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Electrochimica Acta 55 (2010) 2338–2343

Contents lists available at ScienceDirect

Electrochimica Acta

journa l homepage: www.e lsev ier .com/ locate /e lec tac ta

he effect of the series resistance in dye-sensitized solar cells explored bylectron transport and back reaction using electrical and optical modulationechniques

eiqing Liua, Linhua Hua, Songyuan Daia,∗, Lei Guoa, Nianquan Jiangb, Dongxing Koub

Key Laboratory of Novel Thin Film Solar Cells, Institute of Plasma Physics, Chinese Academy of Sciences, P.O. Box 1126, 350 Shushanhu Road, Hefei, Anhui 230031, PR ChinaCollege of Physics & Electronic Information Engineering, Wenzhou University, Wenzhou, Zhejiang 325035, PR China

r t i c l e i n f o

rticle history:eceived 2 September 2009eceived in revised form8 November 2009ccepted 20 November 2009vailable online 26 November 2009

a b s t r a c t

The influence of the series resistance on the electron transport and recombination processes in dye-sensitized solar cells (DSC) has been investigated. The series resistances induced by some parts of DSC,such as the transparent conductive oxide (TCO), the electrolyte layer and the counter electrode, influencethe performance of DSC. By combining three frequency-domain techniques, specifically electrochemi-cal impedance spectroscopy (EIS), intensity modulated photocurrent spectroscopy (IMPS) and intensity

eywords:eries resistanceransportecombinationye-sensitized

modulated photovoltage spectroscopy (IMVS), we studied the relationship between the series resistanceand the dynamic response of DSC. The results show that the series resistance induced by the TCO orcounter electrode predominantly affects the electron transport under short circuit conditions and has nosignificant influence on the recombination under open circuit conditions. However, the resistance relatedto the electrolyte layer not only limits the carrier transport but also influences the recombination. Possiblereasons for the influence of the series resistance on the electron transport and recombination processes

.

olar cells in DSC are also discussed

. Introduction

Dye-sensitized solar cells (DSC) are regarded as a potentialow-cost alternative to conventional solar cells and have attractedonsiderable interest during the past decades [1–6]. A typicalSC is normally made into sandwich-type photoelectrochemicalells, the electrolyte being filled between the photoelectrode andounter electrode. Dyed-TiO2 film, as one of the components ofhe photoelectrode, is nearly insulating and becomes electricallyonducting under illumination or by applying a bias voltage. Thelectron transport and recombination process in the DSC underllumination or under forward bias are distinct. Under light irra-iation, electrons generated by photo-excited dye molecules are

njected into the conduction band of the TiO2 and transported fromhe injection sites to the contact electrode. Finally, electrons areollected and pass through the external circuit. Meanwhile, thexidized dye molecules are regenerated by the redox couple (usu-

lly iodide/tri-iodide) in the electrolyte. However, the direction oflectron flux is reversed under forward bias in the dark. Electronsre injected by the applied potential at the TCO/TiO2 contact andransported from the TCO/TiO2 contact to the TiO2/dye/electrolyte

∗ Corresponding author. Tel.: +86 551 5591377; fax: +86 551 5591377.E-mail address: sydai@ipp.ac.cn (S. Dai).

013-4686/$ – see front matter © 2009 Elsevier Ltd. All rights reserved.oi:10.1016/j.electacta.2009.11.065

© 2009 Elsevier Ltd. All rights reserved.

interface. Simultaneously, electrons are transferred to tri-iodideat the TiO2/dye/electrolyte interface and iodide is oxidized to tri-iodide at the counter electrode.

Under these conditions, electron transport and recombination inDSC can be investigated with frequency-domain techniques, suchas intensity modulated photocurrent spectroscopy (IMPS) [2,7],intensity modulated photovoltage spectroscopy (IMVS) [3,8] andelectrochemical impedance spectroscopy (EIS) [9–12]. IMPS/IMVSmeasures the current/voltage response to a modulated light inten-sity superimposed on a steady light intensity, whereas EIS measuresthe current response to a modulated applied bias superimposedon a constant applied voltage. An analysis of IMPS/IMVS has beenpresented with models based on differential equations, whereasEIS can be evaluated using resistance and capacitance elements asan equivalent circuit [2,3,7,8,11,12]. EIS is a powerful techniqueto identify and study the transport and recombination in DSC. Inprinciple, the EIS spectrum of standard DSC includes the diffusionimpedance of the electron transport in TiO2 film [13,14]. However,the Warburg feature associated with electron transport may over-lap with other processes in the spectrum of EIS so as to show the

significantly small electron transport resistance in TiO2. Thus theelectron transport process in TiO2 becomes immeasurable [15]. TheIMPS technique is suitable to investigate the electron transport pro-cess in TiO2 films and obtain the transit time directly over a rangeof light intensities [7,16]. The process of transfer across both the

ica Acta 55 (2010) 2338–2343 2339

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Fig. 1. Equivalent circuit used for the impedance spectra of DSC. Iph is a constantcurrent source, Rh is the transport resistance of the TCO, C1 is the capacitance ofelectrolyte/Pt-TCO interface, R1 is the electron transfer resistance associated with

hcovered with silver grid lines, Rh significantly changes from 48.6 �to 3.4 �. For TCO without silver grid lines, a significant part of theforward bias voltage (Vbias) loss occurs on the TCO, so the Vbias doesnot drop on the Z completely and the potential V that drops on

Table 1Parameters determined by fitting the impedance spectra using the equivalent circuitof Fig. 1 for DSC with or without silver grid lines.

W. Liu et al. / Electrochim

iO2/dye/electrolyte interface and the electrolyte/Pt-TCO interfacean be investigated by EIS at any bias under illumination or in theark. The IMVS mainly deals with the process of electron trans-er across the TiO2/dye/electrolyte interface at open circuit underllumination. But, the IMVS yields information on the characteristicime for electron recombination and is not affected by the factorsssociated with the conducting glass or counter electrode [17].

In fact, parts of DSC, such as the TCO, the electrolyte layer,nd the counter electrode, give rise to some additional ohmic loss12,18]. The series resistance is an important factor that influenceshe performance of DSC. Several groups applied EIS and I–V mea-urements to discuss the influence of series resistance upon thehotovoltaic performance of DSC from the macroscopic perspective9–12,18]. However, the influence of series resistance on the trans-ort and recombination processes in DSC has not been fully studied.

n this paper, a detailed analysis and discussion are made about thenfluence of series resistance on the transport and recombinationrocesses in DSC with EIS, IMPS and IMVS. This study aims to fur-her investigate the relationship between the series resistance andhe dynamic response of DSC. It is important to understand theseelationships for improving the performance of DSC. The values oferies resistance can be changed by varying the electrical proper-ies of TCO, the thickness of the electrolyte layer and the catalyticctivity of the counter electrode. Therefore, by taking these com-ositions into account, the influence of the series resistance on theransport and recombination processes of DSC are discussed.

. Experimental

The TiO2 paste was prepared from a colloidal dispersionbtained by the hydrolysis of titanium tetraisopropoxide asescribed elsewhere [1,19]. TiO2 films of a thickness of about 14 �mere obtained by screen printing on the TCO (TEC-15, LOF) sub-

trate, then sintering at 450 ◦C for 30 min in air.The photoelectrodes were immersed in an ethanol solu-

ion (0.5 mM) of N719[cis-dithiocyanate-N,N′-bis-(4-carboxylate-′-tetrabutylamonium-carboxylate-2,2′-ipyridine) ruthenium(II)]ye at room temperature for 12 h. The platinized counter elec-rodes were obtained by spraying H2PtCl6 solution to TCO glassollowed by heating at 410 ◦C for 20 min. Then the counter elec-rode was placed directly on the top of the dyed-TiO2 film sealedith thermal adhesive films (Surlyn, Dupont). The electrolyte waslled from a hole made on the counter electrode, which was laterealed by a cover glass and thermal adhesive films. The silverrid lines were printed on conductive glass substrate by screenrinting followed by heating at 450 ◦C for 30 min. The active areaf DSC for investigating the influences on the electrical proper-ies of TCO was 1.5 cm × 1.5 cm = 2.25 cm2 and the others were.5 cm × 0.5 cm = 0.25 cm2.

IMPS/IMVS measurements were carried out on IM6ex (Ger-any, Zahner Company) using light emitting diodes (� = 455 nm)

riven by Expot (Germany, Zahner Company). The LED providedoth dc and ac components of the illumination. A small ac compo-ent was 10% or less than that of the dc component. The frequencyange is 3 kHz to 0.1 Hz.

EIS measurements were performed with the same instrumentsed for IMPS/IMVS measurements. The frequency range wasxplored from 3 MHz to 10 mHz and the ac amplitude was 10 mV.mpedance measurements were carried out under illuminationrom LED.

. Results and discussion

The electrical properties of DSC have been analyzed with anquivalent circuit, as shown in Fig. 1. In this equivalent circuit, a

the flow of electrons across the electrolyte/Pt-TCO interface, Z is the impedance forelectron transfer across the TiO2/dye/electrolyte interface, R2 is the electron transferresistance, C2 is the capacitance of TiO2, Zn is the diffusion impedance of redoxspecies in the electrolyte, and R3 is the dc resistance of the diffusion impedance.

constant current source (Iph) in which electrons are generated bydye molecules is in parallel with an impedance (Z) associated withelectron transfer at the TiO2/dye/electrolyte interface. (The mostsimple representation of Z is a reaction resistance (R2) and a capac-ity (C2) in parallel.) The series resistance (Rs) can be described as[11,12]

Rs = Rh + R1 + R3 (1)

where Rh is the resistance for electron transport in the TCOsubstrate, R1 is the resistance for electron transfer across the inter-face of electrolyte/Pt-TCO, and R3 relates to the Nernst diffusionimpedance Zn within the electrolyte.

3.1. Impact of Rh at the TCO interface

Under short circuit conditions, the injected electrons flowthrough the TCO layer to the counter electrode via the exter-nal circuit. The resistance of TCO mainly contributes to Rh, whichincreases in proportion to the sheet resistance of TCO [11,12]. TheRh should be reduced in order to improve the efficiency of DSC.Although Rh can be decreased with low sheet resistance TCO, thetransmittance of TCO will be reduced at the same time [12]. It isunsuitable to investigate the influence of Rh on the performance ofDSC by changing the sheet resistance of TCO, due to the effect of var-ied transmittance. Here we print silver grid lines on TCO to decreasethe transport resistance through TCO and investigate the influenceof this resistance on the transport and recombination processes ofDSC.

Fig. 2(a) shows electrochemical impedance spectra in a Nyquistpresentation of a DSC at −0.7 V in the dark. The fitted values for TCOwith and without silver grid lines are summarized in Table 1. R3 israther small because the thickness of the electrolyte layer for thismeasurement is extremely thin. Rh and R2 are distinctly differentin the spectrum for TCO with and without silver grid lines. Whenthe TCO is not covered by silver grid lines, the transport resistanceof TCO is very high, which leads to a large R (48.6 �). But, if TCO is

Bias Silver grid lines Rh/� R1/� R2/� R3/�

OCV With 3.4 3.1 9.0 1.7OCV Without 48.0 3.3 10.0 1.9−0.7 V With 3.4 2.7 5.8 1.6−0.7 V Without 48.6 2.9 21.4 3.4

2340 W. Liu et al. / Electrochimica Acta 55 (2010) 2338–2343

Fsu

tspliic

DaTciTtwtod

aIat

�

aofflrsowdsltert

c

�n =2�f IMVS

min

(3)

Fig. 4 shows the intensity dependence of lifetime �n for TCOwith and without the silver grid lines. The �n for TCO without

ig. 2. Impedance spectra for DSC with or without silver grid lines. (a) Impedancepectra measured at −0.7 V in the dark and (b) impedance spectra measured at OCVnder illumination (� = 455 nm; light intensity: 10 mW cm−2).

he Z is V = Vbias − IRs (I is current). It is expected that Rs becomesmaller when the TCO covered with grid lines and Vbias almost com-letely drop on the Z. When V becomes more negative, the Fermi

evel rises and the reaction resistance at the TiO2/dye/electrolytenterface becomes smaller due to the increasing electron densityn TiO2 [20]. In this case, R2 with silver grid lines is smaller (5.8 �)ompared with TCO without silver grid lines (21.4 �).

Fig. 2(b) shows impedance spectra in a Nyquist presentation ofSC at OCV under illumination. Compared with EIS measurementst −0.7 V in the dark, R2 is almost the same in the spectrum forCO with and without silver grid lines. Under OCV and illuminationonditions, all of the photogenerated electrons are captured by tri-odide and the absorbed photo energy is converted into heat [21].here is no net current flowing through the DSC, so V is equal tohe open circuit voltage and R2 is almost the same despite of TCOith or without silver grid lines. The changes of Rh are the same as

hat of the impedance spectra at −0.7 V in the dark. The influencef TCO with or without silver grid lines on Rh have been previouslyiscussed.

The most useful tools to obtain characterization informationbout electron transport and recombination processes in DSC areMPS and IMVS [2,7]. The electron transit time (delay times), �d, isssociated with the electron transport from the injection sites tohe substrate and can be obtained from IMPS by [7]

d = 1

2�f IMPSmin

(2)

Fig. 3 shows the light intensity dependence of �d of the TCO withnd without silver grid lines. The double logarithmic representationf data allows the intensity dependence of �d to be expressed in theorm of the power law �d ∝ I0ˇ (ˇ is slope). In the incident photonux range of 1.0 × 1015 cm−2 s−1 to 2.3 × 1016 cm−2 s−1, the IMPSesults show that the power exponents ˇ for TCO with and withoutliver grid lines are −0.52 and −0.38, respectively. The lower valuef the slope indicates a weaker dependence on the light intensity,hich may be caused by the involvement of processes that are notependent on light intensity in a first approximation [16]. In thistudy, the higher transport resistance of the TCO is a reason for aower slope value. The �d for TCO without silver grid lines is longerhan that for TCO with silver grid lines, which indicates that the

lectron needs much more time during the transport process. Theesults of IMPS show that the high resistance of TCO may hinderhe electron extraction from the TiO2 film to the external circuit.

Under short circuit conditions, the series resistance and theapacitance of the TCO/TiO2 and TCO/electrolyte interfaces intro-

Fig. 3. Electron transit times measured at different light intensities for TCO with orwithout silver grid lines.

duce an additional time constant, the RC time [2,22,23]. Theexperimentally measured IMPS response is affected by RC atten-uation. The transit time of the photogenerated electron throughthe TiO2 film can be obtained from the IMPS by Eq. (2) whenthe RC time is shorter than this transit time [24]. Taking a typicalvalue for the series resistance (10–20 �/cm2) and the capacitanceof the TCO/TiO2 and TCO/electrolyte interfaces (15–30 �F cm−2)[2,22,23,25,26], the RC time range is estimated at (1.5–6) × 10−4 s.

When the TCO is without silver grid lines, the Rs is very high,and the RC time is longer than that for the TCO with silver grid lines.Furthermore, it has been found that �d decreases with increasingincident light intensity [7]. The collective effect of both the silvergrid lines and incident light intensity may result in a RC time longerthan �d. In this case, the �d no longer reflects the time of the pho-togenerated electron through the TiO2 film. As shown in Fig. 3, the�d of TCO without silver grid lines is evidently limited by RC timeabove 2.3 × 1016 cm−2 s−1.

The electron lifetime �n is determined by back reaction and canbe calculated directly from IMVS response by [7]

1

Fig. 4. Electron lifetimes measured at different light intensities for TCO with orwithout silver grid lines.

W. Liu et al. / Electrochimica Acta 55 (2010) 2338–2343 2341

Fue

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3

bscRtor

c(ssceeePiPa

tR�ehnra

el elDel is the diffusion coefficient of tri-iodide, ı is the diffusion length,kB is the Boltzmann’s constant, T is the temperature, N is Avogadro’sconstant, c0 is the bulk concentration of tri-iodide, and n is thenumber of electrons transferred.

ig. 5. Impedance spectra for the counter electrode with or without Pt at OCVnder illumination (� = 455 nm; light intensity: 10 mW cm−2). Insert represents annlargement of the area marked with the circle.

ilver grid lines shows almost no deviations from that with sil-er grid lines over the experimental light intensity range. Thentensity dependence of �n can be expressed in the form of theower law with almost the same power exponent for two cases.ecause �n is obtained by IMVS measurements at open circuit andhe IMVS mainly studies the process of electron transfer at theiO2/dye/electrolyte interface, the factors (e.g., sheet resistance)ssociated with the conducting glass and counter electrode do notontribute to the IMVS response [17]. The results of IMVS measure-ents are consistent with EIS at OCV under illumination.

.2. Impact of R1 at the electrolyte/Pt-TCO interface

It is well known that the iodide/tri-iodide redox system cane catalyzed by dissociative adsorption of iodine on some metalsuch as platinum [27]. The platinized TCO is generally used as theounter electrode, where the reduction of tri-iodide takes place.1 is the resistance associated with the electron transfer acrosshe electrolyte/Pt-TCO interface. Counter electrodes with and with-ut Pt were prepared and used to investigate the influence of thisesistance on the transport and recombination processes of DSC.

Fig. 5 shows a distinct difference in impedance spectra for theounter electrode with and without Pt at OCV under illumination� = 455 nm; light intensity: 10 mW cm−2). A typical impedancepectrum of the DSC (the counter electrode with Pt) exhibits threeemicircles in the Nyquist plot. In contrast, there is a large semi-ircle in the impedance spectrum of the DSC when the counterlectrode without Pt is used. This semicircle associated with thelectrolyte/Pt-TCO interface overlaps with other processes, so thextra large semicircle is mainly attributed to R1. In the absence oft, electron transfer at the bare TCO electrode is much slower, so R1ncreases markedly. The R1 of the DSC (the counter electrode witht) is 20.6 �, but R1 of the DSC (the counter electrode without Pt)pproaches 1806.0 �.

Figs. 6 and 7 show the intensity dependence of �d and �n forhe counter electrode with and without Pt. The influence of various1 on electron transport and recombination are similar to Rh. Thed (the counter electrode without Pt) is larger than �d (the counter

16 −2 −1

lectrode with Pt) below 2.3 × 10 cm s , indicating that R1 alsoinders the electron extraction from the TiO2 film to the exter-al circuit. Due to the fact that R1 does not contribute to the IMVSesponse, the �n for the counter electrode with and without Pt arelmost the same.

Fig. 6. Electron transit times measured at different light intensities for the counterelectrode with or without Pt.

3.3. Impact of R3 between the TCO/TiO2 and electrolyte/Pt-TCOinterfaces

The standard electrolyte consists of the iodide/tri-iodide redoxcouple dissolved in organic solvent. The steady state concentra-tions of the redox couple in the electrolyte under illumination orunder forward bias are distinct and are space dependent [21,28].The distance between the photoelectrode and the counter electrodeaffect the performances of DSC. To investigate the influence of thediffusion of the redox couple on the transport and recombinationprocesses of DSC, the thicknesses of the bulk electrolyte layer arevaried.

At the low-frequency region (1 Hz to 20 mHz), the Nyquist plot ofDSC generally shows a small semicircular arc that can be attributedto the diffusion of tri-iodide in the electrolyte [11]. The Nernstimpedance Zn is more suitable to describe this diffusion process[14,18],

Zn = R3

(i�elω)0.5tanh (i�elω)0.5 (4)

where R3 = kBT/(n2q2c0NDelı) is the dc resistance of the diffusionimpedance, � = ı2/D is the characteristic diffusion time constant,

Fig. 7. Electron lifetimes measured at different light intensities for the counterelectrode with or without Pt.

2342 W. Liu et al. / Electrochimica Acta 55 (2010) 2338–2343

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tftsrrtittiwt

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iitA

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Fig. 9. Photocurrent measured at different light intensities for DSC with variationsof distance between two electrodes.

phenomenon is that the concentration of tri-iodide decreases withincreasing distance. Further research must be conducted to verifythis.

ig. 8. Impedance spectra for DSC with variations of distance between two elec-rodes over a range (60–370 �m) at OCV under illumination (� = 455 nm; lightntensity: 10 mW cm−2).

Fig. 8 shows the impedance spectra with variations of distanceetween two electrodes over a range (60–370 �m). The semi-ircles in these impedance spectra at the low-frequency regionre remarkably different and become larger with an increase inistance from 60 �m to 370 �m. The fitted values for DSC atifferent distances are summarized in Table 2. The R3 increasesrom 22.4 � to 49.8 � as the electrolyte layers of the cellsecome thicker. The diffusion length ı increases with increasingistance between the two electrodes (here ı = 0.5d; d, distanceetween the two electrodes), so that tri-iodide requires a longime to reach the counter electrode. To decrease the diffusionmpedance, it is necessary to shorten the thickness of the electrolyteayer.

The transport processes of iodide and tri-iodide in the elec-rolyte under short circuit conditions are distinct. Iodide diffusesrom the counter electrode to the TiO2 network and then reduceshe oxidized dye molecules. In contrast, the oxidized tri-iodidepecies is transported through the electrolyte layer and finallyeaches the counter electrode. Due to the large excess of iodideelative to tri-iodide in the electrolyte, iodide does not contributeo the diffusion impedance and only the diffusion of tri-iodide lim-ts the current [18]. Fig. 9 shows the photocurrent plotted versushe incident light intensity for different thicknesses of the elec-rolyte layer. The photocurrent is linear with the light intensityn our experiments. At high intensity, the photocurrent decreases

ith increasing distance from 60 �m to 370 �m due to limitingransport of the tri-iodide in the electrolyte.

Fig. 10 shows the values of �d, which are calculated from theMPS plots according to Eq. (2). As the diffusion of tri-iodide to theounter electrode is a limiting factor for current, electrons mustpend a long time in the TiO2 film before these can be collected.

Fig. 11 shows the photovoltage plotted versus the incident light

ntensity at different thicknesses. The experimental results show-ng that photovoltage slightly increased with increasing distance inhe experimental range are consistent with literature reports [9].lthough the basis for this reason has not been fully understood

able 2arameters determined by fitting the impedance spectra using the equivalent circuitf Fig. 1 for DSC with variations of distance between two electrodes.

d/�m Rh/� R1/� R2/� R3/�

60 37.1 20.6 85.1 22.4190 38.3 36.4 90.6 30.2370 44.3 37.9 97.1 49.8

Fig. 10. Electron transit times measured at different light intensities for DSC withvariations of distance between two electrodes.

[8], the results of IMVS (Fig. 12) and EIS (Table 2) have verified thatthe rate of electrons transferred from the TiO2 film to tri-iodide inthe electrolyte becomes slow. We speculate that the reason for this

Fig. 11. Photovoltage measured at different light intensities for DSC with variationsof distance between two electrodes.

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ig. 12. Electron lifetimes measured at different light intensities for DSC with vari-tions of distance between two electrodes.

. Conclusions

This work investigated the influence of the series resistance onhe electron transport and recombination processes of DSC usingIS, IMPS and IMVS. It was shown that, under short circuit condi-ions, electron transport was predominately affected by the seriesesistance Rh in TCO and R1 at the electrolyte/Pt-TCO interface.hese resistances had no significant influence on the charge recom-ination under open circuit conditions. As the Rh or R1 increased,he transit times became longer and the lifetime of the electronsemained invariant. Compared with Rh and R1, the resistance R3elated to the electrolyte between the cathode and anode influ-nces both the electron transfer and charge transport. R3 not onlyimited the electron extraction from the TiO2 film to the externalircuit under the short circuit conditions, but also influenced thelectron transfer from the TiO2 film to tri-iodide in the electrolyte.

cknowledgements

This work is financially supported by the National Basic Researchrogram of China (Grant No. 2006CB202600), Anhui Province Key

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ta 55 (2010) 2338–2343 2343

Technologies R&D Program (Grant No. 07010201005) and theKnowledge Innovation Foundation of the Chinese Academy of Sci-ences (Grant No. KGCX2-YW-326).

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