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Low trap-state density and long carrier diffusion in organolead trihalide perovskite single crystals

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Science  30 Jan 2015:
Vol. 347, Issue 6221, pp. 519-522
DOI: 10.1126/science.aaa2725

Large-crystal perovskite films

The performance of organic-inorganic hybrid perovskite planar solar cells has steadily improved. One outstanding issue is that grain boundaries and defects in polycrystalline films degrade their output. Now, two studies report the growth of millimeter-scale single crystals. Nie et al. grew continuous, pinhole-free, thin iodochloride films with a hot-casting technique and report device efficiencies of 18%. Shi et al. used antisolvent vapor-assisted crystallization to grow millimeter-scale bromide and iodide cubic crystals with charge-carrier diffusion lengths exceeding 10 mm.

Science, this issue p. 522, p. 519

Abstract

The fundamental properties and ultimate performance limits of organolead trihalide MAPbX3 (MA = CH3NH3+; X = Br or I) perovskites remain obscured by extensive disorder in polycrystalline MAPbX3 films. We report an antisolvent vapor-assisted crystallization approach that enables us to create sizable crack-free MAPbX3 single crystals with volumes exceeding 100 cubic millimeters. These large single crystals enabled a detailed characterization of their optical and charge transport characteristics. We observed exceptionally low trap-state densities on the order of 109 to 1010 per cubic centimeter in MAPbX3 single crystals (comparable to the best photovoltaic-quality silicon) and charge carrier diffusion lengths exceeding 10 micrometers. These results were validated with density functional theory calculations.

Solution-processed hybrid organolead trihalide (MAPbX3) perovskite solar cells (PSCs) have now achieved 20.1% certified power conversion efficiencies (1), following a rapid surge of development since perovskite-based devices were first reported in 2009 (2). A key to the success of PSCs is the long diffusion length of charge carriers in the absorber perovskite layer (3). This parameter is expected to depend strongly on film crystallinity and morphology. Thermally evaporated MAPbI3 films fabricated using a Cl-based metal salt precursor were reported to exhibit carrier diffusion lengths three times those of the best solution-processed materials, yet no measurable Cl was incorporated in the final films, hinting at a major but unclear mechanism in the control of crystallinity and morphology (4, 5). These observations suggest that there may be room to improve upon already remarkable PSC efficiencies via the optimization of three key parameters: charge carrier lifetime, mobility, and diffusion length.

The quest for further improvements in these three figures of merit motivated our exploration of experimental strategies for the synthesis of large single-crystal MAPbX3 perovskites that would exhibit phase purity and macroscopic (millimeter) dimensions. Unfortunately, previously published methods failed to produce single crystals with macroscopic dimensions large enough to enable electrode deposition and practical characterization of electrical properties (6). Past efforts based on cooling-induced crystallization were hindered by (i) the limited extent to which solubility could be influenced by controlling temperature, (ii) the complications arising from temperature-dependent phase transitions in MAPbX3, and (iii) the impact of convective currents (arising from thermal gradients in the growth solution) that disturb the ordered growth of the crystals.

We hypothesized that a strategy using antisolvent vapor-assisted crystallization (AVC), in which an appropriate antisolvent is slowly diffused into a solution containing the crystal precursors, could lead to the growth of sizable MAPbX3 crystals of high quality (with crack-free, smooth surfaces, well-shaped borders, and clear bulk transparency). Prior attempts to grow hybrid perovskite crystals with AVC have fallen short of these qualities—a fact we tentatively attributed to the use of alcohols as antisolvents (7). Alcohols act as good solvents for the organic salt MAX (8) due to solvent-solute hydrogen bond interactions; as a result, they can solvate MA+ during the ionic assembly of the crystal, potentially disrupting long-range lattice order.

We instead implemented AVC (Fig. 1A) using a solvent with high solubility and moderate coordination for MAX and PbX2 [N,N-dimethylformamide (DMF) or γ-butyrolactone (GBA)] and an antisolvent in which both perovskite precursors are completely insoluble [dichloromethane (DCM)]. We reasoned that DCM, unlike alcohols, is an extremely poor solvent for both MAX and PbX2 and lacks the ability to form hydrogen bonds, thus minimizing asymmetric interactions with the ions during their assembly into crystal form. When combined with a slow and controlled diffusion rate into DMF or GBA, our approach established the conditions for all the ionic building blocks of the perovskite to be coprecipitated from solution stoichiometrically.

Fig. 1 Crystal growth and diffraction.

(A) Schematic diagram of the crystallization process. (B) Experimental and calculated powder XRD profiles confirming the phase purity of MAPbX3 crystals grown at room temperature (fig. S1). Single-crystal XRD data are given in (9).

Using this method, we grew high-quality, millimeter-sized MAPbBr3 and MAPbI3 single crystals (fig. S1) (9) whose shape conformed to the underlying symmetry of the crystal lattice. The phase purity of the as-grown crystals was confirmed by x-ray diffraction (XRD) performed on powder ground from a large batch of crystals (Fig. 1B).

The synthesized crystals were of sufficient quality and macroscopic dimensions to enable a detailed investigation of the optical and charge transport properties. The absorbance of MAPbX3 (X = Br or I) (Fig. 2) shows a clear band edge cutoff with no excitonic signature, which suggests a minimal number of in-gap defect states. For comparison, the absorption spectrum from the polycrystalline MAPbBr3 (fig. S2) (9) and MAPbI3 (5) thin films shows a peak near the band gap, which is often attributed to an excitonic transition. This observation is consistent with a substantial amount of disorder and lack of long-range structural coherence in nanostructured thin films (10). By extrapolating the linear region of the absorption edge to the energy-axis intercept (fig. S3) (9), we determined the optical band gaps of MAPbBr3 and MAPbI3 single crystals to be 2.21 and 1.51 eV (Fig. 2), respectively. Both materials in their single-crystalline form exhibit a substantially narrower band gap than the corresponding films, which could enhance photon harvesting and hence improve photocurrent generation.

Fig. 2 Steady-state absorbance and photoluminescence.

(A) MAPbBr3 single crystal. (B) MAPbI3 single crystal. Insets: Absorbance versus photon energy and the determined band gap Eg. PL excitation wavelength was 480 nm.

As also shown in Fig. 2, both MAPbBr3 and MAPbI3 exhibit a narrow photoluminescence (PL) that peaks near the band edge. A noticeable shoulder at ~790 nm in the PL of MAPbI3 single crystals is in agreement with the PL from thin films (5), with the main PL peaking at 820 nm attributed to the intrinsic PL from the MAPbI3 crystal lattice. A more structured PL spectrum was observed for polycrystalline MAPbBr3 thin films (fig. S2) (9).

We investigated the key quantities that directly affect a material’s potential for application in PSCs: carrier lifetime τ, carrier mobility μ, and carrier diffusion length LD. In addition, we estimated the in-gap trap density ntraps in order to correlate the trap density with the observed diffusion length. For MAPbBr3 single crystals, we first measured carrier mobility using the time-of-flight technique (11). The transient current was measured for various driving voltages (V), and the corresponding traces are shown in Fig. 3A on a bilogarithmic scale. The transit time τt, defined as the position of the kink in the time traces, is marked by the blue squares, and the corresponding values are plotted in Fig. 3B as a function of V–1. The mobility μ [μ = μp ≈ μn, where μp and μn are the hole and electron mobility, respectively (12, 13)] can be directly estimated from the transit time τt, sample thickness d, and applied voltage V as μ = d2/Vτt (Fig. 3B) (9). Estimating mobility via a linear fit of τt versus V–1 led to an estimate of 115 cm2 V–1 s–1. Complementary Hall effect measurements at room temperature confirmed a carrier (holes) concentration of between 5 × 109 and 5 × 1010 cm–3, and provided a mobility estimate in the range from 20 to 60 cm2 V–1 s–1. Slightly lower mobilities obtained via the Hall effect may be ascribed to surface effects that are negligible for time-of-flight, which constitutes a bulk probe.

Fig. 3 Carrier mobility and lifetime measurements.

(A) Time-of-flight traces showing the transient current after photoexcitation at time t = 0 in a bilogarithmic plot; the transit time τt is identified by the corner in each trace and marked by blue squares. (B) Linear fit of transit time versus inverse voltage V–1. (C) Transient absorption in MAPbBr3 crystals, evaluated at 590 nm, showing a fast component (τ ≈ 74 ± 5 ns) together with a slower decay (τ ≈ 978 ± 22 ns). (D) Time- and wavelength-dependent photoluminescence (PL) color map, with the time trace at λ = 580 nm superimposed (blue markers). (E) PL time decay trace on a MAPbBr3 crystal at λ = 580 nm, with bi-exponential fits showing a fast (τ ≈ 41 ± 2 ns) and a slow transient (τ ≈ 357 ± 11 ns). (F) PL time decay trace on a MAPbI3 crystal (λ = 820 nm, also showing a fast (τ ≈ 22 ± 6 ns) and a slow (τ ≈ 1032 ± 150 ns) component.

For MAPbI3 single crystals, we estimated the carrier mobility using the space-charge-limited current (SCLC) technique. We measured the current-voltage (I-V) trace for the crystals and observed a region showing a clear quadratic dependency of the current on the applied voltage at 300 K (see fig. S8 for details). From this region, we could conservatively estimate the carrier mobility, obtaining the value μ = 2.5 cm2 V–1 s–1. From the linear ohmic region, we also identified the conductivity of the crystal to be σ = 1 × 10−8 (ohm·cm)–1. Combining the information on mobility and conductivity, we estimated a carrier concentration of nc = σ/eμ ≈ 2 × 1010 cm−3 (where e is the electronic charge).

We estimated the carrier lifetime τ from transient absorption (TA) and PL spectra. Nanosecond pump-probe TA spectroscopy was carried out over a window covering the nanosecond- to- microsecond time scales in order to evaluate the fast (τ ≈ 74 ns) as well as the slow (τ ≈ 978 ns) carrier dynamics, as determined from biexponential fits. Time (t)– and wavelength (λ)–resolved PL maps IPP(t, λ) (Fig. 3D) of single-crystalline MAPbBr3 were acquired in the wavelength region around the main band-to-band recombination peak at 580 nm (λ = 500 to 680 nm). The time-dependent PL signals in single-crystalline samples of MAPbBr3 and MAPbI3 are shown in Fig. 3, E and F, respectively; the data were measured at the wavelength of the main PL peak— i.e., λ = 580 nm and λ = 820 nm for MAPbBr3 and MAPbI3, respectively (see insets).

The time-resolved traces are representative of the transient evolution of the electron-hole population after impulsive (Δt ≈ 0.7 ns) photoexcitation. Biexponential fits were performed to quantify the carrier dynamics (fig. S4, blue traces) (9). Both the bromide- and iodide-based perovskite crystals exhibited a superposition of fast and slow dynamics: τ ≈ 41 and 357 ns for MAPbBr3, and τ ≈ 22 and 1032 ns for MAPbI3. We assign these two very different time scales to the presence of a surface component (fast) together with a bulk component (slow), which reveals the lifetime of carriers propagating deeper in the material. The relative contribution of these two terms to the static PL can be readily evaluated by integrating the respective exponential traces (the integral is equal to the product of the amplitude A and the decay time τ), which shows that the fast (tentatively surface) component amounts to only 3.6% of the total TA signal in MAPbBr3, and to 12% and 7% of the total PL signal in MAPbBr3 and MAPbI3, respectively. Ultimately, by combining the longer (bulk) carrier lifetimes with the higher measured bulk mobility, we obtained a best-case carrier diffusion length LD = (kBT/e · μ · τ)1/2 (where kB is Boltzmann’s constant and T is the sample temperature) of ~17 μm in MAPbBr3; use of the shorter lifetime and lower mobility led to an estimate of ~3 μm. The same considerations were applied for the MAPbI3 crystals to obtain a best-case diffusion length of ~8 μm and a worst-case length of ~2 μm.

For comparison, we also investigated the PL decay of solution-processed thin films of MAPbBr3 (fig. S5). We again found two dynamics: a fast decay (τ ≈ 13 ns) and a longer-lived component (τ ≈ 168 ns), in both cases faster than the single crystals. This result suggests a larger trap-induced recombination rate in the thin films, which are expected to possess a much higher trap density than the single crystals. Previous studies on non–Cl-doped MAPbI3 nanostructured thin films also corroborate this trend, revealing a PL lifetime of ~10 ns and a carrier diffusion length of ~100 nm (3, 5).

Crystalline MAPbX3 is characterized by a charge transport efficiency that outperforms thin film–based materials in mobility, lifetime, and diffusion length. To unveil the physical origins of this difference, we investigated the concentration of in-gap deep electronic trap states. We measured the I-V response of the crystals in the SCLC regime (Fig. 4). Three regions were evident in the experimental data. At low voltages, the I-V response was ohmic (i.e., linear), as confirmed by the fit to an IV functional dependence (blue line). At intermediate voltages, the current exhibited a rapid nonlinear rise (set in at VTFL = 4.6 V for MAPbBr3 and 24.2 V for MAPbI3) and signaled the transition onto the trap-filled limit (TFL)—a regime in which all the available trap states were filled by the injected carriers (14). The onset voltage VTFL is linearly proportional to the density of trap states ntraps (Fig. 4A). Correspondingly, we found for MAPbBr3 single crystals a remarkably low trap density ntraps = 5.8 × 109 cm–3, which, together with the extremely clean absorption and PL profiles (see again Fig. 2A), points to a nearly defect-free electronic structure. At high fields, the current showed a quadratic voltage dependence in the Child’s regime. In this region, we extracted the value for the trap-free mobility μ. We found μ = 38 cm2 V–1 s–1 (Fig. 4A), a value in good agreement with the mobility extracted using time-of-flight and Hall effect measurements (fig. S7) (9). We determined a comparable low trap density ntraps = 3.3 × 1010 cm–3 for MAPbI3 single crystals using the same method (Fig. 4B).

Fig. 4 Current-voltage traces and trap density.

Characteristic I-V trace (purple markers) showing three different regimes for (A) MAPbBr3 (at 300 K) and (B) MAPbI3 (at 225 K). A linear ohmic regime (IV, blue line) is followed by the trap-filled regime, marked by a steep increase in current (IVn>3, green line). The MAPbBr3 trace shows a trap-free Child’s regime (IV2, green line) at high voltages.

The defect density measured for the room temperature–grown MAPbX3 crystals was superior to a wide array of established and emerging optoelectronic inorganic semiconductors including polycrystalline Si (ntraps ≈ 1013 to 1014 cm–3) (15, 16), CdTe/CdS (ntraps ≈ 1011 to 1013 cm–3) (17), and copper indium gallium selenide (CIGS) (ntraps ≈ 1013 cm–3) thin films (18), as well as organic materials such as single-crystal rubrene (ntraps ≈ 1016 cm–3) (19) and pentacene (ntraps ≈ 1014 to 1015 cm–3) (20). Only ultrahigh-quality crystalline silicon, grown at high temperatures, offers comparable or better deep trap densities (108 < ntraps < 1015 cm–3) (21, 22). The exceptionally low trap density found experimentally can be explained with the aid of density functional theory (DFT) calculations performed on MAPbBr3, which predict a high formation energy for deep trap defects when MAPbBr3 is synthesized under Br-rich conditions (e.g., from PbBr2 and MABr), such as is the case in this study (9).

Supplementary Materials

www.sciencemag.org/content/347/6221/519/suppl/DC1

Materials and Methods

Figs. S1 to S12

References (2344)

References and Notes

  1. See supplementary materials on Science Online.
  2. Acknowledgments: We thank N. Kherani, B. Ramautarsingh, A. Flood, and P. O’Brien for the use of the Hall setup. Supported by KAUST (O.M.B.) and by KAUST award KUS-11-009-21, the Ontario Research Fund Research Excellence Program, and the Natural Sciences and Engineering Research Council of Canada (E.H.S.).
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