Direct Measurements of Carrier Transport in Polycrystalline

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

Direct Measurements of Carrier Transport in Polycrystalline Methylammonium Lead Iodide Perovskite Films with Transient Grating Spectroscopy Dylan H. Arias, David T. Moore, Jao van de Lagemaat, and Justin C. Johnson J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b02245 • Publication Date (Web): 11 Sep 2018 Downloaded from http://pubs.acs.org on September 11, 2018

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The Journal of Physical Chemistry Letters

Direct Measurements of Carrier Transport in Polycrystalline Methylammonium Lead Iodide Perovskite Films with Transient Grating Spectroscopy Dylan H. Arias, David T. Moore, Jao van de Lagemaat, Justin C. Johnson* National Renewable Energy Laboratory, 15013 Denver West Pkwy, Golden, Colorado 80401, USA AUTHOR INFORMATION Corresponding Author *[email protected]

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Abstract

Hybrid organic-inorganic halide perovskites have been proposed in many optoelectronic applications, but critical to their increasing functionality and utility is understanding and controlling carrier transport. Here, we use light-induced transient grating spectroscopy to probe directly carrier transport in polycrystalline methylammonium lead iodide perovskite thin films using a weakly perturbative and non-contact method. The data reveal intrinsic diffusion characteristics of the charge carriers in the material and agree well with a simulated model of charge transport in which grain boundaries act as barriers to carrier movement.

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Within the last decade, hybrid organic-inorganic perovskites have become one of the most intensively studied materials in optoelectronics research. Combining relatively simple, low temperature solution processing with tunability, perovskites have the potential to revolutionize the optoelectronics industry, in applications ranging from photovoltaics to light emitting diodes and lasers. The first solar cells utilizing perovskite layers heralded today’s state-of-the-art devices of more than 20% power conversion efficiency,1 which rival the efficiencies of commercialized technologies.2 In addition, reports of low-threshold lasing,3 efficient light emission diode schemes,4 nonlinear optical effects,5 and color tunability via material composition or nanoparticle size,6 hint at the enormous potential of this material class. To realize this potential, a thorough understanding of the transport of energy and charge through these materials is necessary. Depending on the perovskite chemical composition, at room temperature electronic energy can move in the form of excitons (bound electrons and holes) or free carriers.7-9 The effects of film defects, impurities, surface passivation, and polycrystallinity on energy transport and how these affect optoelectronic device performance are still not fully understood. The role of grains and grain boundaries and interfaces is pointed to as a key element influencing transport, but the exact nature of the boundaries and their effects are unclear. In particular, chemical composition, film chemistry and processing, and post-processing, e.g. solvent and thermal annealing,10,11 all affect the boundaries and exciton and charge diffusivity, and techniques to probe the microscopic mechanism of energy transport are critical for comprehensive perovskite film engineering. The surface chemistry and passivation of grain boundaries is a topic of intense study, as it has a clear relevance for carrier lifetime and ultimately efficiency. Experimental techniques characterizing the transport mechanisms often include conductivity and mobility measurements


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utilizing electrical contacts,12,13 which have provided useful information but involve semiconductor/metal interfaces and have yet to produce a clear picture of the role of grain boundaries. Non-contact optical methods include fluorescence quenching, transient absorption (TA) microscopy,14-16 terahertz6 and microwave conductivity,17,18 steady-state photocarrier grating,19 and light-induced transient grating.20 From these techniques have arisen a variety of results about the effects of grain boundaries on recombination and transport. Although diffusion constants for high-quality methylammonium lead iodide (MAPI) crystals or films generally fall in a fairly narrow range (0.2 - 2 cm2/s) and variations can be attributed to sample or experimental conditions, there are several reports of very long diffusion lengths using indirect methods.21,22 However, often in these examples crystallite sizes are large and thus boundaries are not a dominant limiting factor. In other cases, diffusion lengths were inferred from diffusion coefficients and lifetimes that are not necessarily connected in terms of timescale, which could result in misleading conclusions. This concern is obviated for techniques that directly image and time-resolve carrier motion. Recent TA microscopy results revealed a factor of two lower diffusion constant near grain boundaries compared to the bulk of crystallites in polycrystalline films.23 Another study involving fluorescence lifetime imaging revealed unique lifetimes for each grain in a polycrystalline film, which suggested strongly hindered transport across grain boundaries.24 Light-induced transient grating (LITG) spectroscopy is an additional non-contact optical technique previously used to explore carrier transport,20,25,26 exciton transport,27 and thermal transport.28 LITG has much in common with time-resolved imaging techniques and potentially elucidates the microscopic scattering and transport mechanisms via high time and spatial resolution. Specifically, LITG can differentiate between, e.g. ballistic, diffusive or sub-diffusive


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motion, or coherent or incoherent transport; and the timescales and length scales over which different transport mechanisms may dominate. A recent report from Webber et al. utilized LITG to investigate MAPI films.29 The diffusion coefficient was measured to be 0.95 cm2/sec at times less than 1 ns. Later times were not probed, and the grating spacing is much larger than the grain size, which may reduce the sensitivity of the technique to the interaction of carriers with grain boundaries. Another recent result employed LITG to monitor the diffusion length in methylammonium lead halide perovskites of varying composition and as a function of photoexcitation density,20 as well as with additives.30 In the present contribution, we use LITG spectroscopy to study carrier transport in polycrystalline films of MAPI. By utilizing grating spacings that approach the average grain size, we show that grain boundaries play a critical role in determining the kinetics of LITG signals from 100 fs to 5 ns, involving a reduction of diffusivity of several orders of magnitude for carriers crossing grain boundaries compared with diffusion within the bulk of the grain. Simulating the LITG results provides additional critical insight into the nature of carrier transport in polycrystalline perovskite films, including the conclusion that additional fast nonradiative recombination due to grain boundaries is not occurring.

Most commonly, LITG signals are analyzed using one-dimensional diffusion with an exponential decay for the excitation lifetime and a sinusoidal initial condition.27 This results in a LITG signal that decays exponentially, with the rate constant kLITG depending on the grating spacing, 𝛬, the diffusion constant, D, and the intrinsic relaxation time constant , 1

2𝜋 2

𝑘𝐿𝐼𝑇𝐺 = 𝜏 + 𝐷 ( 𝛬 )

(1)


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A plot of the rate constant versus the square of the wavevector, ∆=

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2𝜋 𝛬

, gives a linear

relationship with the slope equal to the diffusion constant. Considering the situation more generally and including nonlinear relaxation terms such as Auger recombination and annihilation effects changes the solution to the 1D diffusion equation to non-exponential decays: 𝜕𝑁(𝑥,𝑡) 𝜕𝑡

𝜕2 𝑁

𝑁

= 𝐷 𝜕𝑥 2 − 𝜏 − 𝑏𝑁 2 − 𝑐𝑁 3

(2)

There is no analytic solution to this equation; however, the diffracted LITG signals can still be modelled as the difference between the peak and null population amplitudes, 𝐿𝐼𝑇𝐺Λ (𝑡) = 𝑁(𝑡, 𝑥 = 0) − 𝑁(𝑡, 𝑥 = Λ⁄2). A simplified approach to accomplish a reasonable fit is to determine the non-linear components and the diffusion coefficients from independent experiments, which we describe below. In many cases it is preferable to reduce fluence levels such that the nonlinear relaxation contributions are minimal and can be ignored. Alternatively, using only the long-time component of the TG decay avoids the nonlinear relaxation contributions because the population densities have decreased to the point where only the linear term is relevant.

Figure 1. Left, Schematic of LITG setup. Pump and probe arms are focused to a phase mask (PM) to generate four beams used in the experiment. The beams are imaged to the sample where the PM pattern is re-created with a grating spacing Λ. Right, Typical SEM image of polycrystalline films. Scale bar is 2 µm.


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The experimental setup is depicted in Figure 1 with details in Methods. A 790 nm, 150 fs laser pulse is split by a beamsplitter with a variable delay of up to ~5.5 ns between the two beams. The beams are collected and focused on a phase mask31,32 with varying grating spacing, and the +1/-1 orders of diffraction are collected and imaged to the sample. The two pump beams create a spatially periodic initial excitation. After a delay, a probe pulse impinges upon the excitation grating and diffracts. A reference local oscillator pulse interferes with the diffracted probe signal for heterodyne detection, allowing separation of absorptive and dispersive components of the signal. Calibration of the absolute phase was achieved using carbon disulfide as a reference, since it has known dispersive and absorptive characteristics (Figure S2).33 The grating decay and subsequent diffracted signal is controlled by excitation relaxation to the ground state and transport between interference peaks and minima which diminishes the grating amplitude. Changing the grating spacing via the diffractive optic allows separation between intrinsic relaxation processes and transport processes. We chose 790 nm as the probe wavelength because it is able to sense the effect of the charge carriers on the index of refraction in a spectral region where absorption is low in polycrystalline MAPI, giving uniform excitation through the film thickness. In the films studied in this report, the exciton binding energy has been reported to be less than kBT at room temperature.7 We therefore expect any photoexcited excitons to quickly dissociate into free charge carriers which are then responsible for relaxation and transport in the time range investigated. The scanning electron microscope (SEM) image on the right of Figure 1 shows the morphological characterization of MAPI thin films studied by LITG spectroscopy. Average grain sizes were found to be 303 ± 60 nm. To ensure that the material was of high quality we chose a


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deposition method that has been shown to produce films with long PL lifetimes and high efficiency devices (18-19% PCE).34,35 The optical properties and laser excitation spectrum are shown in Figure S3a. The absorption edge and PL peak are near 780 nm, and the laser spectrum is centered at 790 nm (film OD

Direct Measurements of Carrier Transport in Polycrystalline

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