Charge transport in dye-sensitized solar cell

The effect of charge transport on the photovoltaic properties of dye-sensitized solar cells (DSCs) was investigated by the experimental results and the ion transport. The short current photocurrent density (Jsc) is determined by the electron transport in porous TiO2 when the diffusion limited current (Jdif) due to the I 3 − ?> transport is larger than the photo-generated electron flux (Jg) estimated from the light harvesting efficiency of dye-sensitized porous TiO2 and the solar spectrum. However, the Jsc value is determined by the ion transport in the electrolyte solution at Jdif < Jg. The J value becomes constant against light intensity, and is expressed as the saturated current ( J sc s ?> ). The J s ?> value depends on the thickness (d) of the TiO2 layer, the initial concentration ( C OX 0 ?> ), and the diffusion coefficient ( D OX b ?> ) of I 3 − ?> . These suitable parameters were determined by using the ion transport.


Introduction
Dye-sensitized solar cells (DSCs) have received much attention because of their high energy-conversion efficiency (η = 12%) and low cost of production [1][2][3]. A DSC as shown in figure 1 is composed of a dye adsorbed porous TiO 2 film on transparent conductive oxide (TCO) glass, an electrolyte solution containing an I − / − I 3 redox couple, and a counter electrode (CE). After light absorption of a dye, the electron is injected from the excited state of the dye to the conduction band of TiO 2 . The oxidized dye is reduced by iodide ions (I − ) in the electrolyte solution. The ions such as I − and − I 3 transport through the porous TiO 2 and bulk phase of the electrolyte solution. The oxidized I − ( − I 3 ) is reduced to I − on the surface of the CE. The injected electron also diffuses through the porous TiO 2 and reaches to the TCO glass.
The leakage of the electrolyte solution is the main problem for the application of DSCs because the electrolyte solution is liquid. Many approaches for long time stability have been carried out by introduction of polymers, TiO 2 particle, and non-volatile solvents [3][4][5][6][7][8][9][10][11][12]. Ionic liquids have been also utilized as the electrolyte in DSCs for improvement of the durability because of the properties of high thermal stability, very low vapor pressure and non-flammability [5][6][7][8][9]. However, the photovoltaic performance of DSCs based on these stabilization techniques of the electrolytes is lower than that based on the normal volatile electrolyte. Especially, the photocurrent density of DSCs based on ionic liquid is lower than that based on volatile solution. The photocurrent is dominated not only by the charge injection from a dye to TiO 2 , but also by the charge transports of electrons, I − and − I 3 . The ion transport rate in ionic liquid is generally slower than that of volatile solution. The lower photocurrent must be due to the slower ion transport. Therefore, the charge transports need to be discussed to explain the mechanism of J sc and to find the suitable condition.

Experimental
1-propyl-3-methylimidazolium iodide (MPImI) was used as ionic liquid electrolytes. All electrolytes were prepared by dissolving 0.6 M 1,2-dimethyl-3-propylimidazolium iodide (DMPImI), 0.03-0.26 M I 2 , 0.05 M LiI, and 0.3 M 4-tertbutylpyridine (TBP). The viscosity of the electrolytes was measured by Viscotech Co., Ltd A carbazole dye with hexylsubstituted oligothiophene, MK-2 (Soken Chemical & Engineering Co., Ltd, Tokyo, Japan) [13] was used as a | Vietnam Academy of Science and Technology Advances in Natural Sciences: Nanoscience and Nanotechnology Adv. Nat. Sci.: Nanosci. Nanotechnol. 6 (2015) [14]. The light intensity from 650 nm laser was controlled by applied bias to measure time course of photocurrent density. The diffusion coefficient (D OX b ) of − I 3 in the electrolyte of MPImI was measured to be 3.5 × 10 −7 cm 2 s −1 by using the reference method [15]. The electrolyte is sandwiched by the Pt counter electrode. The diffusion coefficient is estimated from the saturated current of I-V measurement. The diffusion coefficient (D OX ) in porous TiO 2 is also measured by the using the porous TiO 2 sandwiched by the Pt vapor deposition.   figure 3(a). The degree of the current decay was enhanced with increase of the light intensity. The current decreases in 5 s over 2.7 mW cm −2 of the light intensity. On the other hand, the current becomes constant against time below 2.7 mW cm −2 of the light intensity. The current decay is strongly related to the J-V curve in figure 2. During the sweep of voltage, the current decrease with time. Therefore, the strange J-V curve is observed. Time-course of current of DSCs at 25.9 mW cm −2 of 650 nm laser with various concentrations of − I 3 is also shown in figure 3(b). The decay of current against time is also observed. The current becomes constant against time with increase of the concentration of − I . 3 The results are in good agreement with the relationship between the I-V curve and the concentration. These I-V curves became normal shape with increase of the concentration of − I 3 because current does not depend on the time. In the measurement of figure 3(a), the orange color of − I 3 around counter electrode disappeared after each measurement over 2.7 mW cm −2 . The phenomenon means that the concentration of − I 3 becomes 0. The concentration of I − is 0.65 M and is larger than that of − I 3 . Therefore, the ion transport Ican be neglected. The concentration of − I 3 around counter electrode decreases with increase of light intensity. The lack of the − I 3 around counter electrode induces the decay of current against time. The ion transport of − I 3 from TiO 2 to the counter electrode influences on the time course of photocurrent when the concentration is 0 around the counter electrode. On the other hand, the lack of − I 3 can be suppressed by the high initial concentration of − I 3 as shown in figure 3(b). The ion transport limited current is  The relationship between current density at short circuit and light intensity is shown in figure 4. The J sc linearly increases with increase of the light intensity at high concentration of − I 3 . The J sc is constant against time. The J sc at 0 s is also linearly related to the light intensity. However, the J sc at 30 s is saturated over a light intensity at lower concentration. The current decays against time at lower concentration. The light intensity in photon flux corresponds to the amount of photons per time. The slow ion transport rate cannot cover the incident speed of photons. The saturated J sc as shown figure 4 corresponds to the value at 30 s from 9.8 mW cm −2 to 25.9 in figure 3(a). The consistency shows the saturated J sc is due to the ion transport in these DSCs. . The reaction rate at counter electrode also influences J dif . However, the rate can be neglected because it is faster than ion transports. The thicknesses of spacer for DSCs and the TiO 2 film are defined as T and d, respectively.

Results and discussion
In the case of J dif > J g , the current in DSCs is explained by the diffusion equation of the electrons in TiO 2 as the following equation [16][17][18][19][20] The current of DSCs is dominated by J g . The fast ion transports can compensate the ions for electron transfer at the interface. The J sc is generally linear related to the light intensity below 1 sun. The response of the J sc depends on the electron transport. In the case of J g > J dif , the surface concentration of I − and I 3 − at interface becomes 0 because the ion transport cannot compensate the ions for electron transfer at the interface. The current depends on the ion transports. The distribution of ions in DSCs has to be considered. Papageorgiou et al [6,7] had investigated the relationship between the charge (electron, I − and I 3 − ) transport in the electrolyte and the photovoltaic performance by the ion transport model. The ion transport model [6,7,9] was modified by the followings to explain J sc s against physical parameters in DSCs and determined the suitable physical parameters for favorable ion transport in ionic liquid.   In porous TiO 2 ( ≦ ≦ x d 0 ), the concentration of − I 3 (C OX ) can be expressed by x OX OX 2 OX 2 0 where x is distance from TCO, t is time, ρ is porosity of porous TiO 2 I 0 is the incident photon flux corrected for reflection loss, ϕ is the electron transfer and transport yield, and α is the absorption coefficient. In the bulk electrolyte solution layer of DSCs ( ≦ ≦ d x T), the concentration (C OX ) of − I 3 can be expressed by The flux (J flux ) of ion transport can be expressed by the followings. The flux (J flux The concentration gradient of C OX at TCO equals 0 as the boundary condition at x = 0 x 0 I assumed that two boundary condition can be fixed at x = d. Because the electrolyte solution is continuous at x = d, the C OX value calculated from equation (2) must equal to that from equation (3) OX OX The flux of equation (4) must be same as that of equation (5) at The total amount of − I 3 has to be conserved in DSCs In steady state, the left side of equations (2) and (3) equals 0. The distribution of C OX can be solved from equations (2)- (9). The C OX is expressed as follows When C OX 0 is defined as the initial concentration of − I 3 , C OX (0) can be expressed by the following equation The concentration distribution (C OX (0)) from TCO to the counter electrode at various light intensity is shown in figure 5(a). The T is 30 μm, d is 13 μm, ϕ is 0.65, C OX 0 is 0.03 M, D OX b is 3.5 × 10 −7 cm 2 s −1 , β is 5, α at 650 nm is 1200 cm −2 , respectively. As the light intensity increases, the C OX (0) increases and C OX (T) decreases.
In the case of J dif > J g , the photocurrent density of DSCs can be expressed as ion flux at x = T where n is electrons per this reaction and F is Faraday constant, respectively. The linear relationship between photocurrent and light intensity can be explained by equation (13).
C OX (T) becomes minus at light intensity of 3.1 mW cm −2 as shown in figure 5(a). In a real device, C OX (T) of equation (11) has to be 0 or over as described as (v). The model needs to be modified to explain the ion transport limitation. When C OX (T) is calculated to be under 0, the C OX (T) must keep being 0, and equation (8) is neglected. This assumption means that (dC OX /dx) x=T becomes constant against I 0 . J SC is dominated by the diffusion of − I 3 and becomes constant against I 0 defined as diffusion limited current (J SC s ). The constant J SC s is due to (dC OX /dx) x=T of equation (13). The relationship between the calculated J sc and the light intensity (I 0 ) is shown in figure 5(b). The calculated J sc s from figure 5(b) was 1.3 mA cm −2 , corresponding to the experimental results in figures 3(a) and 4.

Saturated photocurrent versus diffusion coefficient of I3−
or initial concentration. J sc s has to be over 30 mA cm −2 which is calculated from the external quantum efficiency (EQE) of 95% from 400 nm to 900 nm in solar light. Otherwise, the solar to energy conversion efficiency of DSCs is limited by the ion transport. The diffusion limited current density (J dif ) can be generally expressed by the following formula [15] dif J dif depends on the diffusion coefficient of ions (D), carrier density (C), and the distance (d) of the ion transport, which respectively corresponds to the diffusion coefficient (D OX b ) of − I 3 , the C OX 0 value of − I 3 , and the d value of the TiO 2 film. Therefore, each parameter needs to be discussed to improve J sc s .
The relationship between the calculated J sc s and D OX b or C OX 0 is shown in figure 6.  The relationship between calculated J sc and the light intensity at the same condition of (a). The black circle is due to this model. The J sc is constant when C OX (T) becomes 0. The white circle is the value calculated from equation (13) when C OX (T) < 0 is permitted in this model.  figure 7(b) is due to J dif of the porous TiO 2 layer and is calculated from equation (14) at C =C OX 0 , d = 13 μm, and D = D OX = 7 × 10 −8 cm 2 s −1 , respectively. The dashed line is due to J dif of the bulk electrolyte and is calculated from equation (14) at C =C OX 0 , d = 17 μm, and D = D OX b = 3.5 × 10 −7 cm 2 s −1 , respectively. The slope of J sc s versus C OX 0 is also similar to that of J dif versus C OX 0 of the porous TiO 2 layer. The results show that the ion transports in the porous TiO 2 layer influence the total ion transport in DSCs.
The β is defined as D D OX b OX . The D OX is usually smaller than D OX b (β > 1). The mechanism of β > 1 is under investigation. The β value seems to depend on the viscosity. The ions can move more randomly when the viscosity is low. Ions easily collide with the surface of porous structure. Therefore, the diffusion rate of ions slows down in porous TiO 2 . On the other hand, the β value seems to decrease with increase of viscosity of the electrolyte. In the case of high viscosity, ions cannot quickly move in the electrolyte solution. The probability of the collision between ions and the surface of porous structure must become smaller.
The relationship between the calculated J sc s and thickness (d) of TiO 2 is shown in figure 8. The results can be explained by using equation (14). The ion can be easily supplied with decrease of the distance. J sc s is exponentially influenced by the d value. The thin TiO 2 films are favorable for the ion transport, especially in the case of small D OX b . However, the light harvesting efficiency of dye on TiO 2 decreases with decrease of d. The high light absorption ability of dyes needs to be designed for DSCs based on ionic liquid. In the case of C OX 0 = 0.05 M, D OX b needs to be 5 × 10 −5 cm 2 s −1 , corresponding to the condition of figure 6(a).

Conclusion
The effect of − I 3 transport in the liquid electrolyte on the photovoltaic properties of dye-sensitized solar cells (DSCs) was investigated by the ion transport model and experimental results. The J sc becomes constant against light intensity when the concentration (C OX (T)) of − I 3 at the counter electrode becomes 0. The saturated J sc is named as the saturated current (J sc s ) and depends on the ion transport in the electrolyte solution of DSCs. The J sc s value has to be over 30 mA cm −2 which is calculated from EQE of 95% from 400 nm to 900 nm in solar light. The