Fundamental Aspects of Photoinduced Charge Flow at a Quantum Dot

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Article

Fundamental Aspects of Photoinduced Charge Flow at a Quantum Dot Sensitized Single Crystal TiO Semiconductor Interface 2

Kevin J. Watkins, Bruce A Parkinson, and Mark T Spilter J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b12803 • Publication Date (Web): 02 May 2018 Downloaded from http://pubs.acs.org on May 3, 2018

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The Journal of Physical Chemistry

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Fundamental Aspects of Photoinduced Charge Flow at a Quantum Dot Sensitized Single Crystal TiO2 Semiconductor Interface

Kevin J. WatkinsA, B. A. ParkinsonA* and M. T. Spitler B * A

Department of Chemistry and School of Energy Resources University of Wyoming Laramie, WY 82071 and B Office of Science, SC 22.13 Department of Energy Washington, D.C. 20585

Abstract The fundamental aspects of charge transfer from photoexcited CdSe quantum dots to a single crystal of TiO2, a wide band gap metal oxide semiconductor, were investigated and compared with that of a dye-sensitized system in relation to the operation of quantum dot sensitized solar cells (QDSCs) and dye-sensitized solar cells (DSSCs). Due to the stark differences, in both physical and electronic properties of quantum dots versus molecular dyes, it was hypothesized that the fundamental behavior of the two systems could differ greatly. The large size and surface area of the quantum dots relative to molecular dyes presents the possibility for the positively charged hole to move a greater distance away from the QD/oxide interface during the electron injection process. This increased distance influences the coulombic interaction between the trapped hole and injected electron, leading to differences and increased complexity of the recombination pathways when compared to the dye system.

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Introduction Both the fundamental aspects of the photosensitization of large band gap semiconductors and the practical aspects for optimizing the energy conversion from these systems have been well studied as evidenced by the extensive research on dye-sensitized solar cells (DSSCs).1 There has been substantial progress over the years in increasing the efficiency and stability of the DSSCs, but many fundamental aspects of the interface between the adsorbed light-absorbing species and the oxide substrate remain unexplored. A good model system for understanding the details of the sensitizer and the oxide/semiconductor interface uses well-characterized oxide single crystal substrates.2,3 We previously investigated the doping density dependence of photocurrents resulting from injection, recombination, and collection of photo-excited chromophores at single crystal rutile TiO2 electrode sensitized with both the ruthenium-based N3 chromophore and a thiacyanine dye.4 As the doping density of the electrodes was varied from 1015 cm-3 to 1020 cm-3, thereby varying the strength of the electric field in the near surface space charge layer, three different regimes of behavior were observed that influenced the magnitude and shape of the dye-sensitized current-voltage curves. Low-doped crystals produced current-voltage curves with a slow rise of photocurrent with potential. At intermediate doping levels, Schottky barrier behavior was observed producing a photocurrent plateau with an electrode bias in the depletion region. At highly doped electrodes, tunneling currents played a significant role in the recombination processes, reducing the quantum yields for electron collection. These different manifestations of the current-voltage curves could be well fit to a one-dimensional Onsager-based model for charge collection at a semiconductor electrode that was sensitive enough to reveal the difference between the dye-electrode distance of the ruthenium based N3 sensitizer as opposed to a carboxylated thiacyanine dye.4 Recently, quantum dot (QD) sensitizers have been incorporated into the nanocrystalline DSSC structure with the justification that their absorption energy can be tuned by simply changing their size, and that they may be more stable than dyes that can tend to bleach.


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Figure 1. Energy level band diagram showing sensitizing CdSe quantum dots on the TiO2 surface and possible kinetic pathways (dashed lines). A photoexcited electron in the quantum dot conduction band can be transferred to the TiO2, with a hole left behind in the valence band. The hole can then be quickly trapped by states at the quantum dot surface (ss). Possible regeneration (black) and recombination (blue) pathways are shown.

However, these semiconducting nanocrystals, and their interface with an oxide surface, can differ from that of the dye system in their physical structure and in the available kinetic pathways for reaction. In dimension, the CdSe nanoparticles extend far beyond the double layer and offer many locations for reduction of a hole state by the regenerating agent that are far from the surface. The reductant can also be trapped between the particle and the TiO2, thus precluding diffusion of the oxidized component away from the surface and creating a buildup of such species at the surface. Also, even a surface with a perfectly packed quantum dot layer will have interstices where the TiO2 is in direct contact with the electrolyte. In addition, the size of the quantum dot also offers a much larger physical cross section for recombination of an electron in the TiO2 with a CdSe hole. The energy level diagram in Figure 1 shows the relationship between the band structures of sensitizing CdSe quantum dots and the TiO2 electrodes to which they are attached. It is evident that a photoexcited electron in the CdSe conduction band can transfer to the TiO2, but the reverse



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reaction is energetically blocked. Also depicted in this diagram are the CdSe valence band level and that of surface states that are known to be present on quantum dots, that can serve as effective traps for holes in the valence band.5,6 Direct recombination is depicted for an electron in the TiO2 conduction band with holes in the CdSe quantum dots, as well as with the trapped hole states and the oxidized form of the ferrocene (Fe(Cp)2) regenerating agent. As is evident from recent reviews,7-12 extensive research has been conducted on the spectral sensitization of photocurrent production at transparent metal oxide semiconductors by attached nanocrystals that absorb visible and near IR radiation. The substrate electrodes under study included ZnO, TiO2 and SnO2, among others as they were sensitized in various combinations with quantum dots such as PbS, PbSe, CdS, CdSe, and CdTe. Most of this work focused on mesoporous forms of the metal oxide with only a few13,14 employing single crystals where the photo-activity of excited quantum dots could be explored at well-defined crystallographic surfaces. It is with single crystal TiO2 sensitized by PbS quantum dots that reports of multiexciton generated photocurrents have been made,13 and that the necessary ultrafast electron transfer from PbS to the TiO2 has been observed and quantified.14 None, however, have studied QD-sensitized single crystal electrodes as model systems, as is done in this work, for the purpose of analyzing current- and photocurrent-voltage behavior to assess the competition between electron collection by the electrode, and the back reaction of the injected electron with an acceptor state in the quantum dot or with the regenerating redox couple. Much of this prior work seeks to determine rates of electron transfer from quantum dots to the metal oxide through employment of transient absorption, photoemission, and terahertz spectroscopies. A large fraction deals with CdS and CdSe sensitized ZnO and mesoporous TiO2, of relevance to the present work.11,15-21 When there is strong electronic coupling between the quantum dot and acceptor solid, exciton broadening can be used as a guide to estimate charge transfer rates, as has been done in studies of PbS on TiO2.22 Usually, however, femtosecond and picosecond transient absorption and photoluminescence measurements are employed to measure these rates, and they are found to vary from tens of femtoseconds to tens of picoseconds.8,15-17 This variation can be attributed to driving force energetics as determined through UPS measurements of donor and acceptor states, as has been done for CdS and CdSe on TiO2.12,23 With donor-acceptor couples, the linker structure between sensitizer quantum dot and metal oxide nanoparticle was also found to play a role, with longer chain mercaptocarboxylic acids


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slowing down the photo-induced transfer to the nanosecond regime.23 With the use of the short mercaptopropionic acid linker between CdSe quantum dots and mesoporous TiO2 in a solvent, the rate constants for electron transfer were found to be a function of quantum dot size;8 for the CdSe sizes in this study of 3-4 nm, the electron transfer rates were found to be in the 10 ps to 500 ps range, with more importantly, non-unity yields for electron transfer of 50-80%. This study and others motivate the use of the short mercaptopropionic acid as a linker and CdSe as a sensitizer of single crystal TiO2 for the study of the competition between the collection of the injected charge as current and recombination with an acceptor at the surface. It is mostly at nanoelectrodes in a solar cell arrangement that measurements of the rate of the back reaction have been made for the injected electron with the donor quantum dot or an acceptor in solution,9,18,20 although spectroscopic studies of direct recombination have been made.11 This has been done through analyses of the decay of the open circuit photovoltage of the solar cell, which is an average system measurement with decays in the picosecond regime. For the CdSe-TiO2 system using ferrocene as the regenerating agent, impedance spectroscopy has revealed the dominance of the back reaction to be with solution ferrocenium rather than with a hole state on the quantum dot.20 Such a result creates the picture of side-by-side pathways for charge transfer at the surface, one where electrons are injected into the TiO2 from CdSe quantum dots and the other where they leave the TiO2 to reduce ferrocenium. This charge transfer scheme is part the Onsager analysis in this work that quantifies the net result of several electron transfer pathways at the CdSe/TiO2 interface. Out of this array of literature, one attempts to extract the parameters that are important to this CdSe sensitized single crystal study of current-voltage curves. There appear to be four of them. The first is the rate of electron transfer from the excited CdSe quantum dot to the TiO2. Various studies on nano-TiO2 have found that Marcus theory provides a good description of the rate constant for electron injection into the TiO2 with the size of the quantum dot determining the driving force of the reaction and its linker spacing controlling the electronic overlap and its rate.8,9 Times for electron injection can be fast or slow, ranging from picoseconds to tens of nanoseconds for 3 nm quantum dots and from one to ten nanoseconds for 4 nm quantum dots. The experimentalist can therefore control this rate through the selection of reaction conditions. This Marcus theory approach may not, however, hold for single crystal substrates which have a continuous density of states to serve as acceptors. However, there are no reports of a lifetime



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measurement for a CdSe hole state at a single crystal. The second parameter is the lifetime for radiative decay, that is an inherent characteristic of the quantum dot. For CdSe of the size used in this work, this has been estimated to be 20-40 ns.24 With this reductive lifetime and the possible slow electron transfer rates to TiO2 mentioned above, the yield for electron transfer from CdSe to TiO2 nanoparticles may not be unity. The yield for single crystals is not known although it is expected to be higher for similar sized CdSe particles. A third parameter is the rate of hole trapping at the surface of the attached CdSe. Measurements of this step in isolated CdSe quantum dots indicate that this at longer than 20 ns.5,25 Such a trapping precludes radiative recombination and favors reaction with the regenerating agent. The last parameter is the time for reduction of the hole by the ferrocene reducing agent in solution, a subject of recent studies,26 in which a single ferrocene will reduce a surface hole within 10-6 s. The large surface area of the CdSe, in comparison to a molecular dye, allows for multiple ferrocenes at the surface with a proportionately faster reduction rate. With the presence of sufficient ferrocenes at the CdSe surface, conditions could be arranged to photo-reduce the excited state of the quantum dot before electron transfer to the TiO2, leaving the conduction band electron free to transfer to TiO2. This collection of reported kinetic behaviors reveal that it is possible to create a range of photochemistries for quantum dots at the surface. It will be seen that the character of this CdSe-TiO2 sensitization process can be deduced from the data and models presented in this work. The photocurrent-voltage analysis of this single crystal work will reveal the nature of the sensitization process, photo-oxidation or photo-reduction, and the parameters that govern it. This will be done through an examination of the efficiency of charge collection and the photocurrent-voltage behavior of photoexcited quantum dots on single crystal rutile electrodes with different doping densities. The developed model can provide insights into the hole position on the quantum dot owing to the sensitivity of photocurrent yield to the coulombic attraction of the hole with the injected electrons at the surface of the TiO2 electrode. It will also give estimates of the absolute and relative magnitudes of the kinetic parameters involved.

Experimental


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The procedure to prepare surfaces of single crystal rutile (110) TiO2 electrodes with a range of doping densities has been previously reported.2,4 In brief, atomically flat terraced surfaces were produced by a series of manual polishing and air annealing steps. Reductive n-type doping of the crystals was achieved by high temperature annealing in vacuum (~5 × 10-6 mbar), with temperatures ranging from 500-1100 ºC and annealing times ranging from 5-30 min. Higher temperatures and longer times resulted in higher doping densities due to the loss of oxygen and production of Ti3+ sites in the lattice. Prepared crystals were mounted in an in-house built electrochemical cell that exposes the desired crystal face to electrolyte with front-side illumination of the crystal through a quartz window and an ohmic contact at the back. CdSe quantum dots were synthesized via a traditional hot injection method where a room temperature selenium powder in trioctylphosphine (TOP) and octadecene solution was injected into a hot solution of CdO in oleic acid and octadecene.6,27 To stop growth, the reaction was quenched, with longer reaction times leading to larger quantum dots. For this work, all experiments, unless otherwise noted, were performed using 3 nm diameter quantum dots. whereas size dependent experiments were done with larger 4 nm diameter quantum dots. After synthesis, the quantum dots were purified by flocculation with methanol and washing with acetone, then dispersed in hexane. The native oleic acid (OA) ligands were exchanged for 3mercaptopropionic acid (MPA) by mixing a 1.0 M MPA in acetonitrile solution with the CdSeOA in hexane in a 2:1 ratio and vigorously shaking until flocculation occurred. The solution was centrifuged, supernatant was decanted, and the CdSe solid was dried under nitrogen and redispersed in 48 mM NaOH. Prior to sensitization of the crystal surface, an above band gap UV illumination was used to clean and activate the crystal surface for QD/ligand adsorption. Immediately following UV treatment, the crystal was rinsed with 18.2 MΩ-cm water and dried under a stream of nitrogen. A destabilized sensitizing solution of MPA capped CdSe quantum dots was prepared 30 minutes prior to adsorbing them to the freshly UV activated TiO2 surface. Destabilization was achieved by diluting a small aliquot of concentrated MPA-CdSe quantum dots in 48 mM NaOH solution with 3 M NaCl in a 1:50 ratio by volume. This “salting out” of the quantum dots was found to drive the equilibrium of dots in solution to bind to the crystal surface, resulting in reproducible formation of a uniform monolayer quantum dot coverage with 15 minutes of immersion time



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(Figure S1). At longer times, the quantum dot sensitization solution was observed to flocculate and so the surface-binding tendency was encouraged between bulk stabilized quantum dot solutions and aggregated quantum dots. After immersion, the crystal surface was rinsed with 48 mM NaOH followed by water and dried in nitrogen. Simply soaking the crystal in stabilized quantum dot solutions resulted in irreproducible coverages with either quantum dot clusters or well below monolayer coverages. Monolayer or near monolayer coverages were required to ensure that all QDs were in contact with the TiO2 surface. An Asylum Research Cypher AFM was utilized (ambient AC mode) to track crystal surface morphology and confirm monolayer coverage of quantum dot nanocrystals. A small area of quantum dots were scrapped from the surface by using the instrument in contact mode, causing the tip to physically move the quantum dots from the scanned area of the surface. Switching back to AC tapping mode, the scraped area becomes visible and the height difference between the bare surface and the quantum dot layer was used to confirm monolayer coverage (Figure S1). Incident photon current efficiency (IPCE) spectra for the sensitized TiO2 crystals were measured in a three-electrode configuration using a Pt-wire counter electrode and a silver-wire as a reference electrode. A 1 mM ferrocene with 50 mM tetrabutylammonium hexafluorophosphate (TBA-HFP) in acetonitrile electrolyte was used for all electrochemical analysis. This electrolyte was degassed with nitrogen and sealed off from ambient air in the electrochemical cell prior to measurements.

Photocurrent measurements were performed with a potentiostat (Princeton

Applied Research EG&G, 174A) and a lock-in amplifier (Stanford Research, SR830), using a Laser-Driven Light Source (Energetiq Technology, LDLS EQ-99) coupled to a computercontrolled monochromator (Jobin Yvon, H20) as the excitation source. The light source was chopped (Stanford Research System Chopper, SR540) at a frequency of 13 Hz, which was synchronized with the lock-in amplifier. Dark and photocurrent-voltage curves, both DC and coupled with the lock-in amplifier with light chopping, were measured immediately following the IPCE evaluation. Excitation light from the same LDLS and monochromator combination for the IPCE measurement was used, with the monochromator wavelength set at either the first or second exciton peak of the quantum dots adsorbed on the surface. Current-voltage (I-V) curves were scanned from positive to negative potentials at 10 mV/s for DC measurements and 5 mV/s for lock-in measurements.


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Results Current-voltage curves were recorded in the dark and in the light for near monolayer CdSe sensitized n-TiO2 electrodes that varied in doping density between 1016 cm-3 and 1020 cm-3. A standard I-V curve is shown in Figure 2a for a system with a substrate doping density of 6 × 1017 cm–3. Quantum dot desorption during these scans was not detected. Starting at an applied potential of 0.5 V, the red curve shows a negative sweep for a dark current-voltage curve for the CdSe/TiO2 electrode in a 50 mM TBA-HFP electrolyte in acetonitrile with 1 mM of added ferrocene. Beginning with a current of 1 nA from oxidation of Fe(Cp)2, the current gradually becomes reductive with a slight bump at -0.3 V before going steeply negative. This is attributed to reduction of Fe(Cp)2+ generated from the oxidative regeneration reaction for the quantum dot sensitizers. On the return sweep a maximum anodic current is reached at -0.35 V before settling down to an oxidative plateau. Under illumination, a sweep shown in blue is offset from the dark baseline current by a constant photocurrent. Similar DC photocurrent-voltage curves were recorded at other doping densities and featured plateaus in photocurrent from 0.5 V negative to about -0.45 V, then a decline negative of that bias potential. The flat-band potential (Vfb) of the bare TiO2 in this electrolyte was determined to be -0.8 V, as determined through impedance analyses (Figure S2). In line with the results of the impedance measurements, it was also observed that the dark reduction currents for CdSe sensitized TiO2 were shifted 200 mV negative of those found for unsensitized TiO2 (Figure S3), to -1.0 V, indicating a shift in Vfb owing to the presence of the attached CdSe. A representative AFM image of a sensitized electrode is provided in Figure 2b to show a typical distribution of quantum dots on the surface where there are only a small number of QD clusters present over the more the 25 square micron area.



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Figure 2. (a) Current-voltage curves in the dark (red) and under illumination of 560 nm light (blue) for a CdSe sensitized TiO2 electrode of 6 × 1017 cm-3 doping density. Dotted green line depicts curve of hand chopped light. Black arrow indicates reduction of Fe(Cp)2+ under the negative direction sweep of the current-voltage curve. (b) AFM image of the single crystal TiO2 substrate with CdSe quantum dots adsorbed onto the surface.

The spectral dependence of the photocurrent is given in Figure 3a for all of the doping densities studied, where the electrodes are held at a bias of +0.5 V. The known excitonic peaks for CdSe quantum dots are evident at about 480 nm and 560 nm. These spectral features confirm the presence of quantized excitations in the samples used and serve to identify the excitation wavelengths for the sensitized photoelectrochemical measurements that follow. No further interpretation of these peaks was necessary for these electrochemical studies. The incident photon current efficiencies at 560 nm measured for these electrodes are plotted in Figure 3b as a function of the electrode doping density. These have been adjusted for variations of about 20% in the surface coverage of under a complete monolayer of the TiO2 by CdSe quantum dots as determined by AFM images (Figure S4). IPCE values for these doped crystals are relatively constant between 1 × 1016 cm-3 and 1 × 1019 cm-3. The absolute magnitude the IPCE values of the CdSe sensitized electrodes are comparable to those found for N3 sensitized TiO2, but are smaller than those found for the higher extinction coefficient cyanine dye G15. However, the IPCE for the highest doping density, 1 × 1020 cm-3 is a hundredfold lower than all of the intermediate doping densities. The highly doped Nb-doped crystals are very dark in color and, as concluded in previous work, the combination of energy transfer quenching by these color centers


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in TiO2 and the large cathodic tunneling currents at positive bias potentials appears to lead to very low sensitization currents. The form and shape of the light and dark currents of the highly doped samples (Figure S5) was found to be very much like those found for molecularlysensitized TiO2, being dominated by tunneling process that can only be approximated in form, and not being found to be informative. Therefore this doping range was not further considered in this work.

Figure 3. (a) Incident photon to current efficiency (IPCE) spectra of CdSe sensitized TiO2 for all doping densities, labeled in legend. A normalized solution absorbance of the CdSe quantum dots used for sensitization is plotted as black dashed line (right axis). (b) The excitonic peak IPCE of CdSe (red), as well as N3 and G15 dyes (blue and green respectively), is plotted for each doping level.

In order to extend the photocurrent measurements to the flat-band potential (Vfb) and beyond, a lock-in technique was employed to extract the in-phase photocurrent component from the relatively large DC dark current background. In the potential regimes where it was possible to measure photocurrents in a DC arrangement with hand-chopped light exposure, the magnitude of the lock-in photocurrents and DC photocurrents were the same. Figure 4 shows that the photocurrent-voltage curves in red using the lock-in amplifier with a potential sweep that extends negative to -1.0 V have the same general form for three different doping densities from 1 × 1016 to 6 × 1017 to 5 × 1018 cm-3. The photocurrent rises from -1.0 V to a shoulder at -0.4 to -0.45 V and remains somewhat constant thereafter. The characteristic features of these curves are the potential of the shoulder relative to Vfb for the doping density and the slope of the photocurrent



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positive of this potential. In Figure 4d the corresponding photocurrent-voltage curve for a 4 nm diameter CdSe quantum dot is also given. A comparison of the DC current-voltage curve in Figure 2a with Figure 4b shows that reduction of the oxidized regenerator ferrocenium by TiO2 electrons occurs faster than direct electron recombination with holes in the quantum dot. At a bias potential such as -0.3 V, where the photocurrent is still at its maximum, dark reduction of ferrocenium produced by regeneration of the CdSe is observed, revealing that ferrocenium reduction reaction is faster. The dark ferrocenium reduction current is also manifest in the lock-in curves as a bump as well as less perceptible transient spikes in the hand chopped DC photocurrent-voltage curves in Figure 2a and in supplementary information (Figure S6). They occur to a greater or lesser extent in all of the curves in Figure 4. These lock-in bumps are an artifact attributed to the transients where in the “on” part of the light chopping cycle, ferrocenium is produced, which is itself reduced in a dark current continuously during the chopping cycle, and is greater under the “on” cycle and decaying in the “off” cycle, thereby producing a component at the fundamental frequency detected by the lock-in. The fact that this bump is larger with 4 nm quantum dots suggests that the regenerator included in the volume between the quantum dots and the surface is the first to be oxidized and reduced since the 4 nm quantum dots create a larger void space. The larger quantum dots also have larger interstices between them, which allows greater diffusion from bulk solution to the surface. The diffusion situation for regenerators at this interface is complicated, including regenerating agent trapped within this space and the standard planar diffusion for the untrapped ferrocenium. Adding to this situation are the imperfections in quantum dot layer on the surface where direct access of the regenerator is possible.


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Figure 4. Normalized experimental photocurrent-voltage curves (red lines) and mathematical fits (black lines) of three different doping densities; 1 × 1016 (a), 6 × 1017 (b), 5 × 1018 cm-3 (c), and a corresponding curve for a doping density of 6 × 1017 cm-3 sensitized with larger 4 nm in diameter quantum dots (d). The different datasets are labeled in the plot legends, where SB represents the Schottky barrier term, BR the branching ratio term, and SB × BR the product of the two. In parentheses are given the value taken in nanometers in the fits for xd of Equation 3, which is the effective distance of the hole in the quantum dot from the TiO2 surface. For (d) krec was taken to be 100. The potential sweep direction is indicated by arrows in all figures.

The form of the photocurrent-voltage curves in Figure 4 support the classic sensitization model where the electron transfer to the TiO2 occurs before reduction of the hole by the regenerator. If



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the hole reduction step had been faster than electron transfer, the negatively charged CdSe would be oxidized by the TiO2 in a dark reaction that would be independent of the bias potential. The current-voltage curves would then be flat over the entire span of the bias. As discussed above, the radiative lifetime of the exciton within CdSe has been reported to be about 20 ns, which should provide ample time for electron transfer to TiO2, and the data above supports that. Hole extraction via a surface state from the core of a core/shell CdSe/CdS QD by ferrocene has been reported to occur within 10-6 s for a single attached ferrocene,26 and occurs proportionately faster for greater numbers of attached donors. It may be possible to attach enough ferrocenes to the quantum dot surface to force a change in the mechanism of the sensitization reaction. In these experiments at 1 mM ferrocene in solution, however, there is an average of 0.1 donor molecules within 1 nm of the quantum dot surface and the electron transfer rate would not be fast enough to quench radiative decay. The governing equation for sensitized photocurrent-voltage curves is given in Equation 1. It states that the current-voltage curve is dependent upon the band bending ∆Φ in the semiconductor and the doping density, ND, as well as , which is total current in A/cm2, of all injected charge from the sensitizer into the electrode that thermalizes in the interior, within the space charge region: =

( + − )

(1)

Here jg is the current density from the surface generation of charge at the thermalized energy of the conduction band edge, such as the oxidation or reduction of redox agents in the dark. Electron injection from oxidation of any photo-reduced quantum dots, for example, would be covered by this term. kes is the escape velocity, in cm/s, of electrons from the surface to the bulk and krec is the recombination velocity in cm/s of electrons in the conduction band with an acceptor at the surface, both in solution and on the surface, and e is the unit electric charge. There are two factors in Equation 1 that describe the experimental features of the photosensitized current-voltage curves. Within the parentheses is found the well-known Schottky barrier (SB) description of current-voltage curves for semiconductor electrochemistry. Electron injection from a sensitizer that thermalizes in the interior of the semiconductor or transfers charge to the surface at the energy of the conduction band edge with a current jinj or jg, is negated by a reverse


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reaction exponentially dependent upon ∆Φ. In the photo-reaction, the electron concentration at

the surface given by reduces the oxidized hole state left in the sensitizer with a rate constant krec. At sufficiently positive bias potentials, this reverse current flow goes to zero to yield the plateau found in Figure 4b and 4c for the intermediate doping levels of 6 × 1017 cm-3 and 5 × 1018 cm-3. As bias potentials are swept from -0.45 to -1.0 V for these two electrodes, however, the rate constant krec allows the reduction of the oxidized sensitizer. As was revealed with molecular sensitizers at these TiO2 electrodes, the recombination rate is multi-exponential in nature.4 The second factor is the branching ratio (BR) pre-factor kes/(kes+krec) where kes is defined as: ) = xs/$ /% &(')/( dx '

(2)

where D is the diffusion constant for electrons in TiO2, xs is the thermalization distance of the electron inside the TiO2 , and Φ(x) is the potential at position x inside the space charge region. This ratio describes the diffusion of the thermalized charge carriers from electron injection on the potential energy surface composed of the Schottky barrier potential and the coulomb potential between the thermalized electron and the positive charge left behind. This overall potential has been approximated4 by the expression:

=

/ / . 0[ ] *+,- ( ' ') 2, 3 , 4

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+ *778 (x - :8 )* − ;? + > ) represents the solution layer and the TiO2 at the surface. The first coulomb term in Equation 3 reflects the discharge of the double layer through the steady state electron injection and the resultant attraction between this layer of injected charge and the surface layer of the hole state left behind. The expression reflects the reduction in potential felt by an electron owing to its image charge in the dielectric of the surface electrolyte layer, which is equal to (>? − > )/(>? + > ).28 For the case of a charge external to a sphere, this image charge reduction is slightly smaller, being expressed formally as (>? − > )/(>? +
)( ) where a is the radius of the quantum dot.29 Given this small change and the subsequent '



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fitting of the data through variations in xd, the simpler expression of Equation 3 is used as an adequate approximation. More complicated and exact expressions for the electrostatics of a spherical dielectric in a dielectric medium adjacent to a planar dielectric surface do exist,30 but their application would have only a minor impact influence upon the potential of Equation 3 and offer little more to this discussion. Overall, this is a dynamic, steady state situation under illumination as the electrolyte diffuses to neutralize any specific local attraction between charges within nanoseconds. The pre-factor BR of Equation 1 controls the yield of escape of a charge from the surface, relative to its loss by reducing a species at the surface. This is a smoothly rising function with potential as the band bending increases. It can be seen through Equation 3 that kes at a position x depends upon the potential at the surface created by the sum of the coulomb potential between electron and hole and the applied, Schottky barrier potential. In contrast to the hole on an oxidized molecular sensitizer attached at a fixed distance from a TiO2 surface, the hole in a quantum dot can range in its distance from the solid and can have a larger xd in Equation 3, being nominally 1.5 nm for a 3 nm dot and 2 nm for a 4 nm dot, in addition to the separation of the mercaptopropionic acid layer. The net result of a reduced coulombic attraction is that the potential position of the rising portion of the current-voltage curve will shift negative relative to the flat-band potential as the coulombic attraction is reduced. Prior work with dye sensitized TiO2 single crystals showed how current-voltage data, such as that in Figure 4, could be fit by Equations 1-3.4 It was learned in that work that the band bending

∆Φ needed in the Schottky barrier factor of Equation 1 to go from zero photocurrent to a plateau feature depended, in a steady state condition for hole concentration, upon the relative rates of recombination from the conduction band to the regenerator reduction for the hole state: ( − / –ΔΦ/( )

=

ABC D

D E 6F G/

(5)

Here k1rec represents only the pseudo first order reduction constant for the hole in the sensitizer CdSe, which can be isolated with the lock-in technique. The conclusion of earlier work was that a dispersion of reduction rate constants H , taken from the dye-sensitized solar cell literature, was necessary to explain the 400 mV band bending required to draw off all of the photocurrent. This dispersion could result from multiple trapping pathways in the TiO2 or the complex 2D diffusion


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process at the interface of an electron seeking a hole. In contrast, single rate constants for H and kreg would result in a rise of photocurrent to the plateau within 60 mV, behavior that has never been observed at a single crystal electrode. The existence of many possible locations of a hole state in the quantum dot with its much greater diameter than a dye would increase this dispersion. However there have been no fast, time-resolved analyses of these recombination rates for quantum dots as there has been for molecular sensitizers. There are no good figures to insert into k’ as there were for the molecularly sensitized TiO2. The overall current in Equation 1 is determined by the product of the SB factor and the BR curve. For higher doped electrodes, BR will tend to go to unity very quickly with band bending, leaving only the Schottky term to describe the photocurrent-voltage curve. It will be seen in Figures 4a through 4b that there are conditions where each of these factors dominate behavior. One begins the fitting of the model to the curves of Figures 4a through 4d with the data from the 1 × 1016 cm-3 doped electrode since the behavior of the lower doped electrodes are the most sensitive to the parameters of Equations 1 through 3. Once an acceptable result is found for Figure 4a for the 1016 cm-3 doped data, these parameters are held constant, changing only the doping density for the calculations of the higher doped electrodes in Figures 4b through 4d. In this 1016 cm-3 calculation, kreg for the hole reduction in CdSe by 1 mM ferrocene was taken to be 105 s-1.

A dispersion of rate constants was used for H in Equation 4, but only with an

acceleration of these rates by a hundred did the calculation place the shoulder of the curve at the correct potential, an approximation that is justified in part because the physical cross section of the quantum dot is far larger than that of a dye molecule. The distance of closest approach xs was taken to be 0.2 nm and (>? + > ) was taken to be (10 + 7), to carry over approximations from earlier work.4 The magnitude of krec in Equation 1 was taken from the magnitude of the dark reduction current at its onset near -0.2 V bias. This velocity should be large since it involves a fast outer sphere electron transfer process, and we estimate this to be 10–100 cm/s given the complicated diffusion situation at a quantum dot covered surface. Through BR, these recombination velocities constrain the range of kes velocities that can influence BR. Given the form of the BR curve in Figure 4a, kes can be seen to increase to several cm/s as the bias potential changes from -1.0 V to +0.5V.



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The resulting curves depicted in Figure 4a reveal that the product SB × BR is very sensitive to the distance xd as it is varied from 0.7 to 1.0 to 1.3 nm, with an xd between 1.0 and 1.3 nm best describing the data. In order to see their form, SB is provided separately, as is BR for an xd of 1.0. It is evident that the upward slope of the photocurrent at positive bias potentials is attributable to the BR. The larger xd values result in a weaker coulombic attraction and a larger kes to compete with the 10 cm/s krec velocity. Carrying these parameters forward to the 6 × 1017 cm-3 doping density curves of Figure 4b, one sees that the calculated curves for xd values of 0.7, 1.0, and 1.3 nm bracket the shoulder and plateau region of the photocurrent. The rise to the shoulder is less well described, but this may be attributed to the lack of dispersion in these calculations to describe rates for the receiving end of the hole in the quantum dot as discussed previously. These deviations also are found at potentials where the dark current is very large compared to the photocurrent. To examine the 5 × 1018 cm-3 data of Figure 4c the calculations bracket the data with the 1.0 and 1.3 nm values for xd. This sensitivity to xd is tested in Figure 4d where a 4 nm quantum dot is used at a doping density of 6 × 1017 cm-3. Ignoring the large bump at the shoulder, which has been discussed earlier, the curves for xd values of 1.6 to 1.9 nm appear to come closest, as is appropriate for the larger QD. In order to create the sloping aspect of this curve, krec in the BR term was increased to 100 cm/s, which the dark current measurements for this sample supports. Discussion There are several ratios of rates that control the photochemistry of these quantum dots at the surface of TiO2, and the efficacy of the resultant sensitization. First is the relative rate of electron transfer of an electron to the TiO2 to that of hole capture by the reducing agent, ket/kreg. At mesoporous TiO2, Marcus behavior was reported for ket as a function of size of the quantum dot. If the ratio is large, then photo-oxidation of the excited quantum dot is preferred, but if it is low, it is possible for photo-reduction of the quantum dot to occur. Both the absolute and relative rates of these are under control of the experimentalist. At single crystal electrodes, ket is most likely fixed and very fast, and this photo-reduction regime is not reachable. In Equations 1, 2, and 3, the ratio of kes/krec controls the ability of an injected charge to escape from the surface, and governs the overall sensitization process. The escape velocity kes is controlled by the structure and nature of components at the sensitizer/substrate interface, and can be designed to maximize


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kes. The recombination rate is less well controlled by the experimentalist, although the selection of the regenerator redox couple plays a major role. Last, it is evident that the back reaction at the surface controlled by the SB is determined by the ratio of direct recombination to the hole recombination rate, H /kreg. This ratio determines the potential position at which the plateau region of the photocurrent occurs. This is important in planar electrode research and provides an electrochemical evaluation of the recombination rate of electron and hole state. Given the lack of a Schottky barrier region in mesoporous electrodes, there is no photocurrent shoulder, but the ratio H /kreg still controls photocurrent yield, for which only the single crystal work can provide a direct electrochemical measure. The analysis provided by the single crystal sensitization study of this work provides insights into these rates and ratios. The calculated curves provide a reasonable description of the experimental photocurrent-voltage curves of Figures 4a through 4d. For the 1016 cm-3 doped crystal, the calculated curves reveal the influence of BR upon the upward sloping current and establish that the effective distance xd of the hole in the CdSe is about 1.0 to 1.3 nm. The curves of Figure 4a are the clearest manifestation of the competition between escape and recombination of the electron as it diffuses within the force field at the semiconductor surface. At this doping density, the field from the Schottky barrier at the surface is weak and the coulombic attraction to the hole layer is sufficient to pull an electron into recombination. The distance xd derived from this doping density was carried forward to the calculation of the higher doped 6 × 1017 cm-3 and 5 × 1018 cm-3 electrodes and appeared to work well in describing the slope of the current in the plateau region. The potential required for the rise of the photocurrent from -1.0 V to -0.45 V is described by the SB term, determined by the ratio of kreg to H , and although calculations place the shoulder at the correct potential versus Vfb, the rise in current is less well described. However, as was previously mentioned, rate constants are not known for the direct recombination of the injected electron with the hole state of the CdSe, and these determine the form of the rise of the photocurrent to the plateau region. Instead, the dispersive rates from dyesensitized modeling were used as an approximation. When a 4 nm quantum dot was used, the curve of Figure 4d was observed where an xd of 1.5 to 1.9 nm matched best. This greater distance reflects the larger radius almost exactly, but both xd distances, 1.0 to 1.3 nm and 1.5 to 1.9 are shorter than what the actual geometry predicts, which should be 1.5 nm + δ and 2.0 + δ where δ is the thickness of the intervening mercaptoproprionic acid layer. The electrostatic



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attraction between the planar electrode and the spherical quantum dot should compress this layer, or displace it completely if the Se sites on the QD bind directly to unsaturated Ti sites on the TiO2 surface, but it should still be several tenths of a nanometer. The results indicate that the average position of the hole state is between the center of the quantum dot and the TiO2, which implies a preferred degree of hole trapping on the surface of the CdSe particles facing the TiO2. The correlation of data with the calculations is not as good as those found in earlier work on dyesensitized TiO2 single crystal electrodes for several reasons. One is because the quality of the quantum dot sensitized interface is not as simple as the dye-sensitized interface. This is evident from the AFM images and the transients in the hand-chopped DC photocurrent curves. There is also a unique geometry to the QD/TiO2 interface, that has an impact upon recombination kinetics. The layer of quantum dots on the TiO2 includes a volume where the regenerator may be included and would not obey a one dimensional diffusion model, whereas the regenerator on the outside surface of the quantum dots will. This would complicate accurate modeling in ways beyond the scope of that employed in this work. In addition, the hole state on the CdSe can be localized at all positions on the surface, from adjacent to the TiO2 to the point furthest distant from the TiO2, leading to a dispersion of electron-hole recombination rates that is also not included in the present calculations. It is clear from the literature reports of Marcus behavior for electron transfer from CdSe quantum dots to mesoporous TiO223 and reports of reduction rates for CdSe holes by Fe(Cp)226 that situations can be manipulated to photo-reduce the excited CdSe sensitizer. However, the data for this work on single crystal TiO2 support the common model for spectral sensitization where the excited CdSe injects an electron into the TiO2 conduction band and the hole is reduced by the regenerator Fe(Cp)2. The current-voltage curves also show that reduction of Fe(Cp)2+ at the surface is very fast and that great care must be taken in preparing such a sensitizing interface for effective charge separation. In summary, the possible reaction pathways involved in the spectral sensitization of semiconductors by quantum dots are more complicated than those for sensitization by molecular species, owing to the greater size of quantum dots and a different physical and electronic structure. These differences offer numerous opportunities for further exploration and discovery.


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Supporting Information AFM images of single crystal TiO2 substrates with adsorbed CdSe; Mott-Schottky plots for electrodes; Current-voltage curves of unsensitized TiO2; AFM images of sub-monolayer coverage of TiO2 by CdSe; 1020 cm-3 high doping density photocurrent-voltage curves for sensitized TiO2.

Acknowledgements The authors acknowledge funding from the Department of Energy Basic Energy Sciences Division of Solar Photochemistry Program under Grant # DE-SC0007115. KJW and BAP acknowledge support from the J. E. Warren Chair of Energy and Environment at the University of Wyoming.

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Fundamental Aspects of Photoinduced Charge Flow at a Quantum Dot

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