Preprint of "Role of Random Texture Scattering on the Absorptance Enhancement in Halide Perovskite Layers"

SUPPORTING INFORMATION Role of Random Texture Scattering on the Absorptance Enhancement in Halide Perovskite Layers Meng-Hsueh Kuo1,2 , Branislav Dzurňák1, Neda Neykova1,2, Lucie Landová1,2, Ivana Beshajová Pelikánová1, Zdeněk Remeš2, Stefaan De Wolf3 and Jakub Holovský1,2 1 Centre for Advanced Photovoltaics, Faculty of Electrical Engineering, Czech Technical University in Prague, Technická 2, 16627 Prague, Czech Republic 2 Institute of Physics, Czech Academy of Sciences, Cukrovarnická 10, 16200 Prague, Czech Republic 3 King Abdullah University of Science and Technology (KAUST), KAUST Solar Center (KSC), Thuwal, 23955-6900, Saudi Arabia Calculations Poruba’s model [1]: Complex refractive index 𝑁 can be defined from refractive index 𝑛 and absorption coefficient 𝛼 as follows ( i is imaginary unit and 𝜆 is wavelength): 𝑁=𝑛+i𝛼𝜆 4𝜋 Fresnel intensity coefficients for perpendicular incidence for reflectance 𝑅 and transmittance 𝑇 (𝑛1 is refractive index of medium on the first, incoming side, 𝑛2 is refractive index of medium on the second, transmitting side) are defined as follows: 𝑡12 =2𝑛1 𝑛1+𝑛2 ,𝑇12=𝑛2 𝑛1|𝑡12|2 𝑟12 =𝑛1−𝑛2 𝑛1+𝑛2 ,𝑅12 =|𝑟12|2 The amount of specularly transmitted or reflected light is obtained by multiplying Fresnel intensity coefficients by scalar scattering theory [2] scattering factors (𝜎 is RMS roughness, 𝑛𝑓is refractive index of film, 𝑛𝑎 is the refractive index of ambient, 𝜑 is the angle of incidence that for trapped light can be approximated by 𝜋/𝑛𝑓 ): 𝑆𝑇=exp[−(2𝜋(𝑛𝑓−𝑛𝑎)𝜎 𝜆)2] 𝑆𝑅,0 =exp[−(4𝜋𝑛𝑓𝜎 𝜆)2] 𝑆𝑅=exp[−(4𝜋𝑛𝑓𝜎cos𝜑 𝜆)2]≅exp[−(4𝜋𝑛𝑓𝜎cos(𝜋/𝑛𝑓) 𝜆)2] The light absorbed directly without scattering event is (𝑑 is the film thickness): 𝐴𝑑𝑖𝑟 =𝑆𝑇(1−𝑒−𝛼𝑑) Relative portion of photons scattered at the hitting the first surface and at the hitting the surface after reflection from the back side of the film is (indices 𝑓and 𝑠 mean film and substrate, respectively): 𝑃0=(1−𝑆𝑇)+𝑆𝑇𝑅𝑓𝑠𝑒−2𝛼𝑑𝑅𝑓𝑎(1−𝑆𝑅0) Probability of scattered light escaping through escape cone into substrate, for Lambertian case is: 𝑃𝑒𝑠𝑐 =(𝑛𝑠/𝑛𝑓)2 The multiplication factor of average optical path increase for Lambertian distribution. Angles 𝛽and 𝛾 are the integration limits that are linked to escape cone: 𝑌𝛽𝛾= ∫𝑠𝑖𝑛 𝛾 𝛽𝜑 𝑑𝜑 ∫𝑠𝑖𝑛 𝛾 𝛽𝜑cos𝜑𝑑𝜑 Figure S1: Illustration of the different contributions into Poruba model. The portion of light (scattered and non-scattered) absorbed between first and second scattering event (𝛾 is the angle of escape cone into substrate for which the condition is sin(𝛾)=𝑛𝑠𝑛𝑓 ⁄): 𝐴1=(1−𝑃𝑒𝑠𝑐)[1 − exp (−2𝑌𝛾𝜋/2𝛼𝑑)]+𝑃𝑒𝑠𝑐[1 − exp (−𝑌0𝛾𝛼𝑑)] The relative intensity reduction between the first and second scattering event is: 𝑃1=(1−𝑃𝑒𝑠𝑐) exp (−2𝑌𝛾𝜋/2𝛼𝑑) The portion of light (scattered and non-scattered, inside and outside of escape cone) absorbed between first and second scattering event (𝛾 is the angle of escape cone into substrate for which the condition is sin(𝛾)=𝑛𝑠𝑛𝑓 ⁄): 𝐴2=[(1−𝑃𝑒𝑠𝑐)(1−𝑆𝑟)+𝑆𝑟)][1 − exp (−2𝑌𝛾𝜋 2𝛼𝑑)]+𝑃𝑒𝑠𝑐(1−𝑆𝑟)[1 − exp (−𝑌0𝛾𝛼𝑑)][1+𝑅𝑓𝑠 exp (−𝑌0𝛾𝛼𝑑)] The relative intensity reduction between each two consecutive scattering events is (of nonscattered light and light scattered outside escape cone): 𝐴2=[(1−𝑃𝑒𝑠𝑐)(1−𝑆𝑟)+𝑆𝑟)]exp (−2𝑌𝛾𝜋 2𝛼𝑑) Altogether the intensity of absorbed light is the sum of an infinite row: 𝐴=𝐴𝑑𝑖𝑟+𝑃0𝐴1+ 𝑃0𝑃1𝑅𝑓𝑎𝐴2 1 1−𝑃2 Transparent conductive oxide (TCO) layers preparation The samples A, B, and C were prepared on Corning glass using RF magnetron sputtering from 2 inch ZnO (99,99%) target with substrate to target distance 35 mm at RF power 75 W, 150 W and 175 W, respectively. Argon pressure was 2×10-2 Pa. Without any additional intentional heating the substrate temperature was approximately100 °C. Deposition time was 10 minutes. FA0.9Cs0.1PbI3 material preparation The 1M FA0.9Cs0.1PbI3 perovskite films were deposited from a precursor solution prepared by dissolving 0.9 mmol of FAI, 0.1 mmol of CsI, and 1 mmol of PbI2 in 1 ml of a mixed solvent consisting of DMF and DMSO in a 4:1 ratio. This precursor solution was continuously stirred at 60 °C for 1 hour and then left to stir overnight. The resulting perovskite solution was then spin-coated onto the substrate, first at 1000 rpm for 10 seconds, followed by 5000 rpm for 30 seconds. During the second spin-coating step, 200 µL of ethyl acetate was dropped onto the spinning substrate 5 seconds before the end. Finally, the samples were annealed at 100 °C for 15 minutes. All fabrication steps were performed in a nitrogen-filled glovebox. CH3NH3PbI3 material preparation Samples MAPI A and MAPI B were fabricated from precursor solutions containing 1mmol of PbI2 and 1 mmol of CH3NH3I dissolved, in 1 ml of DMF. Different amount of MACl (2.5 wt% for MAPI A and 1.5 wt% for MAPI B) were added to these solutions. After stirring overnight, the solutions were spin-coated onto glass substrates at 4500 rpm for 40 seconds. The resulting films were then annealed at 100 °C for 3 minutes to create the CH3NH3PbI3 ·MACl layers. Once cooled to room temperature, the films were briefly exposed to CH3NH2 gas for about 2 seconds. After the gas was released from the films, the films were subjected to a final annealing at 150 °C for 10 minutes to produce high-quality CH3NH3PbI3 films. All the steps were performed in a nitrogen-filled glovebox. More details can be found in publication [3] Sample MAPI C was deposited on corning glass substrates from a precursor solution performed by dissolving 1.5 mmol PbI2 and 1.5 mmol MAI in 1.5 ml solvent mixture of GBL and DMSO in a ratio of 3:2. This mixture was continuously stirred at 60 °C. The resulting perovskite solution was then spin-coated onto the substrate, first at 1000 rpm for 10 seconds and then at 5000 rpm for 30 seconds. During the second spin-coating step, 150 µL of chlorobenzene was dropped onto the spinning substrate 5 seconds before the end. Finally, the samples were annealed at 100 °C for 10 minutes. All the steps were performed in a nitrogen-filled glovebox. Photothermal Deflection Spectroscopy measurements The Photothermal Deflection Spectroscopy measurements were performed by a home-made setup equipped with 150W Xe lamp and Andor Kymera 328i. Slits were set to 1 mm. Focusing optics with magnification 1:1 was used. Combination of grating number of grooves and slit widths gave theoretical resolution ∆𝐸/𝐸≈0.01, where E was photon energy. Real resolution, according to spectral linewidth measurements, was ∆𝐸/𝐸≤0.02. As a thermal sensitive liquid, Flutec PP1 was used. Refractive index was 1.25. Simultaneously, transmittance and reflectance were measured by integration spheres in front and behind the cuvette (not directly in front or behind the sample), cuvette internal dimensions were 10 x10 mm. Absorptance from PDS effect was absolutely scaled according to 1−𝑅−𝑇 measured by integrating spheres. Absorption coefficient was then evaluated from absorptance/transmittance ratio from a smooth sample on glass according to equations from ref. [4]. For other purposes of absorptance comparison the simple equation is assumed to be 𝐴≅1 − exp (−𝛼𝛿𝑑). More accurately, the equation reads 𝐴𝑒𝑥𝑝 ≅(1−𝑅0) [ 1− exp (−𝛼𝛿𝑑𝑒𝑥𝑝)] , where 𝑅0 is the reflectance on the first surface, 𝑑𝑒𝑥𝑝 is actual thin-film thickness. In high absorption region, the 𝑅0 reflectance equal to the experimentally observed reflectance of the real stack, but for the purposes of this study we assume 𝑅0≅𝑅 everywhere. From experimentally obtained 𝐴𝑒𝑥𝑝 we calculated absorptance 𝐴 that is corrected to reflectance effects and corrected to thickness variations as 𝐴≅1 − exp [𝑑/𝑑𝑒𝑥𝑝 ∗ ln(1−𝐴0/(1−𝑅))]. 1.4 1.6 1.8 2.0 2.2 2.4 2.6 102 103 104 105 MAPbI3 absorption coefficient (1/cm) photon energy (eV) 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 2.3 2.4 2.5 2.6 2.7 refractive index (-) photon energy (eV) MAPbI3 Figure S2: Absorption coefficient and refractive index of MAPI perovskite layer obtained from PDS measurement and numeric fitting procedure. Fourier Transform Photocurrent Spectroscopy measurements On the samples dedicated for FTPS measurements, the planar electrodes were prepared by evaporation gold trough mechanical mask. The contact distance is 0.5 mm. The electrode pattern is in Figure S2. Figure S3: electrode pattern for FTPS measurements. Figure S4: Sketch of the FTPS sample arrangement and the effect of the illumination direction and the role of trapped light. In the case of glass side the long travelling photons contribute more to the measurement. FTPS was performed by FTIR Thermo Nicolet 8700 equipped with external tungsten light source and external voltage source and pre-amplifier Keithley 428. Voltage bias 10 V was applied, giving DC current in the range of ~10 nA. Preamplification 108 V/A was applied. Infrared glass optical filter RG 780 from Thorlabs was used to suppress visible part of the spectrum and to collect sub-bandgap part of the spectrum. Scan speed velocity was 0.16 cm/s leading to modulation frequency around 4 kHz. Frequency dependence was corrected based on the measurements at twice and three times higher modulation frequencies. Scanning Electron Microscopy measurements The thicknesses of the perovskite thin films were determined from sample cross sections using scanning electron microscope MAIA 3, TESCAN at voltage of 5 kV. S 160 (int. no. 2024 23a) M 160 (int. no. 2025 I3) L 160 (int. no. 2025 C3) S 250 (int. no. 2025 G3) M 250 (int. no. 2025 B3) L 250 (int. no. 2025 A3) S 500 (int. no. 2024 C2) M 500 (int. no. 2025 D15) L 500 (int. no. 2024 E1) Figure S5: SEM images of CH3NH3PbI3 samples. Atomic Force Microscopy Surface roughness was measured by AFM using WiTec alpha300 SNOM system utilizing non-contact AFM method with Si probes. Measured sample area was 5 × 5 µm. RMS=51 ± 8 nm RMS=72 ± 17 nm S 160 (int. no. 2024 23a) M 160 (int. no. 2025 I3) RMS=67 ± 13 nm L 160 (int. no. 2025 C3) RMS=125 ± 19 nm RMS=105 ± 23 nm S 250 (int. no. 2025 G3) M 250 (int. no. 2025 B2) RMS=210 ± 40 nm L 250 (int. no. 2025 A2) RMS=210 ± 70 nm RMS=390 ± 60 nm S 500 (int. no. 2024 C2) M 500 (int. no. 2025 D15) RMS=63 ± 14 nm L 500 (int. no. 2024 E1) Figure S6: Morphology of native roughness of MAPI samples. ZnO A, RMS = 26 ± 6 nm ZnO A with Au, RMS = 26 ± 6 nm ZnO B, RMS= 34 ± 10 nm ZnO B with Au, RMS= 32 ± 9 nm ZnO C, RMS = 50 ± 17 nm ZnO C with Au, RMS = 61 ± 17 nm FTO, RMS = 173 ± 42 nm FTO with Au, RMS = 150 ± 50 nm Figure S7: Morphology of nano-rough TCO substrates before (left image) and after (right image) the deposition of gold layer.