. Interfaces 2013, 5, 11858.

(30)

Chang, J.-Y.; Lin, J.-M.; Su, L.-F.; Chang, C.-F. ACS Appl. Mater. Interfaces 2013, 5, 8740.

(31)

Yang, J.; Kim, J.-Y.; Yu, J. H.; Ahn, T.-Y.; Lee, H.; Choi, T.-S.; Kim, Y.-W.; Joo, J.; Ko, M. J.; Hyeon, T. Phys. Chem. Chem. Phys. 2013, 15, 20517.

(32)

Li, L.; Pandey, A.; Werder, D. J.; Khanal, B. P.; Pietryga, M.; Klimov, V. I. J. Am. Chem. Soc. 2011, 133, 1176.

(33)

Li, L.; Coates, N.; Moses, D. J. Am. Chem. Soc. 2010, 132, 22.

(34)

Castro, S. L.; Bailey, S. G.; Raffaelle, R. P.; Banger, K. K.; Hepp, A. F. J. Phys. Chem. B 2004, 108, 12429.

(35)

Chen, B.; Zhong, H.; Zhang, W.; Tan, Z.; Li, Y.; Yu, C.; Zhai, T.; Bando, Y.; Yang, S.; Zou, B. Adv. Funct. Mater. 2012, 22, 2081.

(36)

Omata, T.; Nose, K.; Kurimoto, K.; Kita, M. J. Mater. Chem. C 2014, 2, 6867.

(37)

Robel, I.; Kuno, M.; Kamat, P. V. J. Am. Chem. Soc. 2007, 129, 4136.

(38)

Burda, C.; Green, T. C.; Link, S.; El-Sayed, M. A. J. Phys. Chem. B 1999, 103, 1783.

(39)

Klimov, V. I. J. Phys. Chem. B 2000, 104, 6112.

(40)

Mohamed, M. B.; Burda, C.; El-Sayed, M. A. Nano Lett. 2001, 1, 589.

(41)

Radich, J. G.; Dwyer, R.; Kamat, P. V. J. Phys. Chem. Lett. 2011, 2, 2453.

(42)

McDaniel, H.; Fuke, N.; Makarov, N. S.; Pietryga, J. M.; Klimov, V. I. Nat. Commun. 2013, 4.

(43)

Robel, I.; Subramanian, V.; Kuno, M.; Kamat, P. V. J. Am. Chem. Soc. 2006, 128, 2385.

(44)

Baker, D. R.; Kamat, P. V. Adv. Funct. Mater. 2009, 19, 805.

(45)

Tvrdy, K.; Frantsuzov, P. a; Kamat, P. V. Proc. Natl. Acad. Sci. U. S. A. 2011, 108, 29.

(46)

El-Ballouli, A. O.; Alarousu, E.; Bernardi, M.; Aly, S. M.; Lagrow, A. P.; Bakr, O. M.; Mohammed, O. F. J. Am. Chem. Soc. 2014, 136, 6952.

(47)

Tvrdy, K.; Frantsuzov, P. A.; Kamat, P. V. Proc. Natl. Acad. Sci. U. S. A. 2011, 108, 29.

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Chemistry of Materials

(48)

Fabregat-Santiago, F.; Garcia-Belmonte, G.; Mora-Sero, I.; Bisquert, J. Phys. Chem. Chem. Phys. 2011, 13, 9083.

(49)

Fabregat-Santiago, F.; Bisquert, J.; Garcia-Belmonte, G.; Boschloo, G.; Hagfeldt, A. Sol. Energy Mater. Sol. Cells 2005, 87, 117.

(50)

Sudhagar, P.; Gonzalez-Pedro, V.; Mora-Sero, I.; Fabregat-Santiago, F.; Bisquert, J.; Kang, Y. S. J. Mater. Chem. 2012, 22, 14228.

(51)

Schneider, C. A.; Rasband, W. S.; Eliceiri, K. W. Nat Meth 2012, 9, 671.

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