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Dye-Sensitized Solar Cells

Electrochemical Impedance Spectroscopic Analysis of Dye-Sensitized Solar Cells

Qing Wang,Jacques-E.Moser,and Michael Gra1tzel*

Laboratory for Photonics and Interfaces,Institute of Chemical Sciences and Engineering,Ecole Polytechnique

Fe´de´rale de Lausanne,1015Lausanne,Switzerland

Recei V ed:May25,2005

Electrochemical impedance spectroscopy(EIS)has been performed to investigate electronic and ionic processes

in dye-sensitized solar cells(DSC).A theoretical model has been elaborated,to interpret the frequency response

of the device.The high-frequency feature is attributed to the charge transfer at the counter electrode while

the response in the intermediate-frequency region is associated with the electron transport in the mesoscopic

TiO2film and the back reaction at the TiO2/electrolyte interface.The low-frequency region reflects the diffusion

in the electrolyte.Using an appropriate equivalent circuit,the electron transport rate and electron lifetime in

the mesoscopic film have been derived,which agree with the values derived from transient photocurrent and

photovoltage measurements.The EIS measurements show that DSC performance variations under prolonged

thermal aging result mainly from the decrease in the lifetime of the conduction band electron in the TiO2

film.

1.Introduction

Dye-sensitized solar cells(DSC)present a promising alterna-

tive to conventional photovoltaic devices.1-4After more than

one decade’s development,it has reached global AM1.5power

conversion efficiencies up to11%.5At the heart of the DSC is

a mesoscopic semiconductor oxide film typically made of TiO2,

whose surface is covered with a monolayer of sensitizer(Figure

1).During the illumination of the cell,electrons are injected

from the photoexcited dye into the conduction band of the oxide.

From there they pass through the nanoparticles to the transparent

conducting oxide current collector into the external circuit.The

sensitizer is regenerated by electron transfer from a donor,

typically iodide ions,which are dissolved in the electrolyte that

is present in the pores.The triiodide ions formed during the

reaction diffuse to the counter electrode where they are reduced

back to iodide by the conduction band electrons that have passed through the external circuit performing electrical work.Although these basic processes are well understood,a deeper comprehen-sion of the electronic and ionic processes that govern the operation of the DSC is warranted.Transient photocurrent/ photovoltage measurements,6-12intensity-modulated photocur-rent/photovoltage spectroscopy(IMPS/IMVS),6,13-22and very recently the open circuit voltage decay technique23,24have been used to scrutinize the transport properties of the injected electrons in mesoscopic film and the back reaction with redox species in electrolyte.

Electrochemical impedance spectroscopy(EIS)is a steady-state method measuring the current response to the application of an ac voltage as a function of the frequency.25An important advantage of EIS over other techniques is the possibility of using tiny ac voltage amplitudes exerting a very small perturbation on the system.EIS has been widely employed to study the kinetics of electrochemical and photoelectrochemical processes including the elucidation of salient electronic a

nd ionic processes occurring in the DSC.15,18,26-34The Nyquist diagram features typically three semicircles that in the order of increasing frequency are attributed to the Nernst diffusion within the electrolyte,the electron transfer at the oxide/electrolyte interface, and the redox reaction at the platinum counter electrode.15 However,owing to the complexity of the system,the unambigu-ous assignment of equivalent circuits and the elucidation of processes occurring on dye-sensitized mesoscopic TiO2electrode is difficult and remains a topic of current debate.

The present study employs EIS as a diagnostic tool for analyzing in particular photovoltaic performance changes detected during accelerated high-temperature durability tests on dye-sensitized solar cells.A theoretical model is presented interpreting the frequency response in terms of the fundamental electronic and ionic processes occurring in the photovoltaic device.From applying appropriate equivalent circuits,the transport rate and lifetime of the electron in the mesoscopic film are derived and the values are checked by transient photocurrent and photovoltage measurements.

We note that during the final stage of preparation of the present particle a paper by Bisquert et al.35appeared presenting a similar approach to electrochemical impedance investigations of the DSC and that concurs with our analysis.

*To whom correspondence should be addressed.E-mail:

Figure1.Scheme of a dye-sensitized solar cell.

14945 J.Phys.Chem.B2005,109,14945-14953

Published on Web07/20/2005

2.Theoretical Modeling of the Frequency Response

The DSC contains three spatially separated interfaces formed by FTO/TiO2,TiO2/electrolyte,and electrolyte/Pt-FTO.Elec-tron transfer is coupled to electronic and ionic transport.In the dark under forward bias electrons are injected in the conduction band of the nanoparticles and their motion is coupled to that of I-/I3-ions in electrolyte.Illumination gives rise to new redox processes at the TiO2/dye/electrolyte interface comprising sensitized electron injection,recombination with the parent dye, and regeneration of the sensitizer.During photovoltaic operation, this“internal current generator”drives all the electronic and ionic processes in the solar cell.31We now derive the equations describing the frequency response of the impedance at the different interfaces.总和生育率

2.1.I3-Finite Diffusion within Electrolyte and Electron Transfer at the Pt-FTO/Electrolyte Interface.In practical electrolytes,the concentration of triiodide is much lower than that of iodide and the latter is diffuses faster than the former ion.Hence,I-contributes little to the overall diffusion imped-ance,which is determined by the motion of I3-.The diffusion of I3-within a thin layer cell is well described by a Nernst diffusion impedance Z N.15,28Using Fick’s law and appropriate boundary conditions Z N becomes

whereωis the angular frequency and R equals0.5for a finite length Warburg impedance(FLW).Z0andτd are the Warburg parameter and characteristic diffusion time constant,respec-tively,which can be expressed by

雷视网

where R is the molar gas constant,T the temperature,F the Faraday constant,c0the bulk concentration of I3-,A the electrode area,D the diffusion coefficient of I3-,and d is the diffusion length.Because of the mesoporous character of the TiO2electrode,a modified Nernst diffusion impedance with R deviating from0.5is used to fit the transport of I3-.Nernst diffusion impedance in the Nyquist plot shows typically a straight line at higher frequency along with a semicircle at lower frequency.Fitting Z0andτd,the diffusion coefficient can be determined.

The charge-transfer resistance R CT associated with the heterogeneous electron exchange involving the I3-T I-redox couple at the electrolyte/Pt-FTO interface is typically given for the equilibrium potential.From the Bulter-Volmer equation, one obtains

where i0is the exchange current density of the reaction.The frequency response of charge-transfer impedance under small sinusoidal perturbation can be expressed as36

where C d is the double layer capacitance.The charge-transfer resistance manifests itself as a semic

ircle in the Nyquist diagram and a peak in the Bode phase angle plot.For electrodes having a rough surface the semicircle is flattened and C d is replaced by a constant phase element(CPE).

2.2.Electron Transport within the Mesoscopic TiO2Film and Electron Loss due to the Reduction of Triiodide at the TiO2/Electrolyte Interface.When a voltage modulation is applied in the dark to the mesoporous TiO2electrode of the DSC,electrons are injected and recovered during the cathodic and anodic parts of the current response.Their collection yield of recollecting the injected electrons depends on their diffusion length

where D e is the diffusion coefficient andτr the lifetime of the electron within the film.

The impedance due to electron diffusion and loss by the interfacial redox reaction in a thin mesoporous layer has been treated by Bisquert.31-34For the case of a mesoscopic TiO2film, the diffusion occurs over a finite length and is coupled with interfacial electron-transfer reaction.The electron charge is screened by the electrolyte,which eliminates the internal field, so no drift term appears in the transport equation.4The continuity equation contains therefore only the diffusion and reaction terms. the boundary condition being

where n is the concentration of electron,n0is their initial concentration,and L is the film thickness.To a

ccount for a harmonically modulated voltage,a frequency term is introduced yielding finally for the impedance response:

where R d and R r are the diffusion and dark reaction impedance, respectively,whileωd′(ωd′)1/τd′)D e/L2)andωr(ωr)1/τr) are the corresponding characteristic frequencies.If R r f∞,eq 9describes a simple diffusion process within restricted bound-

aries.For a DSC exhibiting a current collection efficiency close to unity,the condition R r.R d applies and eq9becomes

Under these conditions,the Nyquist plot shows a short straight line at higher frequencies due to diffusion and a large semicircle in the lower frequency regime,indicating fast electron transport and long lifetime of electron in the film.By contrast,if the electron collection efficiency is ,a major part of the electron reacts with I3-in the electrolyte before they are recovered at the current collector,the condition R d.R r applies leading to Gerischer impedance34,37

Z N )

(iω)R

tanh(iτ

ω)R(1)

)

n2F2c

A D

(2)

)d2/D(3)

)

i0南无拳

(4)

花木兰袁咏仪下载

i-R

(5)

) D eτr(6)

∂n

∂t

∂2n

∂x2

(n-n

)

(7)

∂n

∂x|x)L)0(8)

Z)(R d R r1+iω/ωr)1/2coth[(ωr/ωd′)1/2(1+iω/ωr)1/2](9)

1+iω/ω

)(10)

Z)(R d R r1+iω/ωr)1/2(R d.R r)(11)

14946J.Phys.Chem.B,Vol.109,No.31,2005Wang et al.

The Gerischer impedance produces response curves similar to a FLW impedance (eq 1).It shows a

Warburg diffusion-like straight line at higher frequencies along with a semicircle at lower frequencies.The diffusion coefficient D e and the lifetime τr of the electron in the film can be obtained from eqs 10and 11.

The above discussion was based on DSC in the dark and under forward bias.Under illumination the continuity equation becomes

where R ′is the effective absorption coefficient,ηinj is the

quantum yield for charge injection,and I is the incident photon flux,the boundary condition being again given by eq 8.

As indicated in Figure 2,under illumination the short circuit photocurrent J SC of the cell is

where J inj is the flux of injected electron and J loss is the current from back reaction loss.Since ηcc )1for distances x <L n ,and ηcc )0if x >L n ,

where J inj,x <Ln is the anodic flux of electron that are injected by the sensitizer and collected at the FTO,while J FTO -TiO 2is the cathodic current flowing from the FTO into the TiO 2film.Thus,

where J inj,x >Ln is the flux of injected electron,which is lost completely before arriving at FTO/TiO 2interface.It is clear that J inj,x <Ln <J FTO -TiO 2as E >V OC (Figure 2a);and J inj,x <Ln >J FTO -TiO 2as E <V OC (Figure 2c).

At open circuit state (Figure 2b),J inj ,x <Ln equals to J FTO -TiO 2,and the total flux is zero.Phenomenologically we can treat the perturbation imposed by the illumination as if a voltage bias was applied in the dark.This applies in particular for a situation where the diffusion length of the electrons is commensurate with or larger than the film thickness.Hence,the same approach as above can be used to analyze its frequency response.Nevertheless,the model may overstate the diffusion rate D e because photons travel through the film faster than conduction band electrons.But the correction is small if the electron

diffusion length is long compared to the film thickness L .31Indeed,as will be shown below,in a DSC L n normally exceeds L rendering this distinction irrelevant.

2.3.Equivalent Circuits and Typical Impedance Spectra of DSC.For a nanoporous electrode,the infinite transmission line is normally used as the equivalent circuit for modeling.For simplicity,only the representative elements displayed in Figure 3are employed here to model DSC at different states.Fr

om left to right,Figure 3shows the electron transport at the FTO/TiO 2interface,electron transport and electron capture by the I 3-at the TiO 2/electrolyte interface,diffusion of I 3-in the electrolyte,and charge transfer at electrolyte/Pt -FTO interface,respectively.For a cell exhibiting a carrier collection efficiency near unity,the condition R r .R d and eq 10applies.In this case,the equivalent circuit for the mesoporous TiO 2film comprises a diffusion element Z W1that is in series connected with the charge-transfer element R REC ,the two being in parallel with a capacitive (constant phase angle)element CPE3,as shown in Figure 3a.On the other hand,for cells where only a fraction of the photogenerated charge carriers are collected,the condition of R d .R r applies and a single Gerischer impedance element Z G describes the diffusion of the electron in the mesoscopic TiO 2film and their recapture by the triiodide ions in the electrolyte (Figure 3b).R FTO/TiO 2is the resistance of the FTO/TiO 2contact and CPE1is the capacitance of this interface.The latter feature,due to overlap with other processes,is not easily distinguished.Z W2is the Warburg impedance describing the diffusion of I 3-in the electrolyte,R CE is the

charge-transfer

Figure 2.Schematic model of photoanode at different voltages.(a)E >V OC ;(b)E )V OC ;(c)E <V OC .L is the film thickness,L n is the electron effective diffusion length,and ηcc is the charge collection efficiency of injected electron.

∂n ∂t

)R ′I ηinj +D e ∂2n ∂x

2-(n -n 0)τr (12)

J SC )J inj -J loss

(13)

J SC )J inj,x <L n -J FTO -TiO 2

(14)

J loss )J inj,x >L n +J FTO -TiO 2

(15)

Figure 3.Equivalent circuits of DSC.(a)a cell showing quantitative collection of photoinjected electrons;(b)a cell showing incomplete collection of electrons.Bottom line shows the interpretation of the electrical elements of the equivalent circuit.(A)electron transfer at the FTO/TiO 2interface;(B)electron transport and back reaction at the mesoscopic TiO 2/electrolyte interface;(C)diffusion of I 3-in the electrolyte;(D)charge at electrolyte/Pt -FTO interface.

Dye-Sensitized Solar Cell J.Phys.Chem.B,Vol.109,No.31,200514947

impedance at the counter electrode,and CPE2is the double layer capacitance at the electrolyte/Pt -FTO interface.

A typical EIS spectrum for a DSC exhibits three semicircles in the Nyquist plot or three characteristic

frequency peaks in a Bode phase plot.This is illustrated in Figure 4showing Nyquist plots of a N719sensitized DSC before and after thermal aging at 80°C for 2days.The response in the intermediate-frequency regime changes greatly upon aging,indicating the conversion of a Nernst to a Gerischer impedance.Apparently,the spectra can be well fitted in terms of the corresponding equivalent circuits in Figure 3.These models will therefore be employed to interpret impedance data in the following sections.3.Experimental Section

3.1.Dye-Sensitized Mesoscopic TiO 2Electrode Prepara-tion and Cell Fabrication.The preparation of mesoscopic TiO 2film has been described in ref 38.The screen-printed double-layer film consists of a 10-µm transparent layer and a 4-µm scattering layer whose thickness was determined by using an Alpha-step 200surface profilometer (Tencor Instruments).A porosity of 0.63for the transparent layer was measured with a Gemini 2327nitrogen adsorption apparatus (Micromeretics Instrument Corp.).The film was heated to 500°C in air and calcinated for 20min before use.Then the still hot spots were dipped into a 2×10-4M 2-fold deprotonated cis-RuL2(SCN)2(L )2,2′-bipyridyl-4,4′-dicarboxylic acid)(N719)or cis-RuLL ′-(SCN)2(L )2,2′-bipyridyl-4,4′-dicarboxylic acid,L ′)4,4′-dinonyl-2,2′-bipyridyl)(Z907)dye (Chart 1)solution in aceto-nitrile/tert -butyl alcohol (1:1)and left for overnight.Finally,the dye-coated electrodes were rinsed with acetonitrile.For transient photocurrent/p

hotovoltage measurements,single trans-parent TiO 2films with the thickness of 12µm were used.A sandwich cell was prepared using the dye-sensitized electrode as the working electrode and a platinum-coated conducting glass electrode as the counter electrode.The latter was prepared by chemical deposition of platinum from 0.05M hexachloroplatinic acid at 400°C.The two electrodes were placed on top of each other using a thin transparent film of Bynel polymer (DuPont)as a spacer.The empty cell was tightly held,and the edges were heated to 130°C in order to seal the two electrodes together.A thin layer of electrolyte was introduced into the interelectrode space from the counter electrode side through a predrilled hole.The hole was sealed with a microscope cover slide and Bynel to avoid leakage of the electrolyte solution.There were two electrolytes used in this paper:electrolyte 1,0.6M PMII,0.1M I 2,and 0.5M NMB in MPN;electrolyte 2,0.6M DMPII,0.05M I 2,0.5M tBuPy,0.1M LiI in AN:VN(1:1).Thermal stress tests were carried out by putting cells in an oven at 80°C and then measuring the I -V curve,impedance and transient photocurrent/photovoltage.3.2.I -V Measurements.A 450-W xenon light source (Osram XBO 450)was used as the irradiation source for the I -V measurements.The spectral output of the lamp matched the AM 1.5solar spectrum in the region of 350-750nm (mismatch <2%).Incident light intensities were adjusted with neutral wire mesh attenuators.The current -voltage character-istics were determined by applying an external potential bias to the cell and measuring the photocurrent us

ing a Keithley model 2400digital source meter (Keithley).The overall conversion efficiency ηof the photovoltaic cell is calculated from the integral photocurrent density (J SC ),the open-circuit photovoltage (V OC ),the fill factor of the cell (ff),and the intensity of the incident light (I Ph ),

3.3.Electrochemical Impedance Measurements.Impedance measurements were performed with a

computer-controlled

王治坪

Figure 4.Typical Nyquist plots of a N719sensitized DSC.Filled squares,fresh cell;open circles,cell after aging for 48h at 80°C.The lines show theoretical fits using the equivalent circuits shown in Figure 3a and b,respectively.The electrolyte is 0.6M PMII,0.1M I 2,and 0.5M NMB in MPN.

CHART 1:Sensitizers Used in This Study

Key:(a)N719;(b)Z907.

η)J SC ‚V OC ‚ff/I Ph

(16)

14948J.Phys.Chem.B,Vol.109,No.31,2005Wang et al.

potentiostat(EG&G,M273)equipped with a frequency response analyzer(EG&G,M1025).The frequency range is0.005-100 kHz.The magnitude of the alternative signal is10mV.Unless otherwise mentioned,all impedance measurements were carried out under a bias illumination of100mW/cm2(global AM1.5, 1sun)from a450-W xenon light source.The obtained spectra were fitted with Z-View software(v2.1b,Scribner Associate, Inc.)in terms of appropriate equivalent circuits.

3.4.Transient Photocurrent/Photovoltage Measurements. Transient photocurrent and photovoltage studies of the DSC were carried out by using weak laser pulses atλ)514nm, superimposed on a relati

vely intense bias illumination.The bias light was supplied by a cw450-W Xe arc lamp,equipped with a water filter and a680-nm cutoff filter.The continuous wave beam was condensed by a lens to irradiate a∼1cm2cross section of the cell,the surface of which was kept at a60°angle to the beam.The red light intensity measured at the cell position was typically120mW/cm2.The cell was oriented to expose the counter electrode side to both the bias light and laser beams. The5-ns-duration laser pulses at a wavelength of514nm were generated by a broadband optical parametric oscillator(GWU,

OPO-355)pumped by the third harmonic of a30-Hz repetition rate,Q-switched Nd:YAG laser(Continuum,Powerlite7030). The laser beam was attenuated by gray filters to restrict the pulse fluence onto the cell to<100µJ/cm2.The514-nm laser light was strongly absorbed by the dye,and therefore,injected electrons were introduced into a narrow spatial region,corre-sponding to where the probe light enters the film.Current transients were measured across a20Ωresistor load using a large bandwidth digital signal analyzer(Tektronix DSA602A). Transient photovoltages were measured by feeding the signal directly into the DSA amplifier,whose impedance was1MΩ.

4.Results and Discussion

4.1.Impedances of DSC Obtained in Dark and Illumina-tion.There are different processes that occur in the cell in the dark or under illumination.At open circuit voltage and in sunlight,there is no net current flowing through the cell.All the injected electrons are recaptured by I3-before being extracted to the external circuit.Meanwhile,the oxidized dye is regenerated by I-.As a result,the absorbed photon energy is converted to heat through the two coupled redox cycles involving sensitized electron injection,dye regeneration,and electron recapture by I3-.The counter electrode is kept at equilibrium,because there is no net current flowing through it. However,in the dark under forward bias,electrons are transported through the mesoscopic TiO2network and react with I3-.At the same time,I-is oxidized to I3-at the counter electrode.The net current density can be large depending on the applied bias voltage.

Figure5shows the impedance spectra of a DSC measured at OCV(-0.68V)under1sun and under forward bias(-0.68 V)in the dark.Strikingly,the impedance due to electron transfer from the conduction band of the mesoscopic film to triiodide ions in the electrolyte,presented by the semicircle in intermedi-ate-frequency regime,is much smaller under light than in the dark even though the potential of the film is the same. Correspondingly,the characteristic frequency shown in Bode phase plots increases two times,suggesting the electron lifetime is shortened by a factor of2.This can be as

cribed to a difference in the local I3-concentration.Under illumination,I3-is formed “in situ”by dye regeneration at the mesoporous TiO2/electrolyte interface,whereas in the dark,I3-is generated at counter electrode and penetrates the mesoporous TiO2films by diffusion.

As indicated by eq17,the higher local I3-concentration

produced in the porous network under light is expected to

accelerate the recapture of conduction band electrons and

shortens their lifetime within the TiO2film.

Here J r is the I3-reduction current,k r is the rate constant of the

reduction reaction,and c ox is the concentration of I3-;the

exponentsγand are the reaction orders for I3-and electrons,

respectively.

4.2.Impedance of DSC with Different Electrolytes.

Electrolytes exert a great influence on the photovoltaic perfor-

mance of the DSC by effecting the kinetics of electronic or ionic

processes.For instance,acetonitrile(AN)-based electrolytes have

much lower viscosity compared with3-methoxypropionitrile

(MPN),the kinetics of dye regeneration,I3-f I-reaction at counter electrode,electron transport within the TiO2film,and

I-/I3-diffusion in electrolyte being faster in the former case.

Consequently,much better photovoltaic performance has been

achieved.In addition,additives in the electrolyte are of great

importance for optimization and stabilization of the TiO2/dye/

electrolyte interface.TBP,39NMB,40and recently guanidinium

salts5have been shown to be effective in increasing the

photovoltage without greatly reducing the photocurrent.

Figure6shows the impedance spectra of a Z907sensitized

cell with two kinds of electrolytes at different light intensity.

From the Bode phase plots,the electron lifetime with electrolyte

2is much longer than that obtained with electrolyte1at the

same light intensity.According to Frank et al.,it is believed

教育手拉手论坛that Li+in electrolyte2plays an important role for the long

lifetime of the electron.11The characteristic time constants of

electron transport and back reaction are obtained by fitting the

spectra with the equivalent circuit shown in Figure3a.The

electron diffusion rate D e of the cell with electrolyte2is2×

10-4cm2/s at1sun,3times higher than that obtained from

IMPS by Peter et al.in an AN-based electrolytes.16,22That of

electrolyte1is1.1×10-4cm2/s,close to the value obtained

from photocurrent transient measurements.12From eq18,the

effective diffusion length L n of the conduction band electrons

is calculated to be∼16.2µm for MPN-based electrolyte1at1

sun and at open circuit voltage.That of electrolyte2is∼

30.1 Figure5.Impedance spectra of a Z907cell measured at OCV(-0.68 V),1sun or at-0.68V in dark.(a)Bode phase plots;(b)Nyquist plots.Electrolyte1is used.

)ek

γ(n -n

)(17)

Dye-Sensitized Solar Cell J.Phys.Chem.B,Vol.109,No.31,200514949

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