Direct Observation of Long Electron-Hole Diffusion Distance in CH3NH3PbI3 Perovskite Thin Film

In high performance perovskite based solar cells, CH3NH3PbI3 is the key material. We carried out a study on charge diffusion in spin-coated CH3NH3PbI3 perovskite thin film by transient fluorescent spectroscopy. A thickness-dependent fluorescent lifetime was found. By coating the film with an electron or hole transfer layer, [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) or 2,2′,7,7′-tetrakis(N,N-di-p-methoxyphenylamine)-9,9′-spirobifluorene (Spiro-OMeTAD) respectively, we observed the charge transfer directly through the fluorescence quenching. One-dimensional diffusion model was applied to obtain long charge diffusion distances in thick films, which is ~1.7 μm for electrons and up to ~6.3 μm for holes. Short diffusion distance of few hundreds of nanosecond was also observed in thin films. This thickness dependent charge diffusion explained the formerly reported short charge diffusion distance (~100 nm) in films and resolved its confliction to thick working layer (300–500 nm) in real devices. This study presents direct support to the high performance perovskite solar cells and will benefit the devices’ design.

an important parameter when calculating the charge diffusion distance by one-dimensional diffusion model 11,12 . It seems that all these conflicts need a better explanation.
To clarify these conflicts, we performed a study of directly observing the charge transfer in perovskite with various thicknesses and with an electron/hole transfer layer, by means of time-resolved transient fluorescence. It shows that the charge diffusion in CH 3 NH 3 PbI 3 is of distance at micrometer scale, which obviously longer than film thickness. The study also explains why former studies provide short diffusion lengths. The results show that hole diffusion is faster than electron within perovskite thin film.

Results
Absorption coefficient of CH 3 NH 3 PbI 3 . All perovskite films discussed here were prepared by a twostep dipping procedure similar to a report 22 and our study recently 23 on flat glass substrates. Figure 1 shows the absorption coefficient of CH 3 NH 3 PbI 3 derived from the absorption spectrum (see details in Supplementary Information, SI). This spectrum, which is in line with former reports, covers the entire UV and visible range up to 760 nm 11,24 . At 517 nm (the wavelength of pump light), a coefficient of 1.2 × 10 5 cm −1 is slightly higher than the reference 11 , corresponding to a penetration depth of 84 nm.
Thickness dependence of lifetime. The thickness of four prepared perovskite films are determined by a profilometer and listed in Table 1. An insulating polymer poly(methylmethacrylate) (PMMA) layer was coated atop the neat perovskite films for all photoluminescence (PL) decay measurement to passivate their moisture sensitivity 25 . By excitation at 517 nm, their transient fluorescent decay for the peak emission wavelength are shown in Fig. 2. The lifetimes for each thickness are also listed in Table 1. For a brief comparing, the curves are fitted by stretch exponential decay function 26 . The lifetimes show thickness dependency. For the films of 63 nm and 156 nm, their decays are 2.8 and 12.6 ns, which is similar to the reports 11,12 . For the two thick films of 254 and 310 nm, they have quite identical fluorescence decay as 90 ns and 91 ns. This means that the fluorescent decay is thickness-dependent in thin films, which disappears in thick ones. CH 3 NH 3 PbI 3 characterization. The thickness-dependent fluorescence lifetime is analogous to previous reports on perovskite crystal grain size 26 . To investigate the influence of crystallite nature on PL properties, a series of scanning electron microscopy (SEM) and X-ray diffraction (XRD) measurement were performed on perovskite films of various thickness. Top-view SEM images of four samples mentioned above are shown in Fig. 3a-d. The thinnest film (made by 0.3 M PbI 2 ) in Fig. 3a is a thin layer of individual nanocrystallites with plenty of voids or pinholes. The average grain size is about few tens to   Table 1. Summary of the stretched exponential fitting for the PL decays in Fig. 2.
100 nm. When films became thicker, as shown in Fig. 3b-d, the undesired voids evidently decreased, generating much more compact morphology. Meanwhile, larger crystallites were obtained in thick film, e.g. in Fig. 3d, the crystal size is of ~250 nm. This evolution of grain growth is in agreement with previous reported thermally annealed perovskite films 13,15 . The corresponding XRD patterns ( Fig. 1 in SI) clearly show the perovskite structure (14.66°, 27.09°, 31.82°) with the presence of residual unreached PbI 2 , in keeping with a previous study about PbI 2 deposited on flat glasses 22 . Moreover, the relative amount of PbI 2 decreases when thickness increases. Since the fabrication procedures for each sample are the same, this tendency should be attributed to the thickness for different samples.

PL decays with and without quenchers.
To examine the charge transfer properties of the CH 3 NH 3 PbI 3 film, transient fluorescence experiments were performed by measuring the PL decay in perovskite film with or without a selected electron or hole acceptor. We made two samples with low and  high PbI 2 concentrations, as listed in Table 2. Figure 4 shows the corresponding PL results of a thick perovskite film (390 nm). As shown in Fig. 4a and Table 2, the perovskite/PMMA film has a long lifetime of 170 ns, which we will explain in discussion. When the film was coated with a charge transfer layer, PCBM, e.g., fast fluorescent quenching happens (Fig. 4b). The decay is as fast as 1.24 ns, which means highly efficient electron transfer to the interface. It is even faster, when Spiro-OMeTAD is coated above perovskite films, as shown in Fig. 4c. The decay is 0.17 ns, close to the instrument response of streak camera. For the thinner film of 95 nm, PL decays show the same trend ( Fig. 2 in SI). The neat perovskite film has a lifetime of 12.4 ns, which decreases to 0.40 ns and 0.16 ns for PCBM and Spiro-OMeTAD coated samples, respectively.

Discussion
The thickness-dependent lifetimes indicate that the fluorescent quenching is neither local, nor to the surfaces. Then this quenching is more like a boundary related effect. We observed that the size of the grain become larger when the films are thicker. In addition, the films become compact with less defects. Then the abundant surface area, void, and defects in thin film should be responsible for the quenching. In thick films, the boundary effect become insignificant. In our study, it is above 250 nm, as shown in Fig. 2. This grain size independency was also shown in D'Innocenzo's report, in which the lifetime of ~100 ns was found for grains between 0.2-2 micron 26 . Smaller grains presenting dramatically reduced lifetime was also presented. This proves that when the grain size becomes too small, it will produce reduced lifetime. However, in an optimized real device of 300-500 nm, the small size grain is avoided and the lifetime is not sensitive to detailed morphology. On the contrary, in semi-transparent device and thin films for photophysical study, small size grain exists with reduced lifetime. Therefore, towards its real applications, we prefer to take film thickness as a basic parameter to describe the lifetime dependency, instead of grain size and defects, which had already been optimized in cells with high efficiency by many groups.
The SEM and XRD studies reveal the mechanism of this dependency. The SEM images manifest the evolution of grain growth, from the level of below 100 nm to ~250 nm, and the diminishing of voids or pinholes. We can rationally assume that long lifetime exists when large size of crystallite are the main species in film, and the boundaries between crystallites have a significant impact on the fluorescence characteristic 27,28 , esp. when the crystal size is small and not compact. Some groups showed that a proper amount of PbI 2 species can fill perovskite grain boundaries, eliminate defect states, and thus slow down the carrier relaxation, whereas a large amount of excessive PbI 2 is detrimental to charge transport 29,30 . This is in according with our XRD results for thick and thinner perovskite films, respectively. We believe this is the quenching mechanism of thickness dependent fluorescent lifetime. In short, when the perovskite layer become thicker, it has larger crystallite size with reduce overall grain boundary area, and much less defects due to reduced PbI 2 at boundary. Both the factors finally make the fluorescence emitted by thick film independent to thickness.
It has been well established that excitons in perovskite are nearly fully ionized because of low binding energy 2,31,32 . So the charge diffusion directly relate to their lifetime. Therefore, the film thickness dependent fluorescent lifetime becomes an important issue here. When the film is thin, the lifetime is short due to the boundary defects. This means that to find out the unaffected charge diffusion distance, the real lifetime needs to be established in advance. As mentioned earlier, in the thicker film of ~280 nm, a long lifetime of 140 ns can be found at lowest pump intensity 21 . In addition, when the perovskite are in large crystal of ~1 μ m, its lifetime is also at ~100 ns timescale 26 . These results are very similar to our observation in thick films. It reasonably suggests that the native lifetime for CH 3 NH 3 PbI 3 without considerable boundary defect is at ~100 ns timescale, though small differences exist among research groups. To our knowledge, for reports whose lifetime is ~100 ns, they are shown as thicker films or larger grain sizes.
We performed a step forward experiment to verify the grain size dependent fluorescent decay. For thick film of 345-390 nm, grain size of 150-350 nm were prepared, shown in SI Fig. 4. We found that grain size has little effects on lifetime. All of them present lifetime of ~200 ns, as shown in SI Fig. 5 and SI Table 1. Therefore, we can conclude that the grain size should have no significant effect on charge  Table 2. Summary of parameters in Fig. 4. The fluorescent decay parameters obtained by rate equation (the monomolecular trapping rate (A), bimolecular radiative recombination coefficient (B), and effective PL lifetime (τ PL ), the PL decay of perovskite coated with and an electron transport layer (ETL, PCBM) and hole transport layer (HTL, Spiro-OMeTAD), the calculated diffusion coefficients (D), and diffusion lengths (L D ) of a thin and a thick CH 3 NH 3 PbI 3 perovskite films.
diffusion. The grain size has large tunable range when it is compact and with less defects. This also explains that high performance perovskite solar cells can be repeated among labs, in spite of morphological variation.
The one-dimensional diffusion model are describe in the SI. The fittings produce diffusion constant, D. The charge diffusion distance L D , is calculated by the equation where τ PL is PL lifetime of 390 nm in this study by simple rate equation 21,31,32 . We take the duration when fluorescence decays to 1/e of initial intensity as the diffusion time for electrons and holes. As summarized in Table 2, we obtain the electron diffusion coefficient of 0.18 cm 2 s −1 and corresponding diffusion length of ~1.7 μ m. This confirms the observation by EBIC method 17 . As a comparing, when taking lifetime of the thinner film, 95 nm, we can calculate the corresponding diffusion constant of 0.06 cm 2 s −1 and diffusion length of 273 nm. This result is close to other reports based on thin films 11,12,33,34 . For diffusion of hole, the D is found 2.3 cm 2 s −1 in perovskite/Spiro-OMeTAD film, which is one order larger than the electron diffusion coefficient. The corresponding charge diffusion distance is calculated as ~6.3 μ m. For the thin film of 95 nm, this distance is 459 nm, as listed in Table 2. It should be remarked here that both the electron and hole's diffusion distances obtained are much longer than the thickness of the perovskite films ever made with top solar energy conversion efficiency.
There are several points should be addressed here. The first is that though the charge diffusion distance are thickness dependent, it is much longer than the film thickness, even for the thin film less than 100 nm. Therefore, both in thin semi-transparent devices and black thick devices, the high cell performance can both be achieved. The long diffusion distances provide a large tunable range for preparing perovskite working layers, both for thickness and morphology. The second is that the charge transfer balance between the electrons and holes is not exactly shown in our study. However, it is less important for currently developed devices, which are usually 300-500 nm. The last one is that the lifetime of CH 3 NH 3 PbI 3 may not be an exact number but a range around 100 ns or larger, since the crystal grain size, defects, preparation procedure, post treatment, pump energy, and fitting methods et al. can not exactly be the same. However, the lifetime variation will not make the diffusion distance lower than micrometer level.
The plain films provide a simple model to study the charge diffusion inside perovskite working layers. Another widely applied cell structure is with mesoporous scaffold such as TiO 2 and Al 2 O 3 . Due to the restricted growth for crystals and large interface area, the charge diffusion inside the structure is much more complicated. E.g. the fluorescent lifetime varies to the size of mesoscopic pores, the type of scaffold, and capping layer 35,36 . High speed charge transfer to TiO 2 of 200 fs was found through ultrafast spectroscopy, which will benefit these devices which possess large interface area 37 . At molecular level, the interface shows oriented permanent dipoles indicating the existence of ordered perovskite layer 38 . In addition, the perovskite inside scaffold shows co-existence of medium range crystalline and local structural coherence 39 . These studies reveal the significant differences of these mesoporous cells compared to the planner structured devices. In spite of these differences, it has been reported that the charge diffusion in mesoporous devices has lower coefficient than the layered cells 40 . It is also reported that the existence of capping layer may recover the longer charge diffusion distance 36 . Base on these study, we can summarize that the charge diffusion distance inside the mesoporous layer is smaller, but may benefit from the large interface area because of the highly efficient charge extraction 5,37 .
In conclusion, we found that the fluorescent lifetime of spin-coated CH 3 NH 3 PbI 3 perovskite thin film depends on the film thickness. The lifetime increases towards the increment of film thickness, till ~250 nm. The lifetime finally increases to > 100 ns. The fluorescent quenching in thin film is due to the defects at grain boundary. Therefore we take a thick film of 390 nm to study the charge diffusion in CH 3 NH 3 PbI 3 . After coating charge-transfer layer, PCBM or Spiro-OMeTAD, and applying one-dimensional diffusion model, we can obtain the charge diffusion distance of 1.7 μ m for electrons and 6.3 μ m for holes. For thin film of 95 nm, a result of short diffusion distance similar to other reports is found. This study resolves the current conflict between the measured short charge diffusion distance and thick working layer in high efficient devices. The result shows that in case of thin and thick films, CH 3 NH 3 PbI 3 both can provide long charge diffusion distance for best cell performance.

Methods
Sample preparation. All samples were fabricated on glass slide substrates. First, glass substrates were cleaned sequentially by ultrasonic bath in detergent water, deionized water, acetone and ethanol for 15 min, respectively, and then exposed to oxygen plasma for 15 min to achieve optically smooth films. The CH 3 NH 3 PbI 3 perovskite were fabricated with a two-step sequential deposition method under nitrogen atmosphere. The pre-cleaned glass substrates were spin-coated a PbI 2 solution (6000 rpm, 0.3 M, 0.5 M, 0.8 M, and 1.1 M) of N,N-dimethylformamide (DMF) at ambient temperature to obtain layers of different thicknesses. After drying at 60 C in ambient environment for 6 h, the films were dipped into CH 3 NH 3 I solution in 2-propanol (15 mg/mL) at 65 C for 90 s and then rinsed with 2-propanol. For the samples fabricated by using various concentration of CH 3 NH 3 I solution (10 mg/mL, 15 mg/mL and 20 mg/mL), PbI 2 was kept at 1.0 M. After CH 3 NH 3 PbI 3 annealing at 100 C for 40 min, Spiro-OMeTAD (10 mg/mL), PCBM (10 mg/mL) or PMMA (20 mg/mL) was spin-coated at 2000 rpm for 60 s atop the CH 3 NH 3 PbI 3 perovskite films.
Characterization details. XRD patterns were obtained using a Philips X'PERT-MRD x-ray diffractometer system with a Cu Kα radiation source (λ = 0.1541 nm) at 45 kV and 40 mA. SEM images were collected using a Hitachi S-4800 microscope, with a working bias of 10 KV. Sample thicknesses were measured using a Veeco Dektak 150 profilometer. Ultraviolet-visible (UV-vis) absorption measurements were recorded with an Agilent 8453 UV-vis Spectroscopy System at room temperature.
Time-resolved photoluminescence. The time-resolved fluorescence spectra were recorded with a high resolution streak camera system (Hamamatsu C10910). We used an amplified mode-lock Ti: Sapphire femtosecond laser system (Legend, Coherent) and a two-stage optical parametric amplifier (OperA Solo, Coherent) to generate the pump beam with a repetition rate of 1 KHz. All the samples were excited by 517 nm at room temperature. The excitation fluence on the sample surface was in the range from 9 nJ/cm 2 to 1.2 μ J/cm 2 per pulse.