Size-Dependent Optical Properties of Zinc Blende Cadmium Telluride

Article pubs.acs.org/JPCC

Size-Dependent Optical Properties of Zinc Blende Cadmium Telluride Quantum Dots John Sundar Kamal,†,‡ Abdoulghafar Omari,†,‡ Karen Van Hoecke,§ Qiang Zhao,∥ André Vantomme,∥ Frank Vanhaecke,§ Richard Karel Capek,†,⊥ and Zeger Hens†,‡,* †

Physics and Chemistry of Nanostructures, Ghent University, Krijgslaan 281-S3, B-9000 Gent, Belgium Center for Nano and Biophotonics, Ghent University, B-9000 Gent, Belgium § Department of Analytical Chemistry, Ghent University, Krijgslaan 281-S12, B-9000 Gent, Belgium ∥ Instituut voor Kern- en Stralingsfysica, K.U.Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium ‡

S Supporting Information *

ABSTRACT: We analyze the optical properties of CdTe quantum dots, including the sizing curve, the absorption coefficient, and the oscillator strength of the band gap transition, by combining absorption spectroscopy, elemental analysis, and electron microscopy imaging. At short wavelengths, the absorption coefficient spectrum is still affected by quantum confinement, yet a largely constant value, close to that of bulk CdTe, is found at around 410 nm. At shorter wavelengths, remaining quantum confinement effects on the CdTe E1 transition are present even for the largest quantum dots studied (11 nm). For the band gap transition, we find an integrated absorption coefficient μgap that scales almost proportionally to the inverse of the quantum dot volume. Especially for the smaller diameters, deviations up to a factor of 3 are found as compared to widely used literature values. The corresponding oscillator strength fgap is almost size-independent in the diameter range 3−7 nm. The correspondence between radiative lifetimes predicted based on fgap and literature values is discussed.

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INTRODUCTION Over the last 20 years, sterically stabilized colloidal nanocrystals have emerged as unique and versatile building blocks of nanostructured materials that combine tunable opto-electronic properties with a suitability for solution-based processing.1 A key technique for the characterization of colloidal nanocrystal dispersions is absorption spectroscopy. In the case of semiconductor nanocrystals or quantum dots (QDs), it gives access to the average QD diameter dQD and the volume fraction f of semiconductor material in solution. Numerous examples show that both quantities are essential for present day research on colloidal QDs. Mapping the size dependence of electro-optical properties is widely used to understand QD properties and to link them to theoretical modeling;2 the time development of the amount of QD material formedaccessible via the volume fractionis one of the starting points to analyze the kinetics and the mechanism of a QD synthesis.3 Furthermore, the knowledge of QD concentrations is needed for the rational development of ligand exchange procedures1,4 or reproducible cytotoxicity studies.5 As a result, the availability of reliable sizing curveslinking dQD to the QD band gap Egand absorption coefficientsenabling the calculation of QD volume fractions from an absorbanceis imperative for QD research. Establishing experimental sizing curves typically relies on the analysis of transmission electron microscopy (TEM) images. Possible systematic errors related to the implementation of the © 2012 American Chemical Society

image analysis can be avoided by bringing together experimental data of different groups, as was done for CdSe,6 CdTe,6 PbSe,7 and PbS.8 The determination of absorption coefficients (μ) is based on elemental analysis. This requires well-purified dispersions, which can be verified by solution NMR.7 On the other hand, an absorption coefficient determination can be checked for consistency since it was found for many materials that μ coincides with the value calculated for the bulk material using the Maxwell−Garnet model at short wavelengths.7−12 Using this consistency check, molar absorption coefficientsa quantity closely related to μfor CdSe QDs published by Yu et al.13, for example, were re-examined by Jasieniak et al.,14 leading to considerably improved values. Here, we present an analysis of the absorption coefficient of CdTe QDs. Together with CdSe and CdS, CdTe is one of the first materials synthesized using the hot injection approach.15,16 By now, various approaches have been described to synthesize them,17−19 control their size and shape,20 and incorporate them in heteronanocrystals.21 Both the sizing curve6,13 and sizedependent molar absorption coefficients13 have been published. Although less widespread than CdSe, CdTe QDs are nowadays used in, for example, LEDs,22 bioimaging,23 and photovoltaics.24 Received: December 20, 2011 Revised: January 25, 2012 Published: January 31, 2012 5049

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aperture with Z-filter has been used. On the basis of the TEM images, the size histogram, mean diameter, and size dispersion of the QDs are determined by analyzing 100−150 particles for each sample. Absorption Coefficient Determination. Absorption coefficients were determined by combining elemental analysis with UV−vis absorption spectroscopy. The concentration of Cd was determined by inductively coupled plasma−mass spectrometry (ICP−MS). Samples for ICP−MS analysis were prepared by drying a known amount of CdTe QD suspension in a nitrogen flow. The dried samples were digested in 500 μL of HNO3 to be analyzed with a Perkin-Elmer SCIEX ELAN 5000 ICP-MS. The Cd:Te ratio R is determined using Rutherford backscattering spectrometry (RBS). Samples for RBS analysis consisted of 10−15 nm thick films of CdTe QDs spin coated on Si substrates. The measurements were done with a 4 MeV He2+ ion beam and an NEC 5SDH-2 Pelletron tandem accelerator with a semiconductor detector at backscattering angles of 124° and 168°. The Cd:Te ratio is obtained from the ratio of the backscattered intensity with Cd (ICd) and Te (ITe) nuclei after Z2 correction (Z: atomic number)

Here, we combine UV−vis absorption spectroscopy, TEM imaging, and elemental analysis to determine the absorption coefficients at short wavelengths and at the band gap transition. At short wavelengths, we find that size quantization persists, but still, wavelength regions exist where the absorption coefficient is size-independent and close to the bulk value. At the band gap transition, integrated absorption coefficients deviate markedly from published values and lead to largely size-independent oscillator strengths in the range 10−13. These results will strongly enhance the accuracy of volume fraction and concentration determination in future research on CdTe QDs.

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EXPERIMENTAL SECTION Chemicals. Methanol and 2-propanol were purchased from VWR BDH Prolabo and had Rectapur grade. Toluene was also purchased from VWR BDH Prolabo and had technical and Normapur grade, respectively. Cadmium oxide (CdO, 99.99+%) was purchased from Aldrich. Tellurium (99.999%) and 1-octadecene (ODE, technical) were purchased from Alfa Aesar. Tetradecylphosponic acid (TDPA, 98%) was purchased from PCI synthesis. Hexadecylamine (HDA, 90%) was purchased from Merck. Synthesis. CdTe QDs were synthesized by adapting the procedure of Dorfs et al.,25 which makes use of CdO, tetradecylphosphonic acid (TDPA), elemental Te, trioctylphosphine (TOP), and hexadecylamine. Octadecene (ODE) is typically used as the solvent. The Cd-TDPA precursor was prepared by mixing CdO and TDPA in a 1:3 molar ratio, degassing under nitrogen flow for 1 h at 100 °C, followed by dissolving the CdO under a nitrogen atmosphere between 250 and 300 °C until the mixture became clear. TOP-Te was typically prepared by dissolving 1.5 mmol of Te in 10 mL of TOP at about 80 °C for one hour under a nitrogen atmosphere. In a typical synthesis (procedure 1), 0.3 mmol of the CdTDPA precursor, 0.9 mmol of HDA, and 7.8 mL of ODE are degassed under a nitrogen flow at room temperature and at 100 °C for 1 h, respectively. The temperature is then raised to 280 °C under a nitrogen atmosphere, and 2 mL of the TOP-Te precursor is subsequently injected. After the injection, the temperature of the mixture is reduced and maintained at 260 °C for the growth of nanocrystals. The reaction is stopped by temperature quenching with a water bath. The product obtained is purified using toluene as the solvent and an isopropanol/methanol mixture as the nonsolvent. By controlling the reaction time, CdTe QDs with a size of 4−6 nm are obtained. Smaller sizes (procedure 2) are obtained by adding stearyl alcohol in a 12:1 ratio to the Cd precursor to the reaction mixture prior to injection. QDs with a diameter above 6 nm (procedure 3) are synthesized using multiple precursor injections. For this, 4.5 mmol of the Cd-TDPA precursor is dissolved in 4 mL of ODE at 280 °C for 15 min and mixed with 1 mL of a 1.5 M TOP-Te solution after cooling. This precursor mixture is added to the reaction mixture with a syringe pump for 1 h at a rate 2 mL/h. Again, the temperature of the reacting mixture was quenched by a water bath, and the product was purified as described above. Size Determination. The mean diameter dQD of the CdTe QDs was determined from bright-field TEM images recorded with a Cs corrected JEM-2200FS transmission electron microscope. The samples for TEM were prepared by drop casting a dilute suspension of CdTe QD on holey carbon film supported by a copper TEM grid. To improve the contrast, a high contrast

I Z2 R = Cd × Te 2 ITe ZCd

(1)

For the absorption measurements, an identical amount of CdTe QDs as used for ICP−MS was dried under nitrogen flow and redispersed in toluene. The absorbance spectrum of the resulting dispersion was recorded with a Perkin-Elmer Lambda 950 UV−vis spectrophotometer. We estimate that the procedure leads to an error of about 10% on the determined absorption coefficients.12

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RESULTS AND DISCUSSION Material Characterization. Figure 1 gives the basic characteristics of a sample of CdTe QDs synthesized following procedure 1. The TEM overview image (Figure 1a) demonstrates that the resulting CdTe QDs are quasi-spherical, in this case with an average diameter of 5.7 nm and a narrow size dispersion of around 4% (Figure 1b). According to the X-ray diffractogram (Figure 1c), the QDs used here have the zinc blende crystal structure. Furthermore, from the ratios of the Z2-corrected integrated intensities of Cd and Te in the RBS spectrum (eq 1), it follows that the CdTe QDs studied here are cation rich, with a Cd:Te ratio R of 1.10 for the sample shown here. A similar result was found for PbSe, PbS, and CdSe QDs.7,8,26−28 As shown in the Supporting Information, these conclusions hold for all sizes. Only for the largest QDs (8− 10 nm), crystal facets are more pronounced, and the size dispersion increases to about 8%. Figure 2a shows the UV−vis absorption spectra of six different batches of CdTe QDs (see Supporting Information for TEM images and size histograms). For all samples, the wavelength λ1S−1S of the first exciton transition can be readily determined. The combination of the resulting λ1S−1S with TEM overview images of the different samples enables us to construct the CdTe sizing curve, which relates the band gap Egas calculated from λ1S−1Sto dQD. Figure 2b represents the different data points we obtain and compares them with sizing curves previously published by Donega et al. and Yu et al.6,13 A good correspondence is overall obtained with the former, with maximum deviations of about 0.3 nm. On the other hand, deviations up to 0.6 nm are found with the sizing curve of Yu et al., 5050

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An advantage of using μi is that its value does not depend on the QD sizing curve, which means that f can be determined irrespective of errors on the size determination. For CdTe QDs, f is related to the molar concentrations of Cd (CCd) and Te (CTe) according to (a: lattice parameter of the CdTe zinc blende unit cell) f=

⎛ a3 a3 1⎞ NA(CCd + C Te) = NACCd⎜1 + ⎟ ⎝ 8 8 R⎠

(4)

As outlined in the Experimental Section, we obtain CCd using ICP−MS and R using RBS measurements. Figure 3(a) shows

Figure 1. Basic characterization of 5.7 nm CdTe QDs synthesized according to procedure 1. (a) TEM overview image. (b) Size histogram, yielding a size dispersion of 4%. (c) (black line) XRD pattern of the CdTe QDs and (red bars) the reference diffractogram of zinc blende CdTe. (d) RBS spectrum indicating the backscattered intensity for Cd (ICd) and Te (ITe), yielding a Cd:Te ratio of 1.10 after Z2 correction. Figure 3. (a) Intrinsic absorption coefficient (μi) spectra of CdTe QDs of different sizes (left to right: 3.10, 3.65, 4.10, 5.00, 5.70, 7.10, and 11.0 nm) in toluene and (black line) intrinsic absorption coefficient (μi,th) calculated for bulk CdTe according to eq 5. (Inset) zoom of the short-wavelength range of the μi spectra. (b) μi at (blue markers) 410 nm and (red markers) 330 nm as a function of the CdTe QD diameter, together with (dashed lines) the respective average μi and (black lines) the corresponding bulk value. (c) Relative standard deviation on μi as a function of wavelength calculated using the seven spectra shown in (a).

seven different μi spectra determined by combining elemental analysis (yielding f) and absorption spectroscopy (yielding A) in toluene. Similar to previous studies on various QDs,7−12 we find that the μi spectra tend to coincide at short wavelengths, especially in the wavelength ranges around 400 and below 340 nm. In the literature, this has always been interpreted as an absence of quantum confinement effects on higher-energy conduction and valence band states. Moreover, excellent correspondence has been demonstrated between the experimental μi and a theoretical value μi,th calculated within the Maxwell−Garnett effective medium theory,30 using the bulk dieletric function εR + iεI of the QD material

Figure 2. (a) Absorption spectra of QDs with sizes of (bottom to top) 3.10, 3.65, 4.10, 5.00, 5.70, and 7.10 nm. (b) Relation between CdTe QD band gap Eg and diameter dQD, including (markers) experimental data obtained here, (full black) best fit according to eq 2, (dotted red) sizing curve of Yu et al.,13 and (dashed blue) sizing curve of Donega et al.6

especially in the range dQD = 3.5−6.5 nm. Taking a value of 1.51 eV for the band gap of bulk CdTe,29 we use the following best fit to our experimental data to link Eg to dQD (black line in Figure 2b) E0(d) = 1.51 +

μi,th =

1 0.048d2 + 0.29d − 0.09

ln(10)A fL

(5)

Here, ns is the refractive index of the solvent, and f LF is the local field factor, i.e., the ratio between the electric field outside and inside the QD. For spherical QDs, f LF is given by (εs = ns2)

(2)

Intrinsic Absorption Coefficient at Short Wavelengths. We quantify the absorbance of dispersed colloidal QDs in the first place by the intrinsic absorption coefficient μi, which relates the measured absorbance A of a QD dispersion to the fraction f of the sample volume occupied by the QDs (the QD volume fraction) μi =

2π |f |2 εI ns λ LF

fLF =

3εs εR + i εI + 2εs

(6)

The bulk μi,th reference spectrum for CdTe in toluene is shown as the black line in Figure 3. It clearly reproduces the overall increase of μi with decreasing wavelength, and the wavelength regions where all μi spectra tend to coincidearound 410 and 320 nmcorrespond to wavelengths where the bulk

(3) 5051

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energy integrated absorption coefficient μi,gap of the first exciton transition. This can be obtained either by using μi spectra obtained by determining f using elemental analysis (see Figure 3) or by normalizing absorption spectra using the average value of μi,410. In this way, μi,gap follows from the integrated absorbance Agap of the first exciton absorbance peak

spectrum does not show particular features. Figure 3b shows μi,410 and μi,330 as a function of dQD. One sees that both values are largely size-independent with an average value lower than μi,th by 16% and 24%, respectively. A similar deviation was found with zb-CdSe at wavelengths below 350 nm.12 As shown in Figure 3c, the standard deviation on μi is lowest in the wavelength range 405−420 nm. Therefore, we propose to use the average absorption coefficient μi,410 as obtained here for the determination of CdTe QD volume fractions in toluene dispersions μi,410 = 75500 cm−1

μi ,gap =

(10)

Figure 5. Energy integrated intrinsic absorption coefficient μgap as a function of QD diameter (bottom axis, calculated according to eq 2) and λ1S−1S (top axis), showing data obtained by (filled blue circles) elemental analysis and (open blue circles) normalization of μi at 410 nm. The blue line is a best fit according to eq 11, and the red squares represent the data according to Yu et al.13

3 N πdQD A

μ 6 ln(10) i

μ A 410 i ,410

Typically, μi,gap is calculated by doubling the integrated lowenergy half of the first exciton peak.7

(7)

The intrinsic absorption coefficient of bulk CdTe shows a pronounced feature at 365 nm, which corresponds to the E1 transition that connects initial and final states along the Λ direction in the Brillouin zone.31,32 Figure 3 shows that this feature is not present in the μi spectra of the smaller CdTe QDs. Only for the largest sizes, a shoulder develops in this wavelength range, which becomes more pronounced and shifts from shorter wavelengths toward 365 nm with increasing size. This is a clear indication of size quantization effects in this particular region of the Brillouin zone, similar to what was found for the E1 transition along the Σ direction in PbSe QDs.33,34 Importantly, this persistence of size-quantization effects implies that normalization of CdTe QD spectra for relative comparison is only viable at those wavelengths where size effects on the absorption coefficient are minimal, i.e., around 410 or 320 nm, respectively. The molar absorption coefficient ε of dispersed colloidal CdTe QDs is obtained as the product of μi and the volume of 1 mol of QDs

ε=

A gap

Figure 5 shows the resulting μi,gap obtained with both procedures. Opposite of μi,410, μi,gap shows a marked increase with decreasing particle size. Since μi gives an absorbance per unit volume of material, this shows that for the same volume of CdTe small QDs absorb more light at their bandgap transition than large QDs. The dependence of μi,gap on dQD in the size range envisaged here (3−7 nm) can be well fitted to a power law. A best fit shows that μi,gap is about proportional to the inverse of the QD volume

(8)

Since μi,410 is independent of dQD, we obviously find that ε410 3 scales proportionally to dQD (see Figure 4). Writing dQD in

μi,gap = (2.68 ± 0.41) × 107 × d(−2.76 ± 0.12) (eV m−1) (11)

Molar absorption coefficients at the band gap for CdTe QDs have been published before by Yu et al.13 To compare these results with the data obtained here, we have combined the molar absorption coefficients and the sizing curve of these authors to calculate a μi,gap (see Supporting Information for more details). Figure 5 gives the resulting values as a function of λ1S−1S (upper horizontal axis) and dQD calculated according to the sizing curve proposed here (lower horizontal axis). Depending on the actual size, the resulting μi,gap according to Yu et al. is up to 3 times smaller than the values reported here. Since our values correspond to a μi,410 that only deviates from the bulk value by 16%, we conclude that the use of the molar absorption coefficients proposed by Yu et al. for volume fraction and concentration determination of CdTe QD dispersions may give considerable errors and is therefore not recommended. Oscillator Strength and Lifetime. The oscillator strength of an electronic transition from a ground (g) to an excited (e) state compares the power absorbed by the electronic transition

Figure 4. Representation of (markers) the molar absorption coefficientʼ of CdTe QDs in toluene at 410 nm as a function of QD diameter and (full line) the cubic fit according to eq 9.

nanometers, a best fit to the experimental data yields (ε410 in cm−1/μM) 3 ε410 = (0.0106 ± 0.0002) × dQD

(9)

Intrinsic Absorption Coefficient at the Band Gap. In the literature, (molar) absorption coefficients are often reported at the band gap transition, typically in combination with a normalization procedure to account for peak broadening due to size dispersion.13,35 A useful quantity in this respect is the 5052

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2 to 3 times smaller than the experimental ones, which range from about 20 to 40 ns over the same diameter range. Although a detailed interpretation of this difference is out of the scope of the present manuscript, a first explanation of this difference could be that instead of an equal occupation probability of all eight exciton levels a dark exciton state is preferentially occupied. However, opposite of the data shown in Figure 6b, this should lead to a better correspondence between predicted and measured lifetimes for larger QDs, which have a concomitantly lower energy splitting between the different exciton levels. Alternatively, the measured lifetimes will exceed the predicted values when additional dark exciton states, not accounted for in the g = 8 assumption, are accessible. This is not unlikely given the small energy spacing between the S3/2 and P3/2 hole states,38 which would mean that a manifold of 16 instead of 8 exciton states is readily accessible for the first exciton. As shown in Figure 6, the assumption of g = 16 leads to a good correspondence between measured and predicted lifetimes, especially for the smaller sizes.

to that of a classical dipole oscillator with the same resonance frequency. It is an intrinsic property of an electronic transition closely related to the g → e transition dipole matrix element. The oscillator strength fgap related to the first exciton transition can be calculated from the experimental μi,gap according to (ε0, permittivity of the vacuum; c, speed of light; me, electron mass; ℏ, Planck’s constant)7 fgap =

3 2ε0nscme 1 πdQD μi ,gap e πℏ |f |2 6 LF

(12)

Figure 6(a) shows the resulting fgap as a function of dQD calculated using the bulk dielectric function of CdTe at the

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CONCLUSIONS We have analyzed the basic optical propertiessizing curve, absorption coefficient, and oscillator strength of the band gap transitionof CdTe QDs by combining UV−vis absorption spectroscopy, TEM, ICP-MS, and RBS measurements. At 410 nm, we retrieve a largely size-independent intrinsic absorption coefficient μi. The resulting value is close to what is expected for bulk CdTe and can be used for determining the volume fraction of spherical CdTe nanocrystals in colloidal dispersions. Despite the size-independent μi at 410 nm, we observe persistent quantum confinement effects on the E1 transition, which appears less pronounced and blueshifted in CdTe QDs relative to its bulk value of 365 nm. Around the band gap, we find an integrated absorption coefficient μgap that scales proportionally to the inverse of the QD volume. Especially for the smaller diameters, significant deviations are found as compared to widely used literature values. The corresponding oscillator strength fgap is almost size-independent in the diameter range 3−7 nm. Radiative lifetimes predicted based on fgap are in line with published values if a 16-fold degeneracy for the first exciton is assumed.

Figure 6. (a) Oscillator strength fgap of the first exciton transition in CdTe QDs, based on (filled blue circles) elemental analysis and (open circles) normalization of μi at 410 nm. (b) Spontaneous emission lifetime calculated according to eq 14 using (filled blue circles) g = 8 and (open blue squares) g = 16 and (filled red triangles) experimental data according to Van Driel et al.36

wavelength of the respective band gap transition. As could be expected from the almost cubic dependence of μi,gap on 1/dQD, fgap is largely constant in the diameter range 3−7 nm, varying only between 10 and 13. In this respect, CdTe QDs differ significantly from CdSe QDs, where the oscillator strength shows a pronounced size dependence and drops to values of around 5 in the 2−4 nm size range.12 On the other hand, a similar sizeindependent oscillator strength was found for InAs QDs.10 The oscillator strength of an electronic transition is related to the decay rate τ−1 of the excited state by spontaneous emission. Summing over all accessible exciton states jpresumed to be in thermal equilibriumτ−1 reads (kB, Boltzmann’s constant; T, absolute temperature) −1

τ

=

e2

ns|fLF 2πε0c 3me

|2 ω2

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S Supporting Information *

∑j fij e−Δεij / kBT ∑j e−Δεij / kBT

Additional experimental details. This material is available free of charge via the Internet at http://pubs.acs.org.

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Here, Δεij denotes the energy difference between the exciton state j and the lowest energy exciton state i. When Δεij ≪ kBT, the spontaneous emission rate can be rewritten as (g, total number of exciton states accessible) τ−1 =

=

e2 2πε0c 3me e2

ns|fLF |2 ω2

ns|fLF 2πε0c 3me

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 0032-9-2644863. Fax: 0032-9-2644983. Present Address ⊥

∑j fij

Schulich Faculty of Chemistry, Russell Berrie Nanotechnology Institute, Technion, Haifa 32000, Israel.

g

Notes

fgap |2 ω2 g

ASSOCIATED CONTENT

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge BelSPo (IAP 6.10 photonics@be), EU-FP7 (ITN-Herodot) and the FWO-Vlaanderen (project (G.0794.10) for financial support. A.O. acknowledges the IWTVlaanderen for a research grant.

Figure 6(b) plots the resulting predicted lifetime τ, calculated taking g = 8,37 together with experimental literature data.36 In the diameter range 3−7 nm, the predicted lifetimes slightly increase from 9 to 13 ns with increasing dQD. These lifetimes are 5053

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