ARTICLE pubs.acs.org/JPCC
Quantum Confinement in CdTe Quantum Dots: Investigation through Cyclic Voltammetry Supported by Density Functional Theory (DFT) Santosh K. Haram,*,† Anjali Kshirsagar,‡ Yogini D. Gujarathi,† Pravin P. Ingole,† Omkar A. Nene,†,|| Ganesh B. Markad,† and Sachin P . Nanavati§ †
Department of Chemistry and ‡Department of Physics, University of Pune, Pune 411 007, India C-DAC, Pune University Campus, Pune 411 007, India
§
bS Supporting Information ABSTRACT: Cyclic voltammetry has been used as a tool to study the quantum confinement in oleic acid stabilized CdTe quantum dot dispersions. The band structure parameters, conduction band edge, valence band edge, and quasi-particle gap, have been estimated as a function of quantum dot size, ranging from ca. 2.4 to 4.7 nm and compared with the corresponding UVvis data. To support the experimental results, density functional theory (DFT) based calculations have been performed for passivated nonstoichiometric CdmTen (m6¼n) clusters, using the projector augmented wave method. The computed HOMOLUMO positions and their energy separations have been found to be in good agreement with the values obtained from UVvis spectroscopy and cyclic voltammetry.
1. INTRODUCTION An understanding of the underlying physics and chemistry of semiconductor quantum dots (Q-dots) in their strong confined regimeparticularly in the evolution of their band structure, as a function of size,14 has an immense importance in view of their direct applications in photovoltaics,5 optoelectronics,6 and biomedical fields.7,8 Furthermore, significant insight can be gained if the simulation methods are used to study such evolutions by mimicking the experimental situation in a physically convincing way. The values of the band structure parameters are generally estimated by photoelectron spectroscopy (PES)9 and scanning tunneling spectroscopy (STS).10 These techniques, however, involve sophisticated instrumentation and tedious sample preparation protocols. The work reported by us1113 and others1416 has demonstrated that voltammetric techniques can instead be readily used to estimate these parameters. The main advantage of voltammetry is the simple experimental conditions under which the measurements are performed, compared to PES and STS. Moreover, the results have been in good agreement with the UVvis spectroscopy measurements and also fit very well with the theoretical predictions.17 In this regard, voltammetric measurements on the quantumdots of CdSe (Q-CdSe) have been reported in more detail. Besides size dependent quantum confinement,13,14 the effect of other physicochemical aspects, such as the nature of solvents18 and ligands (charge, dielectric constant, etc.)16,19,20 on the voltammograms have been studied in the case of Q-CdSe. All of these studies summarize that the cathodic and anodic peaks noted in the voltammograms of Q-CdSe can be directly correlated with the electron transfers mediated through the highest occupied r 2011 American Chemical Society
molecular orbital (HOMO) or valence band edge (h1) and lowest unoccupied molecular orbital (LUMO) or conduction band edge (e1) and are not drastically affected by the nature of ligands, capping agents, or the solvents used. In the present work, we have tried to gain further insight on such an evolution in the case of Q-dots of CdTe (Q-CdTe) by cyclic voltammetry (CV), corroborated with the simulated results, using density functional theory (DFT). CdTe is a p-type direct band gap (1.44 eV) semiconductor and is viewed as an ideal window material for the heterojunction photovoltaic systems.21,22 Having a large Bohr exciton radius,23,24 it is expected to exhibit a size quantization effect (SQE) in the wider size range. Thus, it would provide a unique opportunity to study the SQE in a more elaborated way. In spite of these promising features, sufficient attention has not yet been paid toward the studies related to SQE in Q-CdTe, especially through voltammetry. To our knowledge, there are three isolated reports which discussed the voltammetric measurements on Q-CdTe with a limited effort to understand the SQE as a function of size. Moreover, the comparison of these results with a suitable theoretical model has not yet been attempted. Gaponik and co-workers25 have reported size dependent electrochemical behavior of thiol capped Q-CdTe, drop casted on a gold electrode in an aqueous medium. The aqueous medium, however, is not a solventof-choice for such measurements, as (1) it cannot provide an adequate electrochemical potential window to observe the redox Received: December 2, 2010 Revised: March 3, 2011 Published: March 21, 2011 6243
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The Journal of Physical Chemistry C peaks which are ca. 22.5 V apart, and (2) after charge transfer, the Q-dots are likely to undergo rapid hydrolysis, which may destabilize the Q-dots and may not provide the desired outcome. Besides, the measurements on drop-casted Q-dots seldom fulfill the fundamental requirement of charge transfer on a physically isolated system, and thus, the results obtained may not in 13,17 All principle be correlated to the quasiparticle gap (εqp gap). of these limitations can be overcome by carrying out measurements on the Q-dot dispersion in polar organic solvents. Bard and co-workers26 have reported differential pulse voltammetry (DPV) and electro-generated chemiluminescence (ECL) response from 3.9 nm trioctylphosphine oxide (TOPO) capped Q-CdTe, dispersed in an acetonitrilebenzene mixture. Poor dispensability of the TOPO capped Q-CdTe27 in the solvent mixture perhaps did not allow them to accomplish the measurements on varied size. Li et al.28 carried out electrochemical characterization of anisotropic shaped Q-CdTe (6.9 nm), dropcasted on the glassy carbon (GC) electrode. Again, the SQE with respect to the particle size has not been studied. Thus, to the best of our knowledge, a complete investigation and related data regarding the band structure parameters of Q-CdTe for varying sizes and their direct comparison with the known theoretical model are lacking in the literature. This gap in the literature has motivated us to undertake a detailed study regarding the size dependent voltammetric behavior of Q-CdTe dispersion in dichloromethane (DCM) medium. Q-CdTe stabilized with oleic acid has been employed in the present studies because of their better dispersibility in the solvent of interest in the wider size range (ca. 2.4 to 4.7 nm). These samples were characterized with UVvis, PL, and CV measurements to provide the information about the band structure parameters, op quasi-particle gap (εqp gap), and optical band gap (εgap) as a function of size. To support the experimental results, density functional theory (DFT) based calculations have been performed for nonstoichiometric CdmTen (m6¼n) clusters using the projector augmented wave (PAW) method. To render the surface of Q-CdTe inert, the active sites have been passivated with fictitious hydrogen atoms (H*) as terminating ligands. The computed HOMO and LUMO positions and the energy gaps (εDFT gap ) as a function of size have been found to be in good agreement with the one obtained from CV measurements.
2. EXPERIMENTAL SECTION 2.1. Materials. Cadmium oxide (CdO), Te powder, and oleic acid were purchased from SD fine chemicals. Octadecene (Across Organics), toluene (Merck), and tri-n-octylphosphine (TOP), (Technical grade, Aldrich) were used as received, without further purification. Methanol, ethanol, and 1-butanol purchased from Merck chemicals were dried over CaH2 and distilled twice before use. Dichloromethane (DCM) (Merck, dried reagent grade) was treated with CaH2, double distilled, and stored over preactivated Linde 4A-type molecular sieves. Electrochemical grade tetrabutylammonium perchlorate (TBAP) was purchased from Fluka and used as received. 2.2. Preparation of Oleic Acid Capped Q-CdTe. Varied sizes of oleic acid capped Q-CdTe were prepared using the method suggested by Peng et al.29,30 The stock solution of TOP-Te was prepared by the reported protocol.29 In brief, 0.159 g of Te and 5.0 mL of TOP was heated gently at ca. 210 °C, until the appearance of pale green-yellow color to the solution. It was then diluted to 25 mL with 1-octadecene to form 0.1 M TOP-Te stock
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solution. CdO (0.064 g) was predried in situ over N2 flow at 200 °C, in the specially designed borosilicate cylindrical cell (Figure-S1, Supporting Information). The temperature of the cell was brought down, and a solution of oleic acid (1.0 mL) in octadecene (2.5 mL) was injected with constant stirring. The temperature was subsequently elevated to 300 °C under continuous flow of N2 until the complete dissolution of CdO was noted. Into this, freshly prepared TOP-Te stock solution (2.5 mL) was swiftly injected with vigorous stirring. After the desired time interval, the reaction was quenched by lowering the temperature, followed by the addition of toluene (ca. 10 mL) to the reaction mixture. To separate the product from the mother liquor, a mixture of dry ethanol and dry n-butanol was used as antisolvents. The resultant ruby-red color precipitate was centrifuged and washed repeatedly with methanol. Eventually, the sample was vacuum-dried and stored in a vacuum desiccator for further analysis. Varied particle sizes were accomplished by withdrawing the aliquots at predecided time intervals. The products thus prepared were used for further analysis within 48 h to avoid possible agglomeration. 2.3. Material Characterization. For routine characterization, UVvis spectra were recorded using an Agilent 8453 diode array single beam spectrophotometer. Steady state photoluminescence (PL) spectra were recorded at room temperature, with the help of a Shimadzu RF-5301PC spectrofluorometer. For the molecular level understanding of the surface passivation of Q-CdTe, FTIR spectra were recorded using a Shimadzu FTIR-8400 spectrophotometer, having the attenuated total reflection (ATR) attachment. Powder X-ray diffractograms (XRD) were recorded on the dried product using a Bruker, D8-Advance, X-ray diffractometer (CukR, 40 kV and 40 mA). Low resolution transmission electron microscopic (TEM) images were recorded on the samples using a Philips CM200 transmission electron microscope (200 kV). 2.4. Electrochemical Characterization. The Electrochemical measurements were performed with the help of Metrohm Potentiostat/Galvanostat (model Autolab PGSTAT 100). A commercial Pt disk electrode (CHI Instruments, USA, 2-mm diameter), Ag wire, and Pt-wire loop were used as working, quasireference, and counter electrodes, respectively. Prior to use, the working electrode was polished over 0.5 μm alumina powder, rinsed with copious amounts of Milli-Q water, and was pretreated electrochemically with 0.5 M H2SO4 by cycling the potential between 1.2 V and 0.55 V (scan rate of 1 V s1), until characteristic H2/O2 adsorption/desorption peaks reported for the clean Pt surface were observed.31 In order to minimize the interference of moisture and CO2, the voltammetric measurements were carried out in an indigenously developed vacuum electrochemical cell, having a special provision to transfer the analytes with minimum exposure to the laboratory atmosphere. After fixing the electrodes to the cell, 0.239 g of TBAP (typically 100 mM for a 5 mL solution) was transferred and vacuum-dried in situ, at 80 °C for an hour. The cell was cooled down to room temperature and brought to atmospheric pressure by relieving the vacuum through high purity Ar gas. Predried 5 mL DCM was injected into the cell through a Silicone septum under Ar atmosphere. The blank or controlled voltammograms were acquired in TBAP-DCM mixture, prior to the measurements. Dispersion of Q-dots in predried DCM (net concentration 1.0 mg mL1) was then injected through a siliconerubber septum, and similar experiments were performed under a slight positive pressure of Ar gas. At the end of each set of experiments, the potentials were calibrated with 6244
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respect to the normal hydrogen electrode (NHE), using ferrocene as an internal standard.
3. THEORETICAL METHODS Bulk CdTe occurs in zinc blende (ZB) and wurtzite structures. The wurtzite structure is higher in energy by 9 meV per CdTe pair than the ZB structure.32 Bulk CdTe is reported to have a direct band gap of 1.44 eV at Γ point. It has been reported that IIVI semiconductor Q-dots possess the same geometric structure as that of respective bulk material with slight variations in lattice parameters. Thus, nonstoichiometric clusters can be considered as fragments of bulk, possessing the same structural symmetry as that of the bulk.33 We have therefore considered the Q-dots as atom-centered ZB fragments. For the computational modeling of electronic structure of Q-dots, surface passivation has to be implemented to mimic the experimental situation. Bare clusters have dangling bonds at the surface. These unsaturated bonds alter the chemical and electronic properties of the Q-dots, and therefore, these unsaturated bonds have to be satisfied. To arrest the growth and to prevent coalescing of the Q-dots, passivating organic ligands are normally employed in experiments. In the present work, we have used the procedure given by Chelikowsky et al.34 satisfying dangling bonds. We have passivated the Q-dots with a suitable number of two types of neutral fictitious hydrogen (H*) atoms. One species having nuclear charge 1.5 is bonded to Cd atoms and the other species having a nuclear charge 0.5 is to be bonded to Te atoms, and the overall charge neutrality of the system is maintained. (For details, the reader may refer to refs 35 and 36.) In our earlier work, we have shown that passivation locks the symmetry for three-dimensional structures;35 hence, no structure minimizations are carried out for the passivated ZB fragments constructed with a lattice constant of 0.645 nm. Computations based on the KohnSham density functional framework37 have been performed. The electronic structure is calculated self-consistently using the PAW method38 as implemented in the VASP package39 within the framework of generalized gradient approximation (GGA). We have used the PerdewBarkeErnzerhof (PBE) exchange correlation energy functional40 for our calculation as it is known to provide decent estimates of the total energy and molecule atomization energy, and therefore, the electronic properties. The valence electronic configurations used for Cd and Te are 5s24d10 and 5s25p4, respectively. The 4d levels in the Te atom are well separated from the 5s levels and hence are included in the core. The size of the basis set was decided by the plane wave cut off energy, which was varied from 205.76 to 274.34 eV, depending on the size of the Q-dot. Calculations were done in a supercell geometry by varying the size from 2.5 to 5.0 nm to be large enough to mimic free Q-dots geometries with enough vacuum region on all sides. The total energy convergence used for the electronic self-consistency is ∼104 eV. Single particle energy values are obtained by solving the KohnSham equations for passivated CdTe clusters of varying sizes as mentioned above. It is well known that DFT underestimates the band gap of semiconductors due to the underneath approximations used for the exchange correlation energy functional. Normally, a scissor operator is applied to make the theoretical band gap match the experimental value for the bulk material. We too have followed a similar procedure. The HOMOLUMO gap (εDFT gap ) obtained from the VASP results for Q-CdTe is corrected by an appropriate factor. To compare the actual HOMO
Figure 1. UVvisible absorption and the corresponding emission spectra recorded for the varied sizes (samples AF) of the oleic acid capped Q-CdTe, redispersed in toluene.
and LUMO energy values, we have rigidly shifted the HOMO levels by the same factor.
4. RESULTS AND DISCUSSION 4.1. Characterization of Oleic Acid Capped Q-CdTe. As described in Experimental Section, the varying sizes of Q-CdTe were obtained by quenching the growth at stipulated time intervals. These dispersions were extracted from the mother liquor in the form of a dry powder. Figure 1 shows the typical UVvis and photoluminescence (PL) spectra obtained for Q-CdTe, redispersed in toluene. The characteristic absorption and emission peaks were observed in the range 500730 nm which are attributed to the size quantization or quantum confinement effect for Q-CdTe.41 The average particle sizes for all the samples were obtained by fitting the absorption peak maxima (refer Figure 1A to F) in the sizing curves reported independently by Yu et al.42 and Dagtepe et al.,43 for identical systems. On the basis of these curves, the average particle sizes were estimated to be in the range of 2.44.7 nm. The size of the Q-dots and their corresponding labels are listed in Table 1. These values match reasonably with the average diameters measured from the low resolution TEM images recorded for these samples (for the representative TEMs refer to Figure-S2 in Supporting Information). The narrow full width at half maxima and symmetry in the PL peaks further suggest that the Q-dots have narrow size distribution which commemorated the TEM images.41 Freshly prepared Q-CdTe is known to give very bright luminescence; however, they lose most of their quantum yield over time due to exposure to ambient conditions. This suggests the formation of surface trap states. Thus, relatively large Stoke shifts in the PL peaks are attributed to the presence of trap states associated with the Q-CdTe surface. Nevertheless, a systematic correlation between the Stoke shift and the particle size has not been observed.44 A powder X-ray diffractogram (XRD) recorded on these samples (for typical XRD refer, Figure-S3 in Supporting Information) displayed reflections at ca. 24.2°, 40.1°, 46.7°, 61.5°, and 71.3°, which fitted faithfully into the d-spacings for (111), (220), (311), (331), and (422) planes of CdTe- cubic phase (JCPDS-15-0770). A comparison between FTIR spectra recorded on pristine oleic acid and oleic acid capped Q-CdTe 6245
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Table 1. Band Structure Parameters of Oleic Acid Capped Q-CdTe, Obtained from UVVis Spectroscopy and Cyclic Voltammetry from UVvis spectroscopy sample
average Q-dot size
ID
(nm)
optical band gap (eV)
from cyclic voltammetry (εop gap)
conduction band edge (e1) vs vacuum valence band edge (h1) vs vacuum Quasi-particle gap (εqp gap) (eV)
(eV)
(eV)
A
4.7
1.88
3.54
5.40
1.86
B C
4.2 3.5
1.94 2.09
3.56 3.65
5.49 5.73
1.93 2.08
D
3.1
2.19
3.57
5.76
2.19
E
2.8
2.33
3.53
5.88
2.34
F
2.4
2.40
3.61
6.02
2.41
Figure 2. Cyclic voltammograms recorded for (b) 100 mM TBAP in DCM, i.e., background, without any sample and (a) after the addition of Q-CdTe (sample-F, 1.0-mg/mL). The scan rate was 100 mV s1. Figure 4. Cyclic voltammograms (CVs) recorded on varied sizes of Q-CdTe (sample-A to sample-F). Scan rates were 100 mV s1 for all the cases.
Figure 3. Plots of (B) cathodic (Ip,c) and (A) anodic (Ip,a)peak current values (0 and O, respectively) vs ν1/2 obtained from scan rate dependent CV response recorded on Q-CdTe dispersions (not shown). The solid lines indicate corresponding linear regression fits for the Randles-Savcik equation, suggesting that the electron transfer is the diffusion controlled one.
(refer, Figure-S4 in Supporting Information) suggested the adsorption of oleic acid molecules on the Q-dot surface. Thus, from all these experimental evidences, we concluded the formation of monodispersed oleic acid capped Q-CdTe in the sizes ranging from ca. 2.4 to 4.7 nm, which are labeled, respectively, as sample-A to sample-F.
4.2. Voltammetric Investigation on Q-CdTe Dispersions. A successful use of CV measurements for the determination of band structure parameters viz. the conduction band edge (e1 LUMO), valence band edge (h1 HOMO), and εqp gap have been described in detail in our earlier report.13 The electron transfer with Q-dots is mediated through e1 and h1, which are manifested as respective cathodic and anodic peaks in the CVs. As the Q-dot size decreases, the cathodic and anodic peaks are expected to shift toward more negative and positive potentials, respectively. Thus, the SQE can readily be confirmed by simple voltammetric experiments. In the present investigation, the CV measurements were carried out on Q-dots dispersions. Thus, the charge transfer can be viewed as a formation of the noninteracting electronhole pair. The potential difference between cathodic and anodic peaks is correlated to the single particle or quasi-particle gap (εqp gap) estimated by scanning tunneling spectroscopy.1317 Figure 2a shows a typical CV recorded for the dispersion of Q-CdTe (sample-F, 2.4 nm) in a TBAP-DCM mixture. The corresponding CV curves obtained for the controlled sample (without Q-CdTe) are superimposed as Figure 2b. The prominent, cathodic and anodic peaks at ca. 0.89 V (marked as C1), 0.60 V (marked as A1), and 1.52 V (marked as A2), respectively, are observed. The potential difference of 2.41 V between 6246
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C1 and A2 is in accordance with the optical band gap of 2.40 eV, observed in the UVvis spectrum (Table 1). Unlike Q-CdS and Q-CdSe,1113 Q-CdTe shows an anodic peak A1, which is found to be complementary to C1. The peak separation between C1 and A1 is observed to be 306 ( 56 mV, which is far higher to qualify as a Nernstian type quasi-reversible case. The complementary peak-pair indicates that the reduction of Q-CdTe forms a relatively stable anion radical (Q-CdTe•) in a given time frame and the solvent system. A similar observation has been made earlier by Bard et al. in which the addition of an oxidant in the electrochemically reduced Q-CdTe led to the observation of the electro-generated chemiluminesence (ECL) and confirmed the formation of stable CdTe radical anions.26 An additional difference of 247 mV over and above the typical reversible case (59 mV) is comparable with the average Stoke shift of ca. 258 ( 39 meV (48 ( 6 nm) observed in the PL spectra. The coincidence in these values further supports the model of surface state mediated electron transfer, during the complementary oxidation. On other side, the anodic peak (A2) does not show such a complementary nature even for fast scan rates (not shown). This feature is attributed to the well known electron transfer followed by the chemical reaction (E-C) mechanism, i.e., an oxidation of telluride to tellurium.26
Figure 5. Plot of valence (b) and conduction (O) band edge positions for Q-CdTe, obtained as a function of size from the respective anodic (A1) and cathodic (C1) peaks (Figure 4). HOMO and LUMO positions obtained from DFT calculation are marked as (1) and (r), respectively. For the comparison, the values reported in ref 26 (marked as 9 and 0) and ref 28 (marked as ( and )) are also included in the plot.
To understand the rate determining steps in the electron transfer reaction, the scan rate dependent CV measurements (not shown) have been carried out. Figure 3 shows a plot of peak current values at C1 and A2 positions vs square root of the scan rates. The linear regression of the data fitted in the Randles-Sevick equation (R2 = 0.98) suggesting that the charge transfer is diffusion controlled, i.e, the electron transfer is taking place on diffusing and isolated Q-CdTe rather than the adsorbed film. Hence, the formation of the noninteracting pair is inferred, and the potential difference 17 between (C1) and (A2) is correlated to εqp gap. Figure 4 shows CVs recorded on varied sizes of Q-CdTe, i.e., from sample-A (4.7 nm) to sample-F (2.4 nm). These voltammograms show similar features, i.e., the presence of cathodic and complementary anodic peak pair and irreversible anodic peak. Moreover, the separation between these two set of peaks increases with decreases in particle size (from samples A to F). This observation is attributed to the quantum confinement of charge, whose energy and thus εqp gap increases upon decreasing the particle size. In few cases, less prominent cathodic and anodic peaks in the potential range of ca. 0.5 to 0.5 V are apparent. These peaks are attributed to the redox activity of degradation products, which are formed during the electron transfer followed by chemical reaction, for example, the reduction of tellurium formed at A2 to telluride. Similar observations were reported previously in the case of Q-CdTe26 and also in the cases of Q-CdS and Q-CdSe.1113 The values of the cathodic and anodic peaks and thus respective positions of e1 and h1 obtained from these data on varied sized Q-CdTe are listed in Table 1 and plotted in Figure 5. For the comparison, the corresponding reported values from Bard et al.26 (marked as 9 and 0) and Li et al.28 (marked as ( and )) are included in the same graph. In spite of the difference in the experimental conditions such as capping agents and solvent systems, both data fall very close to the present findings for oleic acid capped Q-CdTe. These results put forward a very important conclusion that the observed voltammograms are the intrinsic properties of Q-CdTe and are not much affected by capping agents or the dielectric of the medium in which CVs are being recorded. To support the experimental results, the DFT based calculations have been performed using the projector augmented wave method, for H*-passivated nonstoichiometric CdmTen (m6¼n) clusters. The calculated HOMO and LUMO levels and εDFT gap for six different particle sizes chosen close to the experimental values are compared in Table 2 and are plotted in Figure 5 (marked as r and 1). From these plots, it is clear that the values of HOMO
Table 2. Band Structure Parameters Computed for the Various Sizes of H*-Terminated CdTe Clusters, Using Density Functional Theory (DFT) size of clusters (nm)
LUMO vs vacuum (eV)
HOMO vs vacuum (eV)
HOMOLUMO energy separation, εDFT gap (eV)
4.0
3.36
5.40
2.26
3.8
3.28
5.49
2.34
3.2 3.0
3.23 3.17
5.61 5.76
2.44 2.49
2.8
3.18
5.88
2.53
2.5
3.04
5.76
2.72
2.1
2.80
5.73
2.93
1.9
2.73
5.91
3.18
1.7
2.55
5.94
3.39
1.4
2.45
6.19
3.74
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assumed in the DFT model than the sterrically stabilized Q-CdTe system.
match reasonably well with h1, in a chosen size range. However, the values of LUMO showed slight deviation by a small factor of 0.2 eV from e1 (8% compared to the magnitude of band gap energies). The values are marginally toward the higher side, especially in the more confined region. Perhaps, the surface properties are more prevalent in this size range. In Figure 6, the optical band gaps (εop gap) obtained from UVvis absorption spectra, quasi-particle gap (εqp gap) determined from CV measurements, and HOMOLUMO gaps (εDFT gap ) obtained from the DFT calculations are plotted as a function of size of Q-CdTe. The values from CV and UVvis data are well overlapped with each other in the chosen size range. This observation is slightly different from similar data reported for qp Q-CdSe where the separation between εop gap and εgap became more prominent in the strong confinement regime, i.e., in the smaller size range.13 This is attributed to the larger Bohr exciton radius and higher dielectric constant of CdTe compared to CdSe, which makes the exciton more delocalized in Q-CdTe than Q-CdSe. The weak electronhole interaction in Q-CdTe as compared to Q-CdSe in a given size range leads to matching qp 23,24 DFT εgap obtained values of εop gap and εgap in the case of Q-CdTe. from DFT calculations shows a trend similar to that of the experimental values. Nevertheless, these are found to be slightly toward the higher side by 0.20.35 eV (810% with respect to the band gap). Thus, the theoretical and experimental data for Q-CdTe matched reasonably well and go hand-in-hand. Figure 6 also carries the interesting comparison of present band gap data with the optical band gaps reported for Q-CdTe by others, in a variety of environments. These are Q-CdTe, in n-tetradecylphosphonic acid (TDPA)42 and hexadecyl amine(HDA)/TOPO mixture, as well as magic size CdTe clusters stabilized in hexylphosphonic acid(HPA),43 and mercaptopropionic acid (MPA) capped Q-CdTe in aqueous media.44 In spite of so many variations in the capping agents, media, experimental procedures, etc., the present data matched very well with the reported one, within experimental errors. The optical band gaps reported for extremely small MPA capped Q-CdTe fall on the line-of-intrapolation of the present data. The magic size CdTe clusters prepared in HPA,43 however, show band gap values toward the slightly higher side in the smaller size range and tend to approach εDFT gap . Perhaps, an absence of surface capping agents in the HPA/HDA stabilized CdTe clusters makes the case closer to the H*-passivated clusters
’ ASSOCIATED CONTENT
bS
Supporting Information. Schematic of setup used for the synthesis of oleic acid capped Q-CdTe; representative low resolution transmission electron micrograph (TEM) obtained for Q-CdTe sample-B and sample-C; representative powder X-ray diffractogram (XRD) recorded on a typical sample of oleic acid capped CdTe Q-dots; FTIR spectra recorded on oleic acid capped CdTe Q-dots and pristine oleic acid; and a list of the size of each Q-CdTe used in the calculation along with the total number of atoms as well as the number of atoms of each species. This material is available free of charge via the Internet at http:// pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*Phone: þ91 20 25691373. Fax:þ91 20 25691728. E-mail:
[email protected]. Present Addresses
)
Figure 6. Comparison of the optical band gaps (εop gap) from UVvis, DFT quasiparticle gaps (εqp gap) from CV, and HOMOLUMO gaps (εgap ) from DFT, for varied sizes of Q-CdTe. For furher comparison, the band gap data reported in refs 42, 43, and 44 are superimposed.
5. CONCLUSIONS Cyclic voltammetric measurements have been performed on diffusing Q-CdTe, pertaining to the determination of their band structure parameters, as a function of size. The effect of size quantization or quantum confinement on Q-CdTe has been studied extensively using these techniques. The band structure parameters determined from voltammetric measurements are found to be in good agreement with the values obtained from density functional theory based calculations and show that the description of the Q-dots as fragments of bulk is justifiable. We believe that the data presented here will have immediate applications in device preparations.
B.tech. student, Department of Metallurgical Engineering and Material Science, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India. This author was on a summer project at University of Pune.
’ ACKNOWLEDGMENT P.P.I. thanks CSIR India, for the fellowship. G.B.M. thanks the BARC-Pune University collaborative Ph.D. program for the fellowship. We are thankful to the CNQS, Department of Physics, University of Pune, for the XRD facility. A.K. acknowledges the research grant from BCUD, University of Pune. O.A.N. acknowledges Professor R.O. Dusane, Head of Department, Metallurgical Engineering and Material Science, IIT Bombay, for giving him kind permission to work under this project. ’ REFERENCES (1) Efros, A. L.; Efros, A. L. Sov. Phys. Semicond. 1982, 16, 772–775. (2) Brus, L. E. J. Chem. Phys. 1983, 79, 5566–5571. (3) Brus, L. E. J. Chem. Phys. 1984, 80, 4403–4409. (4) Brus, L. E. J. Phys. Chem. 1986, 90, 2555–2560. (5) Huynh, W. U.; Dittmer, J. J.; Alivisatos, A. P. Science 2002, 295, 2425–2427. (6) Colvin, V. L.; Schlamp, M. C.; Alivisatos, A. P. Nature 1994, 370, 354–357. 6248
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