Linear Absorption in CdSe Nanoplates: Thickness and Lateral Size

Article pubs.acs.org/JPCC

Linear Absorption in CdSe Nanoplates: Thickness and Lateral Size Dependency of the Intrinsic Absorption Alexander W. Achtstein,†,‡ Artsiom Antanovich,§ Anatol Prudnikau,§ Riccardo Scott,† Ulrike Woggon,† and Mikhail Artemyev*,§ †

Institute of Optics and Atomic Physics, Technical University of Berlin, 10623 Berlin, Germany Institute for Physico-Chemical Problems, Belarusian State University, Leningradskaya str. 14, Minsk 220030, Belarus

§

Downloaded by UNIV OF NEBRASKA-LINCOLN on August 25, 2015 | http://pubs.acs.org Publication Date (Web): August 19, 2015 | doi: 10.1021/acs.jpcc.5b06208

S Supporting Information *

ABSTRACT: We investigate the optical absorption properties of colloidal CdSe nanoplatelets and compare them to CdSe quantum dots. Starting from inductively coupled plasma−atomic emission spectroscopy (ICP-AES) measurements on their intrinsic absorption coefficients μi, we compare these results with a theoretical approach by a continuum absorption Lorentz local field model. We show that the platelets’ intrinsic absorption coefficients μi are strongly thickness and aspect ratio dependent, which results in the possibility to tune the absorption properties of this material class by the lateral size and thickness. The continuum intrinsic absorbance of the platelets is considerably larger if compared with quantum dots making them more efficient absorbers with higher light−matter interaction that is essential for their use in, for example, solar cells. The obtained μi values can be used for concentration determination of CdSe nanoplatelets in solution and solid films which is essential for all optical experiments with controlled generated population density upon optical excitation.

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INTRODUCTION In recent years, the influence of size and shape on the linear absorption properties of semiconductor nanoparticles has gained growing interest with respect to nanoparticles in dispersion or polymeric matrices. Recent investigations1−6 have shown that the absorption properties of II−VI semiconductor nanoparticles can be strongly altered not only by the electronic and dielectric carrier confinement but also by the dielectric environment of these particles. This is because the light−matter interaction (e.g., absorption or emission of radiation) is connected to local fields inside the nanoparticles and the effective medium dielectric constant.7 Different kinds of CdSe, CdS, PbS, and PbSe1−6,8,9 particles in the shape of dots, rods, and wires were investigated. They exhibited a strong shape, aspect ratio, and dielectric contrast (semiconductor vs surrounding medium) dependence of their optical properties such as a shape dependent intrinsic absorption coefficient, polarized emission and absorption, and a varying oscillator strength and exciton lifetime.2,7 In recent years, a new class of colloidal nanoparticles has been synthesized, the colloidal II−VI nanoplatelets (NPLs).10−13 These ultrathin and flat nanocrystals (made of CdSe, CdS, or CdTe) exhibit lateral dimensions of the order of tens of nanometers and thicknesses of several monolayers.10−12,14−19 Strong anisotropic quantum confinement in the NPLs results in spectrally narrow absorption and photoluminescence peaks even at room temperature. Because lateral dimensions of NPLs are much larger than their thicknesses, NPLs can be considered as the colloidal analogue © XXXX American Chemical Society

of ultrathin semiconductor quantum wells (QWs) prepared by molecular beam epitaxy (MBE).20,21 For many, for example, optical investigations, linear absorption cross sections or intrinsic absorption coefficients are necessary to determine the absolute particle concentrations of nanoparticles in colloidal solutions. Therefore, in this report, we study dependence of the linear absorption properties of CdSe nanoplatelets on their aspect ratio and thickness by means of inductively coupled plasma−atomic emission spectroscopy (ICP-AES) and theoretical calculations.

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MATERIALS AND METHODS Zinc blende (ZB) CdSe NPLs of different thicknesses and lateral sizes were synthesized according to published procedures.22 Details of the synthesis of 2.5 monolayer (ML) NPLs and purification procedures can be found in the Supporting Information. Produced NPLs were stirred in 10% solution of oleic acid in chloroform for 2 h at room temperature, and the excess of precursors was removed by centrifugation at 7000 rpm for 10 min. Only the CdSe NPLs were deposited at these conditions because of their large size/ weight, whereas all residuals in the molecular form (cadmium oleate, etc.) remained in the solution. A repeated procedure of centrifugation/dissolution produces colloidal solutions of CdSe NPLs practically free from inorganic contaminations. Optical Received: June 29, 2015 Revised: August 6, 2015

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DOI: 10.1021/acs.jpcc.5b06208 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C Table 1. Characteristic Parameters of the CdSe Nanocrystal Samplesa size sample 3.5 ML 4.5 ML 5.5 ML MS dots

lx (nm)

ly (nm)

20 19 42 diameter

8 5 11 1.829

lz (nm)

aspect ratio reff

1st exciton absorption peak (nm)

stoichiometry

μi at 309 nm (105 cm−1)

μi at 1st exciton (105 cm−1)

1.06 1.37 1.67

0.08 0.14 0.10 1

460 511 552 407

Cd1Se0.75 Cd1Se0.80 Cd1Se0.83 (CdSe)3429

2.5 (0.27) 4.06 (0.44) 4.8 (0.25) 1.7 (0.09)

3.68 (0.4) 2.27 (0.25) 1.24 (0.15) 2.8 (0.15)

The μi results at 309 nm and first exciton from ICP-AES (with statistical errors from three independent measurements) are displayed in the last two columns. The effective platelet aspect ratio is defined as reff = lz/(lx × ly)0.5, where lx, ly, and lz are NPLs’ length, width, and thickness, correspondingly.


a

absorption spectra of the purified colloidal solutions of NPLs were measured with an Ocean Optics HR2000+ spectrometer at room temperature in a 1 cm quartz cuvette. After the optical measurements, the CdSe NPLs were finally deposited by the addition of acetonitrile and centrifugation at 4000 rpm for 10 min, the solvent was discarded, and the solid precipitate was dried at room temperature overnight. Then, the nanocrystals were treated with concentrated nitric acid (90 °C, 24 h), and the resultant solution of cadmium nitrate and other watersoluble compounds was diluted with bidistilled water. The concentration of cadmium ions in the resultant solution was determined with ICP-AES analyzer (Varian Liberty Sequential) against a cadmium nitrate analytical standard.

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RESULTS AND DISCUSSION The intrinsic absorption coefficient μi can be experimentally derived from the absorbance A of the NPLs solution, the volume fraction of semiconductor material f V in the solution, and the optical path length L of the cuvette (L = 1 cm) μi =

ln(10)A fV L

Figure 1. Intrinsic absorption spectra (relative to pure chloroform) of 3.5, 4.5, and 5.5 ML CdSe NPLs and magic size CdSe clusters from ICP-AES (solid lines). Absorption spectra were normalized to the ICP-derived intrinsic absorption at first exciton. Dots of respective colors indicate our calculated theoretical intrinsic absorption values at 4.4 eV (280 nm) and 4 eV (309 nm) for the corresponding NPL thicknesses and the magic size CdSe clusters. The result for zinc blende CdSe spherical quantum dots from Č apek et al.23 is inserted as well. The inset shows the experimental intrinsic absorption at λ = 309 nm with corresponding error bars.

(1)

The volume fraction f V is determined from the Cd weight concentration CCd obtained by ICP-AES and the cadmium-toselenium molar ratio RCd/Se according to ref 23 fV = CCd

MCdSe ⎛ 1 ⎞ ⎟ ⎜1 + 2ρCdSe MCd ⎝ R Cd/Se ⎠

AES measurements for each type of NPL, we determined μi for three different solutions of each NPL with volume concentrations differing by a factor of 2 from one to the other. The inset in Figure 1 shows the averaged μi at 309 nm for all types of studied NPLs with corresponding error bars, while the optical absorption spectra in a μi scale are drawn relative to average μi values depicted in the inset. Table 1 summarizes the experimentally determined averaged μi at 309 nm for CdSe NPLs of different thicknesses and MS CdSe cluster sizes along with the wavelength of the first exciton absorption peak. The errors of ICP-AES based determination of the intrinsic absorption coefficients are about 10% (see Table 1 for detailed statistical errors). To make our study more general, we also synthesized the thinnest 2.5 ML CdSe NPLs. We also determined the μi for 2.5 ML NPLs and compared it with those for other thickness classes of CdSe NPLs family. The collective spectra are presented in Figure S2. It can be seen that the character of the optical transitions for 2.5 ML NPLs differs significantly from those of 3.5−5.5 ML NPLs both by the relative intensities and the energy gap between hh- and lh-bands. We believe that the electronic structure of 2.5 ML CdSe NPLs is influenced by the surface and the ligands because of the ultrastrong transversal quantization to 0.76 nm. In this case, the exciton wave function extends significantly into the oleic acid ligands where the

(2)

where MCd and MCdSe are the molar masses of Cd and CdSe, respectively. For large CdSe quantum dots (QDs) and nanorods (NRs), the Cd/Se molar ratio can be assumed to be 1, while for small QDs it can be greater than 1 because of surface termination by Cd atoms.24 Although the Cd/Se molar ratio for CdSe core NPLs is still a disputable parameter, the recent results of She et al.,25 Lim et al.,26 and Li and Peng19 pointed to a double-sided Cd-termination. On the basis of these data, we calculated μi for both sided Cd-terminated NPLs. To examine the μi dependence of the NPL thickness, we synthesized 3.5, 4.5, and 5.5 ML thick CdSe core NPLs. The lateral sizes of corresponding NPLs determined by transmission electron microscopy (TEM) are indicated in Table 1. We assumed the thickness of one CdSe monolayer to be 0.304 nm according to She et al.25 and Li and Peng.19 However, other, slightly different sheet thicknesses have been reported.27,28 As a reference, we additionally included a spherical, magic size CdSe cluster (MS) sample synthesized according to published procedures.29,30 Figure 1 shows optical absorption spectra of corresponding NPLs in chloroform normalized to their μi at first exciton determined by eq 1. To estimate the reproducibility of the ICPB


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The Journal of Physical Chemistry C

permutations of a, b, c. With the semiconductor refractive index n and extinction k, Li represents the orientation and aspect ratio dependent depolarization factor. Here, εm, nm, and km denote the matrix dielectric function, refractive index, and absorption coefficient, whereas εs, ns, and ks denote the same for the CdSe semiconductor. Equation 3 already takes into account the random orientation of our particles in solution with respect to the optical light field.7 In our notation, the platelets have r values of 0 < r < 1, dots r = 1, and rods of 1 < r < ∞. Because the high-frequency dielectric constant of chloroform (ε = 2.1932 at 4 eV) is very similar to the dielectric constant of the ligands ε ≈ 2, we can neglect the changes of the local Lorentz field introduced by the ligand/chloroform interface and use chloroform as the dielectric surrounding. Our applied local field theory has already proved applicability for describing dielectric effects in the continuum absorption of CdSe, CdS, and PbSe nanodots and nanorods.5,7,23 Because μi(E) = δ(1)(E)/VP (with the particle volume VP) is valid, it is possible to calculate the intrinsic absorption μi for randomly oriented nanoplatelets (dots, rods) according to eq 3 by numerical integration of eq 5. Figure 2 shows the obtained aspect ratio dependence of μi at 4 eV for zinc blende (ZB) CdSe particles (with lateral aspect

carriers experience a different dielectric environment and effective mass. We excluded the 2.5 ML sample from further examination for the above-mentioned reasons but show the data in the Supporting Information. Figure 1 is difficult to interpret as it contains information about the platelet thickness for platelets of different lateral sizes and, hence, different aspect ratios. To analyze the aspect ratio dependence of the intrinsic absorption coefficient theoretically, we use a Lorentz local field theory in connection with an effective medium Maxwell-Garnett approach.1,3,4 In this case, the linear absorption cross section δ(1) in the continuum absorption region of a semiconductor nanoparticle is calculated. To introduce a particle-independent quantity, we use the volume-independent intrinsic absorption μi given by μi(ω) = δ(1)(ω)/VP with VP being the platelet volume and δ(1) the linear absorption cross section. The transition wavelength λ is related to the transition energy E and frequency ω by E = ℏω= hc/λ. Because the nanoplatelets have a 2D sheetlike shape, the concept of the intrinsic absorption of a sphere1,3,4 has to be extended to nonspherical particles. We assume dilute nanoparticle dispersions in chloroform (measured volume fractions f V are about 10−6), so that we can neglect the changes in the surrounding effective medium dielectric constant by mixture and Förster transfer interactions. The CdSe nanoparticles in dispersions (nanodots, rods, or platelets) can be approximated as spherical, prolate, or oblate ellipsoids for which their linear absorption cross section is related to the local field factor f i depending on the particle shape and dielectric contrast between the semiconductor inclusion and solvent. Here, we define the aspect ratio r of our nanoplatelets as thickness lz divided by the largest lateral size lx (in case of nonquadratic platelets). For our investigated platelets, r is in the range between 1/8 and 1/33. Nonquadratic platelets are treated by the introduction of the lateral aspect ratio R = ly/lx. For different values of R and r and platelet orientations relative to the optical excitation light field, we expect strongly different local field factors f i,7 defining the relation between the external excitation light field in the solvent and the field in the nanoparticles. We approximate the platelets as oblate ellipsoids, and we obtain for the linear absorption cross section δ(1) P of an arbitrary shaped ellipsoid taking into account its random orientation in the solvent7 δ P(1) =

Figure 2. Aspect ratio dependence of the intrinsic absorption coefficient μi at 4 eV for randomly oriented ZB CdSe rotationally symmetric ellipsoids (spheroids, R = 1) with respect to the symmetry axis z according to eq 3 (thick line). The graph shows the cases of oblate (r < 1) and prolate (r > 1) ellipsoids as well as the case of a sphere (r = 1 and R = 1). Particles of unequal side length (R < 1), e.g., platelets with different lateral sizes lx and ly or rods with elliptical cross section, are also plotted (dotted/dashed lines). It can be seen that an unequal side length decreases the intrinsic absorption of platelets (because the local field factor is lowered in the direction of shorter lateral extent (ly) with respect to the long one (lx)), while for rods of unequal cross section, we observe an increase of the intrinsic absorption as they evolve into sheetlike rods for cross-sectional aspect ratios R = ly/lx < 1. Therefore, the lateral aspect ratio R, e.g., of nanoplatelets, is a relevant parameter for their intrinsic absorption.

2ω VP(|fx (ω)|2 + |f y (ω)|2 + |fz (ω)|2 )ns(ω) 3nm(ω)c ks(ω)

(3)

with fi (ω) =

1 1 + Li(ϵs(ω)/ϵm(ω) − 1)

(4)

for which the depolarization factors Li [with Lz along the short platelet (ellipsoid) semiaxis c = lz/2 (half thickness) and Lx,y along the long extended lateral platelet semiaxes a = lx/2 and b = ly/2] are given by the integral31 Lz =

∫0

∞

abc ds 2(s + c 2)3/2 (s + a 2)(s + b2)1/2

ratio R = 1, e.g., symmetric platelets and R < 1, e.g., asymmetric platelets) using bulk dielectric function data for CdSe33 and our solvent chloroform32 for our colloidal dispersion of randomly oriented particles. We observe a strong aspect ratio dependence for the oblate ellipsoids (platelets) which have r < 1. Please note again that prolate ellipsoids (rods) are described by r > 1 and oblate (platelets) by r < 1 in the calculations. Especially for very thin platelets, the results let us expect a strong lateral size and aspect ratio dependence. Our both sided Cd-terminated

(5)

where we use the platelet size parameters a = lx/2, b = ly/2 = R × lx/2, and c = lz/2 = r × lx/2 for the surface normal in the z direction and thickness lz. Lx and Ly are obtained by cyclic C


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and 309 nm in Figure 1 and see that we obtain slightly higher values, which shall be discussed later. To determine the influence of the lateral platelet size on the intrinsic absorption, we synthesized three different batches of 4.5 ML CdSe NPLs with different average lateral sizes as indicated in Table 2. The lateral size was controlled by the reaction time (4.5a, 3 min; 4.5b, 10 min; and 4.5c, 20 min) and was measured by TEM. Figure 3 shows the μi spectra for 4.5 ML CdSe NPLs having the lateral sizes of 16 × 3 nm2, 19 × 5 nm2, and 23 × 9 nm2. It can be seen in Figure 3 that the experimental intrinsic absorption in the continuum region from 280 to 309 nm is practically independent of the lateral size within our measurement uncertainty (Table 2). The results of a calculation of the continuum intrinsic absorption for wavelengths from 280 to 309 nm are indicated in Figure 3 as dots along with experimental and calculated results for magic size quantum dots. The calculated intrinsic absorption coincides for the smallest platelets while it predicts a slight increase for larger lateral sizes (smaller corresponding r). This is the result of an increasing (lateral) local field factor because of the increase of the lateral aspect ratio of the platelets with growing reaction time. This behavior originates from the dielectric mismatch in-between the solvent/ligand dielectric constant and the semiconductor particle dielectric constant. Therefore, for very slender oblate particles, an increase of the continuum intrinsic absorption is expected from the Lorentz local field model. We observe a good agreement of the theoretically calculated intrinsic absorption from 280 to 309 nm for our platelet size series in Figure 3 even if we cannot reproduce the abovementioned trend with the given accuracy of our ICP measurements. However, the main critical point is the exact particle lateral size, lateral aspect ratio R, and volume deduced from TEM used in the theoretical model. Because we can assume that the size determination error is at least about 7% for our small particles, we infer a resulting uncertainty of about 14% for the calculated intrinsic absorption values according to Gaussian error propagation taking errors in both lateral directions into account. The experimental intrinsic absorption curves of Figure 3 agree with the calculated intrinsic absorption from 280 to 309 nm within these estimated errors. In Figure 1, we observe a lower agreement of the experimental results with the theoretical calculations for the platelets with 3.5 ML. To check whether this might be related to an inaccuracy in the ICP-AES concentration determination method, we additionally studied magic-size ZB CdSe clusters with first exciton absorption at λ = 407 nm which we synthesized according to Kasuya et al.30 (shown as a blue line in Figure 1). For reference, we also plot the intrinsic absorption values of spherical ZB CdSe particles deduced from Capek et al.23 at 300 nm and our local field theory result at 280 and 309 nm in Figure 1. We observe a good agreement with our ICPAES result. Therefore, we conclude that the observed deviations of the ICP-AES results from the calculations at

NPL samples are included in the calculations by assuming an (n + 1/2) monolayer ZB CdSe platelet thickness lz as suggested earlier. Because not only absorption but also scattering may contribute to the total extinction, we investigate whether light scattering at the particles results in a contribution to the measured extinction. Therefore, we calculate the scattering contribution (index s) to the total extinction cross section (intrinsic extinction) μe = μi + μs as34 μs =

⎞ σs k4 ⎛ 1 1 1 ⎜ = |αx|2 + |αy|2 + |αz|2 ⎟ ⎠ Vp 6π ⎝ 3 3 3

(6)

with


αi =

πlxlylz 6

εs − εm εm + Li(εs − εm)

(7)

with i = x, y, z and k = 2π/nλ. A calculation shows that for all of our platelet and dot samples the intrinsic scattering contribution to μe of an individual particle is less than 1% of the intrinsic absorption contribution μi at 4 eV, so that the values for our particles obtained from eq 3 practically coincide with μe and Rayleigh scattering at the particles plays only a minor role. Analyzing Figures 1 and 3 carefully, we see that

Figure 3. Intrinsic absorption spectra of 4.5 ML CdSe NPLs of different average lateral dimensions: a, 16 × 3 nm2; b, 19 × 5 nm2; c, 23 × 9 nm2. Dots indicate the theoretical intrinsic absorption values from 4.4 to 4 eV (280 to 309 nm, respectively) for the corresponding platelets. As a reference, the experimental and calculated results for magic size quantum dots (MS QD) are added. The inset shows the experimental intrinsic absorption of the platelets at λ = 309 nm.

there is indeed no observable scattering background which would result in a ∝ 1/λ4 background signal. For comparison of the experimental and calculated intrinsic absorption, we plot the calculated intrinsic extinction (absorbance) values at 280

Table 2. Characteristic Parameters of 4.5 ML CdSe NPLs of Different Lateral Sizes size sample lx (nm) 4.5a 4.5b 4.5c

16 19 23

ly (nm)

lz (nm)

aspect ratio reff

1st exciton absorption peak (nm)

stoichiometry

μi at 309 nm (105 cm−1)

μi at 1st exciton (105 cm−1)

3 5 9

1.37 1.37 1.37

0.20 0.14 0.10

509 511 512

Cd1Se0.80 Cd1Se0.80 Cd1Se0.80

3.85 (0.19) 4.06 (0.44) 4.00 (0.7)

1.98 (0.1) 2.27 (0.25) 2.04 (0.35)

D


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investigated colloidal semiconductor nanoplatelets are further cheap to produce in large amounts as analogues of epitaxial quantum wells, for example, for the light-harvesting applications. Their thickness, quantized to integer monolayer multiples, and their lateral size can be precisely controlled during the synthesis. New type II heteronanoplatelets may be used for photovoltaic applications because of their efficient charge separation properties, making semiconductor nanoplatelets interesting systems for solar cell applications, for example, for flexible solar cells.

280 and 309 nm are not related to systematic errors in the ICPAES method. A further reason for the deviations of the calculation results from ICP-AES measurements is related to differing dielectric constants for ZB CdSe at 309 nm given by different authors33,35 that were used in the theory. This already results in a ∼10−16% variation of the calculated intrinsic absorption coefficient according to eq 3. However, within the mentioned uncertainties in theory (lateral size and aspect ratio determination (∼14%) and dielectric constants (10−16%)) and ICP measurements (∼10%)), we observe good agreement of our theory and experimental results for most of the samples. Last quantifiable factor for some differences in Figure 1 which is not within the presented measurements, is a slight change in the dielectric constants of CdSe at 4 eV in the continuum because of the ultrastrong anisotropic confinement of the platelets, especially for the thinnest (1 nm) 3.5 ML platelets. For CdSe quantum dots, Č apek et al.23 also found a slight decrease of the intrinsic absorption with decreasing particle diameter which may be attributed to a change in the dielectric constants of CdSe. The intrinsic continuum absorption of the nanoplatelets is always larger as compared to nanodots or rods of the same material. As seen in Figures 1 and 3, the absorption can be tailored both in the continuum absorption region and at the first exciton transition by altering the lateral and transversal quantum confinement. Figure 2 indicates that the nanoplatelets have always higher intrinsic absorption values as compared to round nanorods of similar aspect ratio or spherical dots because of their very slender shape in two directions. This is the result of a higher optical field penetration in the x and y planes (a and b axes) of the nanoplatelets, where the local field factor in these two directions approaches unity. Compared to slender rods, where the local field factor approaches unity only in one direction along the rod axis, and compared to dots, where f i is always much smaller than 1, higher orientationally averaged optical field penetration in the platelets makes them superb materials with higher light−matter interaction. The intrinsic absorption can be further tuned by the lateral aspect ratio and size of the nanoplates. Both high intrinsic absorption and narrow absorption spectra make the nanoplatelets an interesting material for photonic applications as modulators or solar cells because of their stronger interaction with optical light fields as compared to conventional quantum dots and rods.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b06208. Detailed synthetic procedure of 2.5 ML CdSe NPLs with the first exciton transition at 389 nm, corresponding optical absorption spectra, TEM images of selected CdSe nanoplatelets (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address ‡

Optoelectronic Materials Section, Department of Chemical Engineering, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands. Notes

The authors declare no competing financial interests.

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ACKNOWLEDGMENTS A.A., A.P., and M.A. acknowledge the CHEMREAGENTS program. A.A. acknowledges support by DFG project AC 290/ 1-1, and R.S and U.W. by DFG project WO477/32-1. We further thank L. Kisiel for help with ICP-AES analysis.

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REFERENCES

(1) Leatherdale, C. A.; Woo, W. K.; Mikulec, F. V.; Bawendi, M. G. On the Absorption Cross Section of CdSe Nanocrystal Quantum Dots. J. Phys. Chem. B 2002, 106, 7619−7622. (2) Protasenko, V.; Bacinello, D.; Kuno, M. Experimental Determination of the Absorption Cross-Section and Molar Extinction Coefficient of CdSe and CdTe Nanowires. J. Phys. Chem. B 2006, 110, 25322−25331. (3) Jasieniak, J.; Smith, L.; Van Embden, J.; Mulvaney, P.; Califano, M. Re-Examination of the Size-Dependent Absorption Properties of CdSe Quantum Dots. J. Phys. Chem. C 2009, 113, 19468−19474. (4) Moreels, I.; Lambert, K.; Smeets, D.; De Muynck, D.; Nollet, T.; Martins, J. C.; Vanhaecke, F.; Vantomme, A.; Delerue, C.; Allan, G.; et al. Size-Dependent Optical Properties of Colloidal PbS Quantum Dots. ACS Nano 2009, 3, 3023−3030. (5) Achtstein, A. W.; Hennig, J.; Prudnikau, A.; Artemyev, M. V.; Woggon, U. Linear and Two-Photon Absorption in Zero- and OneDimensional CdS Nanocrystals: Influence of Size and Shape. J. Phys. Chem. C 2013, 117, 25756−25760. (6) Achtstein, A. W.; Ballester, A.; Movilla, J. L.; Hennig, J.; Climente, J. I.; Prudnikau, A.; Antanovich, A.; Scott, R.; Artemyev, M. V.; Planelles, J.; et al. One- and Two-Photon Absorption in CdS Nanodots and Wires: The Role of Dimensionality in the One- and Two-Photon Luminescence Excitation Spectrum. J. Phys. Chem. C 2015, 119, 1260−1267. (7) Hens, Z.; Moreels, I. Light Absorption by Colloidal Semiconductor Quantum Dots. J. Mater. Chem. 2012, 22, 10406−10415.

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CONCLUSIONS In conclusion, we have shown that the new class of CdSe nanoplatelets has strong thickness and lateral size dependent absorption properties in the continuum absorption region as well as at the first excitonic transition. A Lorentz local field theory in connection with an effective medium MaxwellGarnett approach gives a quite adequate model of the intrinsic absorption coefficient μi in the nanoplatelet absorption continuum. Slight deviations have been attributed to size determination, dielectric constants, and ICP errors. The high aspect ratio of these platelet particles leads to a significantly increased intrinsic continuum absorption of these quasi-2D nanoparticles as compared to nanodots or rods, which can be understood in terms of the local field inside the nanoparticles. Therefore, the nanoplatelets are more efficient light absorbers as compared to other colloidal particles. This increased light− matter interaction might be used for efficient modulators or solar cells and will be the subject of further investigations. The E


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Linear Absorption in CdSe Nanoplates: Thickness and Lateral Size

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