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Theoretical Demonstration of Efficiency Enhancement of Dye-Sensitized Solar Cells with Double-Inverse Opal as Mirrors Cheng-an Tao, Wei Zhu, Qi An, and Guangtao Li* Key Lab of Organic Optoelectronic and Molecular Engineering, Department of Chemistry, Tsinghua UniVersity, Beijing 100084, People’s Republic of China ReceiVed: March 12, 2010; ReVised Manuscript ReceiVed: May 09, 2010
Herein we describe the employment of double-inverse opal (DIO) as a novel optical element and present a theoretical analysis of the efficiency enhancement of the designed DSSCs. We find that, compared to inverse opal (IO) as the optical element, the presence of small spheres in IO (i.e., DIO structure) produces a great light-scattering effect and broader reflection region, leading to considerable enhancement of the photocurrent efficiency of cells. Dye-sensitized solar cells (DSSCs) with one DIO layer as a mirror has a photocurrent efficiency enhancement up to 47%, which is a large improvement compared to that of the IO-coupled one (28%). More remarkably, double DIO layers as a scattering layer lead to efficient enhancement of the absorptances of DSSCs in the whole visible spectrum range (400-800 nm) and a distinct increment of about 80% of photocurrent efficiency with respect to standard ones. In this work, the optimum structural parameters of such DIO optical elements needed to achieve an efficient photocurrent efficiency enhancement are provided. Introduction Since originally reported in 1991 by Gra¨tzel and co-workers,1 dye-sensitized solar cells (DSSCs) have attracted increasing attention2-13 as inexpensive and relatively efficient promising alternatives to expensive silicon solar cells. In the most common and most efficient devices to date, DSSCs are composed of a photoanode, typically a 5-10 µm thick film of nanocrystalline titania (nc-TiO2) sensitized with a ruthenium dye such as N719, a platinum counter electrode, and the redox active electrolyte (I-/I3-), which permeates into the nanocrystalline mesoporous TiO2, giving the device a sandwich configuration.14 DSSCs have achieved record light-to-electric power conversion efficiencies of around 11%.15,16 Nevertheless, still much lower efficiency than the silicon counterpart is a major obstacle for the practical application of DSSCs. In this sense, diverse strategies have been followed to enhance the performance of DSSCs. Development of a new photoanode17,18 having more negative conduction band potential to improve photovoltage, and use of new types of dyes19-21 having a wider and stronger absorption band to increase photogenerated current are two main ways explored to enhance the performance of DSSCs based on upgrading the components of cells.22 As an interesting and complementary approximation, rational optical design of the cell by introducing scattering structures to optimize its lightharvesting efficiency (LHE), thus making a more efficient use of the solar spectrum, presents another promising approach to improve the performance of cells.23 A special attractive feature of this approach lays in the efficient increase of the absorption path length of photons and thus LHE by means of simply coupling optical elements to a conventional DSSC. Polydisperse packings of submicrometer-sized spheres were initially used as highly diffusive reflecting layers.24 In 2003, photonic crystals (PCs)25,26 as a novel optical element to further improve the efficiency of DSSC were reported by Mallouk’s * To whom correspondence should be addressed. E-mail:
[email protected]. Tel: (+86) 10-6279-2905. Fax: (+86) 10-62792905.
group.27 An enhancement of up to 26% of the photogenerated current efficiency of DSSCs was achieved compared to the standard ones, by coupling a TiO2 inverse opal (IO) PC layer to a conventional nc-TiO2-based DSSC. Theoretical investigation by Miguez et al. revealed that the effect of the presence of a PC on the optical absorption of DSSC is mainly the consequence of partial localization of light within the nc-TiO2 layer.28 Moreover, it is noted that there is no need to sensitize the scattering layer: efficient absorption could be attained as long as highly reflecting PC is implemented. Recently, Miguez further theoretically analyzed the efficiency of DSSCs in which IO PCs as optical elements are introduced in different configurations.29 After optimization of structural features, 28% enhancement could be achieved for only one IO scattering layer-coupled DSSC, and 48% for double IO (DIO) layer-coupled DSSC with respect to standard DSSCs. When three IO layers are employed in the device, a large efficiency enhancement of about 60% in a broad spectrum range (450-720 nm) should be possible. Later, experimental work satisfactorily confirmed their theoretical predictions.30 Slow photon resonant modes or photon localization partially confined within the absorbing part of a cell by the mirror behavior of the photonic superlattice is the origin of the observed efficiency enhancement in photonic-crystal-coupled DSSCs.28 As a key point in this enhancement scheme, the properties such as the position and the width of the stop band of the used PCs determine the spectral range, in which the mirror effect takes place, and thus the enhancement effect. These results clearly indicate that the rational design and utilization of photonic structure as an optical element could provide tremendous opportunities for improving the performance of DSSCs. In this direction, Miguez’s group29 has exhibited exciting results by using IOs as optical elements. It can be conceived that, if an additional scattering element is introduced into optical elements, further enhancement of light absorption in the real full spectrum could be achieved. In this work, we describe the employment of DIO as a novel optical element and present a theoretical analysis of the
10.1021/jp1022604 2010 American Chemical Society Published on Web 05/19/2010
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Figure 1. Schemes of the DSSC models under analysis: standard DSSC (a); PC-coupled DSSC: DSSC with one IO layer (b, IO DSSC), one DIO layer (c, DIO DSSC), and two DIO layers (d, DIO DSSC) above a dye-sensitized nc-TiO2 layer. The dye-sensitized slab of all four cells has the same average RI and length.
efficiency enhancement of the designed DSSCs. DIO is a special and accessible IO structure with a scattering sphere embedded in its each lattice pore.31 We found that, compared to IO as the optical element, the presence of small spheres in IO produces a great light-scattering effect and broader reflection region, leading to considerable enhancement of the photocurrent efficiency of cells. DSSCs with one DIO layer as a mirror has an efficiency enhancement up to 47% through optimizing the structural features, comparable to that of two IO layer-coupled DSSC (48%). More remarkably, double DIO layers as a scattering layer lead to a distinct increment of about 80% of photocurrent efficiency in the whole visible absorption range (400-800 nm), which is much larger than that of the three IO layer-coupled device (60%). Results and Discussion Figure 1a-d illustrates the configurations of conventional, IO-coupled and DIO-coupled DSSCs, respectively. To start our analysis, we carefully considered the structure and the values of all relevant parameters of the systems. For simplicity, the theoretical model considers that the embedded sphere is fixed in the center of each pore. One or two DIO layers are placed after the dyed nc-TiO2 layer, each one made of spherical shells of different inner pore radius (R1 and r1). In both cases, light first impinges onto a conductive transparent substrate (with refractive index (RI) n1 ) 1.45), on which a 7 µm thick film of ruthenium dye N535-sensitized nc-TiO2 has been deposited. The RI of this film, assuming that the electrolyte fills all the mesopores, is n2 ) 1.966, and the RI of the electrolyte (TG50) is n4 ) 1.433. The absorption coefficient of the ruthenium dye has been simulated as in ref 28. The (111) planes of the DIO crystals are parallel to the solar cell conducting substrate and therefore perpendicular to the incident light in our study. The RI of these nc-TiO2 spherical shells is nshell ) 2.39. The number of close-packed sphere monolayers (MLs) composing the DIOs is fixed at 17 MLs. All above parameters are set the same as in Miguez’s work (ref 29) except the ones about DIO. Similarly, the theoretical model considers the first conductive glass as the first media (n1 ) 1.45) and the electrolyte as the last one (n4 )1.433). For the sake of comparison, theoretical analysis of IO-coupled systems was also performed in this work. An estimation of the increase in photocurrent generation effienecy can be obtained by comparing the value of photogenerated current density (Jsc) for IO- or DIO-coupled DSSCs with respect to that for the standard DSSC, which is explained as follows. The incident photon-to-current conversion efficiency
(IPCE) is proportional to the LHE or absorptance (A) and is given by the expression1
IPCE ) (LHE)φη ) Aφη
(1)
where Φ is the quantum yield of charge injection, and η is the charge-collecting efficiency by the glass supported electrode. From this magnitude it is possible to gain the generated photocurrent density in short-circuit (Jsc) by using the equation9
Jsc )
∫ qIPCE(λ)F(λ) dλ ) ∫ qA(λ)Φ(λ)η(λ)F(λ) dλ (2)
where q is the electron charge, and F(λ) is the incident photon flux under AM 1.5 spectral irradiance.32 Since Φ(λ) and η(λ) are, in the range of interest, weakly dependent on λ, and it is presumed that Φ and η keep constant in different configured DSSCs. Thus, the increment of photocurrent density ∆Jsc is defined as
∆Jsc )
∫ APC(λ)F(λ) dλ -1 ∫ Astandard(λ)F(λ) dλ
(3)
where APC is the absorption of the DSSCs coupled with different PCs, and Astandard refers to that of the standard DSSC. Both cells have the same amount of dye and total width. The simulation was carried out in each case using a scalar wave approximation (SWA)33,34 method implemented in the MATLAB code. Let us overview the assumptions we made when using SWA method.28 First, as the name implies, is that the polarization of light (i.e., its vector nature) is neglected. The wave equation for the electric field is then
-∇2E(b) r -
ω2 ω2 ε(b)E( r b) r ) 2 ε0E(b) r 2 c c
(4)
where c is the speed of light in a vacuum, ω is photon frequency, ε0 is the volume-averaged dielectric constant of the crystal, and ε(r b) is its periodically modulated part. ε0 is given by the expression
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ε0 ) ffεs + (1 - ff)εb
(5)
where ff is the filling fraction of the spheres, εs and εb are the dielectric constant of the spheres and background materials, respectively. As for electrons in periodic potentials, we can expand the electric field wave function into a Fourier series
E(b) r )
r ∑ Ck exp(ikbb)
(6)
to the [111] lattice planes. One need only consider diffraction off of these planes. More specifically, we are only concerned about the optical properties at frequencies close to the first Brillouin zone boundary in that direction (i.e., the L-point), and only keep terms with G ) 0 or G ) GL, where GL ) 2π/d[111]. Thus, ε(r b) contains only one Fourier component UGL)U-GL. Also, the eq 6 will now be a function of just one spatial variable, we just consider the contribution of a mode corresponding to k and k ) k - GL
k
where the wavevector b k lies within the first Brillouin zone. The periodic dielectric function is also expanded in a Fourier series, in which the sum is performed over all reciprocal lattice vectors G
ε(b) r )
r ∑ UG exp(iGbb)
E(x) ) Ckeikx + Ck-GLei(k-GL)x
The second assumption reduces the problem to a onedimensional analytic form, in which the infinite set of equations reduces to only two. These may be written as
(7)
(
G
k2 - ε0
where UG is the Fourier coefficients with U0 ) 0, and UG(G * 0) is given by the well-known Rayleigh-Gans expression33
3ff UG(G * 0) ) (εs - εb)[sin(GR) - GR cos(GR)] (GR)3 (8) where R is the radius of the spheres and G is the magnitude of the reciprocal lattice vector G associated with UG. While in the DIO case, ε0 is given by the following expression:
ε0 ) Pf2 · ε2 + (Pf1 - Pf2) · ε1 + (1 - Pf1)εb
(9)
where Pf1 and Pf2 are the filling fractions of the lattice cavity and the embedded spheres. Correspondingly, the Fourier coefficient UG is given as35
UG(G * 0) )
3Pf1 (GR1)3
(ε1 - εb)[sin(GR1) -
GR1 cos(GR1)] +
3Pf2 (Gr1)3
-
(
2
∑ k2Ckeikx - ωc2 ∑ ∑ CkUGei(k+G)x) ωc2 ε0 ∑ Ckeikx k
G
k
)
k
(11) A second assumption of the SWA aims to simplify this manydimensional eigenvalue problem. It is assumed that the conditions of the experiment strongly favor scattering off of one particular set of lattice planes, and that the effects of all other lattice planes may be neglected. Thus, only the shortest reciprocal lattice vectors contribute significantly. In the case under consideration, the incoming radiation propagates normal
(13a)
ω2 ω2 2 U C + (k G ) ε Ck-GL ) 0 G k L 0 c2 L c2
(13b)
In order for these two equations to be simultaneously satisfied, their determinant must vanish. Thus, one may determine the wave vector of the radiation inside the PC, k(ω),
GL ( 2
kC(ω) )
GL2 ω2 + ε0 2 4 c
GL2ε0
ω2 ω4 + UGL2 4 2 c c (14)
Substituting this result in the homogeneous set of equations (eq 8 or 10) provides us with the relation between coefficients of the field within the lattice (see eq 15). Thus, we have transformed a three-dimensional vector problem into a onedimensional scalar one.
kC2 - ε0
Gr1 cos(Gr1)] (10)
2
)
ω2 ω2 C UG Ck-GL ) 0 k c2 c2 L
(ε2 - ε1)[sin(Gr1) -
where ε1 and ε2 are the dielectric constants of the cavity and the embedded sphere, respectively, and R1 and r1 are the corresponding radii. Substitution of eqs 6 and 7 into eq 4 yields
(12)
η) UGL
ω2 c2
ω2 c2
(15)
It is clear from eq 3 that, to estimate the changes in the photocurrent generation efficiency of the cells depicted in Figure 1, we need to calculate their absorptance. To do so, calculataion of the reflection and transmission coefficients of the fields in the incident and outgoing media is required. The following set of equations defining the electric field in each medium needs to be solved:
E(x) )
{
eikix + re-ikix (substrate) C1eiksx + C2e-iksx (nc-TiO2 slab) C3(eikcx + ηei(kc-G)x) + C4(e-ikcx + ηe-i(kc-G)x) teiktx
(PC layer 1)
(electrolyte)
(16)
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Figure 2. Absorptance spectra of (a) IO DSSC: R1 ) 101 nm, (b) BiIO DSSC: R1 ) 90 nm for layer 1, R2 ) 110 nm for layer 2, (c) DIO DSSC: R1 ) 107 nm, R2/R1 ) 0.9, ε2 ) 1, and (d) BiDIO DSSC: R1 ) 150 nm, r1/R1 ) 0.9, and ε2 ) 9 for layer 1, R2 ) 80 nm, r2/R2 ) 0.7, and ε′2 ) 11 for layer 2. In all cases, the absorptance spectra of the equivalent standard solar cell (Astandard) is also presented, and each PC slab has 17 MLs.
Reflection (R) and transmittance (T) are determined by calculating the coefficients r and t and using the following relations (eq 17-18):
R ) |r| 2
(17)
T ) |t| 2
(18)
The absorptance (A) spectra are then obtained by employing the equation
A)1-R-T
(19)
We first analyzed the effect of the presence of an IO PC on the optical absorption of DSSCs. Figure 2a,b displays the absorptances of IO-coupled DSSCs, which are in excellent agreement with the results reported by Miguez’s group.29 Using the same approach, the absorptance of the DIO-coupled DSSC was simulated, and the dependence of the efficiency on the radius of the lattice pore (R1), the radius of the embedded spheres (r1), and the dielectric constants of the embedded spheres (ε1) was investigated. In Figure 2c, the absorptance of DIO DSSCs is plotted. In this case, the increment of Jsc of the DIO DSSC is maximized when R1 ) 107 nm, r1/R1 ) 0.9, and ε1 ) 1. With these structural features, increments in the photocurrent as large as ∆Jsc ) 47% can be achieved, while in the case of IO-coupled DSSCs an increment of only 28% is found at best. This enhancement effect induced by one DIO layer is comparable to that (48%) of two IO-coupled DSSCs. Inspecting Figure 2a,c, we can see that the introduction of an additional scattering
sphere in normal IO cavities (i.e., DIO structure) leads to efficient LHE enhancement of DSSCs in a much wider spectral response range. Bandgap analysis confirmed that the DIO structure possesses a much wider band gap width than the IO counterpart (Figure 3), making the occurrence of photon localization in a wider spectrum range within the dye sensitized layer. Stacking a second DIO layer (i.e., BiDIO configuration in Figure 1d) can further extend the wavelength range at which optical absorptance enhancement occurs, as shown in Figure 2d. Compared to the IO counterpart in Figure 2c, the extent of widening the absorptance amplification range by DIO as an optical element is significant. With this double DIO structure, it is possible to attain full spectrum enhancement of the LHE of the ruthenium dye. In fact, the increment of 80% in the photocurrent in double DIO configuration largely exceeds that (60%) of DSSC with three-IO stacking. In order to visualize the dependence of the maximum of ∆Jsc with the lattice constants of the double DIO layer, we have plotted a two-dimensional (2D) contour plot of ∆Jsc,max by varying R1 and R2. At each pair of R1 and R2, the radius and the dielectric constant of embedded spheres in each DIO layer were optimized to get the maximum of ∆Jsc. This photocurrent maximum enhancement map is shown in Figure 4. The abscissas correspond to the sphere radius of the second DIO layer (R2) and the ordinates to that of the first layer (R1), which is in contact with the absorbing layer. It can be clearly seen that, as long as the DIOs with suitable lattice cavity radius were used, the greatest improvement would be received in a wide region via changing the parameters of the embedded spheres. Concretely, as long as the R2 is between 60-95 nm, r2/R2 ) 0.7-0.9, and
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Figure 3. Photonic band structure of optimized DIO (a) and IO (b) PCs. Shaded region represents the Γ-L bandgap width. The bandgap width of DIO is about 100 nm, while only 60 nm for IO PC.
Figure 4. Photocurrent density enhancement maps (% ∆Jsc) for a twoDIO layer-coupled DSSC (BiDIO DSSC). The maximum of ∆Jsc is obtained by optimizing the radius and the dielectric constant of embedded spheres in each DIO layer at each pair of varied R1 and R2. Both lattices present a similar thickness of 17 ML.
the dielectric constant of the embedded sphere is between 9-11 in the second DIO layer, and the suitable lattice cavity radius (115-160 nm) of the first DIO are satisfied, around 80% improvement would be achieved in a wide region. Since the whole visible spectrum is already amplified with the double DIO structure, further enhancement by building a more complex structure could be unnecessary. The origin of LHE enhancement by using a PC as a reflection mirror is that multiple resonant modes localized within the absorbing dyed layer36 lead to longer matter-radiation interaction time. The light wave incidents from the dye-sensitized TiO2 slab side and with frequencies within the stop-band range are evanescent and therefore penetrate the PC slab to a limit depth. An effective resonant cavity is then formed, and the photon is localized preferentially at the absorbing nanocrystalline slab deposited onto the IO, which implies slow propagation speed. This, in turn, yields a much higher probability of the photon being absorbed by the dye molecules in that slab. Thus, the enhancement efficiency strongly depends on the overlap region between the absorption spectrum of dye and the stop band of the PC mirror. It is well-known that higher contrast in the RI between ordered cavities and background medium leads to a broader photonic stop band37 since the light scatters more severely in the interface between two dielectrics. Compared to the case of an IO PC as the mirror, when an additional scatting sphere is introduced into each lattice pore of the normal IO, the light will scatter not only in the interface mentioned above,
but also in the new interface between the added spheres and the electrolyte. If the RI of the embedded spheres is lower than that of the electrolyte ( 9). A material such as air (ε ) 1) does not exist, but according to effective medium theory,47 hollow silica spheres with thin compact shells37 have an ε of approximately 1, which can be easily accessible by using polymer/silica/polymer core-shell-shell spheres48 instead of silica/polymer core-shell spheres in the fabricating procedure. For the second case, DIO with high RI embedded spheres could be created through Se/polymer core-shell spheres as an example. Monodisperse Se spheres have been synthesized and fabricated into PCs successfully.49 In fact, we have successfully
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prepared monodisperse nanoparticles with hollow silica spheres as central cores. The related experimental study to confirm the theoretical predictions described above is ongoing in our lab. Conclusion Making a more efficient use of the solar spectrum by including optical elements into the design of DSSCs is a promising approach to improve the photon-to-current conversion efficiency of the constructed cells. In this work, we describe the employment of DIO as a novel optical element and present a theoretical analysis of the efficiency enhancement of the designed DSSCs. Interestingly, we found that the introduction of an additional scattering sphere into the lattice cavities of the conventional IO could produce a great light-scattering effect and broader reflection region, leading to considerable enhancement of photocurrent efficiency of cells. By adapting a double DIO structure, the whole spectrum enhancement of the dye absorptance with about 80% increment of the photocurrent efficiency of the DSSC can be realized. We predict that this extraordinary improvement might not only lead to more competitive DSSC devices, but also boost the related fields which are needed to enhance the LHE, such as photocatalysis, water-splitting, and so on. Acknowledgment. We acknowledge the financial support from the NSFC (50873051, 20772071, and 50673048), the MOST Program (2006CB806200 and 2007AA03Z307), and the transregional project (TRR61). References and Notes (1) Oregan, B.; Gratzel, M. A Low-Cost, High-Efficiency Solar-Cell Based on Dye-Sensitized Colloidal TiO2 Films. Nature 1991, 353, 737– 740. (2) Sauve, G.; Cass, M. E.; Coia, G.; Doig, S. J.; Lauermann, I.; Pomykal, K. E.; Lewis, N. S. Dye Sensitization of Nanocrystalline Titanium Dioxide with Osmium and Ruthenium Polypyridyl Complexes. J. Phys. Chem. B 2000, 104, 6821–6836. (3) Asbury, J. B.; Hao, E. C.; Wang, Y. Q.; Lian, T. Q. Bridge LengthDependent Ultrafast Electron Transfer from Re Polypyridyl Complexes to Nanocrystalline TiO2 Thin Films Studied by Femtosecond Infrared Spectroscopy. J. Phys. Chem. B 2000, 104, 11957–11964. (4) Paulsson, H.; Hagfeldt, A.; Kloo, L. Molten and Solid Trialkylsulfonium Iodides and Their Polyiodides as Electrolytes in Dye-Sensitized Nanocrystalline Solar Cells. J. Phys. Chem. B 2003, 107, 13665–13670. (5) Horiuchi, T.; Miura, H.; Sumioka, K.; Uchida, S. High Efficiency of Dye-Sensitized Solar Cells Based on Metal-Free Indoline Dyes. J. Am. Chem. Soc. 2004, 126, 12218–12219. (6) Geary, E. A. M.; Yellowlees, L. J.; Jack, L. A.; Oswald, I. D. H.; Parsons, S.; Hirata, N.; Durrant, J. R.; Robertson, N. Synthesis, Structure, and Properties of [Pt(II)(diimine)(dithiolate)] Dyes with 3,3′-, 4,4′-, and 5,5′-Disubstituted Bipyridyl: Applications in Dye-Sensitized Solar Cells. Inorg. Chem. 2005, 44, 242–250. (7) Altobello, S.; Argazzi, R.; Caramori, S.; Contado, C.; Da Fre, S.; Rubino, P.; Chone, C.; Larramona, G.; Bignozzi, C. A. Sensitization of Nanocrystalline TiO2 with Black Absorbers Based on Os and Ru Polypyridine Complexes. J. Am. Chem. Soc. 2005, 127, 15342–15343. (8) Martinson, A. B. F.; Elam, J. W.; Hupp, J. T.; Pellin, M. J. ZnO Nanotube Based Dye-Sensitized Solar Cells. Nano Lett. 2007, 7, 2183– 2187. (9) Shi, D.; Pootrakulchote, N.; Li, R. Z.; Guo, J.; Wang, Y.; Zakeeruddin, S. M.; Gratzel, M.; Wang, P. New Efficiency Records for Stable Dye-Sensitized Solar Cells with Low-Volatility and Ionic Liquid Electrolytes. J. Phys. Chem. C 2008, 112, 17046–17050. (10) Bai, Y.; Cao, Y. M.; Zhang, J.; Wang, M.; Li, R. Z.; Wang, P.; Zakeeruddin, S. M.; Gratzel, M. High-Performance Dye-Sensitized Solar Cells Based on Solvent-Free Electrolytes Produced from Eutectic Melts. Nat. Mater. 2008, 7, 626–630. (11) Yen, Y. S.; Hsu, Y. C.; Lin, J. T.; Chang, C. W.; Hsu, C. P.; Yin, D. J. Pyrrole-Based Organic Dyes for Dye-Sensitized Solar Cells. J. Phys. Chem. C 2008, 112, 12557–12567. (12) Yip, C. H.; Chiang, Y. M.; Wong, C. C. Dielectric Band Edge Enhancement of Energy Conversion Efficiency in Photonic Crystal DyeSensitized Solar Cell. J. Phys. Chem. C 2008, 112, 8735–8740.
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