Photophysical Model for Non-Exponential Relaxation Dynamics in

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Photo-Physical Model for Non-Exponential Relaxation Dynamics in Hybrid Perovskite Semiconductors Rishabh Saxena, Ayush Kumar, Nakul Jain, Naresh Kumar Kumawat, Krishnamachari L. Narasimhan, and Dinesh Kabra J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11503 • Publication Date (Web): 05 Dec 2017 Downloaded from http://pubs.acs.org on December 5, 2017

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The Journal of Physical Chemistry

Photo-Physical Model for Non-Exponential Relaxation Dynamics in Hybrid Perovskite Semiconductors Rishabh Saxena1, #, Ayush Kumar2, #, Nakul Jain1, Naresh K. Kumawat1, K.L. Narasimhan3, Dinesh Kabra1* 1

Department of Physics and 3Electrical Engineering, Indian Institute of Technology Bombay,

Powai, Mumbai 400076, India 2

Space Applications Center, Indian Space Research Organization, Ahmedabad 380015, India

*E-mail: [email protected]; Phone No. +91-022 2576 7589

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT The photoluminescence (PL) decay of hybrid halide perovskite single crystals (MAPbX3, MA=CH3NH , Pb=Pb2+, X= Br- and I-) is measured over four orders of magnitude in intensity over the time scales of 100s of ns to few microseconds. This long PL decay is non-exponential suggesting the presence of a distribution of carrier relaxation times. Spectro-temporal studies show that the emission peak red-shifts with increasing time. The physics of this problem is closely related to donor-acceptor pair recombination in crystalline semiconductors and recombination in a-Si:H. Based on these models, we present a simple model to account for the recombination dynamics in the perovskite systems. This model also accounts for the fluence dependence of the recombination kinetics. In this model, a fraction of the photo generated electrons and holes are trapped in localized states. The electrons tunnel to the hole sites for recombination. The broad distribution of lifetimes is a consequence of the fact that the tunneling probability is very sensitive to the separation of electron-hole pairs and PL decay dynamics is function of excitation fluence, i.e., carrier density generated by optical excitation. The red shift arises from the fact that holes and electrons are trapped at different energies.


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INTRODUCTION Methylammonium lead halide perovskites (MAPbBX3) have emerged as an important optoelectronics material in recent years.1 These materials are attractive as they are solution processible with very good optoelectronic properties. MAPbBX3 perovskites are direct band gap semiconductors2 with high carrier mobility (164 ± 25 cm2 V−1 s−1 in CH3NH3PbI3 crystal3), large diffusion length of charge carriers (175 µm in CH3NH3PbI3 crystal and 1µm in films4), high absorption coefficient (105 cm-1), low exciton binding energy (comparable to room temperature thermal energy5), high photoluminescence yield with narrow PL FWHM6 (full width at half maximum) and low Urbach energy.7-9 In a very short time these materials have emerged as an important material for solar cells,10,

11

light emitting diodes,12,

13

detectors14 and other

optoelectronic applications.15 Photo-excitation gives rise to both free charges and excitons in this material.5,

16, 17

Despite

achieving high PCE (Power Conversion Efficiency), an exact underlying photo-physics is lacking in the understanding of long-lived PL components for perovskite materials. Timeresolved photoluminescence (TRPL) spectroscopy is extremely helpful for determining the recombination lifetime and exploring how charge carrier density, structure perfection affects recombination dynamics.18 Many TRPL experiments show that the PL decay stretches to long times.19, 20 This has been attributed to effects such as photon recycling.4, 21, 22 However, assuming a PL efficiency of ~20% at low fluence level at which TRPL is carried out, it is difficult to account for the fact that TRPL data extends to microseconds.19, 20 Fang et.al. reported photon recycling efficiencies were less than 0.5% in MAPbI3 and MAPbBr3 single crystals and that photon recycling is likely to be unimportant.21 According to their study the surface and bulk PL was different in the perovskites and could account for the observed 3 ACS Paragon Plus Environment


behavior. Molecular dynamics study by Walsh et. al.23,

24

suggested that while the average

structure may appear to be cubic the local PbI6 octahedra is distorted. Pb-I-Pb bond angles are not found to be 180° in the relaxed structure. Molecular rearrangements, octrahedra distortion and ion movement creates fluctuations in electrostatic potential of energy landscape of crystal and results in separation of electrons and holes in real space.23 Moreover, since conduction and valence band are hybridized states of Pb and I atomic orbitals, causing the band edges to separate (relativistic splitting, i.e., Rashba-Dresselhaus effect) in momentum space, leading to a suppressed recombination rate.24 Also, another theoretical investigation25 based on Rashba splitting suggests that since inversion symmetry is broken at the surface, the band structure of the surface is different from that of the bulk. The authors suggest that the surface band structure is that of an indirect band gap semiconductor which results in long lifetimes. This could explain the observed red shift and weak luminescence at longer times. Also, very recently, Bernard et. al.26 suggested a diffusion model to explain the early part of PL decay dynamics and long-lived component is explained using trap model. It is known that steady state and transient optical properties of MAPbI3 perovskites are found to be affected by the localized states found below the optical gaps in these materials27, 28 and the density of these trap states is estimated to be only one order of magnitude less in single crystals (1015 cm-3)26 than polycrystalline films. In this paper, we present a model invoking these localized states to explain the long-lived PL component that is spectrally red-shifted w.r.t. the main PL peak and the large distribution of lifetimes seen in TRPL measurements .


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EXPERIMENTAL SECTION Perovskite Single Crystal Growth Hybrid perovskite single crystals were grown using the method of Inverse Temperature Crystallization.29,

30

The solubility of the precursor MAPbX3 solutions decreases in certain

solvents at elevated temperatures and this inverse solubility phenomenon is used to synthesize MAPbX3crystals as illustrated in Fig. 1(a). For the growth of single crystals, 1 molar solutions of MAPbI3 in g-butyrolactone (GBL) and MAPbBr3 in N,N-dimethylformamide (DMF) were prepared and were heated in an oil bath at 120°C and 80°C respectively. Figure 1 (b) and (c) show images of MAPbI3 (6mm x 5mm x 2mm) and MAPbBr3 (6mm x 6mm x 2.5mm) crystals with centimeter ruler. (for detailed procedure, see Supplementary Information). X-ray Diffraction Studies For structural phase characterization, PAN analytical made Horizontal X'Pert PRO diffractometer with Goniometer radius 320mm was used. It is working at 1.2kW (40kV and 30mA) and is equipped with Nickel fillet and X’Celerator (1D silicon strip) detector. Few crystals were powdered in mortar and pestle. Powder was speeded on glass plate homogeneously and mounted the plate on diffracting stage of XRD. (See Supplementary Information Figure S2). Steady State and Transient Photoluminescence Measurement Nd-YAG laser (1KHz repetition rate and 840 ps pulse width) was used as a power source. For MAPbI3 532 nm excitation wavelength and for MAPbBr3 355 nm excitation wavelength were used. To vary the laser fluence, neutral density filter of different optical density was used. Laser light was focused on crystals with the planoconvexlens. PL from the sample was collected with a planoconvex lens of a big aperture on the reflection side. We used 400 nm long pass filter for



MAPbBr3 and 600 nm long pass filter for MAPbI3 to discriminate laser light from PL. PL was coupled to an opticalfibre which feeds to the Shamrock SR303i spectrometer. The SR303i was integrated with Andor istar Gated ICCD. The ICCD is triggered by the Laser. The gate width of 2ns delay time were dynamically varied to collect the PL decay. For steady-state PL, peak is centered around 770 nm (1.61 eV) and 535 nm (2.32 eV) for MAPbI3 and MAPbBr3 crystals respectively.


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RESULTS AND DISCUSSION Perovskite single crystals were prepared by a method based on the reduced solubility of MAPbX3 in certain solvents with increase in temperature.29,

30

The procedure adopted for the

growth of these single crystals is depicted in Figure 1(a). 1 molar solutions of MAPbX3 were prepared in GBL (γ-butyrolactone) and DMF (N,N-dimethylformamide) for X = I-, Br- and were heated to obtain different single crystals.29, 30 Figure 1 (b) and (c) show images of MAPbI3 (6mm x 5mm x 2mm), and MAPbBr3 (6mm x 6mm x 2.5mm).

Figure 1: (a) Pictorial diagram of single crystal growth, (b) and (c) images of the MAPbI and 3

MAPbBr single crystals respectively with scale. 3

These crystal sizes are comparable to the sizes reported earlier.30-32 MAPbI3 single crystal is black in color and grows in rhombic dodecahedral type crystal structure, which is typical faceting for the I4/mcm space group32. MAPbBr3 appears brown-red and grows in cubic crystal 7 ACS Paragon Plus Environment


structure which is the stable phase at room temperature.33 The steady state photoluminescence (PL) spectrum of the two samples MAPbI3 and MAPbBr3with peak emission at 1.61 eV (770 nm) and 2.32 eV (535 nm) respectively are shown in Figure S5. The PL FWHMs of both the single crystals (MAPbI3 and MAPbBr3) are comparable (≈ 100 meV). a) 2 ns PL (arb. unit)

4 ns 6 ns 12 ns 22 ns 30 ns

740

760

780

800

λ (nm)

b) 2 ns PL (arb. unit)

4 ns 6 ns 8 ns 14 ns 16 ns

500

t (ns) 540 λ (nm)

520

c) 1.61 PL Peak (eV)

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560

2.34 MAPbI3

MAPbBr3

Diffusion model

1.60

Tunneling model

1.59

2.32 2.30 2.28

1.58 1.57 0

50

100 150 t (ns)

200

2.26 250

Figure 2: PL spectra at different decay time (fluence = 6 µJ/cm2) for (a) MAPbI3 and (b) MAPbBr3 (c) Spectral peak shift of MAPbI3 and MAPbBr3.


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PL spectra for MAPbI3 and MAPbBr3 are shown in Figure 2(a) and (b) respectively for increased time delays. Figure 2(c) shows the peak position as a function of time for clarity for both the crystals. It can be observed that the peak position red shifts with increasing time. This is in agreement with the observations of other reports.4,

21, 22

The luminescence decays as obtained

from Figure 2(a) and (b) for MAPbI3 and MAPbBr3 are non-exponential (Figure S2 and S3). Various hypotheses to explain the red shift of the luminescence with time have been proposed, like photon-recycling4,

22

and Rashba splitting,25 as discussed in introduction. Fang et. al.34

conducted one-photon and two-photon experiments to show that the spectral shift can be attributed to the diffusion of charged carriers from the surface to bulk. An explanation for the long PL decay (in microseconds) and the spectral shift of the PL peak with time can arise from the existence of donor-acceptor pairs. As a starting point, we borrow from the literature of donor acceptor pairs35 which are well known in crystalline semiconductors. In nitrogen doped GaP, excitons are bound to nitrogen atoms. With time these excitons tunnel to pairs of nitrogen atoms resulting in a shift in the emission peak with time.35 A similar effect is seen in a-Si:H.36 In this scenario, after excitation and thermalization, electron-hole pairs (excitons) are localized in space. The density of such localized states is calculated to be 1015 cm-3 (see supplementary information). The calculated localized state density is in agreement with many reports26, 37, 38 but is higher than that reported by Yamada and co-workers.39 Electrons tunnel to hole states and recombine non-radiatively. The long lifetimes arise due to the separation in space R of the tunneling pairs. Non-radiative transitions occur when the electron (hole) tunnels to a defect site. Thus, the initial red-shift can be explained by the diffusion of photo-generated charged carriers from the surface to bulk and, the long-lived PL components and the spectral shift at longer time scales can be attributed to the tunneling of charged carriers via localized centers (as depicted in



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Figure 2(c)). Applying the tunneling model to this recombination process, the decay time τ is then given by35, 36

τ = τ . exp (1)

where, τ is the radiative lifetime (≈ 10-8 sec.) and R0 is the Bohr radius. The distribution of lifetimes is essentially due to the distribution of the ratio R/R0. A critical radius RC is defined such that at RC the non-radiative tunneling rate given by ωo.exp (-2R/R0) is equal to the radiative recombination rate PR, and thus36, 40 =

. ln (2)

where ωo is the vibrational frequency of molecules (≈ 1012 sec-1).36 If RRC radiative tunneling is more probable. The model of Tsang and Street36 explains both - the long lifetimes and the spectral diffusion of the luminescence with time in a-Si:H. We argue here that the spectral diffusion and the long lifetimes seen in Figures 2(a) and (b) are adequately explained by this model. The essential features of this model are briefly summarized below. Optical excitation results in a distribution of different decay times given by a relative probability distribution G(τ). At the end of the excitation the number of pairs created by the excitation pulse of length T is given by41 N(T,τ) = A.G(τ) τ (1-exp (-T/τ)), for T

Photophysical Model for Non-Exponential Relaxation Dynamics in

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