Received Date: October 26, 2016; Accepted Date: October 28, 2016; Published Date: October 31, 2016
Citation: Yang A, Bai M, Bao X, Wang J, Zhang W (2016) Investigation of Optical and Dielectric Constants of Organic-Inorganic CH3NH3PbI3 Perovskite Thin Films. J Nanomed Nanotechnol 7:407. doi: 10.4172/2157-7439.1000407
Copyright: © 2016 Yang A, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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CH3NH3PbI3 thin films with thicknesses in the region of 230-365 nm were prepared. The films were characterized by scanning electron microscope (SEM), x-ray diffraction (XRD), ultraviolet-visible (UV-Vis) absorption and transmittance spectra. Based on the Kramers-Kronig relation and the transmittance spectra, the optical constants of the CH3NH3PbI3 thin films were investigated. Our results show that the absorption coefficient, extinction coefficient, refractive indices, real and imaginary components of the dielectric constant of the CH3NH3PbI3films are basically independent on the thicknesses of the films, which indicate our results are reliable. At 500 nm, above parameters of the films are ~1.38 × 105 cm-1, 0.55, 2.70, 7.01, and 3.13, respectively. The band gap is 1.595 eV. The refractive index of CH3NH3PbI3thin films is 2.84 at 633 nm, which imply that CH3NH3PbI3-based solar cells are ideal antireflection coatings for silicon solar cells (SCs) and are applicable to be top solar cell in monolithic silicon-based tandem solar cells for beyond the efficiency limit of Si SCs. Our results are meaningful for designing optoelectronic devices related to the perovskite thin-films.
CH3NH3PbI3 perovskite thin films; optical constants; Kramers-kronig relation
Organic-inorganic pervoskite of CH3NH3PbX3 (X=Cl, Br, I) families have attracted extreme attention as light-harvesting materials in SCs. Within past six years, power conversion efficiency of pervoskite SCs has been enhanced from 3.8%  to 20.1% , which is the fastest increasing rate in the history of SCs. The impressive photovoltaic efficiency of perovskite SCs attribute to their unique optical and electrical properties, such as an appropriate band gap (1.50 eV) [2,3], high absorption coefficient [2,4], high open-circuit voltages (1.3 V) , long hole-electron diffusion length (~100 nm) and excellent carrier transportation . The quality of perovskite films is very important for SCs. A variety approaches have been employed to fabricate perovskite films, such as single step solution method [7-9], sequential deposition of inorganic and organic precursor , co-evaporation of the precursors  and vapor assistant solution process .
Expect for perovskite SCs, organic-inorganic perovskite are also promising materials for light-emitting diodes , lasers  and thinfilm electronic devices . For designing thin-film optoelectronic devices, optical parameters such as absorption coefficient, extinction coefficient, refractive index, optical band gap and dielectric coefficient are very important parameters.
So far, the optical and dielectric properties of CH3NH3PbI3 thin film have been little studied. Hirasawa et al.  obtained the dielecttric constant of 6.5 in visible range at temperature of 4.2 K. Stefaan De Wolf et al.  found a high absorption coefficient with particularly sharp onset by photothermal deflection and photocurrent spectroscopy. Xie Zhang et al.  fabricated the CH3NH3PbI3 thin films by dualsource evaporation technique and studied the refractive index and extinction coefficient of CH3NH3PbI3 layer by spectroscopic ellipsometry in the range of 300-2000 nm, the refractive index of CH3NH3PbI3 thin film is of 2.8-3.4 in the visible range, and almost a constant (2.6) in nearinfrared range. Philipp Loper et al.  investigated the complex refractive index of planar CH3NH3PbI3 thin films at room temperature by variable angle spectroscopic ellipsometry and spectrophotometry. The authors modeled the dielectric function according to the Forouhi- Bloomer formulation. In the visible range, the refractive index of
CH3NH3PbI3 thin film is of 2.5-2.8, and in near-infrared range, the refractive index is 2.3-2.6. Qianqian Lin et al.  achieved the refractive index and extinction coefficient in the visible to near-infrared wavelength range by a combination of spectroscopic ellipsometry, total transmittance and near-normal incidence reflectance measurements. The refractive index is 2.5-3.2. There are two peaks at 510 nm and 775 nm with refractive index of 3.2 and 2.8 respectively. Chang-Wen Chen et al.  determined the refractive index and extinction coefficient of CH3NH3PbI3-xClx single sample by using a combination of reflection and transmission ellipsometric measurements of a single sample, which eliminates the risk of sample to sample variation that could occur in a multi-sample analysis. And the refractive index is approximately 2.4-2.6 in the visible to near-infrared wavelength range. The films shows extinction coefficient peaks at 355 nm, 460 nm, 630 nm and 730 nm with extinction coefficient values of 1.29, 0.75, 0.30 and 0.26, respectively. From the published results about the refractive index and extinction coefficient of CH3NH3PbI3 perovskite films we can see that different research groups obtained different data. The main reasons are reflection and transmission ellipsometric measurements are different for the samples with different film quality.
In this paper, high-quality CH3NH3PbI3 perovskite films with different thicknesses were prepared. The features of the films were characterized by SEM, XRD, UV-Vis absorption and transmittance spectra. Based on the Kramers-Kronig relation [21-23] and the transmittance spectra, the optical and dielectric constants of the CH3NH3PbI3 perovskite films were calculated. Our results show that the band gap of the films, absorption coefficient, extinction coefficient, refractive indices, real and imaginary components of the dielectric constant of the CH3NH3PbI3 films are basically independent on the thicknesses of the films, which indicate our results are reliable.
Materials and characterization
Methylamine (33 wt% in ethanol), hydroiodic acid (57 wt% in water), PbI2, N, N-Dimethylformamide (DMF), and diethyl ether were purchased from Aladdin reagent, Shanghai, China. γ-Butyrolactone (GBL), dimethylsulphoxide (DMSO), N-methyl-2-pyrrolidone (NMP) were also purchased from Aladdin reagent. The above materials were used as received. The morphology of CH3NH3PbI3 films was characterized by SEM (Hi-tachi4800). The XRD pattern was obtained on a Bruker D8 ADVANCE instrument (Billerica, MA). A Lamda-25 UV-Vis spectrophotometer was used to measure the absorption and transmission spectra. The thicknesses of the films were measured by a Veeco Dektak150 surface profiler.
Fabrication of the CH3NH3PbI3 films
The fabrication of CH3NH3PbI3 films is similar to our previous method  with a small change. Under argon at 0°C, CH3NH3I was synthesized by methylamine (36 mL) and hydroiodic acid (15 mL) reacting in 150 mL ethanol for 2 h. The white precipitate of CH3NH3I was gained by rotary evaporation at 50°C then dissolved in ethanol followed by sedimentation in diethyl ether under stirring the solution for 30 min. Above steps were repeated three times and the white CH3NH3I powder was finally collected and dried at 50°C in a vacuum oven overnight. The CH3NH3I and PbI2 (1 M) were dissolved in a mixture of anhydrous GBL: DMSO (7:3), with 5 v/v% NMP. To strengthen dissolution of solid material, the solution was heated at 70OC overnight, then cooled down to room temperature and act as a precursor solution of the films. Before spin-coating, the precursor solution was filtered with a 0.22 mm PTFE filter. ITO glasses were as the substrates of the CH3NH3PbI3 films. Before spin-coating, the ITO glasses were cleaned in an ultrasonic bath with detergent, ultrapure water, acetone, and isopropyl alcohol for 20 min, respectively. After being treated in oxygen plasma for 6 min, the precursor solution was spin-coated onto the ITO glasses. During the spin-coating, toluene was used to wash the surface to form high-quality surface coverage, as reported by Seok  and Bao . Finally, the films were thermal treated at 90 oC for 20 min in a glovebox. By adjust the rotating speed, CH3NH3PbI3 films with 230 nm, 260 nm, 295 nm and 365 nm thicknesses were prepared. The experimental error in measuring the film thickness is about 5 nm.
Characterization of the films
Figure 1 shows the representative SEM image. We can see that the CH3NH3PbI3 thin film on the ITO coated glass is composed of uniform grains. The perovskite film fully covered on the ITO layer without any cracks, pinholes and other serious aggregations. The quality of the film is good.
Figure 2 is the XRD pattern of CH3NH3PbI3 thin film. The four main peaks located at 14.18°, 28.50°, 31.92°, 34.24° correspond to the lattice plane (110), (220), (310) and (312) respectively. It is similar to the result of Ref. 12. The peaks related to CH3NH3I and PbI2 were not observed in the synthesized perovskite layer, which indicates CH3NH3I and PbI2 completely reacted and transformed into CH3NH3PbI3.
Figure 3 shows the UV-Vis absorption spectra of the four CH3NH3PbI3 thin films. The films have wide absorption range from UV to NIR regions with two distinct peaks positioned at 480 nm and 756 nm respectively. The first absorption peak (480 nm) is attributed to the direct gap transition from lower valence band (VB2) to the conduction band minimum (CB1), which is near to 2.58 eV [6,17]. And the second absorption peak (756 nm) is assigned to the direct gap transition from the first valence band maximum (VB1) to the conduction band minimum (CB1), which is approximate to 1.64 eV [6,17] .
Figure 4 indicates the transmission curves of the four CH3NH3PbI3 thin films. In the UV-Vis range, the thicker the films, the higher the transmittance. The transmittance of the films is less than 10% when the wavelength is less than 540 nm. In the range of 540-750 nm, the transmittance almost increases linearly from 10% to 30%. And in the region of 750-800 nm, the transmittance increases quickly near to 70%. The highest transmission is 76% at 800 nm for the film with 295 nm thickness. In the range of 800-1000 nm, the transmittance decrease slightly. The change tendency is consistent with the experiment result reported by Philipp LÖper et al. .
The absorption coefficient α(λ) of the CH3NH3PbI3 thin films can be calculated by the transmittance spectra as following equation ,
where T is the transmittance and d is the thickness of thin film. Figure 5 shows the calculated results. From 320 nm to 775 nm, α(λ) exhibits independence on the film thicknesses. In the range of 310-510 nm, α(λ) are almost constant of 1.4 × 105 cm-1. And in the range of 510-750 nm, α(λ) decrease from 1.4 × 105 cm-1 to 4 × 104 cm-1. The absorption coefficient curves of CH3NH3PbI3 films show a sharp shoulder near the wavelength of 756 nm, which corresponds to the position of the band gap. Our results coincide with Ref. 4. Comparison to GaAs, CdTe, CIGS and c-Si, this shoulder occurs at higher absorption coefficients . So very thin absorber films are suffice for perovskite SCs fabrication . In the NIR range of 756-800 nm, α(λ) decrease again till to the fundamental absorption edge. The magnitude of α(λ) and spectral shape are good agreement with previous reports [4,18].
The extinction coefficient k(λ) can be calculated by below equation :
Figure 6 shows the curves of extinction coefficient of CH3NH3PbI3 thin films. At 510 nm and 750 nm, the peaks of k(λ) are near to 0.55 and 0.25 respectively. The values of k(λ)in the visible regions are larger than that in the NIR regions. From 340 nm to 510 nm, k(λ) increase with wavelengths till the peak value of 0.55 at 510 nm. In the range of 510- 750 nm, k(λ) decrease slowly down to 0.25. In the NIR range of 750-800 nm, k(λ) decrease again and follow a linear trend till to 0.14 (230 nm thickness) and 0.05 (295 nm thickness). In the range of 800-850 nm, k(λ) are almost constants and show dependence on the thickness of films.
The classical Tauc equation  was used to calculated the optical band gap Eg
Where A is a constant, h and c are the Planck’s constant and light speed respectively. For the direct band gap semiconductor, m=1/2 or 2/3 . When m=1/2, the calculated results gives the best linear plot in the band edge region for the CH3NH3PbI3 thin films. Representative plots of (αhν)2 verses photon energy were showed in Figure 7. The band gap of CH3NH3PbI3 thin films were obtained by extrapolation α to zero. For the four films with different thicknesses, the band gap is same (1.595 eV), which is almost as same as Ref. 2, Ref. 3 and Ref.17.
The integration range is from 0 to ∞, which means one has to know α(λ’) in the range of [0, ∞] for calculation the refractive index at λ. But from experimental transmittance spectrum, one can only obtain α(λ’) in a limited wavelength range . In the regions of and , one has to speculate α(λ’). So Eq. (4) can be written as
Where ji (i=1, 2 and 3) are the integrations of Eq.(4) in the ranges of , and , respectively.
At the short wavelength, we suppose that there is only one absorption band and α(λ’) match Eq. (3) and m=1/2. By combining Eq. (4) and (3), j1 can be written as the sum of the integration under three cases,. In Ref. 23, we corrected the equations to calculate j1 in the above three cases and calculated the optical constants of ZnO nano-thin films. The same equations were used here to calculate j1. The equations to calculate j2 and j3 are as same as Ref. 21.
Figure 8 shows the dependence of refractive indices on the wavelengths. There are three peaks of the refractive indices. One sharp peak with value of 3.0 is at 350 nm, which resembles the result of Ref. 17 and Ref.18. Another slowly change peak near to 2.84 is at 550 nm. There is a small peak at 760 nm. In the region of 350- 400 nm, the refractive indices decrease from 3.0 to 2.53, then increase to 2.84 at 550 nm. From 550 nm to 750 nm, the refractive index is almost a constant (around 2.8). At 633 nm, the refractive index of CH3NH3PbI3 films is near to 2.8, which imply that CH3NH3PbI3 is an ideal antireflection coating for silicon SCs. The tandem SCs of CH3NH3PbI3/Si are promising to beyond the efficiency limit of Si SCs.
The complex dielectric ε=ε1 + iε2 characterizes the optical properties of solid material. The real and imaginary parts of the complex dielectric constants are expressed as :
Figure 9 shows the real and imaginary components of the complex dielectric constants of CH3NH3PbI3 thin films. The real components follow the same pattern as the refractive indices changing with wavelengths (Figure 8). There is a sharp peak at 350 nm. In the region 300-350 nm, the real components ε1 increase from 4.7 to 9.0, then decrease to 6.18 at 400 nm. In the region of 400-560 nm, ε1 increase from 6.18 to 7.95. After 560 nm, ε1 is almost a constant near to 8.0. Our result for the real components of the complex dielectric constants is in good agreement with Ref. 18. Hirasawa et al.  obtained the dielectric constant of 6.5 in visible range at temperature of 4.2 K. For the imaginary component ε1, the peaks are at 350 nm and 510 nm. The first cuspidal peak at 350 nm resembles to the result of Ref. 18. In the region of 360-510 nm, ε1 increase from 2.00 to the peak value of 3.03 at 510 nm then decrease down to 1.39 at 775 nm.
In this work, CH3NH3PbI3 thin films with thicknesses in the range of 230-365 nm were prepared. The features of the films were characterized by SEM, XRD, UV-Vis absorption and transmittance spectra. The optical constants including in absorption coefficient, extinction coefficient, refractive indices, real and imaginary components of the dielectric constant were calculated based on the Kramers-Kronig relation. These optical and dielectric constants are basically independent on the thicknesses of the films, which indicate our results are reliable. At 500 nm, above parameters of the films are ~1.38 × 105 cm-1, 0.55, 2.70, 7.01, and 3.13, respectively. Our results agree well with previously reported data. The band gap of the films is 1.595 eV. The real part of the refractive index at 633 nm is 2.84, which indicates that CH3NH3PbI3-based SCs are applicable to top cell in monolithic silicon-based tandem SCs. Our results are meaningful for designing optoelectronic devices related to the perovskite thin-films.
This work was supported by the National Natural Science Foundation of China (Grant No. 41172110 and 41576170).