Transport of a Charge Carrier Packet in Nanoparticulate ZnO Electrodes

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Transport of a Charge Carrier Packet in Nanoparticulate ZnO Electrodes Volker Noack,a Horst Weller,b and Alexander Eychmüller*b a

Present Address: Wenzel & Kalkoff, Patent Attorneys, Grubes Allee 26, 22143 Hamburg, Germany Institute of Physical Chemistry, University of Hamburg, Bundesstrasse 45, 20146 Hamburg, Germany *Corresponding author: Email: [email protected]

b

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The apparent changes in the transient photocurrents of nanoparticulate ZnO layers have been investigated by varying the extrinsic conditions of the measurement such as the composition of the electrolyte solution, the intensity of the incident light and the temperature. The effect of the light intensity on the transient photocurrents is interpreted in terms of a local increase of the electron density in the charge carrier packet. From the analysis of measurements performed at different temperatures, the mechanism of an electron exchange between adjacent particles is identified as a tunnelling process. A simple model is derived from which information about the height and the width of the potential barrier between the particles is gained. The energetic position of the conduction band edge of the ZnO is found to follow the Nernst equation with respect to the pH of the electrolyte solution. In comparison with the steadystate measurements, the transient photocurrents obtained for different hole scavenger concentrations in the electrolyte solution are explained by kinetic arguments. The changes of the charge transport by varying the concentration of the supporting electrolyte is interpreted in terms of the tunnelling approach by a screening of the potential barrier by the cations in the electrolyte solution. 1 to the data curves. The rate constants k1 and k2 refer to the electron transport through the illuminated part of the ZnO layer and the ITO substrate, respectively. The charge transport through the illuminated volume of the ZnO film is correlated strongly with the initial charge separation which competes with a recombination of electrons and holes. Thus, information about this process is included implicitly in the parameter n10 which, according to the underlying model, refers to the amount of charge transported. The electron transport through the ZnO layer was found to be a diffusion process. By using the approach of a random walk, the fit parameter k1 was reinterpreted in terms of the diffusion coefficient D resulting in the relation

Introduction Wide band gap semiconductors such as TiO2 and ZnO play a major role in the design of photovoltaic1,2 and photocatalytic devices.3,4 Thus, information about the mechanism of a charge transport in these systems is crucial for an improvement of the present technology. In general, photocurrent measurements have proven to be a valuable tool in the investigation of semiconductors employed in electrochemical cells. Steady-state and dynamic experiments provide detailed information about the processes arising in these electrodes, especially about the dynamics of a charge transport, competing recombination pathways, and chemical reactions occurring at the boundary to the electrolyte solutions such as photocorrosion or photocatalysis.5-9 In comparison to other techniques (e.g. intensity modulated photocurrent spectroscopy8,10,11), the illumination by a laser pulse in a transient experiment usually imposes a strong disturbance on the system under examination. However, this experimental approach allows to monitor the transport of a single packet of charge carriers across the electrode which is of high interest for applications in signal transmission or fast sensors. In conventional single-crystalline electrodes, only a small part of the semiconductor is in direct contact with the electrolyte solution. Thus, the phase boundary is only important for a charge injection from or into the electrolyte. However, by the use of nanoparticulate electrode materials, the electrolyte solution interpenetrates the porous network and might thus affect not only Faradaic processes but also a charge transport through the semiconductor. In this case, additional information about the system can be gained by simply changing the composition of the electrolyte solution.9,12,13

d = 0.39 ⋅ a D k1 −1 / 2

e n10

A (k2

−1

−1

− k1 )

[exp( -k 2 t ) − exp( -k1 t )]

(2)

where d denotes the thickness of the ZnO film and a is a parameter which depends on the directions available for the propagation of the electron. Since only the photocurrent signal is detected which results from a current flow perpendicular to the plane of the back contact, it is reasonable to restrict the random walk to the one-dimensional case and thus to a = 2. As a consequence of this simplification, the diffusion coefficient obtained from the measurement is not the “true” diffusion coefficient D but the effective one-dimensional diffusion coefficient D*. Additionally, it should be mentioned that the transport mechanism described by Eqns. 1 and 2 is restricted to ZnO layers having a thickness between 260 nm and 2.9 µm for our experimental conditions. For very thin ZnO films (up to a thickness of 260 nm corresponding to the threefold penetration depth of the incident light), no contribution of the transport through the ZnO to the transient photocurrents is observed since the whole volume of the ZnO layer is illuminated and the transport through this part of the electrode is considerably fast. For ZnO films with a thickness of more than 2.9 µm, the total number of deep trap states is larger than the number of photogenerated electrons. Thus, all charge carriers become trapped before they reach the back contact and a slower transport mechanism via these trap states is expected to take place. This latter transport mechanism is not taken into account by the simple model (cf. Eqns. 1 and 2). Besides the film thickness, more factors might possibly change the electron transport through particulate electrodes in

Evaluation Procedure: In a previous publication, we have given a very basic description of the transient photocurrent jP(t) in a ZnO nanoparticulate layer onto an ITO substrate14. The photocurrent transient can be modelled by using two exponential functions, j P (t ) =

,

(1)

,

where e is the elementary charge and A denotes the electrode area. The parameters k1, k2 and n10 are obtained from a fit of Eq.

1


previous publication14. For excitation, the 266 nm line of a Nd:YAG laser system (SLT804T, Spectron Laser Systems, Polytec) with a pulse duration of 10 ns was used. The respective photocurrents were recorded using an oscilloscope (64522A Oscilloscope, Hewlett Packard). In order to ensure the illumination of the whole area of the working electrode, the laser beam was widened using a quartz lens. A Rm-3700 universal radiometer equipped with a RjP-375 energy probe (Laser Probe Inc.) was employed to monitor the light intensity. Unless otherwise stated, the laser beam was attenuated to an energy density of 20-30 µJ/cm2 per pulse. In all experiments, the electrode was illuminated by the laser light from the front side (i.e., not from the substrate side). Before and after exposure to the laser light, absorption spectra of the electrodes were taken and cyclovoltammetric measurements were performed in order to ensure that the samples had not suffered damage during the experiments. In order to remove the DC component of the current from the transient signal, the respective transient dark currents were subtracted from the data. The thus obtained photocurrents were corrected with respect to the actual area of the ZnO film in order to obtain current densities. Measurements at different temperatures were performed using a quartz tube cell. This small cell was tightly fit into a copper block which had an additional bore to allow an illumination with the laser light. The temperature of the cell was adjusted by an external flow-thermostat (Lauda) which was connected to the copper block. The resulting temperature of the electrolyte solution was monitored with a digital thermometer. The cell and the copper block were embedded in an evacuated double-wall quartz dewar to minimise a heat exchange. In this experimental set-up, the counter electrode was a glassy carbon rod whereas for spatial limitations of the small cell a platinum wire as a quasi-reference electrode was employed. Prior to the experiments, the potential of the quasi-reference electrode was measured under current load between the working and the counter electrode with respect to an external Ag/AgCl/3 M NaCl reference electrode, which was not part of the three electrode arrangement. From the potential difference at 298 K, the relation between the two different potential scales was obtained. Steady-State Photocurrent Measurements: Steady-state photocurrents were recorded under potentiostatic control during illumination with 360 nm light of a Xe lamp (XBO 450W/4, Range D, Osram). The lamp was equipped with a 15 cm water cuvette to remove the IR part of the lamp spectrum. The light was focussed onto the entrance slits of a monochromator (Photon Technology International; grating: 600 lines/mm). The respective photon flux (about 1 nmol/cm2s @ 360 nm) was monitored with a calibrated thermopile (6M, Laser Components). The photocurrent was calculated as the difference between the current flow under illumination and the dark current measured without illumination. By dividing the photocurrent by the respective electrode area and the photon flux, the incident photon to current efficiency (IPCE) was obtained. Cyclic Voltammetry: Cyclic voltammograms were recorded in the potential range between +200 mV and –800 mV with a xyrecorder (PM 8277, Philips). For the potential sweep, a rate of 10 mV/s was used. Prior to the measurements, one potential cycle was performed to guarantee the reproducibility of the data. By this first scan, electrochemically active substances were removed from the surface of the ZnO which were possibly adsorbed during the storage of the electrodes under ambient air.

electrochemical cells and thus a refinement of the model described above is reasonable. In general, the charge transport depends on intrinsic and extrinsic factors. The first ones refer to the specific properties of the electrodes such as the materials, the geometry of the electrode, the size and the size distribution of the particles as well as the morphology and the thickness of the film. Other factors that may possibly have an effect on the charge transport are extrinsic in nature, e.g., the composition of the electrolyte solution, the cell geometry, the intensity of the light source or the temperature. The subject of this publication are the extrinsic factors affecting the charge transport through a nanoparticulate ZnO electrode on an ITO substrate.

Experimental Section Preparation of the ZnO/ITO Electrodes: The preparation of the ZnO particles and of the ZnO/ITO electrodes has been described in detail elsewhere.15 Briefly, a colloidal solution of ZnO particles 2 nm in size was prepared according to the method of Spanhel and Anderson16 from a suspension of zinc acetate dihydrate in ethanol in the presence of lithium hydroxide. From this solution, larger ZnO particles (6 nm) were obtained by addition of a small aliquot of water at 60 °C. After a thorough purification of the resulting precipitate by repeated washing and centrifugation, the ZnO particles were spin coated onto cleansed ITO substrates (25×25 mm2, 25 Ω/sq., Schott) in subsequent coating steps. Each of these steps was followed by heating the sample in a furnace at 100 °C for 5 min in order to remove the residual solvent. The thickness of the resulting ZnO film was monitored using a stylus profilometer (Alphastep 200, Tencor Instruments). With this method, transparent samples with a film thickness of up to 2.1 µm were achieved which showed no light scattering in the visible range of the spectrum. Finally, the sample was annealed for 30 min at 300 °C. For the preparation of the electrodes, a copper wire was attached to the sample using a conductive epoxy resin (3021, EpoxyProdukte) and the contact area was sealed with an insulating resin (Scotchcast No. 10/XR5241, 3M). General Set-up: Photoelectric Measurements were performed using the ZnO/ITO electrodes as working electrodes in an electrochemical cell equipped with a quartz window. The counter electrode was a platinized platinum grid and the reference electrode was an Ag/AgCl/3 M NaCl electrode (+207 mV vs SHE). The reference electrode was connected with the cell compartment via a salt bridge filled with an electrolyte solution of the same composition as the solution in the cell. All potentials in this study are reported against this Ag/AgCl/3 M NaCl electrode. The experiments were performed under potentiostatic control using a home-built potentiostat with a potential rise time under short circuit conditions of less than 300 ns (depending on the capacitance of the respective sample) and a low input impedance (< 1 Ω). Unless otherwise reported, the electrolyte solution used was an aqueous borate buffer solution (pH=8.0) containing 1 M LiClO4 (p.a., Fluka) as the supporting electrolyte and 30 vol.-% ethanol as a hole scavenger. For the preparation of the buffer solutions, a stock solution was employed which contained 12.404 g H3BO3 (p. a., Merck) in 1000 mL 0.1 M aqueous NaOH solution. Buffer solutions with different pH were obtained by mixing this stock solution with various amounts of 1 M solutions of HCl (for pH between 7.8 and 9.2) or NaOH (for pH between 9.4 and 11.0) and carefully adjusting the pH of the degassed solution under control of a pH-meter. Prior to the electrochemical experiments, the electrolyte solution was deaerated with high purity nitrogen for at least 20 min. The nitrogen was allowed to flow over the solution surface during the experiments. Transient Measurements: A detailed description of the experimental set-up and the data acquisition was given in a

Results and Discussion I) General Considerations

2


0.6 0.4

0

10

19

ITO

-300 -600

φ [mV]

ITO

-10

10

18

10

17

10

16

10

15

ZnO

φ [mV] 0

0

-200

-400

-600

φ [mV vs Ag/AgCl/3 M NaCl]

-800

0

electrode

ZnO

-20 200

0

-200 -400 -600 -800

10 -1 10 -2 10 -3 10 -4 10 -5 10

nP

0

0.0

-3

2

10

20

2

j [µA/cm ]

0.2

ITO

10

Ne [cm ]

ZnO 20

Q [mC/cm ]

30

-200

-400

ZnO

-600


-800

Fig. 1 Cyclic voltammogram of a particulate ZnO/ITO electrode and a bare ITO substrate. The thickness of the ZnO film was 1.6 µ m. Inset: Total amount of charge flown during the voltammetric experiment with the ZnO/ITO electrode.

Fig. 2 Electron density at different potentials applied for a bare ITO electrode (dotted line), a ZnO covered ITO electrode (dashed line) and for the ZnO part of the ZnO/ITO electrode (full line). Inset: electron density of the ZnO layer, recalculated as electrons per ZnO particle.

In Fig. 1, the cyclic voltammograms of a bare ITO electrode and a ZnO/ITO electrode are shown. Both electrodes exhibit a similar current response at positive potentials applied whereas the current density of the ZnO/ITO electrode increases strongly at negative potentials. For this electrode, the shape of the current response is symmetric with respect to the abscissa (despite the hysteresis at the negative reversal point referring to the porous structure of the ZnO film17). Furthermore, it was found that the current density of both electrodes scales linear with the potential sweep rate. It is thus reasonable to assume that the current response of both systems arise mainly from a capacitive charging and decharging process of the respective materials. By integrating the current in the time region, the total charge transferred into or from the electrodes is gained (shown in the inset in Fig. 1). By comparing the data obtained for positive potentials applied, it is found that the current density of the bare ZnO/ITO electrode is only 60 % of the current density of the bare ITO. At these potentials, ZnO has only little available electronic states and thus the contribution of the particulate film to the capacitive current has to be neglected. Since the whole electrode area is covered uniformly by the particulate film,18 this observation might be explained by the porous nature of the ZnO layer; therefore, it can be assumed that about 40 % of the surface of the substrate is covered by the ZnO film and 60 % is still accessible to the electrolyte solution interpenetrating the porous ZnO network. Consequently, by subtracting 60 % of the charge of the bare ITO electrode from the total charge flown of the ZnO/ITO electrode and by taking into account the space filling of the porous film being 60 %,15 the respective densities Ne of electrons in the ZnO can be calculated for all potentials applied. In Fig. 2, these data are given for the bare ITO electrode, the ZnO/ITO electrode and the ZnO film. In the inset, the latter contribution is depicted as recalculated in terms of the number nP of electrons per particle (by assuming a uniform particle size of 6 nm). It is seen from this diagram, that at positive potentials applied, the conduction band of the particles is virtually empty. At negative potentials, the density of available electronic states increases continuously. For example, at -450 mV, every tenth particle can be considered to bear one electron in the conduction band, whereas at -790 mV an occupation of three electrons per particle is achieved. These findings lead to two important conclusions: (i) It is impossible to establish a significant electric field across the ZnO layer due to the porous structure of the particulate film and the shielding of the charge by the interpenetrating electrolyte. This shielding is very effective since it enables not only the charging of adjacent particles but also an occupation of more than one electron on the same particle. Consequently, if the transport of a single packet of charge carriers is considered,

migration of the electrons in an electric field is unlikely to occur, even for the case of an internal field arising from the moving carrier packet. (In contrast to the propagation of a charge packet, a transport based on the concept of the electron mobility in an electric field was shown by Meulenkamp to apply for the constant current in dc conductivity measurements at ZnO electrodes.19). Thus, the transport occurring in photocurrent transients should preferentially be discussed in terms of a diffusion. (ii) Due to the good shielding of the electrolyte and the low occupation by electrons, any differences in the charge transport through a ZnO film consisting of 6 nm particles are unlikely to base only on the electron density in the system for potentials positive of -450 mV. This conclusion is supported by the absorption spectra of the respective electrodes which still exhibit a shift of the absorption edge corresponding to a slight size quantization.15 Consequently, the particles are electronically separated in the film and thus an electron can hardly be affected by other charges in a distance of more than 50 nm (corresponding to one electron per ten particles). However, if an effect of the potential applied is observed for potentials even positive of –450 mV, this should rather be explained in terms of a change in effective height of the energetic barrier between adjacent particles than simply by the electron density in the system. With these considerations, an analysis of the photocurrents within the framework of a diffusive transport can be performed. In a previous study, we pointed out that the transient photocurrent in nanoparticulate ZnO/ITO electrodes can be modelled by using only three parameters, n10, k1 and k2. Since the latter of these quantities refers only to the transport through the ITO substrate, no effect of the extrinsic factors on the parameter k2 was observed in our experiments. Thus, we restrict our report to the results obtained for the rate k1 referring to the charge transport through the ZnO layer and for the amount of charge n10 which is transported via the mechanism described by Eqns. 1 and 2. II) Effect of the Experimental Conditions a) Laser Intensity In the lower part of Fig. 3, the parameter n10 is given for different intensities of the laser pulse. The respective data for the lowest intensity could be analysed only for a small potential range due to the small photocurrent signal. In general, n10 corresponds to the amount of charge transported according to the model (cf. Eqns. 1 and 2). All data curves show a similar shape

3


φ [mV vs Ag/AgCl/3 M NaCl] + 200

-200

-400

0.8

-600

6

Laser Intensity

0.6 2

n1 [µC/cm ]

10

0

5

10

0

-1

10

0.4

e

k1 [s ]

10

d

0.2

c

4

Laser Intensity

b

a

0.0

3

0

100

200

2

Pulse Energy [µJ/cm ]

300

Fig. 4 Change of the parameter n10 obtained for positive potentials

2

n1 [ µC/cm ]

applied (cf. Fig. 3) with respect to the intensity of the laser. The arrow indicates the laser intensity corresponding to the generation of two electron-hole pairs per particle in the first layer. (ZnO film thickness: 1.7 µm; electrolyte solution: pH 8 buffer containing 30 vol.-% ethanol and 1 M LiClO4).

e

0.8

d c

0

0.4

25 µJ/cm2 was employed (corresponding to 0.6 absorbed photons per particle in the outermost layer) to ensure moderate conditions for the photoexcitation. In the upper part of Fig. 3, the rate constant k1 is given for the different the laser pulse intensities. For all potentials applied, the rate constant increases by increasing the laser intensity. At the first sight, this observation is in contradiction to a model of a charge transport which should be of first order with respect to the number of electrons in the ZnO layer and thus no influence of the light intensity on the rate constant k1 is expected. To account for this observation, first of all, the effect of a possible electrostatic repulsion by different numbers of electrons in the propagating charge carrier packet is analysed. At a laser pulse intensity of 80 µJ/cm2, a maximum of two electron-hole pairs per particle are generated. From the charge density n10, the corresponding conversion efficiency with respect to the number of incident photons can be calculated. For a unity quantum yield process, this would correspond to a total charge of 17 µC/cm2. If the value for n10 (380 nC/cm2) is interpolated from Fig. 4, an IPCE of 2.2 % is calculated. Thus, even though two electronhole pairs are generated in the outermost layer of the ZnO particles, less than one electron per 22 particles on average are still in an excited state after the recombination has taken place. For an intensity of 300 µJ/cm2, the maximum numbers of photogenerated electron-hole pairs increases to 7.3 per particle whereas the IPCE drops to 1.2 %. Thus, even under these conditions, the maximum electron density in the carrier packet is not larger than about one electron per eleven particles. Since the electrostatic charge is screened by the electrolyte solution interpenetrating the particulate network, an electrostatic repulsion of the electrons in the packet is unlikely to explain the acceleration of the charge transport at higher light intensities. Furthermore, in a closed packing of spheres, the number of nearest neighbours is eight. Since the maximum electron density in the propagating packet is smaller than this value, even under strong illumination conditions, the electrons might be regarded to propagate freely to adjacent particles. Since the increase of k1 by increasing the laser intensity is unlikely to be explained by a simple electrostatic repulsion, an effect of the total electron density might be taken into consideration: By shifting the potential applied in negative direction, the total electron density in the system is raised (cf. Fig. 2) which is concomitant with an increase of k1. Thus, by increasing the laser intensity, more electrons become photoexcited leading likewise to an increase of the total number of electrons in the electrode. To allow a comparison of both effects on k1 -the increase of the electron density by the potential applied and by the laser

b a 0.0 + 200

0

-200

-400


-600

Fig. 3 Parameters k1 (upper part) and n10 (lower part) as obtained from a fit of Eq. 1 to the transient photocurrent of a ZnO/ITO electrode. The respective data were obtained for various intensities of the 266 nm laser pulse. (curve a (squares): 5 µJ/cm2; b (circles): 20 µJ/cm2; c (uptriangles): 50 µJ/cm2; d (diamonds): 150 µJ/cm2; e (down-triangles): 300 µJ/cm2). (ZnO film thickness: 1.7 µ m; electrolyte solution: pH 8 buffer containing 30 vol.-% ethanol and 1 M LiClO4).

differing solely in the magnitude of n10: By increasing the intensity of the light, n10 increases as well. At positive potentials applied, n10 is independent of the actual potential applied. Negative of an electrode potential of about -150 mV, the parameter n10 increases by shifting the potential in negative direction until it passes a maximum at –250 mV. As the potential is shifted to even more negative potentials, n10 decreases until it drops to zero at a potential of about –550 mV. The dependence of n10 from the potential applied was discussed in detail in a previous paper.14 Briefly, the decrease of n10 at positive potentials applied was explained in terms of a trapping of electrons in deep trap states. These trapped charge carriers are not accounted for by the underlying model. In Fig. 4, for different illumination intensities the mean values of n10 obtained for positive potentials applied are depicted. Below a pulse energy of about 80 µJ/cm2, n10 increases linearly with the light intensity, whereas at higher intensities the slope of the curve decreases. Due to the linear slope, at moderate excitation conditions, the processes competing with a charge separation are most likely assumed to scale also linearly with the number of electrons. For a laser pulse of 80 µJ/cm2, the total number of photons incident on an area of 28 nm2 (corresponding to the cross section area of the 6 nm particles) is calculated to be 30. If the penetration depth of the porous ZnO layer (being 90 nm for 266 nm light14) is taken into account, the maximum number of photons absorbed in the first layer of particles (which are located in the outermost part of the electrode) is estimated to be 2.0. Thus, at higher laser pulse intensities, higher order recombination processes might occur (e.g., Auger recombination). Consequently, the inflection point in the diagram in Fig. 4 might be explained by a higher rate of recombination under such conditions. It is noted that for all other experiments outlined in this study, an intensity of about

4


10

6

8000

5µJ/cm

2

a -1

k1 [s ]

1.7µm

6000

-1

k1 [s ]

10

5

10

270nm

b

c

d

e

4

4000

+ 200

0

-200

φ [mV vs Ag/AgCl/3 M NaCl (298 K)]

-100

-200

-300

-400


-500

Fig. 6 Rate constant k1 obtained for different ambient temperatures (curve a (squares): 278 K; b (circles): 295 K; c (up-triangles): 304 K; d (diamonds): 314 K; e (down-triangles): 323 K). (ZnO film thickness: 1.9 µm; electrolyte solution: pH 8 buffer containing 30 vol.-% ethanol and 1 M LiClO4).

Fig. 5 Rate costants k1 related to the effective potential (see text) of the photoexcited electrons. Open symbols: electrons are distributed uniformly over the whole ZnO film (1.7 µ m). Solid symbols: electrons are distributed uniformly over the threefold penetration depth (270 nm). Curve a from Fig. 3 is plotted as a reference (dotted line).

packet of charge carriers (and thus of a local increase of the electron density) reflects better the situation, but the effective potentials are somewhat higher than the corresponding real electrode potential for the same value of k1. This indicates that the real extension of the charge carrier packet might be slightly larger than the threefold penetration depth. Finally, it has to be pointed out, that by reducing the effect of the laser intensity on the electron density, only a phenomenological relationship between two quantities is gained. Consequently, this interpretation provides no information about the physical nature of this observation as it will be given in the next section.

intensity- the total numbers n10 of photoexcited electrons reaching the back contact were converted into a corresponding effective electrode potential according to the following procedure: First, the contribution of the photoexcited charge carriers to the electron density is calculated from the n10 by division of the spatial extension l of the electrons by considering also the porosity of the ZnO film. Doing this, two different approaches were chosen: The electrons might be assumed to be spread uniformly over the entire ZnO layer (i.e., for l = d = 1.7 µm) before they are detected at the back contact or they might propagate in a distinct packet of charge carriers. For the first case, the electron density of the whole ZnO film is raised, whereas for the second case, only a local increase of the electron density in the propagating packet of charge carriers has to be considered. Since no additional broadening of the electron packet is assumed, for this latter situation, the spatial extension of the packet corresponds to the depth of the volume initially illuminated by the laser pulse. As a rough estimate, for this value the threefold penetration depth of the incident light is taken (l = 270 nm). However, since a homogenisation of the initially created profile of charge carriers due to diffusive processes is likely to occur, the electrons are also assumed to be distributed uniformly over this distance. As a simplification, only the data obtained for positive potentials applied are taken into account, since under these conditions, the basic electron density of the non-illuminated ZnO is very low (1019 cm-3), this mechanism can also be ruled out to be the predominant effect by increasing the electrolyte concentration since the electron density is considerably lower even for negative potentials applied (cf. Fig. 2). Thus, it might be reasonable to interpret the acceleration of the charge transport for higher electrolyte concentrations also within the framework of the tunnelling model: The exchange of electrons between adjacent particles is dominated by the potential barrier at the boundary. The height of this barrier might be reduced by the field of positive countercharges in the electrolyte solution like Li+ ions. If the barrier consists of negatively charged impurities buried inside the solid state contact, this weakening of the barrier would be a pure electrostatic effect. If the origin of such a barrier is assumed to be a radial distribution of the energy of the electronic states inside the particle, the decrease of the height is explained as a counteracting effect of the field of the external charges in the electrolyte solution. The extent of this weakening would be dependent on the concentration of the positive countercharges at the surface of the particles. At positive potentials applied, the increase in k1 by increasing the concentration of the supporting electrolyte is much stronger than at negative potentials (cf. Fig. 11). To account for this observation, the different situations obtained for the different potentials has to be distinguished: As the particles are positively (or slightly negatively) charged, the surface concentration is dominated by the concentration of the cations in the electrolyte solution. (A potential accumulation or depletion of cations in the pore electrolyte is neglected since it qualitatively leads to the same conclusion). When a more negative potential is applied, the particles become negatively charged due to the injection of electrons via the back contact. Thus, the surface of these particles is assumed to be covered continuously by the positive countercharge in the electrolyte solution even before illumination by the laser. Due to the strong electrostatic interaction, the surface concentration of the cations is less sensitive to a change of the electrolyte

concentration. The same effect might contribute also to a better initial charge separation and thus to the increase in n10. Concluding it might to be mentioned that it is intriguing to see that by using our simple evaluation approach an interpretation of the experimental data can be given to a large extent even concerning a tunnelling of electrons between adjacent particles. Though several conclusions possibly might also be drawn from other approaches, the simplicity of the underlying model motivates strongly further application of this approach to the analysis of transient photocurrents arising in ZnO/ITO electrodes in order to obtain a deeper insight into the mechanisms of a charge transport in these porous electrodes.

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