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Refractive index and extinction coefficient of CH3NH3PbI3 studied by spectroscopic ellipsometry Xie Ziang,1 Liu Shifeng,2 Qin Laixiang,1 Pang Shuping,3 Wang Wei,1 Yan Yu,1 Yao Li,1 Chen Zhijian,1 Wang Shufeng,1 Du Honglin,1 Yu Minghui,4 and G. G. Qin1* 1

3

State Key Lab for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China 2 Horiba Jobin Yvon S.A.S Beijing office, Beijing 100080, China Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101, China 4 OKeanos Technology Co. Ltd., 29 Yongxing Road, Daxing District, Beijing 102600, China *[email protected]

Abstract: Research concerning CH3NH3PbI3 solar cells (SCs) has attracted great attention. However, the CH3NH3PbI3 material’s critical dispersion relationships, i.e. the refractive index and the extinction coefficient, n(λ) and k(λ), as functions of λ, have been little studied. Without this knowledge, it will be difficult to quantitively investigate the optical properties of the CH3NH3PbI3 SCs. We studied n(λ) and k(λ) of CH3NH3PbI3 with spectroscopic ellipsometry. The CH3NH3PbI3 film was fabricated by dualsource evaporation, and the surface roughness was investigated to facilitate SE modeling. With the acquired n(λ) and k(λ), we applied the finite difference time domain method to calculate the ultimate efficiency, η(d), without considering carrier recombination, of the planar CH3NH3PbI3 SC as a function of the film thickness, d, from 31.25 nm to 2 μm, and compared with those of GaAs, c-Si, and a-Si:H(10%H) SCs. It is demonstrated that, η(d) for CH3NH3PbI3 SC is a little smaller than, but very close to that for the GaAs SC, however, much larger than that for the c-Si SC, for all d calculated; and much larger than that for the a-Si:H(10%H) SC when d > 100 nm. Apart from an appropriate band gap near 1.5 eV, the larger k(λ) and smaller n(λ) of CH3NH3PbI3 explain why the CH3NH3PbI3 SC has high efficiency. ©2014 Optical Society of America OCIS codes: (350.6050) Solar energy; (260.2030) Dispersion; (160.4760) Optical properties; (160.4890) Organic materials.

References and links 1. 2. 3. 4. 5. 6. 7. 8.

H. Chen, X. Pan, W. Liu, M. Cai, D. Kou, Z. Huo, X. Fang, and S. Dai, “Efficient panchromatic inorganicorganic heterojunction solar cells with consecutive charge transport tunnels in hole transport material,” Chem. Commun. (Camb.) 49(66), 7277–7279 (2013). S. Pang, H. Hu, J. Zhang, S. Lv, Y. Yu, F. Wei, T. Qin, H. Xu, Z. Liu, and G. Cui, “NH2CH═NH2PbI3: An Alternative Organolead Iodide Perovskite Sensitizer for Mesoscopic Solar Cells,” Chem. Mater. 26(3), 1485– 1491 (2014). N.-G. Park, “Organometal perovskite light absorbers toward a 20% efficiency low-cost solid-state mesoscopic solar cell,” J Phys. Chem. Lett. 4(15), 2423–2429 (2013). T. Leijtens, G. E. Eperon, S. Pathak, A. Abate, M. M. Lee, and H. J. Snaith, “Overcoming ultraviolet light instability of sensitized TiO₂ with meso-superstructured organometal tri-halide perovskite solar cells,” Nat Commun 4, 2885 (2013). O. Malinkiewicz, A. Yella, Y. H. Lee, G. M. Espallargas, M. Graetzel, M. K. Nazeeruddin, and H. J. Bolink, “Perovskite solar cells employing organic charge-transport layers,” Nat. Photonics 8(2), 128–132 (2013). J. Burschka, N. Pellet, S. J. Moon, R. Humphry-Baker, P. Gao, M. K. Nazeeruddin, and M. Grätzel, “Sequential deposition as a route to high-performance perovskite-sensitized solar cells,” Nature 499(7458), 316–319 (2013). M. Liu, M. B. Johnston, and H. J. Snaith, “Efficient planar heterojunction perovskite solar cells by vapour deposition,” Nature 501(7467), 395–398 (2013). D. Bi, S.-J. Moon, L. Häggman, G. Boschloo, L. Yang, E. M. J. Johansson, M. K. Nazeeruddin, M. Grätzel, and A. Hagfeldt, “Using a two-step deposition technique to prepare perovskite (CH3NH3PbI3) for thin film solar cells based on ZrO2 and TiO2 mesostructures,” RSC Advances 3(41), 18762 (2013).

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Received 29 Sep 2014; revised 6 Nov 2014; accepted 7 Nov 2014; published 3 Dec 2014 1 Jan 2015 | Vol. 5, No. 1 | DOI:10.1364/OME.5.000029 | OPTICAL MATERIALS EXPRESS 29

9. G. Hodes, “Applied physics: perovskite-based solar cells,” Science 342(6156), 317–318 (2013). 10. C. Toccafondi, M. Prato, G. Maidecchi, A. Penco, F. Bisio, O. Cavalleri, and M. Canepa, “Optical properties of yeast cytochrome c monolayer on gold: an in situ spectroscopic ellipsometry investigation,” J. Colloid Interface Sci. 364(1), 125–132 (2011). 11. R. M. A. Azzam and N. M. Bashara, “Ellipsometry and polarised light,” Nature 269(5625), 270 (1977). 12. M. Richter, C. Schubbert, P. Eraerds, I. Riedel, J. Keller, J. Parisi, T. Dalibor, and A. Avellán-Hampe, “Optical characterization and modeling of Cu(In,Ga)(Se,S)2 solar cells with spectroscopic ellipsometry and coherent numerical simulation,” Thin Solid Films 535, 331–335 (2013). 13. J.-H. Lee, B. Lee, J.-H. Kang, J. K. Lee, and S.-W. Ryu, “Optical characterization of nanoporous GaN by spectroscopic ellipsometry,” Thin Solid Films 525, 84–87 (2012). 14. Q. Chen, H. Zhou, Z. Hong, S. Luo, H. S. Duan, H. H. Wang, Y. Liu, G. Li, and Y. Yang, “Planar heterojunction perovskite solar cells via vapor-assisted solution process,” J. Am. Chem. Soc. 136(2), 622–625 (2014). 15. T. Baikie, Y. Fang, J. M. Kadro, M. Schreyer, F. Wei, S. G. Mhaisalkar, M. Graetzel, and T. J. White, “Synthesis and crystal chemistry of the hybrid perovskite (CH3NH3)PbI3 for solid-state sensitised solar cell applications,” J Mat. Chem. Anal. 1, 5628–5641 (2013). 16. R. Yusoh, M. Horprathum, P. Eiamchai, P. Chindaudom, and K. Aiempanakit, “Determination of optical and physical properties of ZrO2 Films by spectroscopic ellipsometry,” Procedia Engineering 32, 745–751 (2012). 17. P. E. D, Handbook of Optical Constants of Solids (Orlando, FL, 1985). 18. http://www.horiba.com/fileadmin/uploads/Scientific/Downloads/OpticalSchool_CN/TN/ellipsometer/Lore ntz_Dispersion_Model.pdf. 19. M. Fox, Optical Properties of Solids (Oxford University, Oxford, 2001). 20. G. He, L. D. Zhang, G. H. Li, M. Liu, and X. J. Wang, “Structure, composition and evolution of dispersive optical constants of sputtered TiO2 thin films: effects of nitrogen doping,” J Phys. D: App. Phys. 41, 045304 (2008). 21. A. R. Forouhi and I. Bloomer, “Optical properties of crystalline semiconductors and dielectrics,” Phys. Rev. B 34, 7018 (1986). 22. http://www.horiba.com/fileadmin/uploads/Scientific/Downloads/OpticalSchool_CN/TN/ellipsometer/New _Amorphous_Dispersion_Formula.pdf.” 23. L. Etgar, P. Gao, Z. Xue, Q. Peng, A. K. Chandiran, B. Liu, M. K. Nazeeruddin, and M. Grätzel, “Mesoscopic CH3NH3PbI3/TiO2 heterojunction solar cells,” J. Am. Chem. Soc. 134(42), 17396–17399 (2012). 24. G. Xing, N. Mathews, S. Sun, S. S. Lim, Y. M. Lam, M. Grätzel, S. Mhaisalkar, and T. C. Sum, “Long-range balanced electron- and hole-transport lengths in organic-inorganic CH3NH3PbI3.,” Science 342(6156), 344–347 (2013). 25. D. Bi, G. Boschloo, S. Schwarzmüller, L. Yang, E. M. Johansson, and A. Hagfeldt, “Efficient and stable CH3NH3PbI3-sensitized ZnO nanorod array solid-state solar cells,” Nanoscale 5(23), 11686–11691 (2013). 26. M. M. Lee, J. Teuscher, T. Miyasaka, T. N. Murakami, and H. J. Snaith, “Efficient hybrid solar cells based on meso-superstructured organometal halide perovskites,” Science 338(6107), 643–647 (2012). 27. H. B. Kim, H. Choi, J. Jeong, S. Kim, B. Walker, S. Song, and J. Y. Kim, “Mixed solvents for the optimization of morphology in solution-processed, inverted-type perovskite/fullerene hybrid solar cells,” Nanoscale 6(12), 6679–6683 (2014). 28. W. H. Lee, S. Y. Chuang, H. L. Chen, W. F. Su, and C. H. Lin, “Exploiting optical properties of P3HT:PCBM films for organic solar cells with semitransparent anode,” Thin Solid Films 518(24), 7450–7454 (2010). 29. S. Kumar, A. K. Biswas, V. K. Shukla, A. Awasthi, R. S. Anand, and J. Narain, “Application of spectroscopic ellipsometry to probe the environmental and photo-oxidative degradation of poly(p-phenylenevinylene) (PPV),” Synth. Met. 139(3), 751–753 (2003). 30. W. Wang, J. Zhang, Y. Zhang, Z. Xie, and G. Qin, “Optical absorption enhancement in submicrometre crystalline silicon films with nanotexturing arrays for solar photovoltaic applications,” J Phys. D: App. Phys. 46, 195106 (2013). 31. X. Ziang, W. Wei, Q. Laixiang, X. Wanjin, and G. G. Qin, “Optical absorption characteristics of nanometer and submicron a-Si:H solar cells with two kinds of nano textures,” Opt. Express 21(15), 18043–18052 (2013). 32. W. Shockley and H. J. J. Queisser, “Detailed balance limit of efficiency of pn junction solar cells,” Appl. Phys. (Berl.) 32(3), 510 (1961). 33. Air Mass 1.5 Direct+Circumsolar spectrum, American Society for Testing and Materials: http://rredc.nrel.gov/solar/spectra/am1.5/,” (American Society for Testing and Materials, 2011). 34. E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72(7), 899–907 (1982). 35. H. W. Deckman, C. B. Roxlo, and E. Yablonovitch, “Maximum statistical increase of optical absorption in textured semiconductor films,” Opt. Lett. 8(9), 491–493 (1983). 36. W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32(3), 510 (1961). 37. K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012). 38. S. Mokkapati and K. R. Catchpole, “Nanophotonic light trapping in solar cells,” J. Appl. Phys. 112(10), 101101 (2012). 39. H.-S. Kim, S. H. Im, and N.-G. Park, “Organolead halide perovskite: new horizons in solar cell research,” J. Phys. Chem. C 118, 5615–5625 (2014).

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40. E. Mosconi, A. Amat, M. K. Nazeeruddin, M. Grätzel, and F. De Angelis, “First-Principles modeling of mixed halide organometal perovskites for photovoltaic applications,” J. Phys. Chem. C 117(27), 13902–13913 (2013). 41. E. J. Juarez-Perez, M. Wußler, F. Fabregat-Santiago, K. Lakus-Wollny, E. Mankel, T. Mayer, W. Jaegermann, and I. Mora-Sero, “Role of the selective contacts in the performance of lead halide perovskite solar cells,” J Phys. Chem. Lett. 5, 680–685 (2014). 42. Y. Zhao, A. M. Nardes, and K. Zhu, “Solid-state mesostructured perovskite CH3NH3PbI3solar cells: charge transport, recombination, and diffusion length,” J Phys. Chem. Lett. 5(3), 490–494 (2014). 43. V. Gonzalez-Pedro, E. J. Juarez-Perez, W. S. Arsyad, E. M. Barea, F. Fabregat-Santiago, I. Mora-Sero, and J. Bisquert, “General working principles of CH3NH3PbX3 perovskite solar cells,” Nano Lett. 14(2), 888–893 (2014). 44. D. Liu and T. L. Kelly, “Perovskite solar cells with a planar heterojunction structure prepared using roomtemperature solution processing techniques,” Nat. Photonics 8(2), 133–138 (2013). 45. M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13(5), 451–460 (2014).

1. Introduction Recently, the organometal halide perovskite solar cells (SCs) have attracted great attention, owing to their amazing characteristics [1–3]. The typical photovoltaic perovskite materials can be expressed as CH3NH3PbX3, in which X represents Cl, Br or I [4–9]. The CH3NH3PbX3 materials have exhibited superb light absorption properties in SC manufacturing, and they are therefore studied extensively, due to their potential utility. However, the material’s critical dispersion relationships, i.e. the refractive index and the extinction coefficient, as functions of λ, n(λ) and k(λ), have been little studied. Without this knowledge, it will be difficult to quantitively study the optical properties of the CH3NH3PbX3 SCs. In this article, we studied CH3NH3PbI3’s n(λ) and k(λ) by spectroscopic ellipsometry (SE), which is a powerful technique in measuring n(λ) and k(λ) of various materials [10–12]. SE is basically a technique for examining the optical properties of film materials with polarized electro-magnetic radiation [11–13]. It is based on the measurement of the polarization transformation that occurs after the reflection (or the transmission) of a polarized beam by the film [13]. After the acquisition of CH3NH3PbI3’s n(λ) and k(λ), we applied the finite difference time domain (FDTD) simulations to calculate the ultimate efficiency, η(d), without considering carrier recombination, of the planar CH3NH3PbI3 SCs, as a function of the film thickness, d. 2. Experiment 2.1 Dual-source vapor deposition of the CH3NH3PbI3 material Uniform planar films of CH3NH3PbI3 were deposited on quartz and glass substrates, via dualsource vapor deposition [7]. The quartz and glass substrates were rinsed with deionized water, and dried with clean air. The CH3NH3PbI3 film layers were then deposited through dualsource deposition from lead iodide (PbI2, by Alfa Aesar, purity > 98%) and methylammonium iodide (CH3NH3I, by Okeanos Tech. Co. Ltd.) simultaneously, following the methods proposed by Liu et al [7]. A vapor deposition apparatus (by DM-450A, Beijing Instrument Factory) with two separately controlled sources was prepared. Each source was monitored using a quartz crystal monitor (Protek 9100) to record the deposition rates of the dual sources, and to ensure a uniform CH3NH3PbI3 film growth speed during the deposition process. The quartz substrates were rotated (approximately 100 rpm) with an axis perpendicular to the horizontal plane. The molar ratio between CH3NH3I and PbI2 sources was chosen as 4:1. We placed 0.636 g or 4 Mmol of CH3NH3I in its source, and 0.461 g, or 1 Mmol of PbI2 in its source. The deposition time was 7 min, during which CH3NH3I and PbI2 were heated to approximately 130 °C and 300 °C, respectively. The deposition rates were approximately 5 Å/s and 1 Å/s, respectively. The as-deposited films were then annealed at 100 °C for 45 min in a N2-filled glove box. After annealing, the thickness of the CH3NH3PbI3 films was measured to be about 330 nm by profilometer (Dektak 150 Surface Profiler). The fabricated PbI2 films are produced with the same vapor deposition methods, different in that only the PbI2 source was used. The thickness of the PbI2 films was measured by profilometer to be 220 nm.

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The X-ray diffraction (XRD) patterns (by X'Pert PRO MRD XL, emission power of 2.2 kW, accelerating voltage of 60 kV) of a CH3NH3PbI3 film and a PbI2 film on glass substrates are presented in Fig. 1. The glass substrates were used instead of quartz substrates to avoid possible interferences in the XRD patterns. It can be seen that in the XRD spectra of CH3NH3PbI3/glass, three major diffraction peaks can be found at 14.10°, 28.44° and 31.80°, respectively. They are assigned to the (110), (220) and (310) peaks for the CH3NH3PbI3 material with a tetragonal crystal structure, respectively [14, 15]. No peak at 12.63° for the (001) diffraction peak for PbI2 [15] can be found in the XRD spectra of CH3NH3PbI3/glass. An environmental scanning electron microscope (ESEM, by Quanta 200 FEG) image of the CH3NH3PbI3 film grown on a glass substrate is presented in Fig. 2. The crystal grains can be observed by the atomic force microscope (AFM, by Agilent 5500) image, as presented in Fig. 3. Via the Gwyddion 2.34 AFM image processing software we acquired that, the average grain size of the CH3NH3PbI3 film is 173.0 nm, and the average grain height is 32.4 nm.

Fig. 1. XRD spectra of CH3NH3PbI3/glass and PbI2/glass. The baselines are offset for easy comparison, and the highest intensities of the two spectra have been adjusted to the same height.

Fig. 2. ESEM image of the CH3NH3PbI3 film grown on glass substrate. It can be seen that after the 45 min 100°C annealing process, the vapor deposited CH3NH3PbI3 film appears uniform on the 5.0 μm scale.

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Fig. 3. AFM image of the CH3NH3PbI3 film grown on glass substrate.

2.2 Acquisition of n(λ) and k(λ) with SE In our experiment, the n(λ) and k(λ) of the CH3NH3PbI3 film, as well as surface roughness were measured by the ellipsometer (Horiba Jobin Yvon Uvisel), and the corresponding data were processed by the DeltaPsi2 software. In our experimental settings, the reflection light from the bottom side of the quartz substrate was shielded, and the influences of the diffusion scattering lights were neglected, due to the relatively smooth surface of the CH3NH3PbI3 film, as demonstrated in Fig. 3. The intensities of the p and s components of the reflected light are expressed as Rp and Rs, respectively. According to the fundamental equation of ellipsometry [11, 16]: Rp

= tanψ ⋅ eiΔ (1) Rs where Δ is the phase difference between the p and s wave components after reflection, and tanΨ is related to the amplitude change. Ψ and Δ are functions of the photon energy, ω. The ellipsometer measures Ψ(ω) and Δ(ω) directly. In our experiment, the measurements were conducted in the photon energy range of 0.60 – 5.50 eV with a step of 0.05 eV at an incident angle of 57°. For easy fitting, Is(ω) and Ic(ω) are defined as: Is(ω) = sin[2Ψ(ω)]·sin[Δ(ω)], and Ic(ω) = sin[2Ψ(ω)]·cos[Δ(ω)], respectively. Surface roughness models corresponding to the quartz substrate and the CH3NH3PbI3 film grown on quartz substrate were set up. For the quartz and CH3NH3PbI3 materials, different dispersion formulae were applied according to their light absorption properties. In each measurement, with the Mueller Matrix method [17], the unknown parameters in the surface roughness models as well as in the dispersion formulae are fitted and decided with the DeltaPsi2 software to acquire the material’s n(λ) and k(λ). For the quartz substrate, we applied the Lorentz dispersion formula to describe its complex dielectric function ɛ̃(ω) as follows [18, 19]:

ε (ω ) = ε ∞ +

(ε s − ε ∞ ) ωt2 ωt2 − ω 2 + iΓ 0ω

(2)

In Eq. (2), ε∞ is the high frequency dielectric constant. εs is the value of the dielectric function at a zero frequency. ωt is the resonant frequency of the oscillator whose energy corresponds to the absorption peak. Γ0 is the broadening of each oscillator also known as the

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damping factor. The material’s dispersion relation, i.e. ñ(ω) = n(ω) + ik(ω), can be acquired from ɛ̃(ω) thereafter [19]. The optical parameters to be fitted and decided are: ε∞, εs, ωt and Γ0. In measuring, we assumed that the quartz substrate’s thickness is nearly infinite compared to that of the CH3NH3PbI3 film. The fitted parameters of the quartz material are listed in Table 1. The experimental and fitting results of Is(ω) and Ic(ω), and the acquired n(λ) and k(λ) of the quartz material are presented in Figs. 4(a) and 4(b). The mean square error χ2 is used to qualify the difference between the experimental and theoretical results [17, 20].

Fig. 4. (a): Experimental and fitting results of Is(ω) and Ic(ω) of the quartz material. (b): The calculated n(λ) and k(λ) results of the quartz material.

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Table 1. Fitting parameters of the quartz substrate. Parameter χ

Value

2

0.09

ε∞

1.2950 ± 0.4746

εs

2.1016 ± 0.0032

ωt (eV)

11.4967 ± 2.7939

Γ0 (eV)

0.0259 ± 0.0654

For the CH3NH3PbI3 material, we applied the new amorphous dispersion formula developed by Horiba Jobin Yvon, which was derived on the basis of Forouhi-Bloomer formula [21], and it adapts to the optical characterizations of amorphous semiconductors. In the new amorphous dispersion formula, for k there is [22]:  N f j ⋅ (ω − ωg )   , for ω ≥ ω g 2 k (ω ) =  j =1 (ω − ω j ) + Γ 2j  , for ω < ω g 0

(3)

And for n there is: N

n (ω ) = n∞ +  j =1

B j ⋅ (ω − ω j ) + C j

(ω − ω ) j

2

+ Γ 2j

(4)

where: fj  2 2  ⋅ Γ j − (ω j − ω g )   B j =   Γj  C = 2 f Γ ω − ω j j ( j g)  j

(5)

In Eqs. (3)-(5), the subscripts j = 1, 2… N label the oscillator considered in the new amorphous dispersion formula. ωg is the band gap energy, ωj is approximately the photon energy at which k(ω) reaches maxima, fj is the oscillator strength, and Γj is the damping factor. The optical parameters to be fitted are: n∞, ωg, fj, ωj and Γj, j = 1, 2, …, N. For the CH3NH3PbI3 film on the quartz substrate, considering the AFM image as presented in Fig. 3, we set up a three-layer surface roughness model as presented in Fig. 5(a), to describe its surface roughness. The bottom layer is full of the CH3NH3PbI3 material, while the middle and the upmost layers are CH3NH3PbI3 material with different percentages of voids. The depths and the void’s occupation percentages of the three layers are to be fitted. The fitted parameters of the CH3NH3PbI3 material are listed in Table 2. The experimental and fitting results of Is(ω) and Ic(ω), and the acquired n(λ) and k(λ) of the CH3NH3PbI3 material are presented in Figs. 5(b) and 5(c).

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Fig. 5. (a): Schematic of the three-layer surface roughness model of the CH3NH3PbI3 film on a quartz substrate. (b): Experimental and fitting results of Is(ω) and Ic(ω) of the CH3NH3PbI3 material. (c): The calculated n(λ) and k(λ) results CH3NH3PbI3 material.

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Table 2. Fitting parameters of the CH3NH3PbI3 material. Parameter χ

2

Value 4.92

Bottom layer thickness (Å)

315.62 ± 57.32

Middle layer thickness (Å)

2960.22 ± 208.84

Upmost layer Thickness (Å)

190.16 ± 13.82

Middle layer CH3NH3PbI3 material percentage (%)

91.26 ± 7.72

Upmost layer CH3NH3PbI3 material percentage (%)

38.96 ± 10.12

n∞

2.3252 ± 0.249

ωg (eV)

1.5925 ± 0.0030

f1 (eV)

0.0956 ± 0.0372

ω1 (eV)

1.5963 ± 0.0056

Γ1 (eV)

0.0134 ± 0.0035

f2 (eV)

0.0686 ± 0.0402

ω2 (eV)

2.5219 ± 0.0609

Γ2 (eV)

0.4341 ± 0.1116

f3 (eV)

0.0689 ± 0.0205

ω3 (eV)

3.5412 ± 0.0419

Γ3 (eV)

0.4460 ± 0.0591

2.3 Analysis of the n(λ) and k(λ) result In Table 2, for the CH3NH3PbI3 material, the band gap, ωg ≈1.59 eV, or λg ≈779 nm, which is close to the ωg range of 1.50 ~1.55 eV obtained in previous experimental studies [9, 23–26]. In Fig. 5(c), the k(λ) result exhibits three major absorption peaks. According to Table 2, in the three absorption peaks, the first one is located at ω1 ≈1.60 eV, or λ1 ≈776 nm, the second one at ω2 ≈2.52 eV, or λ2 ≈492 nm, and the last one at ω3 ≈3.54 eV, or λ3 ≈350 nm. To examine the k(λ) result of the CH3NH3PbI3 material, we measured the CH3NH3PbI3 film’s absorbance (by Agilent 8453, measurement ranges from 390 to 1000 nm), i.e. optical density, referred to as D(λ). In previous studies, some researchers measured the CH3NH3PbI3 material’s D(λ) [27], or the absorption coefficient, α(λ) [24]. There is k(λ) ≈(loge10/(4π))·D(λ)·λ/d, where d is the thickness of the CH3NH3PbI3 film, and k(λ) = α(λ)·λ/(4π). In Fig. 6 we compared the k(λ) result obtained by the SE method with that obtained by our absorbance measurement, as well as with the k(λ) results deduced from D(λ) [27] and α(λ) [24]. From Fig. 6 it can be seen that, the decreasing tendencies of k(λ) as λ increases beyond ~400 nm are the same in all the four k(λ) results. In the SE curve shown in Fig. 6, there is a λ1 ≈776 nm absorption peak, and in all the other three curves there are absorption peaks near λ1. In the SE curve, there is a λ2 ≈492 nm absorption peak, and nearby peaks can be found in the absorbance curve and the Ref [27]. curve. However, the lowest measured wavelength of the Ref [24]. curve is 500 nm, therefore it is difficult to judge whether there is an absorption peak near 492 nm. In Ref [24]. it has been pointed out that the λ1 ≈776 nm absorption peak is attributed to the CH3NH3PbI3 material’s direct gap transition from the first valence band maximum to the conduction minimum, which is approximately 1.63 eV (which corresponds to 760 nm). The λ2

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≈492 nm absorption peak is attributed to the transition from lower valence band to the conduction band minimum, which is approximately 2.58 eV (which corresponds to 480 nm). In the SE curve, there is a λ3 ≈350 nm absorption peak, and a nearby peak can be found in the Ref [27]. curve. The lowest wavelength of our absorbance measurement is 390 nm, and the measurement range does not include λ3, therefore it is difficult to judge whether there is an absorption peak near 350 nm. However, similar to the SE curve, as λ decreases from 450 nm, a rapid rising tendency in the absorbance curve can also be observed. We have also checked that the acquired n(λ) and k(λ) satisfy the Kramers-Kronig relations. Both the SE curve and the k(λ) result calculated from n(λ) by the Kramers-Kronig relations are given in the inset of Fig. 6, and they are almost identical. In our calculation we only applied n(λ) data from 300 nm to 2000 nm. The small deviation between the SE curve and the Kramers-Kronig relations result derives from this data limitation. The absorption coefficient, α(λ), of the four kinds of important light absorption materials: c-Si, a-Si:H(10%H), GaAs and CH3NH3PbI3, are compared in Fig. 7. It can be seen that in the visible light wavelength range, α(λ) of CH3NH3PbI3 is better than c-Si, which has an indirect band gap, and is comparable to those of a-Si:H(10%H) and GaAs, which both have direct band gaps. As far as we know, up till now no previous experimental studies concerning n(λ) of CH3NH3PbI3 have been published. We compared n(λ) for CH3NH3PbI3, a metallo-organic hybrid, with those for the inorganic semiconductors and the organics. We selected c-Si [17] and GaAs [17], as representative of the inorganic semiconductors; and selected P3HT:PCBM [28] (poly (3-hexylthiophene) (P3HT):6,6-phenyl C61-butyric acid methyl ester (PCBM), 100° annealed for 10 mins) and PPV [29] (poly(p-phenylenevinylene),exposed to air for 470 mins) as representative of the organics, and showed the comparison results in Fig. 8. As can be seen in Fig. 8, the n(λ) of the CH3NH3PbI3 material lies between those of the inorganic semiconductors and the organics.

Fig. 6. Comparison of the k(λ) results obtained from SE, absorbance, Ref [24]. and Ref [27]. Inset: comparison of the k(λ) results obtained from SE and the Kramers-Kronig calculation.

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Fig. 7. α(λ) of c-Si, a-Si:H(10%H), GaAs and CH3NH3PbI3 materials.

Fig. 8. Comparison of n(λ) for c-Si, GaAs, CH3NH3PbI3, P3HT:PCBM and PPV.

3. FDTD simulation Based on the n(λ) and k(λ) acquired, we studied the light absorption properties of the CH3NH3PbI3 planar SCs with FDTD simulations, and compared the results with those of c-Si [30], a-Si:H(10%H) [31], and GaAs (n(λ) and k(λ) obtained from Ref [17].). The FDTD simulations were carried out with the software of Lumerical FDTD Solutions (Edition 8.6). In simulation, an x-polarized plane wave broadband source was cast upon the plane-structured CH3NH3PbI3 material from the positive z-axis direction [30]. Anti-symmetric

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and symmetric boundary conditions were set in the x and y axis directions. The depths of the planar SCs, d, were set as 31.25 nm, 62.5 nm, 125 nm, 250 nm, 500 nm, 1 μm and 2 μm. The basic calculation method in FDTD simulations is to find out the values of reflectance ratio (R) and transmittance ratio (T) of the plane-structured light absorption material. The absorptance ratio (A) was therefore determined by A(λ) = 1 - R(λ) - T(λ). The expression of the ultimate efficiency η, i.e. the ideal efficiency without considering carrier recombination, is defined as [30–32]:

λ  I (λ ) A(λ ) λ λg

η=

0

dλ

g



∞

0

I (λ ) dλ

(6)

where I(λ) stands for the solar intensity per wavelength interval [33]. The solar spectrum and intensity is after the standard AM 1.5 Direct Circumsolar spectrum [33]. A(λ) is the absorptance ratio, λ is the wavelength, and λg is the wavelength corresponding to the band gap of the light absorption materials. After acquiring A(λ), the corresponding η was calculated following Eq. (6), with the Matlab 2011b programs. Apparently η is a function of the layer depth, d. In our previous studies, η(d) of c-Si and a-Si:H(10%H) SCs have been investigated in Ref [30]. and Ref [31], respectively. In this article, we calculated η(d) of GaAs and CH3NH3PbI3 planar SCs. η(d) of the planar structure SCs made of these four kinds of materials are compared in Fig. 9. In Fig. 9 we also compared η(d) of c-Si, a-Si:H(10%H), GaAs and CH3NH3PbI3 planar SCs with their corresponding Yablonovitch limits [34, 35], which are functions of d, and their Shockley-Queisser limits [36].

Fig. 9. η(d) of c-Si, a-Si:H(10%H), GaAs and CH3NH3PbI3 planar SCs. The Yablonovitch limits and the Shockley-Queisser limits of the four kinds of materials are also presented.

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Generally, assuming perfect antireflection and perfect light trapping, the absorption spectrum in a thin film with thickness d is given by the Yablonovitch limit: AYablonovitch(λ) = 11/(4(n(λ))2·α(λ)·d) [37]. We applied the corresponding AYablonovitch(λ) of the four kinds of materials into Eq. (6) to acquire their Yablonovitch limits in the ultimate efficiency. The Yablonovitch limit is applicable when d > λ/(2n(λ)) [38], therefore in Fig. 9 we only plotted the d > 125 nm cases. From Fig. 9 it can be seen that, similar to c-Si, a-Si:H(10%H) and GaAs, the CH3NH3PbI3 SCs have much potential to improve efficiency, via fabricating nano textures on the planar surface. The Shockley-Queisser limit has long been recognized as the theoretical limit of the efficiency of an ideal single p-n junction solar cell. For the CH3NH3PbI3 material, we have measured that its band gap, ωg ≈1.59 eV. Its Shockley-Queisser limit was then calculated to be 30.4%. As presented in Fig. 9, for the CH3NH3PbI3 material, when d = 250 nm, η = 16.8%, when d = 500 nm, η = 23.0%. In current research, the thicknesses of the light absorption layers containing CH3NH3PbI3 in perovskite SCs are mostly 200 nm ~500 nm [39–43]. For example, the ITO/ZnO/CH3NH3PbI3/spiro-OMeTAD/Ag structure SC exhibited a power conversion efficiency (PCE) of 15.7%, when the planar CH3NH3PbI3 layer is as thick as 300 nm [44]. Through linear interpolation we obtained that η(300 nm) = 18.0%. Apparently, when d = 300 nm, the experimental PCE result in planar SC is already near the ultimate efficiency η. From Fig. 9 it can also be seen that in the planar SCs, η(d) for the CH3NH3PbI3 SC is a little smaller than, but very close to that for the GaAs SC, however, much larger than that for the c-Si SC, in all d calculated; and much larger than that for a-Si:H(10%H) SC when d > 100 nm. When the solar light is perpendicularly incident on the planar material from the air, the reflectivity, R0(λ), depends on both n(λ) and k(λ) [19]:  n ( λ ) − 1 +  k ( λ )  R0 ( λ ) =  2 2  n ( λ ) + 1 +  k ( λ )  2

2

(7)

Fig. 10. R0(λ) of c-Si, a-Si:H(10%H), GaAs and CH3NH3PbI3.

For the SCs, their reflection properties are also important. In Fig. 10, we compared the R0(λ) results of plain plates of c-Si, a-Si:H(10%H), GaAs and CH3NH3PbI3. It can be seen that compared with the inorganic semiconductor materials: c-Si, a-Si:H(10%H) and GaAs,

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CH3NH3PbI3 has much smaller R0(λ). Apart from an appropriate band gap near 1.5 eV, the larger k(λ) and smaller n(λ) of CH3NH3PbI3 explain why the CH3NH3PbI3 SC has high efficiency. As can be seen in Fig. 9, η(d) of the c-Si material is the lowest among the four kinds of materials. Apart from being an indirect band gap material, another important reason for the low η(d) of the c-Si material is due to its high n(λ). However, in practice, an anti-reflection coating layer can be introduced to largely reduce the reflection [45]. From this point of view, the comparison above may be unfair. Considering that an ideal anti-reflection coating can be introduced, we made another comparison as follows. We considered a condition, in which the incident light traveled through a background material with the same n(λ) as that of the light absorption material and it does not absorb light, i.e. k(λ) = 0. It is equivalent to an ideal anti-reflection coating, so that the incident light penetrates the upper surface without reflection. The downside material of the planar SC is still air. The intensity of the incident light is I0. When the light traveled through the light absorption layer and arrived at the downside surface of the planar SC, its intensity was reduced to I0e-αd. Reflection happened at the downside surface, in which the light with an intensity of I0(1-R0)e-αd is transmitted downwards to the air. The rest of the light was reflected upwards. Its intensity was reduced to I0R0e−2αd when it passed the upside surface of the planar SC. In this process, the absorption of the SC is: A = 1-R0e−2αd-(1-R0)e-αd. With this assumption, for the four kinds of materials: c-Si, a-Si:H(10%H), GaAs and CH3NH3PbI3, we calculated their A(λ) and acquired η(d), as presented in Fig. 11. The schematic of the planar SC, the light propagation process and the light intensities are illustrated in the inset of Fig. 11.

Fig. 11. η(d) of c-Si, a-Si:H(10%H), GaAs and CH3NH3PbI3 planar SCs, when R = 0. Inset: schematic of the planar SC, the light travelling process and the light intensities.

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From Fig. 11 it can be seen that, with ideal background materials, the GaAs SCs have the highest η(d). With the same depth, η(d) of the CH3NH3PbI3 SCs are only 3% ~5% lower than those of the GaAs SCs, and obviously higher than those of the a-Si:H(10%H) and c-Si SCs. Conclusions In this article, we studied n(λ) and k(λ) of CH3NH3PbI3 with SE. With the acquired n(λ) and k(λ), the FDTD method was used to calculate the ultimate efficiency, η(d) of the planar CH3NH3PbI3 SC. We demonstrated that, η(d) for CH3NH3PbI3 SC is a little smaller than, but very close to that for the GaAs SC, however, much larger than that for the c-Si SC, in all d calculated; and much larger than that for the a-Si:H(10%H) SC when d > 100 nm. Combined with our calculation results, we predict that PCE approaching 20% is realistically possible in the perovskite SCs. Acknowledgments This work was supported by the National Natural Science Foundation of China under Grants 61176041, 61036005, and 11074015.

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