Influence of electrolyte in transport and ... - Universitat Jaume I

ARTICLE IN PRESS

Solar Energy Materials & Solar Cells 87 (2005) 117–131 www.elsevier.com/locate/solmat

Influence of electrolyte in transport and recombination in dye-sensitized solar cells studied by impedance spectroscopy Francisco Fabregat-Santiagoa,, Juan Bisquerta, Germa` Garcia-Belmontea, Gerrit Boschloob, Anders Hagfeldtb a

Department de Cie`ncies Experimentals, Universitat Jaume I, Avda. V. Sos Baynat s/n, Castello´ 12071, Spain b Department of Physical Chemistry, Uppsala University, Husarg 3, P.O. Box 579, Uppsala 75123, Sweden Received 18 May 2004; received in revised form 22 July 2004; accepted 26 July 2004 Available online 23 November 2004

Abstract The main features of the characteristic impedance spectra of dye-sensitized solar cells are described in a wide range of potential conditions: from open to short circuit. An equivalent circuit model has been proposed to describe the parameters of electron transport, recombination, accumulation and other interfacial effects separately. These parameters were determined in the presence of three different electrolytes, both in the dark and under illumination. Shift in the conduction band edge due to the electrolyte composition was monitored in terms of the changes in transport resistance and charge accumulation in TiO2. The interpretation of the current–potential curve characteristics, fill factor, open-circuit photopotential and efficiency in the different conditions, was correlated with this shift and the features of the recombination resistance. r 2004 Elsevier B.V. All rights reserved. Keywords: Dye-sensitized solar cell; Transport; Electrochemical impedance spectroscopy; Band shift

Corresponding author. Tel.: +34 964 728 094; fax: +34 964 728 066.

E-mail address: [email protected] (F. Fabregat-Santiago). 0927-0248/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.solmat.2004.07.017

ARTICLE IN PRESS 118

F. Fabregat-Santiago et al. / Solar Energy Materials & Solar Cells 87 (2005) 117–131

1. Introduction The optimization of dye-sensitized solar cells for their commercial use as an alternative power source of energy is the origin of research dedicated to the identification and description of the physical processes, such as injection, transport, accumulation and recombination of charge, that determine and limit the performance of the device [1]. Impedance spectroscopy is a well-known technique used for the study of electrochemical systems. The method is easy to measure but the correct interpretation of results needs the use of a suitable model. In the case of dye-sensitized solar cells the structure is a complex network of interconnected titanium dioxide (TiO2) nanosized colloids deposited on a transparent conducting oxide (TCO) and permeated with a redox electrolyte. This is the reason why impedance models published so far, to describe the behavior of the dye-sensitized solar cell, are restricted to certain working conditions [2,3] or apply only to separate parts of the cell [4,5]. In this work we aim to describe the general features of impedance spectroscopy of complete dye-sensitized solar cells in a broad range of experimental conditions, both in the dark and under illumination, for the full range of operating conditions, i.e. from open circuit to short circuit passing through the different possible loads attainable by the solar cell under illumination. The results are interpreted using impedance models based on transmission lines [6] that describe the transport, accumulation and recombination of electrons in the semiconductor phase of the cells. Furthermore, the effect that electrolytes with different ion composition have on these properties is also analyzed in order to monitor the displacement of the conduction band of the semiconductor [7] and to describe differences found in parameters such as the open-circuit potential, fill factor, short-circuit current and efficiency of the different samples.

2. Experimental Dye-sensitized solar cells were made from 12 nm diameter colloids deposited onto bare TCO (F:SnO2, Hartford 8 O/&), sintered at 450 1C for half an hour and sensitized with cis-(NCS)2(2,20 -bipyridyl-4,40 dicarboxylate)2Ru(II) (N3 dye from Solaronix) overnight. Three different electrolytes were used in this study as shown in Table 1,

Table 1 Characteristics of the samples. Performance data were taken at 0.1 sun Sample name

Electrolyte composition

#noMBI #Li #Na #TCO

0.5 M 0.5 M 0.5 M 0.5 M

LiI, 0.05 M I2 in 3-MPN LiI, 0.05 M I2, 0.5 MBI in 3-MPN NaI, 0.05 M I2, 0.5 MBI in 3-MPN LiI, 0.05 M I2, 0.5 MBI in 3-MPN

Z (%)

Voc (V)

Isc(mA)

FF

2.0 4.7 4.5

0.31 0.58 0.70 Bare TCO

1.26 1.23 0.96 blank

0.52 0.66 0.67

ARTICLE IN PRESS F. Fabregat-Santiago et al. / Solar Energy Materials & Solar Cells 87 (2005) 117–131

119

20

-Z'' (kΩ)

-0.2 V

-0.35 V

4

-0.4 V

2

10 1

2

0

(a)

0

0 0

10

20

30

(b)

0

2

4

6

(c)

0

1

2

3

4

Z' (kΩ) 20

300 200 1000

-Z'' (Ω)

-0.45 V

-0.6 V

0

500

0

0

(d)

10

100

100

100

200

300

0

50

160

170

180

0 0

500

1000

1500

(e) Z' (Ω)

0

50

100

150

Fig. 1. Impedance spectra of a dye-sensitized solar cell, #Li (Table 1), at different applied potentials: (J) experimental data; (—) fit result. Insets represent enlargement of the area marked with the circle.

where 3-MPN stands for 3-methoxypropionitrile, and MBI for 1-methylbenzimidazole, which is expected to have a similar effect as 4-tert-butylpyridine (4-TBP). Cells were sealed with Surlyn (Du Pont) and a piece of lightly platinized TCO was used as counter electrode. A sample of bare TCO was also prepared to be used as blank. Electrochemical measurements were done using a CHI-660 electrochemical work station with impedance analyzer in a two-electrode configuration. Bias potentials ranged between 0.2 and 0.8 V depending on the open-circuit photopotential of the cell under illumination at 0.1 sun. To enable comparisons, the same potentials were applied in the dark. For impedance measurements, a 10 mV AC perturbation was applied ranging between 10 kHz and 10 mHz. 0.1 sun illumination was obtained from a 50 W halogen lamp.

3. Results and modeling Typical impedance spectra of a dye-sensitized solar cell at different applied potentials are shown in Fig. 1. Experimental data (J) have been fitted (—) to the model represented by the equivalent circuit shown in Fig. 2(a). In this figure, the representation of the network of colloids of TiO2 has been simplified to a columnar model. The equivalent circuit elements have the following meaning [6]:

C m (=cmL) is the chemical capacitance that stands for the change of electron density as a function of the Fermi level [8].



RS

rt RTCOrr

rt

rt rr

cµ

rt

TCO+Pt

rr

rr cµ

solution

rt

cµ

cµ

CTCO

CPt

(a) TCO

TiO2

solution

RS

TCO+Pt

R TCO

CTCO CPt (b) TCO

TiO2

RS

solution

TCO+Pt

Rr Cµ

(c)

TCO

CPt TiO2

Fig. 2. (a) Equivalent circuit for a complete solar cell. (b) Simplified circuit for insulating TiO2 (potentials around 0 V) as currents are low, Zd may be skipped. (c) Simplified circuit for TiO2 in the conductive state.

Rt (¼ rt L) is the electron transport resistance. Rr (¼ rr =L) is a charge-transfer resistance related to recombination of electrons at the TiO2/electrolyte interface. Rs is a series resistance accounting for the transport resistance of the TCO. RTCO is a charge-transfer resistance for electron recombination from the uncovered layer of the TCO to the electrolyte. CTCO is the capacitance at the triple contact TCO/TiO2/electrolyte interface [9]. Zd(sol) is the impedance of diffusion of redox species in the electrolyte [4,5]. RPt is the charge-transfer resistance at the counter electrode/electrolyte interface [2,3]. CPt is the interfacial capacitance at the counter electrode/electrolyte interface [2,3].

The first three mentioned elements are denoted in lowercase letters in Fig. 2(a) meaning the element per unit length for a film of thickness L, because they are distributed in a repetitive arrangement of a transmission line. The physical meaning


121

of this network corresponds to the impedance of diffusion and reaction that is discussed in previous papers [6,10–12]. The equivalent circuit indicates the internal distribution of electrochemical potential (Fermi level for electrons) in response to the modulated small perturbation of the external electrical potential at a steady state [12]. The impedance function of the diffusion–reaction model is Z¼

Rt Rr 1 þ io=ok

1=2

coth½ðok =od Þ1=2 ð1 þ io=ok Þ1=2 ;

(1)

where od ¼ Dn =L2 ¼ 1=Rt C m is the characteristic frequency of diffusion in a finite layer (Dn being the electron chemical diffusion coefficient [13]), ok ¼ 1=R pffiffiffiffiffiffi ffi r C m is the rate constant for recombination, o is the angular frequency and i ¼ 1: Note that od and ok are related, respectively, with the inverse values of the more commonly used parameters of transit (or transport) time and lifetime [10]. The model of Eq. (1) is strictly valid for a homogeneous distribution of electrons in the semiconductor, which yields to constant elements in the transmission line. It has been shown that even in the case of strong inhomogeneity this model is approximately valid [12]. Fig. 3 illustrates the theoretical shapes of impedance spectra corresponding to Eq. (1), i.e. the transmission line model of Fig. 2(a) without considering the effects of the uncovered TCO, the Pt electrode or the diffusion in the electrolyte. The different shapes are obtained by changing only one parameter, the charge-transfer resistance Rr. It is interesting to describe here some cases of Eq. (1) corresponding to particular physical situations, see Refs. [10,11] for a more extended discussion. In the conditions of low recombination, Rt oRr (or ok ood ), Eq. (1) reduces at low frequencies to the expression of a semicircle Z¼

1 Rr Rt þ 3 1 þ io=ok

(2a)

Fig. 3. Simulations of the impedance spectra of Eq. (1) varying Rr from a very high value, curve 1, to a low value, curve 8, while keeping Rt constant. In curves 1–5, Rt oRr while in curves 7–8, Rt 4Rr :



and to the expression of a straight line of slope 1, the conventional Warburg impedance o 1=2 Z ¼ Rt i (2b) od at high frequencies. od indicates the frequency of transition from one behavior to the other. Theoretical curves 1–5 in Fig. 3 are well described by these equations. Note that for very large values of Rr (ok very small), curves 1–3, the 451 line of diffusion given by Eq. (2b) is a minor feature at high frequencies. The impedance is largely dominated by the reaction arc, the second term in Eq. (2a), with the characteristic frequency ok. On the other hand, in conditions of large recombination, Rt bRr ; the general impedance of Eq. (1) becomes the Gerischer impedance 1=2 Rt Rr Z¼ (3) 1 þ io=ok that corresponds to curve 8 in Fig. 3. This behavior is similar to diffusion and reaction in semi-infinite space [11]. As in the preceding case, at high frequency the impedance shows a diffusion line of slope 1, corresponding to Eq. (2b), which is implied by Eq. (1) at obok : Note in Fig. 2(a) that the impedance of the TCO/electrolyte interface is connected as a terminal (boundary) element to the diffusion–reaction impedance of electrons in TiO2. The analytical model is an extension of Eq. (1) that is discussed in Ref. [14]. The different impedance elements in the equivalent circuit are determined by the stationary distribution of carriers that will change strongly depending on the steadystate illumination and potential. This is the reason for the strong variations that can be observed in the shape of the impedance spectra of Fig. 1. We will see that the major factor controlling the impedance spectra is the state of the semiconductor TiO2 at the different potentials [6], and this will allow us to extract important information on the processes of the dye-sensitized solar cell. The dye molecules adsorbed in the semiconductor surface control the rate of injected electrons in the colloids and, in addition, decrease the area that is active for recombination, as it is usually thought that recombination of electrons in the semiconductor with the electrolyte dominates over charge losses through oxidized dye molecules [15,16]. However, the dye molecules are not directly acted upon by the modulation of the Fermi level that is applied in impedance spectroscopy, and are therefore not represented distinctly as a separate element in the impedance model. We discuss now the interpretation of the measured spectra according to the previous model. At the lower applied potentials, Fig. 1(a), the main characteristic is a simple semicircle displaced from the origin by a quantity RS. As will be explained below, in this case the TiO2 is an insulator and the equivalent circuit of Fig. 2(a) may be reduced to the parallel association of the resistance RTCO and the capacitor CTCO, in series with RS, Fig 2(b). At higher frequencies, a small deformation of this single arc occurs (not shown). This effect arises from the contribution of the platinized


123

counter electrode and may be modeled by the parallel combination of the platinum charge transfer resistance, RPt, and double layer capacitance CPt. In this case currents flowing through the complete cell are very small, so that diffusion effects of triiodide are negligible and Zd(sol) may be ignored. The spectrum shown at intermediate potentials, Fig. 1(d), corresponds to the behavior of the whole transmission line [6] as described above in relation to Eq. (1) and in Fig. 3 for Rt oRr : The diffusion behavior is clearly appreciated in the highfrequency wing, with a slope close to 1, see the inset of Fig. 1(d). The low-frequency semicircle is the result of the parallel association of the electron chemical capacitance C m with the charge-transfer resistance, Rr, along the TiO2, as given by Eq. (2a). Zd(sol) is also negligible in this case. As mentioned before, Fig. 1(d) appears in the case in which the charge-transfer resistance is considerably larger than the transport resistance (lifetime4transit time). The opposite case, Rt 4Rr ; is the Gerischer impedance that implies a strong recombination rate relative to conductivity observed under illumination where, as will be shown later, Rr decreases significantly with respect to its value in the dark, Fig. 4. In these conditions, rising up the Fermi level position with the applied potential turns into the case of Rt oRr that yields again the shape of Fig. 1(d). We remark that in the case represented in Fig. 1(d) RTCO bRr : This fact has allowed to clearly identify the characteristic spectrum of diffusion–reaction given by the condition Rt oRr and as consequence, the model of Fig. 2(a) can be simplified by eliminating RTCO. In the potentials that range between Figs. 1(a) and (d), the complete model of Fig. 2(a) is needed to fit the data, and the spectra have an intermediate shape between both, Figs. 1(b) and (c). In these cases, the responses of the TCO, the TiO2 and even the counter electrode overlap in the frequency domain and cannot be separated without using the model. At more negative potentials the Fermi level in TiO2 approaches the lower edge of the conduction band, and both Rt and Rr become smaller due to the increasing electron density. At a certain potential the TiO2 becomes sufficiently conductive so that Rt is negligible and C m bC TCO : In this case the circuit of Fig. 2(a) reduces to the one in Fig. 2(c). It consists of the parallel connection of Rr and Cm in series with RS plus the effects of the counter electrode and diffusion in the electrolyte. At these

-Z'' (Ω)

200

100

0 100

200

300

400

Z' (Ω) Fig. 4. Impedance spectra of the solar cell #Na (Table 1) under 0.1 sun illumination at 0.55 V: (J) experimental data; (—) fit result. This set of data is well described by the Gerischer impedance.


Rt / Ω

10 10 10 10

5

10-2

4

10

Cfilm / F

10

3

2

10 10

1

10

-0.8

(a)

-0.6

-0.4

-0.2

10 5

-3

-4

10 4 10 3 10 2

-5

10 1 -6

10 0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4

-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4

0.0

Potential / V

10 6

Rct / Ω

124

Potential / V

(b)

Potential / V

(c)

Fig. 5. Results from the impedance data for the three samples: #Na (r), #Li (J) and #noMBI (&) in the dark at the different applied potentials. (a) Evolution of transport resistance in TiO2. (b) Capacitance of the cell without the contribution of the platinum capacitance. (c) Charge transfer resistance of the cell, after subtracting platinum and series resistance.

10

3

10 6

10-2

10 5

2

10 10

10

(a)

1

-0.8

-0.6

-0.4

-0.2

Potential / V

10

0.0

(b)

-3

Rct / Ω

10

Cfilm / F

Rt / Ω

10

-4

10 4 10 3 10 2

-5

10 1 10 0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4

-6

-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4

Potential / V

(c)

Potential / V

Fig. 6. Same as Fig. 5 under 0.1 sun illumination: #Na (r), #Li (J) and #noMBI (&).

potentials we found typical spectra as that shown in Fig. 1(e). The high-frequency semicircle is the result of the evolution with the potential of the small deformation mentioned for lower potentials, related to the parallel connection of RPt and CPt from the counter electrode. The intermediate semicircle is the combination of Rr and C m : Finally, the small feature at the lowest measured frequencies, see inset, is the effect of the diffusion of the ions in the electrolyte [3–5]. In this work we are not considering a detailed description of this effect. Impedance data of three cells with different electrolytes indicated in Table 1 were measured within a range of bias potentials in the dark and under illumination. The main physical parameters obtained from the impedance model by fitting to the equivalent circuits are plotted in Figs. 5 and 6.

4. Discussion The observation of the impedance spectrum of Fig. 1(d) has two important implications on the description of the behavior of the dye-sensitized solar cell. The


125

first one is related with the Rt oRr that yields to a value of the normalized ffiffiffiffiffiffiffiffiffiffiffiffiffi pcondition diffusion length Ld =L ¼ Rr =Rt [10] greater than 1. A diffusion length of electrons larger than the thickness of the film means that the transit time is shorter than the lifetime, and this is a necessary condition to efficiently collect the charge injected by the dye when illuminating the solar cell. Therefore, the impedance shape of Fig. 1(d) is an important characteristic feature of an efficient nanocomposite solar cell device. Furthermore, the condition Ld =L41 implies nearly homogeneous distribution of the Fermi level along the nanoporous structure, at least in the vicinity of open circuit [12]. The second implication is that at this potential and at the more negative ones, electron losses are mainly produced at the TiO2/electrolyte interface provided that RTCO 4Rr : Therefore, to improve the performance of the cell the recombination through this interface needs to be diminished as remarked by many authors [17,18]. In the following, we discuss the trends and interpretation of the main impedance parameters as a function of steady-state conditions for the different electrolyte compositions. 4.1. The transport resistance Figs. 5(a) and 6(a) show the change of transport resistance of electrons in TiO2, from a very high to a very low value when the applied potential is displaced toward negative values. The resulting Rt–potential curves are dependent on the electrolyte composition. Both observations may be explained as follows. The conductivity of a semiconductor is s ¼ emncb

(4)

with e the electron charge, m the mobility (that is proportional to the free electrons diffusion coefficient) and ncb the density of electrons in the conduction band (cb) given by E F E cb ncb ¼ N cb exp ; (5) kT where N cb is the effective density of states in the conduction band, k the Boltzmann constant, T the temperature, E cb the position of the lower edge of the cb and E F the position of the Fermi level in the semiconductor that is governed by the applied potential, V a ¼ ðE F E F0 Þ=e: If we consider that the mobility is constant, from Eqs. (4) and (5) we obtain that E F E cb Rt ¼ R0 exp ; (6) kT with R0 constant for all the samples provided that their geometrical dimensions are similar. Eq. (6) presents the exponential behavior shown in Figs. 5(a) and 6(a), with a theoretical slope of 60 mV per decade that agrees with the values obtained in the dark (66 mV per decade). On the other hand for the data taken under illumination it is obtained as 130 mV per decade. This difference is related to the



presence of the injected charge in the sample, that yields smaller values of Rt at the same potentials, but this feature has not been successfully modeled yet. Focusing the attention on the shift of the transition potentials now, it follows from Eq. (6) that it can only be attributed to a displacement of the conduction band energy levels. For samples #Na and #Li, the shift in Ecb, that was attributed to the difference in the cation size in a previous work [7], agrees quite well with the measured open-circuit photopotential difference, see Table 1. On the other hand, the relative displacement in Ecb between samples #Li and #noMBI, is associated with the surface adsorption of this basic compound that also shifts upwards the conduction band in TiO2. However, this shift is only partially responsible for the total VOC difference. The other part has its origin in the recombination process as will be explained below. 4.2. The capacitance Fig. 5(b) shows the capacitance of film in the dark which, according to Fig. 2(a) is the sum of the exposed substrate and the TiO2 capacitances: C film ¼ C TCO þ C m : In good agreement with data from transport of Fig. 5(a), the capacitance of the film starts to rise exponentially only when the TiO2 has a measurable conductivity. This exponential rise is a behavior typical of the chemical capacitance of TiO2 that is related to the total density of electrons, n, by the expression [8,19] e2 n; (7) kT where n / nbcb and 14b40 indicate an exponential distribution of traps below the conduction band edge ðb 2 ½0:2; 0:3 Þ as found in our results here and in previous work [20]. The case b=1 means that all the electrons belong to the conduction band. Eqs. (6) and (7) imply that both Cfilm and Rt should switch to exponential behavior at the same potential. This fact is confirmed by Figs. 5(a) and (b). Before this happens, Cfilm is due exclusively to CTCO, as can be directly deduced from the comparison of the capacities of the #Li complete cell and the #TCO blank, Fig. 7(a). Under illumination, due to the electron injection from the dye to TiO2, transport resistance and consequently charge accumulation in TiO2 become dominant at slightly lower externally controlled potentials, Figs. 6(a) and (b). Cm ¼

4.3. Recombination resistance The overall charge transfer resistance of the film, Rct, that is the parallel combination of RTCO and Rr, is represented in Figs. 5(c) and 6(c). Rct has also two well-defined regions of behavior: When the TiO2 is an insulator, electron recombination takes place mainly at the uncovered TCO that presents a transfer factor a 0:25; see below. When the TiO2 becomes electronically conducting, Rct changes its slope indicating that recombination occurs through the colloids surface, yielding a0 0:5: To avoid the recombination through the TCO, it can be covered by a thin layer of compact TiO2 or polymer, but from these figures we can

ARTICLE IN PRESS F. Fabregat-Santiago et al. / Solar Energy Materials & Solar Cells 87 (2005) 117–131 106

10-2

#TCO #Li

105

10-3

Rct / Ω cm2

Cfilm / F cm-2

127

10-4

104 103 102

10-5 101

-0.9

(a)

-0.6

-0.3

Potential / V

-0.9

0.0

(b)

-0.6

-0.3

0.0

Potential / V

Fig. 7. Comparison between the results of Cfilm (a) and Rct (b) obtained for bare TCO and a complete dyesensitized solar cell.

conclude that a large difference could not be expected for these samples as most of the recombination at the potentials of maximum efficiency occur at the TiO2 interface. The values of Rct under illumination, Fig. 6(b) are lower than those obtained in the dark. Once discarded, recombination losses through the unregenerated dye [15,16], this decrease may be related to the higher concentration of I 3 ions near the surface of the colloids produced during the regeneration of the dye and to the recombination of the photogenerated electrons, specially at the more positive bias. In order to show graphically the potential region in which TCO response dominates the behavior of Rct and its transition to the region dominated by the TiO2 nanocrystalline network, in Fig. 7(b) the results for the sample of bare TCO and the complete sample #Li, both with the same electrolyte composition, are presented. To make a better comparison, the obtained Rct have been normalized to the geometric area and the exposed factor of TCO, e ¼ Rct ð#LiÞ=Rct ð#TCOÞ ¼ 0:90ð0:05Þ calculated at the most anodic potentials in the dark. Thus, Fig. 7(b) shows clearly that electron recombination in the region of potentials more positive than 0.4 V is given mainly at the uncovered TCO. The change in the slope of Rct in the complete dye-sensitized solar cell for potentials more negative than 0.4 V indicates that electron recombination takes place through the TiO2. Note that the low coverage of the bottom TCO, 10% (=(1e) 100), obtained here agrees very well with previously obtained values that were attributed to the mismatch between the crystal lattices of TiO2 (anatase) and SnO2 in the TCO (cassiterite) [9]. Analytical description of charge transfer resistance for the TCO follows: Fluorinedoped SnO2 is a high conductivity degenerated semiconductor that behaves very similarly to a metal. Current of charge transfer in a semiconductor/electrolyte phase is thus governed by the Buttler–Volmer relation [21] ha i ð1 aÞ E j 0 exp E ; (8) j BV ¼ j 0 exp kT kT



j0 being the exchange current density, a the transfer factor and E ¼ E F E redox the energy difference between the Fermi level in the semiconductor and the redox level. In a two-electrode configuration, for small potential drops in the counter electrode, the E is governed by the applied potential, V a ¼ E=e; and it is possible to calculate the charge transfer resistance as 1 di RTCO ¼ e ; (9) dE i being the current flux. Applying Eq. (9) to Eq. (8) we obtain the resistances h ae i Va RC ¼ R0C exp (10) kT and ð1 aÞe Va ; RA ¼ R0A exp (11) kT for cathodic and anodic applied potentials, respectively. From the cathodic and anodic slopes of the data of the bare TCO sample, we obtain very good agreement with theory as a ¼ 0:25 and 1 a ¼ 0:69: On the other side, for sample #Li, in the region of TiO2 recombination, Eq. (10) is followed with a0 ¼ 0:5; as commented before. This change in the transfer factor thereby provides a way to distinguish between the two recombination processes. However, the description of recombination from TiO2 through Eq. (10) can be considered only a phenomenological expression, indeed, note that the dependence of Rct in Fig. 6(c) is not exponential but tends to a Gaussian shape. Electrons may recombine not only from the conduction band but also from localized intraband states and from an exponential distribution of surface states in the bandgap [13]. In addition, the different surface states differently match the fluctuating energy levels of the acceptors in solution, depending on the reorganization energy. Henceforth, the charge-transfer resistance for recombination from the nanostructured TiO2 network necessitates a more complete model that will be presented in future work. Note that in a previously reported analysis [22] the value obtained for the transfer factor for the TCO was 0.5. We attributed this difference to the use of acetonitrile as solvent and methylhexylimidazolium iodide, MHII, as salt in that case. Preparation of cells with similar electrolytes, yielded the same value of a as theirs. This suggests that an electrolyte with these components induces a recombination process involving the double number of electrons (most likely 2 instead of 1) than in the case of its absence, that yields to a value of a00 =2a. 4.4. Effect of bandshift and steady-state characteristics A comment has to be made about the origin of the change in slope observed at the more negative potentials of Figs. 6(b) and (c), for C film and Rct : Under illumination at these potentials Rct and RPt have values within the same order of magnitude. Therefore, a significant drop of potential takes place in the counter electrode. The


129

pertinent correction in these figures (not shown) yields the same tendency as that in the dark. Taking into account this last comment, let us discuss the effect of bandshift on charge transfer resistance under illumination shown in Fig. 6(c). In the region of the more negative potentials, where the recombination takes place through the TiO2, we observe that the shift in the potential at which Rct reaches the same values for the samples #Na and #Li, is nearly the same as the conduction band change observed in Fig. 6(a). However, if we compare this shift for samples #Li and #noMBI, we find that it is larger than the conduction band displacement. At the same time it agrees very well with the difference obtained in the open-circuit voltage, Table 1. A reasonable explanation for this fact may be partial passivation of TiO2 by MBI adsorbed at the surface of the colloids that reduces the effective area available for recombination. The consequent rise in Rct ; that can be observed in Figs. 5(c) and 6(c) for the samples with MBI, produces an increment in Ld =L in the region of transition from insulating to the conducting state of TiO2. Thus, Ld =L passes from slightly minor to greater than 1 and is the element responsible for the increment in the fill factor. Thus, the addition of MBI in the electrolyte, similar to what happens with 4-TBP, has two effects on the performance of the cell: it rises up the conduction band position and reduces recombination yielding higher V OC ; fill factor and efficiency. Differences in I SC between #Li and #Na are mainly due to the different thicknesses of the sample, around 17% in average, but there are also two other minor contributions due to the rise of the conduction band of the semiconductor: The first, a lower matching/driving force for the injection of the electrons from the excited levels in the dye towards the TiO2 [23]. The second, a higher driving force for recombination that would lead to a decrease in Rct : Our data do not give sufficient resolution to evaluate these corrections. Finally, note that Eq. (10) follows the behavior of a diode for V a 4e=kT: Thus, diode models typically used to fit the I–V curves data may be applied, and indeed the origin of the diode equation is the recombination rate dependence on electron concentration [8]. We remark that in the present case, in a first approximation (considering the peculiarities of electron recombination from the TiO2 nanoparticles and the particular physical meaning of the parameters obtained), the proper model would need two diodes of different exponents to fit the data. 4.5. Chemical diffusion coefficient From the data of transport and the chemical capacitance, the effective (chemical) diffusion coefficient, Dn ¼ L2 =Rt C m ; was calculated and results in the dark and under illumination are shown in Fig. 8. Together with the same shifts described before, two new features that affect Dn under illumination should be remarked: (i) It is much larger than the value in the dark, which is consistent with the electron injection in the semiconductor network that yields the better conductivity shown in Fig. 6(a). (ii) Its exponential behavior flattens as could happen if it approached the conduction band diffusion coefficient [13]. However, the values of Rt and Cm from


F. Fabregat-Santiago et al. / Solar Energy Materials & Solar Cells 87 (2005) 117–131 -3

10

-4

D / cm2 s-1

10

-5

10

-6

10

-7

10

-0.8

-0.6

-0.4

-0.2

0.0

Potential / V Fig. 8. Chemical diffusion coefficient for samples in the dark #Na (.), #Li (K) and #noMBI (’) and under illumination #Na (r), #Li (J) and #noMBI (&).

which it is calculated do not present the expected tendency for a cb mechanism. Thus, this last point remains open for further research.

5. Conclusions A transmission line-based model was successfully used to describe the electrochemical behavior of dye-sensitized solar cells with different electrolytes in the dark and under illumination from the results of impedance spectroscopy. The characteristic impedance spectra have been discussed and the conditions needed to obtain an efficient dye-sensitized solar cell were commented on. The parameters for transport, accumulation and recombination processes have been separated and determined using the impedance model. The range of potentials at which recombination of electrons is given through the TCO or the TiO2 is distinguished and related to the conducting/insulating state of TiO2. Conduction band shifts were clearly monitored when varying the electrolyte composition. In combination with recombination data these displacements of the band were utilized to describe the changes observed in the changes in photopotential, fill factor and short-circuit current that govern the efficiency of the cell.

Acknowledgments The authors want to acknowledge Eric Lewin for the preparation of the cells. This work was supported by projects BFM2001-3604 from MCyT, 02G014.31/1 from Fundacio´ Bancaixa and JMB/JG/AP from Generalitat Valenciana, and by the


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