We determined the carrier diffusion lengths in TiO2 nanoporous layers of dye-sensitized solar cells by using scanning photocurrent microscopy using an ultraviolet laser. Here, we excited the carrier directly in the nanoporous layers where the diffusion lengths were found to 140 μm as compared to that of visible illumination measured at 90 μm. The diffusion length decreased with increasing laser modulation frequency, in which we determined the electron lifetimes and the diffusion coefficients for both visible and UV illuminations. The diffusion lengths have been studied in terms of the sintering temperatures for both cells with and without binding molecules. We found a strong correlation between the diffusion length and the overall light-to-current conversion efficiency, proving that improving the diffusion length and hence the interparticle connections, is key to improving cell efficiency.

Nanoporous (NP) films fabricated by TiO2 nanoparticles have attracted considerable attention since they have been widely used in dye-sensitized solar cells (DSCs)1–7 and artificial light harvesting systems.8,9 In DSCs in particular, optimizing the charge collection efficiency of the electrons transferred from dyes to the external circuit is essential for maximizing the total cell efficiency. It has been explicitly demonstrated that the diffusion length is the key parameters maximizing the charge collection efficiency.10–13 Both transient and steady-state methods have been used to determine the electron diffusion length in DSCs.12–17 In both these approaches, the diffusion lengths are measured indirectly, which requires appropriate modeling and exact knowledge of other optical parameters. Recently, scanning photocurrent microscopy (SPCM) has been proven to be a very effective tool for addressing the diffusion length in DSCs, without the knowledge of additional parameters.11,18–21 Diffusion lengths of ∼100 μm have been reported for conventional DSCs, and, more importantly, their correlation to the total cell efficiencies has been demonstrated explicitly.

Previous experiments have primarily focused on the phenomenon of carriers being transferred to NP layers from dyes that absorb visible light. The study on the microscopic transport properties due to the light absorption of the dyes provides us with information that is directly correlated to the total efficiency of DSCs.11 It is sometimes important to address the optical and electrical properties of the NP films, in which the carriers are directly generated in TiO2. This is because the transport properties of carriers in the NP layer, transferred from the light absorbing dyes, are likely to be influenced not only by the layer's interparticle connectivity but also by other parameters such as the dye-NP transfer rate and the absorption efficiency of the dyes. In other words, studying the diffusion length of TiO2 NP films under ultraviolet (UV) illumination (since they are materials with wide band-gaps) even without the presence of dyes can be very useful in searching for the optimal NP fabrication procedures for various optoelectronic applications.

In this study, we measured the diffusion lengths in the NP layers of DSCs by using SPCM under UV illumination (UV-SPCM). This process involves direct excitation of the carriers in the NP layers. This enabled us to investigate the carrier transport properties of the photoelectrode unambiguously without suffering from dye-sensitization processes. By imaging the localized photocurrent captured through a partially etched front-electrode, we obtained diffusion lengths and found their correlation to the light-current conversion efficiency of the cells sintered at different temperatures.

Fig. 1(a) shows the device configuration to measure diffusion length. We fabricate DSCs using conventional procedures, except that a part of the transparent conducting electrode, the fluorine-doped tin oxide (FTO) layer, is removed.11 The partially etched front-electrodes were patterned on the FTO electrodes using photolithography followed by the wet etching process, in which the photoresist (maN-1420, micro resist technology GmbH) was used as an etching mask. Hydrochloric acid and zinc dust were used as the etchant and catalyst, respectively. The conventional titania nanoparticle paste with binding molecules (Dyesol Inc.) was deposited on the partially etched FTO electrodes using the doctor blade method and sintered at various temperatures ranging 300°C–500°C to form NP films (∼12 μm thick). We also used homemade binder-free nanoparticle paste, sintered at 150°C–450°C for comparison, that was ∼12 μm thick. Both types of the NP electrodes were placed in dry methanol with (Bu4N)2[Ru(dcbpyH)2-(NCS)2] (N-719 dye, Dyesol Inc.) for 24 h in order to allow them to adsorb the dyes. The photoelectrode was sandwiched with a platinized FTO counter electrode, separated by 60 μm thick hot melt spacers. The internal space of the cell was filled with a liquid electrolyte (EL-HSE, Dyesol Inc.) by capillary action.

FIG. 1.

(a) Schematic of a DSC device structure with partially etched FTO electrode for the diffusion length measurements illuminated with a focused UV laser. (b) I–V curve with (red) and without (black) UV illumination for a cell without dye-sensitization. (c) Photocurrent as a function of focused laser position (x0) from the FTO edge. Light used to illuminate the DSC sample with dyes had wavelengths of 355 nm (black), 405 nm (blue), and 532 nm (red). (d) Diffusion length for the three different laser wavelengths.

FIG. 1.

(a) Schematic of a DSC device structure with partially etched FTO electrode for the diffusion length measurements illuminated with a focused UV laser. (b) I–V curve with (red) and without (black) UV illumination for a cell without dye-sensitization. (c) Photocurrent as a function of focused laser position (x0) from the FTO edge. Light used to illuminate the DSC sample with dyes had wavelengths of 355 nm (black), 405 nm (blue), and 532 nm (red). (d) Diffusion length for the three different laser wavelengths.

Close modal

The diffusion lengths can be measured explicitly by using SPCM on the DSCs with partially etched front-electrodes. The focused laser spot illuminates the TiO2 NP layer, creating localized electron-hole pairs that contribute to the current through the diffusion process in the film. A schematic of this is shown in Fig. 1(a). Since the collected photocurrent decreases as we move the laser spot away from the FTO layers, we can determine the diffusion length by scanning the laser position. Diode-pumped solid-state lasers at UV (355 nm) and visible (405 nm and 532 nm) ranges were focused individually using an objective lens (Numerical Aperture = 0.1, 4X) and scanned using a two-axis galvo scanner. The full-width at half-maximum of the focused laser spot size was less than 4 μm. When we illuminate the DSCs with the UV laser, we can induce the carriers in the TiO2 layers directly because the laser's energy is above the band-gap of the TiO2. By illuminating the DSCs with the visible laser, we can address the carriers that are transferred from the dye molecules to the NP layers.

Fig. 1(b) shows a plot of I–V measurements on the dye-free DSCs, with (red line) and without (black line) the focused UV illuminations, when the laser with an intensity of 2.0 mW is incident on the unetched region of the NP layer. The I–V curves exhibit the rectifying behaviors determined by the band alignment of the TiO2 layers and the redox potential of the electrolyte solution. UV illumination induces a photocurrent signal. This indicates that the excess electron carriers were collected by the photoelectrode even without the light-absorbing dyes. Similar to conventional DSCs, hole carriers were used for the oxidation of the electrolyte solution.22 Visible light illuminations did not induce noticeable current generation without the dye-sensitization since they are below the TiO2 band-gap.

We first show the results on the diffusion length measurement resulting from laser illuminations at different wavelengths. We used a conventional DSC with the NP layers sintered at 525°C and sensitized with dyes, except that part of the photoelectrode has been removed to measure the diffusion length as mentioned previously.11 The photocurrent signal was large when we illuminated the photoelectrode onto the remaining FTO areas and decreased as we moved the focused laser spot away from the etching interface as described in the inset of Fig. 1(c). We used a very slow scanning speed of 10 μm/s, because the total energy conversion process in DCSs occurs over a long period of time. The line profile of the photocurrent is plotted in Fig. 1(c) as a function of the distance (x0) between the laser spot and the FTO edge for the three different wavelengths. Starting from a 2D diffusion model in the thin film limit, the photocurrent collected by the semi-infinite FTO electrode analytically leads to the simple 1D exponential curve as a function of x0.11 

\begin{equation}I_{col} = \frac{{eG}}{2}exp( - x_0 /L)\end{equation}
Icol=eG2exp(x0/L)
(1)

Here, e is the electron charge, G is the electron generation rate, and L is diffusion length. Therefore, the diffusion length can be extracted explicitly by fitting the photocurrent curve with Eq. (1), without knowledge of additional optical and transport parameters of DSCs.

The fitting results on the diffusion lengths for different wavelengths of illuminating laser are shown in Fig. 1(d). The measured diffusion lengths were larger than the optimal thickness of NP films (10–18 μm) as previously reported.11 This has been attributed to the fact that the effective travel distance (leff) of photogenerated carriers in a highly disordered NP layers can be much larger than the film thickness (d). Our results of Ld are more relevant to the prediction based on the transient methods than those of the steady-state methods that yield Ld in general.12,16 In particular, it is found that the diffusion length is larger (∼140 μm) when we illuminate the DSCs with the UV laser relative to those of the visible-range illumination (∼90 μm) under the same light intensity (0.8 mW). Increase in the diffusion coefficient likely dominates the carrier lifetime reduction because a large amount of carriers is generated under the UV illumination,12,23,24 which will be discussed later. There was no noticeable change in the photocurrent magnitude and the diffusion length values found over the course of repeated measurements.

In order to properly measure the diffusion length of NP layers using SPCM, the scanning speed has to be chosen carefully since it strongly influences the diffusion length. To investigate the frequency dependence of the diffusion lengths of NP films, we modulated the laser light from 10 Hz to 30 kHz using an optical modulator (Boston Micromachine Corperation). The photocurrent is recorded through a lock-in amplifier (Signal Recovery) as a function of position. As we increase the modulation frequency, the measured diffusion length decreases for both visible (532 nm) and UV illuminations, as shown for the visible case in Fig. 2(a). The diffusion lengths are best fitted with the simple exponential function of Eq. (1) and Fig. 2(b) shows the diffusion lengths plotted as a function of the modulation frequency. In the visible case (red circles), the diffusion length decreases from DC value of 98 μm toward the detection limit of about 3 μm. Conversely, the diffusion length decreases (DC value at 143 μm) rather slowly with increasing frequency in the UV case (black squares).

The frequency-dependent diffusion length has been studied in semiconductor thin films, which show a similar tendency towards decreasing with increasing frequency.25,26 When the light modulates, the diffusion length decreases as L(ω) = L0/(1 + iωτ)1/2, where L(ω) is the frequency-dependent diffusion length, L0 is the DC diffusion length, and τ is the carrier lifetime. By taking the real part of Icol in the high frequency regime (ωτ ≫ 1), the above expression leads to L(ω) ≈ L0 × (2/ωτ)1/2.26 By fitting the data in Fig. 2(b), we extracted τ of 6.95 ms and 33.4 ms for UV and visible illuminations, respectively. The short carrier lifetime for the UV illumination is reasonable considering that a large amount of carriers is generated in TiO2 layers, which leads to a significant reduction in the lifetime, as reported elsewhere.11,12,23,24 We also note that τ will decrease further because both the electron and hole carriers are present upon the UV illumination, which increases the recombination probabilities.

The longer diffusion lengths as well as the smaller lifetime suggest that the diffusion coefficient D will be much larger in UV illumination compared to the visible case, according to the relation L0 = (Dτ)1/2. The estimated D is about ten times larger in the UV case (2.94 × 10−2 cm2/s) than in visible case (2.89 × 10−3 cm2/s). The larger diffusion coefficient can be attributed to the increased ratio of free to trapped electrons since the carrier density is significantly large for the UV case.23 In other words, we demonstrated explicitly that the increase in the diffusion coefficient dominates the decrease in the carrier lifetime, resulting in an overall increase in the diffusion length for UV illumination.

The information obtained by the UV-SPCM, which is not obscured by the presence of dyes, is directly linked to the interparticle connectivity of the photoelectrodes fabricated from the TiO2 nanoparticles. Here, we were primarily interested in the charge transport properties in TiO2 layers sintered at the different temperatures (without dye-sensitization). The cell efficiency as a function of sintering temperatures (Ts) has been addressed before.27,28 However, the diffusion length has not been studied in terms of various sintering conditions especially in conjunction with the cell efficiency. We first show scanning electron microscope (SEM) images sintered at two different temperatures of 300°C and 500°C in inset of Fig. 3(a). As reported earlier, there is no significant change in the morphology between the NP layers sintered at different temperatures. This is because the interparticle necking for achieving better carrier transport properties is primarily due to the dehydration process not the change in the morphology. However, they exhibit noticeable changes in the diffusion length with the increase in Ts as shown below.29 

FIG. 3.

(a) Photocurrent as a function of position x0 for the four different value of Ts from 300°C and 500°C. Light modulation frequency is kept at 100 Hz. Solid lines are fits to the data. Inset: SEM images for sintering temperatures (Ts) of 300°C and 500°C. (b) Diffusion length as a function of Ts for both types of pastes with (red squares) and without (blue circles) binding molecules. (c) External QE as a function of Ts for both types of pastes. (d) Plot of external QE versus diffusion length, reconstructed from (b) and (c).

FIG. 3.

(a) Photocurrent as a function of position x0 for the four different value of Ts from 300°C and 500°C. Light modulation frequency is kept at 100 Hz. Solid lines are fits to the data. Inset: SEM images for sintering temperatures (Ts) of 300°C and 500°C. (b) Diffusion length as a function of Ts for both types of pastes with (red squares) and without (blue circles) binding molecules. (c) External QE as a function of Ts for both types of pastes. (d) Plot of external QE versus diffusion length, reconstructed from (b) and (c).

Close modal

We prepared a series of dye-free cells fabricated from the TiO2 paste with conventional binding molecules for different values of Ts on the partially etched FTO electrodes. This time we used 100 Hz for the frequency of light modulation, with which a considerable current (and diffusion length) could be achieved for UV illumination. High-frequency modulations enable us to address the photoresponse with the enhanced signal to noise ratio with fast measurement times. At 100 Hz, the diffusion length reaches ∼50% that of the DC measurement conditions as shown in Fig. 2. The normalized photocurrent is shown in Fig. 3(a) as a function of the distance x0 for the four different values of Ts from 300°C to 500°C. It is clear that the diffusion length noticeably increases at high sintering temperatures.

FIG. 2.

(a) Plot of photocurrent as a function of position x0, with 532 nm laser modulated between frequencies of 10, 20, 50, and 100 Hz. (b) Diffusion length as a function of modulation frequency for both UV (355 nm, black squares) and visible (532 nm, red circles) laser illuminations. Solid lines are fits to the data for ωτ ≫ 1.

FIG. 2.

(a) Plot of photocurrent as a function of position x0, with 532 nm laser modulated between frequencies of 10, 20, 50, and 100 Hz. (b) Diffusion length as a function of modulation frequency for both UV (355 nm, black squares) and visible (532 nm, red circles) laser illuminations. Solid lines are fits to the data for ωτ ≫ 1.

Close modal

A plot of the diffusion length as a function of Ts is shown in Fig. 3(b) for the cells fabricated from the conventional paste with binding molecules (red squares). For each value of Ts, we averaged the diffusion lengths of fifteen samples and then plotted the averages. As expected, the diffusion length increases noticeably from 6 μm at 300°C to 75 μm at 500°C. This is associated with the fact that, generally, the cell efficiency increases with increasing Ts. We also plotted the external quantum efficiency (QE) in Fig. 3(c), which is the light-to-current conversion efficiency, measured when the UV laser illuminated the unetched area of the device. The QE strongly correlates with the diffusion length at the different temperatures even when the diffusion length is much larger the film thickness (∼12 μm). This shows that the diffusion length (and hence the interparticle connectivity) in the NP layer would dominate the light-to-current conversion efficiency and possibly the total cell efficiency, in DSCs. It is also very interesting that the diffusion length reaches its highest value at Ts = 400 °C because it is empirically known that the optimal cell efficiency Ts is above 500°C. Although it has been reported that the binding molecules are supposedly removed completely for Ts > 500°C,30 our results imply that Ts = 400°C could be high enough to remove most of binding molecules in term of the good interparticle connectivity. However, it is likely that the remaining binding molecules at Ts = 400°C would inhibit the adsorption of dye molecules to the TiO2 nanoparticles (or reduce the charge transfer from dyes to the nanoparticles), resulting in reduced cell efficiency when illuminated with visible light.

We also performed similar experiments on NP films formed by homemade, binder-free TiO2 pastes. These pastes are useful for fabricating flexible DSCs without high-temperature processes.27,29 The blue circles in Fig. 3(b) and 3(c) represent the diffusion length and QE as a function of the Ts, respectively. More than fifteen cells have been measured at each temperature. The diffusion length of these NP layers formed from binder-free paste (103 μm for Ts = 450°C) were relatively larger than the lengths of layers with binding molecules. In addition, the diffusion length, which can be as large as 73 μm for Ts = 150°C, does not vary significantly with temperature. Again, we found a strong correlation between the diffusion length and the QE. Finally, QE is plotted as a function of the diffusion length for both sample types in Fig. 3(d). The QE shows an excellent correlation to the diffusion length regardless of the type of paste used in cell fabrication. The total cell efficiency as a function of the diffusion length has been addressed before.31 A clear linear dependence of QE on L suggests that the electron travel length leff of the TiO2 layer is still longer than L (even for L > 100 μm) for the devices we tested. In addition, the large diffusion length together with the resultant large current generation in the binder-free case strongly suggests that the presence of the binding molecules is a primary cause for poor interparticle connectivity in conventional DSCs. This also indicates that the use of binder-free paste could provide an important step forward in the fabrication of DSCs with superior cell efficiency.

To conclude, the diffusion length of NP layers in conventional DSCs with and without dye-sensitization was measured using SPCM with a UV laser source. The diffusion length of 140 μm has been obtained for UV illumination. The dependence of the diffusion length has been investigated, in which we found that the higher diffusion length for UV illumination is due to increased diffusion coefficient, which dominates the reduced lifetime. By measuring the diffusion length as a function of sintering temperature, we determined the optimal conditions of interparticle connectivity in TiO2 layers. In addition, the diffusion length correlates well with the efficiency of the cells sintered at different temperatures even when the diffusion length is larger than film thickness. This confirms that improvement in the diffusion length of the present NP layers will be an important step toward fabricating devices with optimum cell efficiency. These results should lead to studies on the diffusion lengths of NP films with various morphologies, electrolyte solutions, and dyes. Our proposed approach can be applied to various contemporary and future photovoltaic devices and light harvesting systems, to obtain important guidelines for optimizing such devices.

We acknowledge a support of Midcareer Researcher Program (2011-0016173), PRC Program (2009-0094046), and Nano-Material Technology Development Program (2011-0030253) through National Research Foundation grant funded by the Korea Government (MEST).

1.
A.
Hagfeldt
,
G.
Boschloo
,
L.
Sun
,
L.
Kloo
, and
H.
Pettersson
,
Chem. Rev.
110
,
6595
(
2010
).
2.
B.
O’Regan
and
M.
Gratzel
,
Nature
353
,
737
(
1991
).
3.
M.
Grätzel
,
J. Photochem. Photobiol. A: Chem.
164
,
3
(
2004
).
4.
Q.
Wang
,
S.
Ito
,
M.
Grätzel
,
F.
Fabregat-Santiago
,
I.
Mora-Seró
,
J.
Bisquert
,
T.
Bessho
, and
H.
Imai
,
J. Phys. Chem. B
110
,
25210
(
2006
).
5.
B.
Tan
and
Y.
Wu
,
J. Phys. Chem. B
110
,
15932
(
2006
).
6.
H.-S.
Kim
,
C.-R.
Lee
,
J.-H.
Im
,
K.-B.
Lee
,
T.
Moehl
,
A.
Marchioro
,
S.-J.
Moon
,
R.
Humphry-Baker
,
J.-H.
Yum
,
J. E.
Moser
,
M.
Gratzel
, and
N.-G.
Park
,
Sci. Rep.
2
(
2012
).
7.
J.
Burschka
,
N.
Pellet
,
S.-J.
Moon
,
R.
Humphry-Baker
,
P.
Gao
,
M. K.
Nazeeruddin
, and
M.
Gratzel
,
Nature
499
,
316
(
2013
).
8.
X.
Chen
,
S.
Shen
,
L.
Guo
, and
S. S.
Mao
,
Chem. Rev.
110
,
6503
(
2010
).
9.
I.
McConnell
,
G.
Li
, and
G. W.
Brudvig
,
Chem. Biol.
17
,
434
(
2010
).
10.
S.
Nakade
,
Y.
Saito
,
W.
Kubo
,
T.
Kitamura
,
Y.
Wada
, and
S.
Yanagida
,
J. Phys. Chem. B
107
,
8607
(
2003
).
11.
J.-K.
Park
,
J.-C.
Kang
,
S. Y.
Kim
,
B. H.
Son
,
J.-Y.
Park
,
S.
Lee
, and
Y. H.
Ahn
,
J. Phys. Chem. Lett.
3
,
3632
(
2012
).
12.
P. R. F.
Barnes
,
A. Y.
Anderson
,
S. E.
Koops
,
J. R.
Durrant
, and
B. C.
O’Regan
,
J. Phys. Chem. C
113
,
1126
(
2009
).
13.
P. R. F.
Barnes
,
L.
Liu
,
X.
Li
,
A. Y.
Anderson
,
H.
Kisserwan
,
T. H.
Ghaddar
,
J. R.
Durrant
, and
B. C.
O’Regan
,
Nano Lett.
9
,
3532
(
2009
).
14.
J.
Bisquert
and
I.
Mora-Seró
,
J. Phys. Chem. Lett.
1
,
450
(
2010
).
15.
J.
Bisquert
and
V. S.
Vikhrenko
,
J. Phys. Chem. B
108
,
2313
(
2004
).
16.
J. R.
Jennings
,
F.
Li
, and
Q.
Wang
,
J. Phys. Chem. C
114
,
14665
(
2010
).
17.
L.
Peter
,
J. Phys. Chem. C
111
,
6601
(
2007
).
18.
J.
Navas
,
E.
Guillén
,
R.
Alcántara
,
C.
Fernández-Lorenzo
,
J.
Martín-Calleja
,
G.
Oskam
,
J.
Idígoras
,
T.
Berger
, and
J. A.
Anta
,
J. Phys. Chem. Lett.
2
,
1045
(
2011
).
19.
Y. S.
Shin
,
D.
Lee
,
H. S.
Lee
,
Y. J.
Cho
,
C. J.
Kim
, and
M. H.
Jo
,
Opt. Express.
(
2011
).
20.
Y.
Yang
,
J.
Li
,
H.
Wu
,
E.
Oh
, and
D.
Yu
,
Nano Lett.
12
,
5890
(
2012
).
21.
A. J.
Das
,
R.
Shivanna
, and
K.
Narayan
,
Nanophotonics
,
1
(
2013
).
22.
W. H.
Leng
,
P. R. F.
Barnes
,
M.
Juozapavicius
,
B. C.
O’Regan
, and
J. R.
Durrant
,
J. Phys. Chem. Lett.
1
,
967
(
2010
).
23.
A. C.
Fisher
,
L. M.
Peter
,
E. A.
Ponomarev
,
A. B.
Walker
, and
K. G. U.
Wijayantha
,
J. Phys. Chem. B
104
,
949
(
2000
).
24.
L. M.
Peter
and
K. G. U.
Wijayantha
,
Electrochem. Commun.
1
,
576
(
1999
).
25.
J. N.
Hollenhorst
and
G.
Hasnain
,
Appl. Phys. Lett.
67
,
2203
(
1995
).
26.
F. N.
Gonzalez
and
A.
Neugroschel
,
IEEE Trans. Electron Devices
31
,
413
(
1984
).
27.
L.-Y.
Lin
,
C.-P.
Lee
,
K.-W.
Tsai
,
M.-H.
Yeh
,
C.-Y.
Chen
,
R.
Vittal
,
C.-G.
Wu
, and
K.-C.
Ho
,
Prog. Photovoltaics: Res. Appl.
20
,
181
(
2012
).
28.
C.-R.
Lee
,
H.-S.
Kim
, and
N.-G.
Park
,
Front. Optoelectron. China
4
,
59
(
2011
).
29.
T.
Miyasaka
,
M.
Ikegami
, and
Y.
Kijitori
,
J. Electrochem. Soc.
154
,
A455
(
2007
).
30.
H. C.
Weerasinghe
,
P. M.
Sirimanne
,
G. V.
Franks
,
G. P.
Simon
, and
Y. B.
Cheng
,
J. Photochem. Photobiol. A: Chem.
213
,
30
(
2010
).
31.
J.
Halme
,
G.
Boschloo
,
A.
Hagfeldt
, and
P.
Lund
,
J. Phys. Chem. C
112
,
5623
(
2008
).