Low surface recombination velocity in solution-grown CH3NH3PbBr3 perovskite single crystal

Organic-inorganic hybrid perovskites are attracting intense research effort due to their impressive performance in solar cells. While the carrier transport parameters such as mobility and bulk carrier lifetime shows sufficient characteristics, the surface recombination, which can have major impact on the solar cell performance, has not been studied. Here we measure surface recombination dynamics in CH3NH3PbBr3 perovskite single crystals using broadband transient reflectance spectroscopy. The surface recombination velocity is found to be 3.4±0.1 × 103 cm s−1, ∼2–3 orders of magnitude lower than that in many important unpassivated semiconductors employed in solar cells. Our result suggests that the planar grain size for the perovskite thin films should be larger than ∼30 μm to avoid the influence of surface recombination on the effective carrier lifetime.

C arrier recombination at semiconductor surfaces has a detrimental impact on solar cell performance because it decreases carrier lifetimes reducing the attainable short-circuit current and open-circuit voltage 1 . Therefore, surface passivation is a necessary component in achieving high efficiency solar energy conversion 2 . The knowledge of surface recombination can also provide guidance for optimizing the grain size in polycrystalline solar cells 3 . Solution processed lead halide based solar cells are undergoing impressive improvements in power conversion efficiency [4][5][6][7][8] . While thorough characterization in transport carrier parameters such as mobility and bulk lifetime shows sufficient characteristics [9][10][11][12][13][14][15][16] , surface recombination has not been studied.
Here we directly probed the carrier dynamics at the surface of CH 3 NH 3 PbBr 3 perovskite single crystals using broadband transient reflectance (TR) spectroscopy. The lead bromide perovskite single crystals are chosen because their sizes are sufficiently large for optical measurements and their native surfaces do not require further polishing or treatments. In the TR measurement, optical excitation of the perovskite single crystal can modulate the reflectance, R, near the bandgap and the relative reflectance change (DR(' o)/R) is recorded by a white-light continuum. We quantitatively reproduce the spectrum using Kramers-Kronig integration of excitonic absorption bleach and find a linear relationship between DR(' o)/R and the total photoexcited carrier density, N, which includes both free carriers and excitons. Pumping at different photon energies with various intensities, we find that kinetics of DR(' o)/R is only sensitive to N near the surface, and is modulated by surface recombination and carrier diffusion that transports carriers away from the surface. The surface recombination velocity (SRV) and carrier diffusion coefficient (D) are found to be 3.4±0.1 Â 10 3 cm s À 1 and 0.27 ± 0.01 cm 2 s À 1 , respectively, by global fitting of a diffusion model to DR(' o)/R kinetics collected at different excitation energies.

Results
Single crystal characterization. The solution-grown CH 3 NH 3 PbBr 3 single crystals studied here have dimensions of B1.4 Â 1.4 Â 0.7 mm 3 (inset of Fig. 1a). We measured the X-ray diffraction using a Bruker D8 Discover diffractometer with two-dimensional area detector. The X-ray beam is located at the front face of the crystal (Fig. 1a). A diffraction pattern of isolated spots, rather than continuous arcs (Debye ring), is observed (Fig. 1b) and it is caused by X-ray diffraction from oriented lattice planes, consistent with high quality single crystals. To obtain the Miller index of the front face, the diffraction intensity is integrated for the region where the crystal front face and the plane determined by the incident and diffracted X-ray beams are perpendicular (inside the black lines in Fig. 1b, where w ¼ 90±5°). Such an integration produces intensity peaks that correspond to diffraction from the lattice planes that are parallel to the front surface of the single crystal (Fig. 1c). These diffraction peaks can be assigned to the family of (001) planes of a cubic phase perovskite crystal, suggesting that the front face belongs to this family of planes. The optical measurements in this work were all conducted with incident light on the front surface. We carried out similar X-ray diffraction measurements on the side face of the crystal and find that it also belongs to the family of (001) planes ( Supplementary Fig. 1). The integration of the whole X-ray diffraction pattern (w integrated from 0 to 180°) produces the diffraction peaks corresponding to other lattice planes ( Supplementary Fig. 1).
Simulation of optical absorption near bandedge. The absorption coefficient (Fig. 1d), determined from ellipsometry ( Supplementary Fig. 2), shows a prominent absorption band at 2.35 eV attributed to excitonic absorption 17,18 . We simulate the spectrum near the bandedge according to Elliott's formula 19,20 : where A is a constant related to the transition matrix element, o is the frequency of light, y is the step function, E g is the bandgap, where R ex is the exciton binding energy, n ex is the principal quantum number and d denotes a delta function. The first term describes the continuum state absorption and the second term is for excitonic states. We modelled the absorption (black line, Fig. 1d) accounting for inhomogeneous broadening by convolving with a Gaussian function (see Supplementary Table 1 for fitting parameters). We neglect the excitonic transitions with n ex larger than 6 because the oscillator strength decreases as 1/n ex 3 . We find the best-fit  values of R ex and E g to be 41.6 meV and 2.394 eV with o0.1 meV fitting uncertainty. The exciton binding energy found here is about half of the calculated value 18 . For photon energies greater than B2.55 eV, the absorption differs from the model because higher energy bands are not included.
Transient reflectance spectroscopy. For the pump-probe TR measurements, the pump is monowavelength with photon energy of 2.48 eV and the probe is broadband with the spectrum ranging from 2.95 to 1.50 eV. The pump penetration depth is calculated as 190 nm from the absorption coefficient while the effective detecting depth is Bl/4pn (n is refractive index) 21 and is B18 nm for probe photon energies near bandgap. The pseudocolor image of the TR spectra is shown in Fig. 2a with a representative spectrum at 2 ps (Fig. 2b). There are two antisymmetric peaks centred at 2.35 eV. At longer delays, the magnitude decreases while the spectral shape persists. Since DR(' o)/R is small (B0.005) and the refractive index n(' o) is much larger than the extinction coefficient k(' o) in the spectral region of interest ( Supplementary Fig. 2), DR(' o)/R can be approximated as: where Dn is the frequency-dependent photon induced change in refractive index associated with a change of absorption coefficient, Da, and is calculated using the Kramers-Kronig transformation 22 : where c is the speed of light, and P means Cauchy principal value of the integral. The photo-induced Da includes both bleach of the exciton absorption and continuum band absorption. However, at low excitation levels, the bleach of continuum band absorption, caused by band filling, is not important because of the low occupation probability. Thus, Da is dominated by the bleach of exciton absorption resulting from photo-induced carriers (free carriers and excitons) due to the phase-space filling effect, and can be expressed as 23,24 : where a 0 is the steady state exciton absorption coefficient (green-dash line, Fig. 1d), N is the total carrier density, equal to the excitation density, and N s is a saturation density (defined to be the carrier density for which 50% of exciton absorption is bleached) and is related to the exciton Bohr radius (note, equation 4 is only valid when No oN S (ref. 25)). We are able to closely simulate DR(' o)/R (blue-dash line, Fig. 2b) by substituting equations (4) and (3) into equation (2) Fig. 3a. The kinetic traces do not display singleexponential behaviour. The decay is faster at early delay and slower at later delay. The initial magnitude shows a linear relationship with excitation density (inset Fig. 3a). At higher excitation levels, the bleach of the continuum band absorption due to the band filling begins to contribute and the exciton contribution saturates, resulting in a Da (as well as TR response) that is no longer linear with the excitation intensity 14 . In this work, excitation intensities are all controlled to be in the linear region (NB0.02N S ) so the photo-induced exciton absorption bleach dominates the TR response. Figure 3b contains the normalized data from Fig. 3a, showing that TR kinetics for a given excitation energy are independent of excitation density, over 1 order of magnitude. The decay of the TR kinetics suggests the carrier depopulation and/or diffusion out of the probing region. In the bulk, the depopulation from first-order radiative and/or Shockley-Read-Hall (nonradiative) recombination is independent of the excitation density. However, they are excluded because the first-order bulk recombination occurs on a much longer time scale (B31 ns, measured by timeresolved photoluminescence, Supplementary Fig. 3). The decay of TR kinetics is therefore attributed to the surface recombination and the carrier diffusion from the surface into the bulk. Since no electric filed is applied, the carriers are expected to diffuse together as either uncorrelated electron-hole pairs or excitons to maintain the charge neutrality.
Diffusion and surface recombination model. To explore DR/R recovery kinetics, we varied the excitation photon energy. In addition to 2.48 eV the sample was excited at 3.10 and 2.28 eV with corresponding penetration depths of 80 nm and 3.7 mm. We confirmed for each photon energy that TR kinetics are independent of excitation density ( Supplementary Figs 4 and 5). However, the DR/R dynamics exhibits a clear dependence on the excitation energy (Fig. 4a). In Fig. 4a the data for different excitation energies are normalized for comparison and we find that the kinetics decays faster for larger excitation energies corresponding to shorter penetration depths. Because of the linear relationship between DR/R and excitation density discussed above, the TR kinetics follow the total carrier dynamics in the effective detecting region. To understand the relationship between carrier density and surface recombination, we use a onedimensional diffusion model that includes surface recombination to reproduce the TR kinetics. The analytical expression for the normalized carrier density distribution as function of time is 26,27 : where t is delay time, x is distance from surface, D is the ambipolar diffusion coefficient, a is absorption coefficient at the excitation energy, S is surface recombination velocity, and w(z) ¼ exp(z 2 )[1 À erf(z)]. Since the pump penetration depths are always larger than effective detecting depth, the carrier density in detecting region can be approximated as the carrier density evaluated at the surface, N(t,0) 28,29 (the validity of this approximation is explored below). A non-linear global fitting routine is used to model the three kinetic traces simultaneously by calculating N(t,0). In the fitting procedure, the absorption  coefficient, a, at each pump-photon energy is determined from the ellipsometry ( Supplementary Fig. 2), and S and D are free fitting parameters. The best-fit results are shown in Fig. 4a with best-fit parameters of S ¼ 3.4 ± 0.1 Â 10 3 cm s À 1 and D ¼ 0.27 ± 0.01 cm 2 s À 1 . To directly compare with reported value, we calculated the ambipolar mobility as 10.8 cm 2 V À 1 s À 1 from D via the Einstein relation. Our value is consistent with that determined from Hall effect measurement of CH 3 NH 3 PbBr 3 single crystals 9 , B1-10 times larger than that obtained for CH 3 NH 3 PbX 3 (X ¼ Br and I) polycrystalline films 11,12,[15][16][17] , and B10 times smaller than that obtained from time-of-flight measurement of the perovskite single crystals 9,10 . The SRV determined here is B2-3 orders of magnitude smaller than those in other important semiconductors (before surface passivation) such as GaAs (SB8.5 Â 10 5 cm s À 1 ) 30 , GaP (SB2 Â 10 6 cm s À 1 ) 31 , InP (SB1.5 Â 10 5 cm s À 1 ) 26 , p-Si (SB2.4 Â 10 5 cm s À 1 ) 32 , n-Si (SB1.2 Â 10 6 cm s À 1 ) 32 , and CdTe (SB5 Â 10 5 cm s À 1 ) 33 .
In Fig. 4b, we display the calculated carrier distributions at various delay times according to equation (5) for 2.48 eV excitation. The carrier density decreases near the surface and increases in the bulk due to diffusion. The inset shows N(t,x) close to surface, where the red shaded region represents the effective detecting depth (B18 nm). The carrier distribution is nearly uniform in this regime, confirming that the carrier density that affects DR/R can be safely approximated by the surface density.

Discussion
We measured TR kinetics for several different single crystals obtained from the same growth method and for different faces of the same crystal ( Supplementary Fig. 6) and find a high degree of reproducibility of our measurement. For single crystal semiconductors, midgap states created by surface defects are primarily responsible for surface recombination. Theoretical calculations suggest that defects at grain boundary or surfaces for CH 3 NH 3 PbX 3 (X ¼ Br and I) perovskite in either cubic or tetragonal phase cause very few midgap states [34][35][36][37] , which may explain the low SRV determined here. Compared with the bromide perovskite, the iodide perovskite likely has less midgap states due to the narrower bandgap, and thus we expect an even lower SRV (ongoing measurements).
For polycrystalline thin films, the surface recombination at grain boundaries can determine the effective carrier lifetime. To minimize the impact from surface recombination, the grain size cannot be too small. The effective lifetime as function of grain size with a given surface recombination velocity (S) is approximated by 38 : where t b is the bulk carrier lifetime measured above, d is planar grain size. The effective lifetimes, t eff , are calculated with D ¼ 0.27 cm 2 s À 1 plotted in Fig. 5 for various SRV. We find that, ultra low SRV (SB10-100 cm s À 1 ) is required to make t eff approach t b when do5 mm, suggesting that surface passivation will be necessary for the perovskite cells with grain size smaller than 5 mm. For unpassivated perovskites (SB10 3 -10 4 cm s À 1 ), the surface recombination influence on the t eff can be eliminated when the grain size is larger than B30 mm. The effective lifetime curve calculated with the measured S and D (Fig. 5, red-dash curve) shows close correspondence with the reported trend of the perovksite solar cell efficiency versus apparent grain size, in which the efficiency was boosted by 10 times as the grain size increased from 1 to B20 mm while efficiency growth slope became much slower when the grain size was larger than B20 mm (ref. 4).
In solar cells, charge recombination across interfaces between active layers and charge transporting layers can also impact the performance. Recently, Tress et al. demonstrated that interfacial charge recombination could be suppressed by optimizing the thickness of the hole transporting layer in perovskite solar cells 39  It should be noted that the surface recombination measured here is from a single crystal surface without post treatment. However, in working solar cells, the surfaces could be unintentionally passivated by contacting with charge transport layers 41 or forming a lead halide over layer 42 , which may lead to a reduction of surface recombination. The passivation dependent surface recombination is beyond the scope of this paper, and will be the subject of the future work.
In summary, we conducted TR measurements for perovskite single crystals. The TR spectra are quantitatively described by excitonic absorption bleach, and carrier dynamics is attributed to surface recombination and carrier diffusion from the surface into the bulk. By simultaneously fitting the carrier decay for different excitation energies, SRV and diffusion coefficient are obtained. The measured SRV is B2-3 order of magnitude smaller than that in many semiconductors used for solar cells. Our result also suggested that the grain size in polycrystalline perovskite film should be larger than B30 mm or grain boundaries should be further passivated to eliminate the surface recombination influence on effective lifetime.

Methods
Transient reflectance spectroscopy. Femtosecond pump-probe TR experiments were performed based on a regeneratively amplified Ti:sapphire laser system that produces B4 mJ laser pulses at 800 nm with 1 KHz repetition rate. The pumps for TR are generated by an optical parametric amplifier pumped by 800 nm fundamental pulses (B1.5 mJ per pulse), which is chopped at a rate of 500 Hz and attenuated by neutral density filter wheels. The broadband probe pulses (420-830 nm) are generated by focusing 800 nm light into a sapphire crystal. The probe pulses are delayed in time with respect to the pump pulses using a motorized translation stage mounted with a retroreflecting mirror. The pump and probe are spatially overlapped on the surface of the sample, and the probe pulses are directed to the multichannel complementary metal-oxide-semiconductor sensor. The size of the focused spot at the sample position for probe and pump beams are 180 and 560 mm, respectively. The total pump-photon flux is determined by measuring the pump power after a pinhole with radius of 200 mm at the sample position. The input photon flux is obtained by subtracting the reflected photon flux from the total photon flux. The excitation density is calculated as the ratio of input photon flux to the effective depth that is 1 over absorption coefficient at pumping energy.
Sample preparation. To a 5 ml dimethylformaide solvent, PbBr 2 (183 mg, 0.5 mmol) and CH 3 NH 3 Br (56 mg, 0.5 mmol) were dissolved. The mixture solution was heated slightly to obtain a transparent solution. This solution was further filtered through a compacted celite column. The filtrate was collected. Two millilitre of this solution was transferred into an inner vial (5 ml in total vial volume) that was placed in a larger outer vial (25 ml in total volume) with 5 ml of toluene inside. Finally the outer vial was carefully sealed. The diffusion of toluene from outer vial into the inner vial was slow and the crystallization process was maintained in dark and undisturbed environment for at least three days. The orange block-shaped single crystals were obtained and characterized by X-ray diffraction.