Materials Chemistry A

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1 Journal of Materials Chemistry A PAPER Cite this: DOI: /c5ta03990h View Article Online View Journal Thermodynamic regulation of CH 3 NH 3 PbI 3 crystal growth and its effect on photovoltaic performance of perovskite solar cells Namyoung Ahn, a Seong Min Kang, a Jin-Wook Lee, b Mansoo Choi* a and Nam-Gyu Park* b Received 2nd June 2015 Accepted 19th August 2015 DOI: /c5ta03990h We report a theoretical analysis on the crystallization of CH 3 NH 3 PbI 3 and the control of grain sizes by varying the two-step reaction temperature from 10 Cto50 C based on the present analysis. The thermodynamic equation for CH 3 NH 3 PbI 3 crystallization is derived by considering the change in Gibbs free energy and the equilibrium concentration of the reaction between the PbI 2 film and CH 3 NH 3 I solution. The photovoltaic performance of a perovskite solar cell is found to depend on the reaction temperature, which is critical in determining the crystal size of perovskite. The reaction temperature was varied between 10 C and 50 C, and the optimal temperature was found to be around 20 C in our two-step process. The performance enhancement controlled by the grain size with the increase of reaction temperature could be compensated by the generation of defects for a large crystal perovskite layer device. Introduction Research on solid-state perovskite solar cells based on the light harvester, methylammonium lead iodide, MAPbI 3 (MA ¼ CH 3 NH 3 ), has received considerable attention due to their lowcost technology, ease of processing and excellent photovoltaic performances. Following the rst report on a 9.7% efficient perovskite solar cell in 2012, 1 the power conversion efficiency (PCE) of the device has been developed during a number of studies. 2 5 As a result, a PCE of 20.1% was reported in 2014, 6 which is the highest certi ed value among organometal halide perovskite solar cells. Solution-processed techniques using onestep 7,8 /two-step 3,9 and vapor deposition methods 10 have been proposed to improve the potential performance of the perovskite solar cells. In particular, a two-step solution process, which involves sequential deposition of PbI 2 and MAI reacting readily to form MAPbI 3, has been used due to the possibility of controlling the fabricated MAPbI 3 grain sizes It is important to note that the grain sizes of the perovskite active layer affect the photovoltaic performances It was reported that MAPbI 3 grain sizes could be controlled by changing the MAI concentration, which led to enhancement of the properties of a Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul , Korea. mchoi@snu.ac.kr; Tel: b School of Chemical Engineering and Department of Energy Science, Sungkyunkwan University, Suwon , Korea. npark@skku.edu; Tel: Electronic supplementary information (ESI) available. See DOI: /c5ta3990h These authors contributed equally to this work. the solar cell device. 9 However, there are many other factors, such as temperature, surface tension and humidity, that affect the performances of perovskite solar cells by engineering the MAPbI 3 grain sizes. 15,17,18 Herein, we report a fundamental analysis using a thermodynamic equation and temperature-controlled two-step solution engineering, which was used to investigate the correlation of the MAPbI 3 grain sizes with reaction temperature. Deriving a thermodynamic reaction model equation from Gibbs free energy, we demonstrate that the grain sizes of the MAPbI 3 active layer can be controlled not only by the MAI concentration but also by the reaction temperature of a two-step process that involves spin-coating MAI on the PbI 2 lm. It is found that the temperature in the two-step coating process is crucial in determining the MAPbI 3 grain sizes and the performance of fabricated solar cells. While we were preparing our manuscript on the temperature-dependent crystal growth mechanism, a similar study was recently reported on temperature-dependent perovskite morphology. 19 However, this did not include the theoretical analysis to support the basis for the temperaturedependent crystal growth. Results and discussion The fabrication process for MAPbI 3 perovskite solar cells using a two-step spin coating method is schematically illustrated in Fig. 1. To form the PbI 2 crystallized lm, 1 M N,N-dimethylformamide (DMF) solution of PbI 2 is spin-coated on the mp- TiO 2 /bl-tio 2 /FTO substrate, where mp and bl stand for mesoporous and blocking, and annealed on a hot plate, as shown in This journal is The Royal Society of Chemistry 2015 J. Mater. Chem. A

2 Fig. 1 Schematic of the fabrication process for perovskite solar cells using a two-step spin-coated method. (a) First, PbI 2 solution (1 M in DMF) was spin-coated on a mesoporous (mp)-tio 2 layer deposited on a fluorine-doped tin oxide (FTO) substrate with a thin blocking (bl)-tio 2 film, followed by annealing to form the PbI 2 film. (b) Second, MAI solution (0.05 M in 2-propanol) was loaded onto the PbI 2 film to crystallize MAPbI 3 perovskite and then spun after 30 s. (b1) MAPbI 3 nuclei were formed, whereas MAI solute molecules constantly collided with the PbI 2 film. (b2) MAPbI 3 nuclei selectively grew, based on a statistical thermodynamic model. (c) Finally, spiro-meotad was spin-coated on the MAPbI 3 film and an Au electrode was thermally evaporated to complete the solar cell. Fig. 1a. Subsequently, MAI solution in 2-propanol is spread on a PbI 2 lm to crystallize MAPbI 3 perovskite (Fig. 1b). 20,21 The chemical reaction to form MAPbI 3 in a two-step procedure can be expressed as eqn (1), PbI 2 (s) + MAI (sol) 4 MAPbI 3 (s) (1) where the MAI concentration in 2-propanol determines the direction of the chemical reaction. Higher MAI concentrations will push the reaction to the right due to a shi of equilibrium, leading to crystallization of perovskite. In the process of forming perovskite, MAI constantly collides with solid PbI 2, which leads to the formation of MAPbI 3 nuclei according to the probabilistic model. Then, the minute nuclei, which have enough energy for crystallization, can selectively grow bigger according to a thermodynamic model. The change in Gibbs free energy per unit volume (DG V ) with a thermodynamic mechanism of crystallization is calculated using eqn (2), 22 DG V ¼ kt ln C (2) V m C 0 ðtþ where k is the Boltzmann constant, T is the temperature of the reaction, C is the concentration of MAI, C 0 is the equilibrium concentration of MAI, and V m is the volume of a solute particle. C 0 depends on temperature. When crystallization occurs in the solution phase, the change in Gibbs free energy and the surface tension between the surface of the crystal and the solution (DG S ) should be considered together, and the relationship between them can be written as eqn (3), DG S ¼ s sl (3) where s sl is the average surface tension. Because MAPbI 3 perovskite is a tetragonal structure at room temperature, 23 the shape of MAPbI 3 can be assumed to be cubic. The total change in Gibbs free energy (DG) for the two-step solution process is thus expressed as eqn (4), DG ¼ a 3kT ln C V m C 0 ðtþ þ 6a2 s sl (4) where a is the length of the cubic edge, a 3 is the volume of the cube, and 6a 2 is the total surface area of the cube. By differentiating eqn (4) with respect to a, a critical point wherein DG is maximized can be calculated by solving eqn (5). ddg da ¼ 3a2kT ln C V m C 0 ðtþ þ 12as sl ¼ 0 (5) using eqn (5), the critical size (a c ) and the critical Gibbs free energy (DG c ) are expressed as eqn (6) and (7). 4s sl a c ¼ kt ln C V m C 0 ðtþ 32s sl 2 (6) DG c ¼ kt ln C 2 (7) V m C 0 ðtþ The change in Gibbs free energy is presented as a function of the size of the perovskite crystal in Fig. 2a, wherein it is noted that Gibbs free energy is predominantly affected by surface tension. Gibbs free energy increases when the size of the perovskite crystal is smaller than the critical size, whereas it J. Mater. Chem. A This journal is The Royal Society of Chemistry 2015

3 Fig. 2 (a) Theoretical plot with Gibbs free energy versus crystal size in the crystal growth process. Top and cross-sectional views of MAPbI 3 crystal using FE-SEM and focused ion beam (FIB) SEM for MAI solution concentrations of (b) M and (c) M. Fig. 3 Plot of theoretically derived MAPbI 3 grain size (Y) as a function of MAI concentration (X). The experimental data (filled square) were fit to a theoretical equation. decreases when the size of the perovskite crystal is larger than the critical size. Consequently, perovskite nuclei, which have higher energy than the critical energy, are expected to grow as a result of a spontaneous chemical reaction. As a result, the perovskite crystal would grow until all PbI 2 are turned into perovskite. Therefore, the average grain size of MAPbI 3 is controlled by two factors: (1) the crystal growth of perovskite is determined by the critical energy (G c ) and (2) each nucleus will spontaneously grow until it comes into contact with surrounding crystals at grain boundaries. Because the energy distributions of the reactants follow a Boltzmann distribution based on statistical thermodynamics, the number of nuclei that have the potential to become crystals is proportional to e DGc kt. 24 The average volume of a perovskite crystal is inversely proportional to the number of nuclei (n) per unit volume because an increase in the number of nuclei inhibits crystal growth due to the decreased space available for crystal growth. Therefore, the grain size (Y) has the following relation. rffiffi 3 1 Yðgrain sizeþfaf fe DGc 3kT (8) n From eqn (7) and relation (8), we can derive the interaction formula between grain size and MAI concentration in eqn (9) (see more details in ESI ), ln Y ¼ 32s sl 3 2 þ C 0 (9) kt 3kT ðln X ln C 0 ðtþþ V m where X is the MAI concentration that is equal to C and C 0 is a constant. It is demonstrated that eqn (9) correctly predicts grain sizes depending on MAI concentrations, which were measured previously elsewhere, 9 as shown in Fig. 3 (see ESI for more details). Top-view and cross-sectional SEM images of MAPbI 3 Fig. 4 Top-view SEM images and cross-sectional FIB-SEM images for the MAPbI 3 crystals grown at different temperatures (MAI solution and substrate have the same temperature) of (a) and (b) at 10 C, (c) and (d) at 20 C and (e) and (f) at 50 C. are shown in Fig. 2b and c. It is clearly shown that the grain sizes are different for differing MAI concentrations. According to eqn (9), the MAPbI 3 crystal size is controlled not only by the concentration of MAI but also by temperature. To see the temperature effect, both the substrate and the MAI solution are pre-heated at different temperatures of 10 C, 20 C and 50 C, in which the MAI concentration is xed at M. As shown in the SEM images in Fig. 4a f, the grain size increases as temperature increases. As the temperature of the MAI solution increases, the equilibrium concentration of the chemical reaction also increases due to the high solubility of MAI. Therefore, the critical free energy at high temperatures is higher than that at low temperatures according to eqn (7), which determines the number of nuclei based on relation (8). As a result, the number of nuclei growing into MAPbI 3 crystals decreased, which leads to an increase in the MAPbI 3 grain sizes. Top-view SEM images (Fig. 4a, c and e) and cross-sectional FIB-SEM images (Fig. 4b, d and f) clearly show that the MAPbI 3 grain size changes with temperature, which can be explained by our theoretical analysis using eqn (9). It is noted that MAPbI 3 grown at 50 C shows large gaps between crystals, which causes direct contact between mp-tio 2 and spiro-meotad. This journal is The Royal Society of Chemistry 2015 J. Mater. Chem. A

4 Fig. 5 (a) Short-circuit current density (J sc ), (b) open-circuit voltage (V oc ), (c) fill factor (FF) and (d) power conversion efficiency (PCE) of the perovskite solar cells with MAPbI 3 crystals grown at different temperatures. Fig. 6 (a) UV-Vis absorption spectra of MAPbI 3 perovskite films depending on the reaction temperature. (b) External quantum efficiency (EQE) of perovskite solar cells employing MAPbI 3 grown at different reaction temperatures. The effect of reaction temperature on photovoltaic parameters is investigated. Fig. 5 shows the measurement results for different reaction temperatures with short-circuit current density (J sc ), open-circuit voltage (V oc ), ll factor (FF) and power conversion efficiency (PCE). As can be seen in Fig. 5a, J sc is improved as the reaction temperature increases, which may be due to an increase in light absorption as a result of an increase in grain size (see Fig. 6). It is noted that the corresponding perovskite colors becomes darker with increasing grain size (see Fig. S1 in ESI ). On the other hand, signi cantly lowered V oc and FF are observed at 50 C (Fig. 5b), which is probably related to the defects in the perovskite layer, as shown in Fig. 4f. The defects caused by increasing grain size provide recombination sites between mp-tio 2 and spiro-meotad. V oc and FF will be dependant on the thickness of the mp-tio 2 layer and the whole perovskite layer. These are slightly improved at 20 C compared to 10 C because of the higher densities of the compressed mp-tio 2 layer (250 nm) and the whole perovskite layer (450 nm), which are thinner than those at 10 C(400 nm and 600 nm, respectively), as shown in Fig. 4d. It is assumed that the compressed mesoporous TiO 2 layer results from the volume expansion of MAPbI 3 capped on the mesoporous TiO 2 layer, due to the increase in the MAI solution temperature. As a result, PCE is highest for a reaction temperature of 20 C. The photovoltaic parameters for the best performing devices are represented in Table 1. Fig. 6a shows that the absorbance is higher at 20 C and 50 C than at 10 C. A decrease in absorbance with decreasing grain size was observed in the earlier study, 9 which is in part related to the higher re ectance. The relatively low absorbance of MAPbI 3 grown at 10 C results from a smaller grain size. Large crystals with gaps between them are bene cial to the external quantum efficiency (EQE), especially at long wavelengths (Fig. 6b), due to enhanced internal light scattering, which is responsible for a higher J sc at 50 C. Table 1 Short-circuit current density (J sc ), open-circuit voltage (V oc ), fill factor (FF) and power conversion efficiency (PCE) dependence on reaction temperature. The data represent the best performing device for each reaction temperature Reaction temperature J sc (ma cm 2 ) V oc (V) FF PCE (%) 10 C C C J. Mater. Chem. A This journal is The Royal Society of Chemistry 2015

5 Conclusions We presented a theoretical approach using a thermodynamic analysis derived from Gibbs free energy to explain the crystal growth of MAPbI 3 and found that the grain size of MAPbI 3 crystals was clearly dependent on the reaction temperature. The grain size increased with reaction temperature, which could be explained by the thermodynamic model. The photovoltaic performance was signi cantly altered by the reaction temperature, which was mainly due to the MAPbI 3 grain size and the morphology of the resultant MAPbI 3 lm. MAPbI 3 grown at 20 C showed a better performance compared to the same compound grown at lower or higher reaction temperatures. Experimental section Materials synthesis Mesoporous 50 nm-sized TiO 2 nanoparticles were hydrothermally synthesized using 20 nm-sized seed particles as described elsewhere g of TiO 2 paste, which consists of nanocrystalline TiO 2, terpineol, ethylcellulose and lauric acid with a nominal ratio of 1.25 : 6 : 0.9 : 0.3 wt%, was diluted in 10 ml ethanol to prepare a mesoporous TiO 2 lm. MAI was synthesized by reacting 27.8 ml of CH 3 NH 2 (40 wt% in methanol, TCI) with 30 ml of HI (57 wt% in water, Aldrich) in a round bottomed ask in an ice bath for 2 h. 20,26 Using a rotary evaporator, the resulting MAI was collected at 50 C for 1 h. This was washed with diethyl ether and dried in a vacuum chamber for 12 h. Fabrication of perovskite solar cells Fluorine-doped tin oxide-coated (FTO) glass substrate (Pilkington, TEC-8, 8 U sq 1 ) was cleaned using UV/ozone treatment for 15 min and sonicated in ethanol a er washing with detergent liquid, acetone and DI water. A thin compact TiO 2 blocking (bl) layer was deposited on FTO by spin-coating 0.15 M titanium diisopropoxide bis(acetylacetonate) (Sigma-Aldrich, 75 wt% in isopropanol) in 1-butanol (Sigma-Aldrich, 99.8%) at a sequentially increasing spin rate of 700 rpm for 8 s, 1000 rpm for 10 s and 2000 rpm for 40 s. The bl-tio 2 layer was heated at 125 C for 5 min. A mesoporous (mp) TiO 2 layer was formed on the bl-tio 2 layer by spin-coating the diluted TiO 2 paste solution at 2000 rpm for 20 s and annealing at 550 C for 1 h. A er UV/ozone treatment for 30 min, the substrate was treated with 20 mm aqueous TiCl 4 (Sigma-Aldrich, >98%) by immersing the mp-tio 2 coated substrate at 90 C for 10 min, followed by annealing again at 500 C for 30 min. The deposition of the MAPbI 3 perovskite active layer on the mp-tio 2 layer was conducted using a two-step process. Firstly, 30 ml of PbI 2 solution (1 M (1.844 g) of PbI 2 (Sigma-Aldrich, 99%) dissolved in 4 ml of N,N-dimethylformamide (DMF, Sigma-Aldrich, 99.8%)) was spin-coated on the mp-tio 2 coated substrate at 6000 rpm for 20 s, which was dried at 40 C for 3 min and 100 C for 5 min. Second, 200 ml of 0.05 M (8 mg ml 1 ) MAI in 2-propanol (Sigma- Aldrich, 99.5%) was spin-coated on the PbI 2 lm at 3000 rpm for 20 s during 30 s of loading time to allow MAPbI 3 crystallization and was dried at 100 C for 5 min. Prior to the MAI coating process, the three MAI solutions with different temperatures of 10 C (in a dry ice chamber), 20 C (room temperature) and 50 C (using a pre-heated hot plate) were prepared. The hole transport material (HTM) was deposited on the substrate by spin-coating 72.3 mg of spiro-meotad solution in 1 ml chlorobenzene, to which 28.8 ml of 4-tert-butyl pyridine and 17.5 ml of lithium bis(tri uoromethanesulfonyl)imide (Li-TFSI) solution (520 mg Li-TSFI in 1 ml acetonitrile (Sigma-Aldrich, 99.8%)) was added, at 4000 rpm for 20 s. Finally, gold (Au) was thermally evaporated on the top of the HTM for the counter electrode under 10 6 Torr vacuum at 1 Ås 1. Characterization The morphologies of the MAPbI 3 layer and the fabricated perovskite solar cells were examined using a high-resolution scanning electron microscope (HR SEM, JSM-7600F, JEOL) and a focused ion beam assisted SEM (FIB-SEM, Auriga, Carl Zeiss). To avoid a charging effect, a 10 nm-thick Pt layer was deposited on the top of the substrate. The absorbance of the MAPbI 3 perovskite active layer was analyzed using a UV/Vis spectrometer (Lambda 45, Perkin-Elmer) in the wavelength range from 500 to 900 nm. Photocurrent density voltage curves were recorded using a solar simulator (Oriel Sol 3A class AAA) equipped with a 450 W xenon lamp (Newport 6279NS) and a Keithley's series 2400 source meter under AM 1.5G one sun illumination (100 mw cm 2 ). An aperture mask was used while measuring the devices in reverse scan mode at 200 ms scan rate. The external quantum efficiency (EQE) was measured using a specially designed EQE system (PV measurement Inc.), wherein a 75 W xenon lamp (USHIO, Japan) was used as a light source to generate a monochromatic beam. Acknowledgements This study was supported by the Global Frontier R & D Program at the Center for Multiscale Energy System and funded by the National Research Foundation under the Ministry of Science, ICT & Future Planning, Korea (under contracts No. NRF , NRF-2012M3A6A and NRF-2012M3A6A ). References 1 H.-S. Kim, C.-R. Lee, J.-H. Im, K.-B. Lee, T. Moehl, A. Marchioro, S.-J. Moon, R. Humphry-Baker, J.-H. Yum, J. E. Moser, M. Grätzel and N.-G. Park, Sci. Rep., 2012, 2, A. Kojima, K. Teshima, Y. Shirai and T. Miyasaka, J. Am. Chem. Soc., 2009, 131, J. Burschka, N. Pellet, S. J. Moon, R. Humphry-Baker, P. Gao, M. K. Nazeeruddin and M. Grätzel, Nature, 2013, 499, M. Lee, J. Teuscher, T. Miyasaka, T. N. Murakami and H. J. Snaith, Science, 2012, 338, H.-S. Kim, I. Mora-Sero, V. Gonzalez-Pedro, F. Fabregat- Santiago, E. J. Juarez-Perez, N.-G. Park and J. Bisquert, Nat. Commun., 2013, 4, Research Cell Efficiency Records, NREL ncpv/. This journal is The Royal Society of Chemistry 2015 J. Mater. Chem. A

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7 Electronic Supplementary Material (ESI) for. This journal is The Royal Society of Chemistry 2015 Supporting Information Thermodynamic Regulation of CH 3 NH 3 PbI 3 Crystal Growth and Its Effect on Photovoltaic Performance of Perovskite Solar Cell Namyoung Ahn 1, Seong Min Kang 1, Jin-Wook Lee 2, Mansoo Choi 1, * and Nam-Gyu Park 2, * 1 Department of Mechanical and Aerospace Engineering, Seoul National University Seoul , Korea 2 School of Chemical Engineering and Department of Energy Science Sungkyunkwan University, Suwon , Korea Derive equation of thermodynamic MAPbI 3 reaction process. From the relation (8) in the manuscript, we could derive a logarithmic formula by introducing constant C'. lny(grain size) = ∠G c 3kT Substituting equation (7), we could derive a formula about relationship between grain size and concentration. lny = 1 3kT 32 ( kt V M ln C C 0 ) 2 + C ' + C' Finally, the equation could be obtained by replacing concentration C with X.

8 lny = 32σ 3 sl 3kT( kt V m (lnx lnc 0 (T))) 2 Here, the equation was summarized as a simple formula with substitution other terms to constant, except for concentration. lny = B (lnx A) 2 + C It would be assumed that the equilibrium concentration is 0.02 M of MAI solution at room temperature since the PbI 2 film could not react with 0.02 M of MAI solution. In this manner, a value of A would be -3.19, which means natural log value of equilibrium constant. The other value of B and C were mathematically evaluated in order that the model was fitted with an actual data in Table S1, as result, B and C were 1.22 and 3.73 respectively (see Figure 3). + C ' Table S1. Grain sizes, short-circuit photocurrent density (J sc ), open-circuit voltage (V oc ), fill factor (FF) and power conversion efficiency (PCE) versus MAPbI 3 concentration. Data were taken from reference S1. MAI M M M M M Concentration Grain Size (nm) J sc (ma/cm 2 ) V oc (V) FF PCE (%)

9 Figure S1. Photograph of MAPbI 3 coated substrates depending on MAI concentrations and reaction temperature. References S1. J.-H. Im, I.-H. Jang, N. Pellet, M. Grätzel and N.-G. Park, Nat. Nanotechnol., 2014, 9,