Crystallization Kinetics and Morphology Control of Formamidinium–Cesium Mixed‐Cation Lead Mixed‐Halide Perovskite via Tunability of the Colloidal Precursor Solution

The meteoric rise of the field of perovskite solar cells has been fueled by the ease with which a wide range of high‐quality materials can be fabricated via simple solution processing methods. However, to date, little effort has been devoted to understanding the precursor solutions, and the role of additives such as hydrohalic acids upon film crystallization and final optoelectronic quality. Here, a direct link between the colloids concentration present in the [HC(NH2)2]0.83Cs0.17Pb(Br0.2I0.8)3 precursor solution and the nucleation and growth stages of the thin film formation is established. Using dynamic light scattering analysis, the dissolution of colloids over a time span triggered by the addition of hydrohalic acids is monitored. These colloids appear to provide nucleation sites for the perovskite crystallization, which critically impacts morphology, crystal quality, and optoelectronic properties. Via 2D X‐ray diffraction, highly ordered and textured crystals for films prepared from solutions with lower colloidal concentrations are observed. This increase in material quality allows for a reduction in microstrain along with a twofold increase in charge‐carrier mobilities leading to values exceeding 20 cm2 V−1 s−1. Using a solution with an optimized colloidal concentration, devices that reach current–voltage measured power conversion efficiency of 18.8% and stabilized efficiency of 17.9% are fabricated.

: Impact of colloids in the precursor solution on the nucleation stage of the FAPb(Br 0.2 I 0.8 ) 3 and the CsPb(Br 0.2 I 0.8 ) 3 perovskite system. A) A series of photographs of FAPb(Br 0.2 I 0.8 ) 3 thin films spin coated and annealed at 70°C under nitrogen for 1 minute, prepared with a 1.15M FAPb(Br 0.2 I 0.8 ) 3 solutions aged in a N 2 atmosphere for various periods of time after the addition of hydrohalic acid. B) A series of photographs of CsPb(Br 0.2 I 0.8 ) 3 thin films spin coated and annealed at 70°C under nitrogen for 5 minutes, prepared with 0.3M CsPb(Br 0.2 I 0.8 ) 3 solutions aged in a N 2 atmosphere for various periods of time after the addition of hydrohalic acid. C) Ultraviolet-visible absorbance spectra of corresponding FAPb(Br 0.2 I 0.8 ) 3 thin film after the nucleation stage. D) Ultraviolet-visible absorbance spectra of corresponding CsPb(Br 0.2 I 0.8 ) 3 thin film after the nucleation stage.

Fig. S4
Impact of mixing colloidal solutions with colloid-free solution on the nucleation stage of the FA 0.83 Cs 0.17 Pb(Br 0.2 I 0.8 ) 3     The thin films were fabricated using precursor solutions that have been aged for 0h, 60h and 292h after the addition of the hydrohalic acids.

Modified Williamson-Hall method for microstrain estimation
Broadening and shifts in the XRD peak can be caused by either a reduction in the grain size (Scherrer broadening) and/or non-uniform strain (microstrain). We note that Scherrer broadening will only be significant when the grains are in the range of or less than 100 nm, and as we will discuss later we do not expect this to be a significant contribution here. Strain is the relative change in size of an object with respect to its ideal size (or size before experiencing an external force). The microstrain in a crystalline material is a result of small fluctuations in the lattice spacing, induced by crystal imperfections/structural defects including dislocations, vacancies, stacking faults, interstitials, twinning, and grain boundaries. [1,2], [3] By simply considering Braggs law for scattering of light of wavelength λ, nλ = 2dsinθ, it is clear that small fluctuations in d spacing (i.e. d) will result in small fluctuations, or broadening, in θ when measuring the X-ray diffraction from the material. We quantify the extent of microstrain in our perovskite crystals by analysing the peak broadening in the diffraction patterns according to the modified Williamson-Hall method. [2,4] The effective observed d-space broadening (d obs ) determined from the XRD peak width broadening, is a convoluted function of the Gaussian full width half maximum broadening in the 2θ scan due to the instrument response (d ins ), the grain size (d size ) and the microstrain (d ε ). These can be de-convoluted from the observed broadening, via, where the unit-less microstrain ε is defined as ε = (d ε / ), where d is the mean d-spacing.
For single crystals, the size effect induced peak width broadening can be neglected, hence if d 2 size << d 2 obs 19 and we can write, Therefore, the slope of (d 2 obs -d 2 ins ) 1/2 versus d, gives the magnitude of the microstrain, ε, in the crystals.   3  , on a substrate pre-heated at 70 ᵒC. The films were dried inside a N 2 glovebox on a hot plate at a temperature of 70 ᵒC for 1 minute. The films were then annealed in an oven in an air atmosphere at 185ᵒC for 120 minutes. During this annealing process, the samples were covered with a large glass container to shield them from any contaminates such as dust particles. For samples annealed at 220ᵒC, the thin films were heated for 10m in air at 220ᵒC. These films were then transferred to a 185ᵒC oven for 110m.

perovskite composition of A) solar cell efficiency B) short-circuit current density C) open-circuit voltage D) Fill-factor
Preparation of tin oxide (SnO 2 ) nanoparticles: SnO 2 nanoparticles were synthesized via hydrothermal method, similarly to the method described by Zhang et al [5] . We dissolve 467 mg of SnCl 4 ·5H 2 O (98%, Sigma-Aldrich) in 20 ml of deionized (DI) water. After 10 minutes of stirring at room temperature, a fully dissolved, clear solution is obtained. This solution is then transferred to a Teflon-lined stainless steel autoclave, and heated for 2 hours at 200 ᵒC. After heating treatment, the autoclave is quenched to room temperature using cold water. The precipitates were centrifuged at a speed of 9000 rpm for 15 min. The nanoparticles were redispersed in ethanol using a spin-coater. This washing treatment was repeated 3 times. After the final washing treatment, the nanoparticles were also re-dispersed in ethanol. 2) Phenyl-C61-butyric acid benzocyclobutene ester (PCBCB): PCBCB synthesized using the method described by N. Deb et al. [6] After FTO cleaning process, a 3 mg ml -1 of PCBCB in anhydrous ethanol (99.5%, Sigma-Aldrich) is spin coated in a N 2 atmosphere on a clean FTO substrate at 2000 rpm for 30s, and annealed in N 2 at 200 ᵒC for 10m.

Hole
Electrode: A 50 nm gold electrode was thermally evaporated under vacuum of ≈10 −6 Torr, at a rate of ≈0.2 nm·s -1 .

Device characterization:
The current density-voltage (J-V) curves were measured (2400 Series SourceMeter, Keithley Instruments) under simulated AM 1.5 sunlight at 100 mWcm -2 irradiance generated by an Abet Class AAB sun 2000 simulator, with the intensity calibrated with an NREL calibrated KG5 filtered Si reference cell. The mismatch factor was calculated to be less than 1%. The active area of the solar cell is 0.0919 cm -2 . The forward J-V scans were measured from forward bias (FB) to short circuit (SC) and the backward scans were from short circuit to forward bias, both at a scan rate of 0.38V s -1 . A stabilization time of 5 seconds at forward bias of 1.4 V under illumination was done prior to scanning. The EQE was measured using Fourier transform photocurrent spectroscopy. The EQE was measured in short-circuit (Jsc) configuration following a 1.4V prebias for 5 seconds, using a simulated air-mass (AM) 1.5 100 mW cm -2 sun light as illumination source.
Substrate Preparation: Devices were fabricated on fluorine-doped tin oxide (FTO) coated glass (Pilkington, 15Ω □ -1 ). Initially, FTO was removed at specific regions where the anode contact will be deposited. This FTO etching was done using a 2M HCl and zinc powder. Substrates were then cleaned sequentially in Hallmanex detergent, acetone, isopropyl alcohol, and dried with a compressed air gun. The FTO was then cleaned using a "3:1 piranha solution" composed of 3 volume parts of sulfuric acid (H 2 SO 4 ) and 1 volume parts of hydrogen peroxide (H 2 O 2 ) for 90 mins. The FTO was then rinsed in two sequential deionized water (DI) water baths and dried with a compressed air gun.

X-ray diffraction:
The one-dimensional and two-dimensional X-ray diffraction spectra of the prepared films were measured using a Rigaku SmartLab X-ray diffractometer with CuK 1 (1.54060 Å) and a HyPix-3000 2D hybrid pixel array detector. All the perovskite films for XRD measurement were deposited on FTO coated glass substrates.

Dynamic Light Scattering:
The dynamic light scattering (DLS) was measured using a Malvern Zetasizer Nano ZS. The measurement was done with a quartz cuvette at room temperature.
Optical pump -THz probe spectroscopy: The optical-pump-THz-probe setup uses a Spectra Physics Ti:Sapphire regenerative amplifier to generate 40 fs pulses at a center wavelength of 800 nm and a repetition rate of 1.1 kHz. Terahertz pulses were generated by optical rectification in a 450 μm thick GaP(110) single crystal and detected by electro-optic sampling in a ZnTe crystal (0.2 mm (110)-ZnTe on 3 mm (100)-ZnTe). Pulses for optical excitation of the samples at 400 nm have been generated using a beta barium borat frequency doubling crystal.
Optical excitation was carried out from the substrate side of the film. The diameters of optical pump and THz probe beams at the sample position were 3.6 mm and 2.4 mm (FWHM), respectively. Measurements were performed with the entire THz beam path (including emitter, detector and sample) in an evacuated chamber at a pressure of <10 -2 bar.

Derivation of photoconductivity and charge carrier mobility from change in THz electric field transmission
Assuming the thickness of the perovskite film is smaller than the THz wavelength, the sheet photoconductivity ΔS of a thin film between two media of refractive indices n a and n b can be expressed as where the product ε 0 c denotes the invert of the vacuum impedance and ΔT/T the photoinduced change in THz electric field transmission over total transmission. As the experiment has been performed in an evacuated box under vacuum, the films are surrounded by vacuum from one side (n b = 1) and in direct contact with the z-cut quartz substrate from the other side (n a = 2.13) through which the photoexcitation of the sample occurs.
The charge-carrier mobility µ can be calculated as follows (4) where is the sheet photoconductivity of a thin film, e is the elementary charge and N is the number of photoexcited charge-carriers. A eff is the effective area of the overlap of optical pump and THz probe pulse calculated as follows The number of photoexcited charge-carriers N can be determined as follows where φ is the ratio of charge-carriers produced following photon absorption, also known as the photon-to-charge branching ratio, which is assumed to be unity. E, is the energy contained in an optical excitation pulse of wavelength λ, R pump is the reflectivity of the sample at normal incidence of the excitation beam, T pump denotes for the portion of pump beam which is transmitted through the sample. As φ is declared unknown, we define an effective mobility ̃ = φµ which can be directly obtained from our experiments The ascertained charge-carrier mobility contains contributions from both electrons and holes.
Hence, the derived values for mobility represent the sum of electron and hole mobilities. As φ ranges between 0 and 1, the effective mobility describes a lower limit.
Furthermore, the effective carrier mobilities have been corrected by scaling the onset value of with the relative surface coverage of the respective films, which were obtained by processing SEM images. The surface coverage procedure suffices our requirements to account for actual effective carrier mobilities in the films as we rule out any excess absorption in possibly thicker films. Due to high absorption coefficients most of the light is being absorbed within the first hundreds of nanometers, for which reason a thickness correction is not required, especially since the thickness of all measured films exceeds 400 nm.