LETTER pubs.acs.org/JPCL
Impact of High Charge-Collection Efficiencies and Dark Energy-Loss Processes on Transport, Recombination, and Photovoltaic Properties of Dye-Sensitized Solar Cells Kai Zhu,* Song-Rim Jang, and Arthur J. Frank* Chemical and Materials Science Center, National Renewable Energy Laboratory, Golden, Colorado 80401, United States
bS Supporting Information ABSTRACT: We report on the relationships between the energy-loss processes in the dark, charge-collection efficiency and photocurrent densityvoltage characteristics of dye-sensitized solar cells (DSSCs). The charge-collection efficiencies (ηcc) of the DSSCs with different electrolytes were close to 100%. Despite the high ηcc values, the DSSCs showed significant loss of photocurrent density and power density resulting from dark processes associated with the exchange current density J0 at the TiO2/electrolyte interface, series resistance of the cells, and diode ideality factor. Even in DSSCs with high ηcc values, making recombination slower and transport faster in the dark would reduce these losses. The opposing effects of J0 and light absorption properties of DSSCs were found to determine the optimum film thickness (Lopt) for the highest output power density. These effects also explain why Lopt is generally much less than the electron diffusion length. SECTION: Energy Conversion and Storage
D
ye-sensitized solar cells (DSSCs; also known as Gr€atzel cells) have received attention as a potential, cost-effective alternative to silicon solar cells.1 Sunlight-to-electrical conversion efficiencies of over 11% at full sunlight (AM1.5 solar irradiance) have been reported for such cells.2,3 Much effort has been expended to develop more effective cell materials and structures, such as light absorbers,48 hole-conducting media,911 and electron-conducting film architectures,1220 for improved cell performance and reliability. The effects of variations in cell components on charge collection have been studied using a number of characterization techniques along with modeling.2125 Charge-collection efficiency (ηcc) is a measure of the percent of photoinjected electrons that reach the electron collector without recombining with either the oxidized dye or oxidized component in the redox electrolyte. The charge-collection efficiency is distinct from the charge-extraction efficiency. Charge extraction refers to the process of extracting photocarriers to the external circuit. It is possible that some photocarriers that reach the collector are not extracted to the external circuit. A related measure of ηcc is the electron diffusion length Ln (Ln = (Dτr)1/2, where D and τr are the respective electron diffusion coefficient and recombination time constant or, equivalently, the electron lifetime). The electron diffusion length describes the statistical average distance that electrons travel in the electron-conducting network before recombining with redox species in the electrolyte. High charge-collection efficiencies require that Ln be much greater than the film thickness used in the DSSCs. For well-engineered DSSCs, ηcc at short circuit is essentially 100% because recombination at short circuit is negligible.26,27 However, the relationship of the charge-collection efficiency to r 2011 American Chemical Society
the photocurrent density and the output power density from DSSCs at various points along the photocurrent densityvoltage (JV) curve, especially at voltages approaching open circuit, is not well understood. For example, measurements of incident photonto-current conversion efficiency (IPCE) and JV characteristics suggest that at the maximum power point about 80% of photoinjected electrons reach the external circuit, whereas at open circuit, only about 3045% of photoelectrons reach it.25,28 This observation appears to be at odds with recent studies showing21,22 that the electron diffusion length increases with increased bias voltage, implying that more charges should be extracted at higher bias. These apparently contradictory results suggest that the electron diffusion length may not be a sufficient measure of the charge delivered to the external circuit. In this Letter, we describe the effects of the energy-loss processes in the dark and the charge-collection efficiency in determining the JV characteristics of DSSCs. The electron transport and recombination kinetics and JV characteristics were investigated by intensity modulated photocurrent/photovoltage spectroscopies (IMPS/IMVS), electrochemical impedance spectroscopy (EIS), and theory. The photocurrent density measured in the external circuit is taken as representative of the collected charge extracted from the DSSCs. Both light- and dark-related factors were found to influence the photocurrent density and output power density extracted from the cells. None of the measurement techniques Received: March 3, 2011 Accepted: April 11, 2011 Published: April 18, 2011 1070
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Table 1. Effect of Electrolyte Composition on the Diode Ideality Factor, Exchange Current Density, and Fill Factor diode ideality
exchange current density
fill factor
electrolyte
factor m
J0 (A/cm2)
FFd
Aa
1.42
8.2 1012
0.81
b
1.53
4.1 1011
0.79
Cc
1.90
1.3 109
0.67
B a
Figure 1. JV characteristics of a DSSC. (1) JF represents the current density at forward applied bias in the dark (denoted by the black JFV curve). (2) Jnet represents the current density at applied biases when the cell is illuminated with 680 nm laser light (denoted by the red JnetV curve). (3) JFJsc corresponds to JF after being shifted downward by Jsc (denoted by the (JF Jsc)V blue curve; eq 3). The shaded area between the JnetV and (JF Jsc)V curves represents the power density loss, and the vertical lines between the curves represent the photocurrent density loss at specific voltages. The data are for a DSSC containing electrolyte A (Table 1).
could provide a direct, reliable measure of the transport time constant at applied voltages approaching open circuit. Nevertheless, analyses of the data suggest that the charge-collection efficiencies of the cells were close to 100% over the voltage range investigated, irrespective of the different electrolytes that were used. Despite the high ηcc values, the DSSCs displayed substantial loss of photocurrent density and output power density resulting from dark processes associated with the exchange current density J0, series resistance of the cell, and the diode ideality factor. The rate of recombination in the dark at the TiO2/redox electrolyte interface is a major factor in determining J0. Although counterintuitive, this study suggests that making recombination slower and/or transport faster in the dark is one way to increase the photocurrent density and output power density from the maximum power point to open circuit, even in DSSCs with charge-collection efficiencies approaching 100%. The knowledge gained from this work will be valuable in devising approaches to improve the performance of sensitized solar cells and other optoelectronic devices. This study provides insight into the energy-loss mechanisms and describes ways to investigate them. Details about sample preparation and experimental methods are available in the Supporting Information. The photocurrent density and output power density can be evaluated by studying the JV characteristics of DSSCs. The net current density Jnet(V) that flows through the external circuit of a DSSC under illumination can be described by the superposition of the dark current density at forward applied bias JF and the light-generated photocurrent density JL. In the case of JF, electrons flow from the transparent conducting oxide (TCO) substrate into the TiO2 film, whereas for JL, photogenerated electrons flow in the opposite direction, from the TiO2 film to the TCO substrate. Figure S5 (Supporting Information) depicts the opposing current flow pictorially. The net current density is given by the expression Jnet ðV Þ ¼ JF ðV Þ JL ðV Þ
ð1Þ
Quite commonly, Jnet is treated as the photocurrent density JL. However, Jnet includes contributions from not only JL but also from
1.0 M 1-propyl-3-methylimidazolium iodide, 0.05 M LiI, 0.03 M I2, 0.5 M tBP (4-tert-butylpyridine), and 0.1 M GNCS (guanidinium thiocyanate) in a mixture of acetonitrile/valeronitrile (85:15, v/v). b 0.6 M 1-butyl-3-methylimidazolium iodide, 0.1 M LiI, 0.05 M I2, 0.5 M tBP, and 0.1 M GNCS in a mixture of acetonitle/valeronitrile (85:15, v/v). c 0.8 M 1-hexyl-2,3-dimethylimidazolium iodide and 0.05 M I2 in methoxypropionitrile. d FF values have been corrected for ohmic losses.
the dark current density (JF). The current density at forward bias JF includes the transfer of electrons across the nanocrystalline TiO2/ electrolyte interface to oxidized redox species in solution that transport electrons to the counter electrode.25 The dependence of charge-transfer current on the applied voltage can be approximated by a simplified ButlerVolmer equation29,30 JF ðV Þ ¼ J0 ½expðqV=mkTÞ 1
ð2Þ
where q is the elementary charge, V is the applied voltage, k is the Boltzmann constant, T is the temperature, m is the diode ideality factor, and J0 is the exchange current density in the dark. The value of m depends on the electron-transfer coefficient, the order of the rate of the recombination reaction of electrons and oxidized species in the electrolyte, and the distribution of recombination sites.30 The value of J0 is related to the rate constant of the recombination reaction, the film thickness, the order of reactions of electrons and oxidized redox species, and the concentrations of background electrons in the TiO2 and oxidized redox species in the electrolyte.29,30 The simplified ButlerVolmer equation (eq 2) is essentially the same as the diode equation describing the dark JV characteristics.30 The maximum photocurrent density obtained from a cell occurs when the photocurrent density equals the electron-injection current Jinj, which is determined by the incident photon flux, the light absorption property of the sensitized film, and the charge-injection efficiency at the TiO2/dye interface. The short-circuit photocurrent density Jsc is generally a good measure of Jinj.26,27 The maximum solar conversion efficiency occurs when the photocurrent density JL is independent of applied voltage and is equal to the short-circuit photocurrent density (i.e., JL(V) = Jsc). In this case, the ideal net current density Jideal net is simply equal to JF after being shifted downward by Jsc ideal Jnet ðV Þ ¼ JF ðV Þ Jsc
ð3Þ
In practice, the actual (observed) net current density Jnet usually deviates from the ideal case (eq 3). The difference between Jideal net and Jnet represents the loss of photocurrent density (i.e., Δloss = Jnet Jideal net ) and, consequently, the loss of solar conversion efficiency. Figure 1 compares the JV characteristics of a DSSC with the N719 dye (N719 = Ru(2,20 -bipyridyl-4,40 -dicarboxylic acid)2(NCS)2/2 tetrabutylammonium) and electrolyte A (Table 1) in the dark and under a 680 nm laser illumination. The black JFV curve in Figure 1 shows the dark current density JF at forward applied bias. The red JnetV curve shows the current density Jnet when the cell is illuminated with laser light at 680 nm. The 1071
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Figure 2. Comparison of (a) transport and recombination time constants for a DSSC as a function of applied voltage (or quasi-Fermi energy) determined from IMPS and IMVS measurements at short circuit and open circuit, respectively, and (b) transport and recombination (charge-transfer) resistances determined from EIS measurements conducted at open circuit under 680 nm laser illumination.
680 nm light is only weakly absorbed by the dye and therefore provides a relatively uniform (constant) generation of photocarriers throughout the 10 μm thick film. From the JnetV curve, it can be seen that Jsc is 9.65 mA/cm2, the open-circuit voltage (Voc) is 0.75 V, the maximum power point occurs at 0.61 V, and the fill factor (FF) is 0.75. The shaded area between the JnetV and (JF Jsc)V curves represents the difference between the actual and ideal JV characteristics of the DSSC. The photocurrent density loss of the DSSC is only about 5% at the maximum power point (0.61 V) but increases significantly to 65% at Voc (0.75 V). Thus, for the ideal case (eq 3), in which there is an absence of loss processes, the total current density at Voc equals 0 mA/cm2, whereas the photocurrent density at Voc equals Jsc. The total power density loss determined by integrating the area between the JnetV and (JF Jsc)V curves is about 12%. When electrolyte C (Table 1) is used for the DSSC, the loss in total power density increases to about 40% (Figure S7 in the Supporting Information). Therefore, what are the principal factors leading to a loss of photocurrent density and power density in the DSSCs? The charge-collection process in DSSCs is determined by the competition between the charge-transport and recombination kinetics. The charge-transport time constant (τt1) is related to the charge-collection time constant (τc1) and to the recombination time constant (τr1) by the relation24,25 τt 1 ¼ τc 1 þ τr 1
ð4Þ
The charge-collection efficiency (ηcc) is determined by the ratio of the time constants for transport and recombination as expressed by24,25 τt ηcc ¼ τc 1 =τt 1 ¼ 1 ð5Þ τr Figure 2a shows the dependence of the transport and recombination times on the applied voltage (or quasi-Fermi energy) determined by IMPS and IMVS measurements at short circuit and open circuit, respectively. For the transport measurements, the quasi-Fermi levels at short circuit were adjusted to correct for the difference in the photoelectron density between the short circuit and open circuit at constant light intensity.31 Before making this correction, the quasi-Fermi level at short circuit was about 180 mV below that at open circuit as determined by charge-extraction measurements (Figure S2 in the Supporting Information). At a fixed voltage (e.g., 0.55 V), the ratio of τr/τt is
about 200, which corresponds to a ηcc of greater than 99% (eq 5) and a Ln of 140 μm (Ln = d(τr/τt)1/2, where d is the TiO2 film thickness). For such large values of the charge-collection efficiency and electron diffusion length, it is reasonable to assume that the photoinduced charge-collection process does not limit the photocurrent density. It is worth noting that there is no direct measurement of the transport times using IMPS at voltages ranging from about the maximum power point (0.61 V) to Voc (0.75 V) (Figure 2). The quasi-Fermi level (or photoelectron density) at open circuit is obtained by extrapolating the transport time constant data (Figure 2); the extrapolation yields a transport time constant of about 0.1 ms at Voc (0.75 V). To establish a Fermi level at short circuit equal to that at open circuit at about 1 sun light intensity would require that IMPS use an extremely high bias light intensity, up to 100 suns at short circuit, which would likely degrade the dye. Figure 2b shows the dependence of the transport resistance (Rt) and recombination (charge-transfer) resistance (Rct) on applied voltage determined by EIS measurements. Rt represents the transport resistance of electrons in the TiO2 film, and Rct is the resistance associated with electron transfer across the TiO2/ redox electrolyte interface; Rct is equivalent to the recombination resistance. From analyses of the impedance spectrum (Figure S3 in the Supporting Information) obtained under illumination at open circuit,32 one can determine the resistances for electron transport in the TiO2 film, recombination at the TiO2/redox electrolyte interface, and charge transfer across the TCO/Pt/ electrolyte and TCO/TiO2/electrolyte interfaces.33 At a fixed voltage (e.g., 0.55 V), the ratio of Rct/Rt (which is equivalent to the ratio of τr/τt) is about 60, which corresponds to a ηcc of greater than 98% (eq 5) and a Ln of 77 μm (Ln = d(Rct/Rt)1/2. At voltages greater than 0.62 V (close to the maximum power point), the values of Rt become independent of applied voltage. This observation agrees with that of others32 and indicates that the EIS fitting is unreliable in this voltage range. From an analysis of the dependence of Rct on the applied bias V using the expression25 Rct µ exp(qV/mkT), the diode ideality factor m (eq 2) can be determined. The best fit of the log(Rct) versus V data to the expression for Rct yields a diode ideality factor of 1.36, signifying that the cell behaves as a nonideal photodiode and that recombination occurs via traps at the TiO2 surface.25,29,34 Although the IMPS/IMVS and EIS measurements yield different values for ηcc and Ln, both measurements are consistent with cells having high charge-collection efficiencies or long electron 1072
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Figure 3. Dependence of dV/dI on 1/(I þ Isc) for the same DSSC used in obtaining the JV data in Figure 1 for voltages ranging from about 0.60 to 0.75 V; I denotes current.
diffusion lengths over the observed voltage range. The large values of ηcc and Ln suggest that the charge-collection process is not the major cause of the photocurrent density loss and that other factors are involved. The resistance losses associated with ohmic (IR) drop across the cell likely affect the observed photocurrent in the currentvoltage plots. If only the resistance losses relating to current are considered, the expression for the net current (Inet) of a DSSC is ( " # ) qðV Inet Rstotal Þ Inet ðV Þ ¼ I0 exp 1 Isc ð6Þ mkT where I0 is the dark exchange current, Isc is the short-circuit is the total photocurrent, Inet is the net photocurrent, and Rtotal s series resistance of a cell. The current Ix = AJx (x denotes net, short circuit (sc), or 0), where A equals the projected area of a sample. From eq 6, one obtains dV mkT 1 ¼ Rstotal þ dInet q 3 Inet þ Isc þ I0
ð7Þ
The dark exchange current I0 is normally orders of magnitude smaller than the sum of Inet and Isc and therefore can be neglected in eq 7. Figure 3 shows the dependence of dV/dI on 1/(I þ Isc) for the same DSSC as that used for the JV data in Figure 1 for voltages ranging from about the maximum power point (0.60 V) to the open circuit (0.75 V). From the best fit of the data to eq 7, we = 25 determined that the total series resistance of the cell is Rtotal s Ω and that the diode ideality factor is m = 1.38. It is noteworthy that the shunt resistance for the DSSCs in this study is ignored because of the presence of a compact blocking layer35 between the TCO substrate and TiO2 nanoparticle film. The diode ideality factor m was also determined from the relationship of the open-circuit voltage to the short-circuit current density with the expression Jsc µ exp(qVoc/mkT). From the best fit of the Voc versus log(Jsc) data (Figure S4 in the Supporting Information), we determined a diode ideality factor of m = 1.44, which is in agreement with the value (m = 1.38) obtained from the analysis of the JV data (Figure 3; eq 7). The similar values of m (m: 1.36, 1.38, and 1.44) obtained by three different methods are consistent with the diode ideality factor being mainly determined
Figure 4. JV characteristics of a DSSC containing electrolyte A (Table 1) (1) in the dark (black circles), (2) under 680 nm laser illumination (red circles), and (3) in the dark current after being shifted downward by Jsc (blue circles). (4) The calculated current (green dashes) illustrates the effect of 10 J0 on the JV characteristics depicted by the blue curve. The JV curves are corrected for ohmic losses. Lines are the fitted or calculated JV curves based on eq 8 (see text for details).
by the recombination reaction at the TiO2/redox electrolyte interface. = 25 Ω) of the cell (eq 7; The total series resistance (Rtotal s Figure 3) represents the contributions from all of the resistances in series with the diode (i.e., in series with the recombination ), resistance Rct) including the sheet resistance of TCOs (RTCO s charge-transfer resistances (Rp1) across the TCO/Pt/redox electrolyte, charge-transfer resistances (Rp2) across the TCO/ TiO2/redox electrolyte interfaces, electron-transport resistance (Rt/3, which was derived from the transmission line model33) in the TiO2 film, and the resistance (Rion s ) associated with ion diffusion in the bulk electrolyte (see the equivalent circuit model in Figure S3 in the Supporting Information). From the best fits of the EIS spectra (Figure S3 in the Supporting Information) to the transmission line model,33 one can show that for voltages ranging from about the maximum power point (0.60 V) to Voc (0.75 V), is 1011 Ω, (2) the sum of (1) the sheet resistance RTCO s interfacial charge-transfer resistance at TCO contacts (Rp1 þ Rp2) is 48 Ω, and (3) the transport resistance (Rt/3) is
