Density of Surface States at CdSe Quantum Dots by Fitting of

Article pubs.acs.org/JPCC

Density of Surface States at CdSe Quantum Dots by Fitting of Temperature-Dependent Surface Photovoltage Transients with Random Walk Simulations Steffen Fengler, Elisabeth Zillner, and Thomas Dittrich* Helmholtz-Zentrum Berlin für Materialien und Energie, Hahn-Meitner-Platz 1, 14109 Berlin, Germany ABSTRACT: Surface photovoltage (SPV) transients were measured for a monolayer of CdSe quantum dots (QDs) on planar indium tin oxide (ITO) substrate at temperatures between 200 and 40 °C. By fitting with a random walk simulation, the energy distribution and density of electronic surface states at the QDs were determined. SPV transients show the relaxation of separated charge carriers. This relaxation was described by a model based on an isolated QD approximation. In this model Miller−Abrahams hopping of holes between surface states and the first excitonic state of CdSe QDs and recombination of holes with electrons separated at the ITO surface were considered as mechanisms leading to charge relaxation. Parameters of the model were obtained by a statistic multiparameter fitting procedure of measured SPV transients. All SPV transients could be excellently fitted by using the same Couchy energy distribution of hole traps at the CdSe QD surface. The number of hole traps at CdSe QD surfaces determined by the simulation was between 11 and 6 per QD and therefore in the range of 1013 cm−2.

1. INTRODUCTION Semiconductor quantum dots (QDs) expand the range of materials suitable for absorbers in solar cells due to their tunable bandgap.1 In addition the extraction of hot charge carriers2 and multiexciton generation3−5 have been shown in QD systems. Both mechanisms can lead to an enhancement of the efficiency of solar cells and even bear the opportunity to overcome the Shockley−Queisser limit.6 Solar cell structures were for example obtained by using PbSe QD layers with Schottky contacts7,8 or PbS QD on nanoporous TiO2,9,10 while energy conversion efficiencies between 4 and 7% were achieved. Charge separation in QD layers is an important aspect for the application of QDs in solar cells. Charge separation in QD systems can be measured by surface photovoltage (SPV). The formation of a heterojunction between CdSe QDs/TiO211 and CdSe QDs/CdTe QDs12 has been demonstrated by surface photovoltage (SPV) measurements. A deeper understanding of limiting factors in the separation and transport of charge carriers is necessary for the further successful development of solar cells based on QD absorbers. Until now only little attention has been paid to trapping of charge carriers at surface states at the extended internal surface area of QD layers. Colloidal QDs consist of an inorganic core and of an organic shell of surfactant molecules. While the inorganic core acts as the absorber, the surfactant molecules are needed for the control of growth and stabilization of QDs in solution. An exchange of surfactants with long chains by surfactants with short chains and/or exchange of surfactants by linker molecules are generally needed to overcome transport limitations.13,14 A © 2013 American Chemical Society

successive decrease of the photoluminescence and an increase of the surface photovoltage related to charge separation from deep defect states were observed with ongoing surface treatment and exchange of surfactants at CdSe QD layers.15 Defect generation at surfaces of QDs has to be taken into account in general, and strategies have to be developed to characterize the density and energy distribution of electronically active surface states at QDs and to minimize their concentration. Recently it has been shown by transient surface photovoltage measurements that initial charge separation at the indium tin oxide (ITO)/CdSe QD interface takes place within the first monolayer of QDs independent of the number of CdSe QD layers.15,16 This was shown for CdSe QDs (diameter of (4.5 ± 0.5) nm) with a center to center distance between (6.2 ± 0.2) nm and (5.5 ± 0.4) nm, capped with trioctylphosphine and oleic acid, pyridine, or 1,4-benzenedithiol (dithiol).15 This means that coupling between delocalized states in neighbored CdSe QDs is weak. Therefore an isolated quantum dot within a monolayer of CdSe QDs adsorbed at an ITO surface can be considered as a model system for the analysis of relaxation of separated charge carriers. Figure 1a shows a transmission electron microscopy (TEM) image of a monolayer of dithiol capped CdSe QDs and (b) a high-resolution TEM image of one QD. Figure 1c depicts a schematic of CdSe QDs with dithiol surfactants adsorbed at the ITO surface. Received: January 9, 2013 Revised: February 26, 2013 Published: February 28, 2013 6462

dx.doi.org/10.1021/jp4002687 | J. Phys. Chem. C 2013, 117, 6462−6468

The Journal of Physical Chemistry C

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capped QDs a suspension of pyridine capped CdSe QDs (c = 5 mg/g) and a withdrawal speed of 1 mm/s were used. The pyridine surfactants were exchanged by dithiol, by dipping the QD layer for 30 min in a solution of 1,4-benzenedithiol in acetonitrile (c = 3.5 mM) and subsequently into acetonitrile to remove excess dithiol.15 For SPV measurements and heating the sample was in a high vacuum chamber (p = 1 × 10−5 mbar). The CdSe QD monolayers were heated in vacuum up to 230 °C for 5 min, and the transient SPV measurements were performed at decreasing temperature starting with 200 °C. The sample temperature was measured with a Pt100 (3 × 3 mm2) contacted directly with the sample. As a remark, it was found in pre-experiments that heating of the CdSe QDs in vacuum to temperatures above 250 °C caused a clear and nonreversible decrease of the SPV signals of the CdSe QDs. 2.2. Measurement of Surface Photovoltage Transients. SPV transients were measured in vacuum in the fixed capacitor arrangement.19 The sample was illuminated with a 5 ns laser pulse at 590 nm. The transient was measured with an oscilloscope (CS-14200 GAGE, sampling rate 100 MS/s). The measurement range, which was limited at short times by the laser pulse width and at long times by the RC time constant of 0.1 s, was between 10 ns and 0.1 s. The transients were red out logarithmically to limit the number of data points to about 1000 over 8 orders of magnitude in time. Transients were averaged over eight measurements with a repetition rate of the laser pulses of 1 Hz. The transients were shifted in time by t0 = 38 ns for getting an impression about the fast onset of the SPV signals.

Figure 1. (a) TEM image of a monolayer of dithiol capped CdSe QDs and (b) a high-resolution TEM image of a CdSe QD (accelerating voltage 120 keV, Philips CM12/STEM, LaB6 kathode). (c) Shows a schematic of a monolayer of quantum dots with dithiol surfactants adsorbed at the surface of an ITO substrate. The red marks illustrate defect states at the surface of the QDs.

SPV transients were simulated recently within a single QD approximation model and compared with measured transients of CdSe QD monolayers after steps of surfactant exchange.15 From this analysis, first approximate numbers of surface states per CdSe QD were obtained for fixed energy density distributions. It should be pointed out that the number of free parameters is relatively large even for the single QD approximation so that a relatively high uncertainty remained for values obtained from the comparison of simulated and measured SPV transients. Recently Ansari-Rad et al. published random walk simulations of charge transport in nanostructured titanium oxide, considering hopping between trap states. However these simulations are limited due to assumptions of the energy distributions of trap states.16,17 In the current work temperature-dependent SPV transients were measured for dithiol capped CdSe QD monolayers deposited on ITO, and a fitting procedure of SPV transients was developed with random walk simulations for getting reliable values for the density and energy distribution of surface states at dithiol capped CdSe QDs. Temperature-dependent measurements of SPV transients are very useful for the accurate determination of the density and energy distribution of surface states at CdSe QDs by employing multiparameter fits. For equal energy distributions of surface defects, changes of the sample by e.g. chemical reactions or restructuring of the QD surface at different temperature have to be avoided. To minimize changes of the sample during the measurement the sample was first heated and then measured during the cooling phase.

3. THE ISOLATED QD MODEL The isolated QD model has been already motivated and applied in a previous publication.15 After excitation of charge carriers in the CdSe QDs the electron is trapped immediately at the surface of the ITO, as was proofed by PL quenching of the first monolayer of CdSe QDs.15 The basic assumption for the isolated QD model is that charge relaxation within one QD is limited by trapping of the hole at QD surface states before recombining with an electron at the ITO surface. This assumption simplifies the model and shortens dramatically the simulation time since electron transport and charge transfer between neighbored QDs are neglected. The simplicity of the isolated QD model and the reduction of the number of electronic states and free parameters to a needed minimum made the simulation of one SPV transient very fast. Therefore a direct fitting of SPV transients by numerical random walk simulations was possible. 3.1. Geometrical Parameters. Figure 2a summarizes the geometry parameters of the model: the radius of the QD (r = 2.25 nm on average), the distance between the QD surface and the ITO surface (variable in a range between 0.3 and 1.2 nm) and the positions of given surface states which are determined by the polar (φ) and zenith (θ) angles. The angles φ and θ were determined for each surface state by random values between 0 and 2π and between −π/2 and +π/2, respectively. The number of the surface states per particle (Nt) was a variable. A matrix including all distances between surface states and between all surface states and the ITO surface was calculated for each QD before starting the simulation of charge relaxation. As a starting point for charge relaxation within one QD the hole was placed randomly in one of the surface states and the electron was accessible for recombination over the

2. MATERIALS AND METHODS 2.1. Sample Preparation and Heating Procedure. Layers of CdSe QDs were prepared by dipping of a precleaned ITO substrate under inert atmosphere into a suspension of CdSe QDs.18 For the preparation of a monolayer of dithiol 6463



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that the measured SPV transients cannot be fitted well with only one Gaussian distribution of localized states at the QD surface. However there is no obvious reason for implementing more than one distribution function. Therefore a Couchy distribution (F, eq 2) with a distribution parameter s was chosen as the distribution function for the localized states at the QD surface. F=

Figure 2. Geometric parameters of an isolated quantum dot with surface states in front of an ITO surface and hole trapped at the quantum dot and electron separated at the ITO before starting the simulation of relaxation (a) and processes of hole hopping via localized states (1), hole transport via the delocalized state (2), and recombination with the electron (3).

(2)

The choice of the Couchy function led to an increase of deep states at the QD surface, in comparison to the Gaussian distribution. A Fermi−Dirac function with a Fermi level EF was introduced to determine the occupation of electronic states. The peak position of the distribution of delocalized hole states in the QD was used as a reference and fixed at 0 eV for the simulations. The fitting procedure is done in two basic steps. First transients were simulated with fixed sets of parameters. In a second step the error square between SPV measurement and simulation were determined. Both steps were repeated until the best fit was found by a systematic change of parameters. 3.4. Simulation of One SPV Transient. The elementary simulation step corresponded to the relaxation of one separated hole in an isolated QD until recombination with the electron on the ITO surface. For each simulation sample randomly distributed values of the energy levels of localized states, the delocalized state and the ITO surface were defined within the given distributions. The number of localized hole states (traps) was also defined within a Gaussian distribution around a fixed value. Before starting the simulation of one sample a matrix of tunneling rates between the different states was calculated. The matrix led to an additional acceleration of the simulations. The starting time of the simulation of each sample was randomly varied regarding to the shape of the exciting laser pulse. The SPV signal corresponded to the distance between the hole and the ITO surface. The simulation of one SPV transient was performed by adding up the distances at the different time steps for N independent samples of relaxation while the times steps were divided into identical intervals as used for the measurements.

whole ITO surface. The latter condition takes into account that the ITO is highly doped with electrons and that the hole can recombine with any electron accessing the ITO surface. 3.2. Processes Considered for Relaxation. Three fundamental processes were included into the isolated QD model. The hole can be transferred between localized surface states by tunneling (hopping, process 1 in Figure 2b). Further, the hole can be excited from a localized state into a delocalized state of the QD from which it can be trapped at any localized state at the QD surface (process 2) or recombine with an electron at the ITO surface. Further the hole can recombine with an electron at the ITO surface by tunneling from a localized state at the QD surface to an occupied electron state at the ITO surface (process 3 in Figure 2b). The tunneling processes are described by Miller-Abrahams hopping.20 In this mechanism the charge carrier can tunnel into states with a different energy than the one of the initial state. For tunneling into a state with a higher energy a thermal activation of the charge carrier is required. The tunneling rates can be described by the following equation: ⎛ −|E i| + |Ef | + |E i − E i| ⎞ 1 1 = × exp(2αR if ) × exp⎜ ⎟ τ τk 2kBT ⎠ ⎝ ⎛ e 1 ⎞ × exp⎜ × ⎟ R eh ⎠ ⎝ 4πεε0

1 s × 2 π s + (Et − E)2

(1)

while τk, α, Rif, Ei, Ef, kB, e, ε, ε0, and Reh denote the hopping time of an elementary step (10−13 s), the inverse tunneling length, the distance between the initial (i) and final (f) states, the energies of the initial and final states of tunneling, the Boltzmann constant, the elementary charge, the relative dielectric constant, the dielectric constant of the vacuum, and the distance between the electron and the hole, respectively. The first, second, and third terms of eq 1 describe the distant dependence of tunneling, the role of thermal activation for tunneling into states with higher energy, and the role of the attractive Coulomb force between the negative and positive charges while the electron charge is considered as the image charge of the hole in front of the highly conducting ITO. 3.3. Energy Distributions of Electronic States. The energy distributions of localized hole states at the QD surface, of delocalized hole states in the QD, and of electron states at the ITO surface are described by their central energy position (Et, Edl, ES, respectively) and by the widths of their distributions. Gaussian distributions were chosen for the delocalized hole states in the QD and for the electron states at the ITO surface. In numerous previous simulations we found

SPV(t ) =

e × εε0

N

∑ [xe(t ) − xh(t )] i=1

(3)

The simulation of one SPV transient was finished when for each time interval (SPVsim j , j = 1 ... 1000; the points were logarithmically distributed) of the simulation in average between 100 and 400 events were received. Several thousand independent samples of relaxation were needed for the simulation of one SPV transient. 3.5. Fitting Procedure. In the first step measured SPV transients were fitted with stretched exponentials. The transients could be well fitted with stretched exponentials21 pointing to one dominating relaxation mechanism at all temperatures. For the fitting the following equation was used, taking the RC time constant (τRC) into account. β⎞ ⎛ ⎡ ⎛ t − t0 ⎞ t − t0 ⎤ ⎟ ⎜ SPV(t ) = A × exp⎜ −⎢ ⎥ ⎟ × exp⎜ − ⎟ ⎝ τRC ⎠ ⎝ ⎣ τk ⎦ ⎠

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where A is the amplitude, t0 is the time shift of 38 ns, τk is the characteristic time constant of the relaxation, and β is the stretching exponent. By fitting of the measured transients with stretched exponentials we get transients without noise. Therefore the fitting with the isolated QD model was applied on the fitted stretched exponentials. The number of variable parameters in the isolated QD model was quite large even in the rather simplified model. The variable geometric parameters were the inverse tunneling length α (range 0.2−2 nm−1) and the ITO/QD distance (range 0.3−1.2 nm) and the number of trap state. The variable energetic parameters were the energy distribution of the substrate, the localized surface states, the delocalized state of the particle, and the Fermi energy (EF). Note that the position of the distribution of the delocalized states was fixed. For a related multiparameter fit, the result depended sensitively on the order by which the parameters were optimized. A statistic approach was developed to find out the most reliable solutions for the free parameters. A random rank number (rα) was ascribed for each free parameter in the fitting procedure within one run. The random rank number defined the order of free parameters by which they were optimized during the fitting. A run is a consecutive optimization cycle of all parameters in the given order by the rank. Each optimization run was performed for a given set of rank numbers up to four times in order to decrease the probability of local solutions. A run was finished when the error square between simulated tra (SPVsim j , j = 1 ... jmax) and measured (SPVj , j = 1 ... jmax) SPV transients (χ2) did not decrease anymore. χ2 =

Figure 3. Surface photovoltage transients of a monolayer of CdSe quantum dots with dithiol surfactants measured at 200, 120, and 40 °C starting from the higher temperature (black symbols). The red lines represent fits with stretched exponentials.

between the measured transients and the fits with one stretched exponential were observed for the transient measured at the lowest temperature for times shorter than 200 ns. The stretching parameters were very low if comparing with an exponential decay (β = 1) and amounted to 0.18, 0.13, and 0.10 at 200, 120, and 40 °C, respectively. The parameters of the stretched exponential, that is, amplitude (A), stretching parameter (β), and time constant (τk), were obtained for all measured transients. The temperature dependencies of A, β, and τk are plotted in Figure 4. The time constant showed no systematic dependency of temperature. Values between 1 and 8 ns, averaging around 4 ns, were determined. The amplitude increased with decreasing temperature from around 0.12 to 0.25 V. A scattered over a relatively

jmax

tra 2 ∑ (SPV sim j − SPV j ) j=1

(5)

The index j in eq 5 denotes the number of the respective time interval. The rank numbers of the variable parameters were also randomly varied. After a cycle of variation of rank numbers the fitted parameters were plotted as a function of χ2. In an ideal case, one sharp value was found for the fitted parameter at the lowest value of χ2. For the next optimization cycle the parameter with the sharpest value of χ2 was set constant so that the number of free fitting parameters was reduced. This procedure was repeated until the last free parameter was fitted. The fits were performed with the same set of parameters, excluding the number of traps, with SPV transients measured at three different temperatures which led to sharper values of free parameters at early stages of fitting cycles. For the number of traps different results for the transients at different temperatures were allowed.

4. RESULTS AND DISCUSSION 4.1. Measured Temperature-Dependent SPV Transients. SPV transients of CdSe QD (dithiol) monolayers on ITO were measured during cooling at temperatures between 200 and 40 °C with temperature steps of 10 °C. Figure 3 shows as an example SPV transients measured at 200, 120, and 40 °C. The positive SPV signals reached the maximum within the duration time of the laser pulse and decayed within 1−10 μs, 0.1−1 ms, and 10−100 ms for 200, 120, and 40 °C, respectively. The solid lines in Figure 3 represent the fits with stretched exponentials (see eq 4). Generally the stretched exponentials gave a very close fit of the measured transients. Deviations

Figure 4. Temperature dependencies of the fitting parameters of the stretched exponentials. 6465



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5, the found values for the parameters were plotted against χ2. Figure 6 shows as an example the error square in dependence

wide range of about 0.03 V. The stretching parameter β showed a systematic decrease with decreasing temperature. It decreased from about 0.2 at the highest temperatures to about 0.1 at the lowest temperatures. The strong variation of τk was due to the limitation of the measurement accuracy at short times. First τk is smaller than the time resolution of our measurement system. Second the shift t0 can vary due to noises in the trigger signal. β decreased systematically with decreasing temperature. β = 1 would be a normal exponent which describes an ordered system; therefore a decrease of β points toward an increase in disorder. The temperature dependence of β was fitted with a quadratic equation. β = 1.5 × 10−6T 2 + 1.7 × 10−4T + 0.085

(6)

Equation 6 was used in the following to generate SPV transients at any temperature and to fit these generated transients within the model of the isolated single quantum dot. For the generation of SPV transients 4 ns were used for τk. The amplitude was irrelevant due to the normalization of the simulated transients. 4.2. Fitting of Temperature-Dependent SPV Transients with the Single QD Model. In the following the stretched exponentials, representing the measured SPV transients were fitted with the single QD approximation. The transients measured at different temperatures were fitted with the same set of parameters, except the number of traps. The number of traps was fitted independently for every transient. A visualization of the fitting procedure at the example of the variable α is shown in Figure 5. The plot shows the change of χ2

Figure 6. Correlation between α and χ2 after one optimization cycle.

of α. Error squares below 0.01 were found for values between 0.5 and 0.8 nm−1. The smallest χ2 was found for α = 0.65 nm−1. Afterward the parameter with the clearest tendency was fixed in the next optimization cycle. The procedure was repeated until values for all parameters were found. The results of the fits by random walk simulations of stretched exponentials, obtained from surface photovoltage transients measured at 200, 120, and 40 °C are shown in Figure 7. The fits were performed with the same parameter set for all

Figure 7. Stretched exponentials obtained from surface photovoltage transients measured at 200, 120, and 40 °C (lines) and fitted by random walk simulations transients (circles). Figure 5. Example for the random rank number of the tunneling distance (rα, a), the run number (b), and χ2 (c) under given simulation conditions as a function of the number of simulated transients.

three temperatures, excluding the trap density. The value of χ2 = 0.0039 was obtained from the sum of all three transients. The transients simulated by the isolated QD model followed well the stretched exponentials obtained from the measurements. With the three fitted transients at 200, 120, and 40 °C a final set of values for the variable parameters was found. The density of traps was found to be dependent on temperature. 4.3. Energy Distribution of Surface States at CdSe QDs. Figure 8 shows the resulting values for parameters valid for the transients at 200, 120, and 40 °C, determined by the fit. The energetic parameters are the distributions of the densities of delocalized hole states in the quantum dot, of the electron states at the ITO substrate and of the localized hole states at the quantum dot surface. The densities were normalized. The values found for the inverse tunneling length and the distance

depending on the number of simulated transients. The order in which the parameters were optimized is given by the rank number, shown here for the example of α. Each run consists of the optimization of all parameters. The runs were repeated four times with equal rank numbers and optimized values from the previous run. After four runs new rank numbers and starting values were generated to avoid local minima of χ2. It can be seen that the minimum value χ2 depends on the rank number and the starting values chosen. χ2 is decreasing with increasing rank number, reaching different local minima for χ2. After the complete optimization cycle, consisting of approximately 100 000 simulated transients shown in Figure 6466



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Figure 9. Correlation between the number of traps per quantum dot and χ2 in the case of fitting the surface photovoltage transient at 60 °C.

Figure 8. Normalized energy distributions of the densities of delocalized hole states in the quantum dot, of the electron states at the ITO substrate, and of the localized hole states at the quantum dot surface (solid lines) which were obtained from the fits of the surface photovoltage transients at the different temperatures. The dashed line shows the Fermi function.

between particle and substrate were 0.65 nm−1 and 0.73 nm, respectively. The position of the substrate states was 0.30 eV above the delocalized hole state; the distribution was very narrow (5.10−4 eV). The delocalized state had a full width at half-maximum (fwhm) of 0.03 eV. The distribution is due to the variation in QD diameter. The maximum of the distribution of the localized states on the particle was 0.33 eV above the delocalized state and thus 0.03 eV above the states of the substrate. A very broad distribution with a fwhm of ∼0.6 eV was found. Therefore the localized states overlap with both the delocalized and the substrate state. Most of the trap states are higher in energy than the delocalized and the substrate state and therefore require energy to be excited into the delocalized or the substrate state. The Fermi energy was localized at 0.79 eV above the delocalized state and therefore cuts of the deepest trap states. 4.4. Density of Hole Traps at CdSe QDs. The solution found for the above-mentioned three temperatures generally applied at all temperatures. The only parameter depending on temperature, the number of traps per QD, was determined at different temperature. Therefore in the final approximation cycle the SPV transients were fitted separately, with the last free fitting parameter, the number of localized surface states per QD. Specific values were determined for the density of traps (Nt) for transients measured at different temperatures. The narrowing of the distribution of the values of Nt with decreasing χ2 is demonstrated in Figure 9 for the final approximation cycle of the SPV transient obtained at 60 °C. Small error squares (below 0.005) were only found between 6 and 10 traps per QD. The value of Nt was about 7 for the lowest values of χ2. Figure 10 shows the dependence of the number of traps per QD on the temperature. A constant number of traps, with an average of 10.5 traps per QD, was found for temperatures above 110 °C. The number of traps decreased with decreasing temperature below 110 °C to 6 traps at 40 °C. We suspect an increasing number of adsorbates on the surface of QDs as the temperature decreases below 110 °C, which can saturate traps on the QD surface. Figure 11 shows the values of χ2 reached for final approximation cycles at the various temperatures used for the measurement of SPV transients. The value of χ2 of the final approximation cycle decreased from about 6 × 10−4 at 40 °C to

Figure 10. Temperature dependence of the number of localized hole states at the CdSe quantum dot surface.

Figure 11. Value of χ2 for final approximation cycles at the various temperatures of measurement.

6 × 10−5 at 200 °C. It seems that this systematic decrease of the accuracy of the fits with decreasing temperature is related to an increasing role of interparticle charge transfer with decreasing temperature, which was not considered in the model. We suspect an increasing role of interparticle charge transfer due to increased life times of charge carriers.

5. CONCLUSIONS SPV transients of monolayers of CdSe QDs could be simulated with a single QD approximation model. A fit with the simulation was possible due to low simulation times (all together around 500 000 simulations were performed) and a 6467



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(11) Mora-Seró, I.; Dittrich, Th.; Susha, A. S.; Rogach, A. L.; Bisquert, J. Large Improvement of Electron Extraction from CdSe Quantum Dots into a TiO2 Thin Layer by N3 Dye Coabsorption. Thin Solid Films 2008, 516, 6994−6998. (12) Gross, D.; Mora-Seró, I.; Dittrich, Th.; Belaidi, A.; Mauser, C.; Houtepen, A. J.; Como, E. D.; Rogach, A. L.; Feldmann, J. Charge Separation in Type II Tunneling Multilayered Structures of CdTe and CdSe Nanocrystals Directly Proven by Surface Photovoltage Spectroscopy. J. Am. Chem. Soc. 2010, 132, 5981−5983. (13) Gyot-Sionnest, P.; Wang, C. Fast Voltammetric and Electrochromic Response of Semiconductor Nanocrystal Thin Films. J. Phys. Chem. B 2003, 107, 7355−7359. (14) Yu, D.; Wang, C.; Guyot-Sionnest, P. n-Type Conducting CdSe Nanocrystal Solids. Science 2003, 300, 1277−1280. (15) Zillner, E.; Fengler, S.; Niyamakom, P.; Rauscher, F.; Koehler, K.; Dittrich, Th. Ligand Exchange at CdSe Quantum Dot Layers for Charge Separation. J. Phys. Chem. C 2012, 116, 16747−16754. (16) Ansari-Rad, M.; Abdi, Y.; Arzi, E. Monte Carlo random walk simulation of electron transport in Dye Sensitized Nanocrystalline Solar Cells; Influence of morphology and trap distribution. J. Phys. Chem. C 2012, 116, 3212−3218. (17) Ansari-Rad, M.; Abdi, Y.; Arzi, E. Simulation of Non-Linear Recombination of Charge Carriers in Sensitized Nanocrystalline Solar Cells. J. Appl. Phys. 2012, 112, 074319. (18) Zillner, E.; Dittrich, Th. Surface Photovoltage within a Monolayer of CdSe Quantum Dots. Phys. Status Solidi RRL 2011, 5, 256−258. (19) Duzhko, V. Photovoltage phenomena in nanoscale materials. PhD Thesis, Technische Universität München, Munich, Germany, 2002. (20) Miller, A.; Abrahams, E. Impurity Conduction at Low Concentrations. Phys. Rev. 1960, 120, 745−755. (21) Kohlrausch, R. Theorie des Elektrischen Rückstandes in der Leidener Flasche. Ann. Phys. Chem. 1854, 167, 179−214.

clear tendency of the parameters toward a sharp value for lowest error squares. Multiparameter fitting is often critical since different parameter sets can lead to identical solutions. The fitting of multiple measurements, at different dynamics, with the same set of parameters, allowed to increase dramatically the accuracy of multiparameter fitting. By fitting with the isolated QD approximation model one solution for the energy distribution was found. A broad energy distribution of hole traps was found on the dithiol treated CdSe QDs. The number of trap states was constant at temperatures above 110 °C with an average of 10.5 traps per QD and decreased with decreasing temperature to 6 traps per QDs at 40 °C. The proposed method of temperature dependent multiparameter fitting can also be applied to other systems which can be treated within the single QD approximation model. The model can be developed toward consideration of charge transfer processes between neighbored QDs.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work was supported by the BMBF (grant: 03SF0363B). The authors are grateful to Bayer Technology Services GmbH for the supply of CdSe quantum dots.

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REFERENCES

(1) Wadia, C.; Alivisatos, A. P.; Kammen, D. Materials Availability Expands the Opportunity for Large-Scale Photovoltaics Deployment. Environ. Sci. Technol. 2009, 43, 2072−2007. (2) Tisdale, W. A.; Williams, K. J.; Timp, B. A.; Norris, D. J.; Aydil, E. S.; Zhu, X.-Y. Hot-Electron Transfer from Semiconductor Nanocrystals. Science 2010, 328, 1543−1547. (3) Nozik, A. J.; Beard, M. C.; Luther, J. M.; Law, M.; Ellingson, R. J.; Johnson, J. Semiconductor Quantum Dots and Quantum Dot Arrays and Applications of Multiple Exciton Generation to Third-Generation Photovoltaic Solar Cells C. Chem. Rev. 2010, 110, 6873−6890. (4) Semonin, O. E.; Luther, J. M.; Choi, S.; Chen, H.-Y.; Gao, J.; Nozik, A. J.; Beard, M. C. Peak External Photocurrent Quantum Efficiency Exceeding 100% via MEG in a Quantum Dot Solar Cell. Science 2010, 334, 1530−1533. (5) Schaller, R. D.; Sykora, M.; Jeong, S.; Klimov, V. I. HighEfficiency Carrier Multiplication and Ultrafast Charge Separation in Semiconductor Nanocrystals Studied via Time-Resolved Photoluminescence. J. Phys. Chem. B 2006, 110, 25332−25338. (6) Shockley, W.; Queisser, H. J. Detailed Balance Limit of Efficiency of p-n Junction Solar Cells. J. Appl. Phys. 1961, 32, 510−519. (7) Luther, J. M.; Law, M.; Beard, M. C.; Song, Q.; Reese, M. O.; Ellingson, R. J.; Nozik, A. J. Schottky Solar Cells Based on Colloidal Nanocrystal Films. Nano Lett. 2008, 8, 3488−3492. (8) Szendrei, K.; Gomulya, W.; Yarema, M.; Heiss, W.; Loi, M. A. PbS Nanocrystal Solar Cells with High Efficiency and Fill Factor. Appl. Phys. Lett. 2010, 97, 203501. (9) Pattantyus-Abraham, A. G.; Kramer, I. J.; Barkhouse, A. R.; Wang, X.; Konstantatos, G.; Debnath, R.; Levina, L.; Raabe, I.; Nazeeruddin, M. K.; Graetzel, M.; et al. Depleted-Heterojunction Colloidal Quantum Dot Solar Cells. ACS Nano 2010, 4, 3374−3380. (10) Ip, A. H.; Thon, S. M.; Hoogland, S.; Voznyy, O.; Zhitomirsky, D.; Debnath, R.; Levina, L.; Rollny, L. R.; Carey, G. H.; Fischer, A.; et al. Hybrid Passivated Colloidal Quantum Dot Solids. Nat. Nanotechnol. Lett. 2012, 7, 577−582. 6468


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