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Electron-Hole Diffusion Lengths Exceeding 1 Micrometer in an Organometal Trihalide Perovskite Absorber

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Science  18 Oct 2013:
Vol. 342, Issue 6156, pp. 341-344
DOI: 10.1126/science.1243982

Unrestricted Travel in Solar Cells

In the past 2 years, organolead halide perovskites have emerged as a promising class of light-harvesting media in experimental solar cells, but the physical basis for their efficiency has been unclear (see the Perspective by Hodes). Two studies now show, using a variety of time-resolved absorption and emission spectroscopic techniques, that these materials manifest relatively long diffusion paths for charge carriers energized by light absorption. Xing et al. (p. 344) independently assessed (negative) electron and (positive) hole diffusion lengths and found them well-matched to one another to the ~100-nanometer optical absorption depth. Stranks et al. (p. 341) uncovered a 10-fold greater diffusion length in a chloride-doped material, which correlates with the material's particularly efficient overall performance. Both studies highlight effective carrier diffusion as a fruitful parameter for further optimization.

Abstract

Organic-inorganic perovskites have shown promise as high-performance absorbers in solar cells, first as a coating on a mesoporous metal oxide scaffold and more recently as a solid layer in planar heterojunction architectures. Here, we report transient absorption and photoluminescence-quenching measurements to determine the electron-hole diffusion lengths, diffusion constants, and lifetimes in mixed halide (CH3NH3PbI3-xClx) and triiodide (CH3NH3PbI3) perovskite absorbers. We found that the diffusion lengths are greater than 1 micrometer in the mixed halide perovskite, which is an order of magnitude greater than the absorption depth. In contrast, the triiodide absorber has electron-hole diffusion lengths of ~100 nanometers. These results justify the high efficiency of planar heterojunction perovskite solar cells and identify a critical parameter to optimize for future perovskite absorber development.

Photovoltaic (PV) solar energy conversion has the potential to play a major role in future electricity generation. Most currently installed PV arrays consist of crystalline or polycrystalline silicon; in second generation thin-film architectures, light is absorbed and charge generated in a solid layer of this semiconductor (1). Beyond these existing technologies are a myriad of other emerging device concepts based on a broad range of materials, all vying to become the cheapest yet suitably efficient technology to enable widespread uptake of solar energy (26). Some of the most promising technologies for ultimate low-cost manufacture are solution-processed, such as organic photovoltaics (OPV), dye-sensitized solar cells (DSSCs), and semiconductor-sensitized or extremely thin absorber solar cells (7, 8). However, these designs typically require a complex distributed donor-acceptor heterojunction to ionize charge because the exciton and charge carrier diffusion lengths in these materials are much shorter than the absorption depth (7, 911). Emerging from the field of DSSCs, the inorganic-organic perovskite family of materials taking the form ABX3 (A = CH3NH3+; B = Pb2+; and X = Cl, I, and/or Br) has within the past 12 months been used to fabricate high-performance hybrid solar cells, with reported power conversion efficiencies (η) of between 7 and 15% (1220). These perovskite absorbers can be solution-processed in air and absorb light broadly across the solar spectrum. In the first experiments, the perovskite absorber was used as a sensitizer on mesoporous titania electrodes, along with a solid-state organic hole transporter (HTM) such as 2′-7,7′-tetrakis(N,N-di-p-methoxyphenylamine)-9,9ʹ-spirobifluorene (spiro-OMeTAD), with the perovskite effectively replacing the dye conventionally used in a DSSC (12, 13, 21). Subsequently, the mixed halide CH3NH3PbI3-xClx perovskite devices have been reported to yield η >12% when the titania is replaced with an insulating mesoporous alumina scaffold in meso-superstructured solar cells (MSSCs), demonstrating that the perovskite itself can at least sustain sufficient electron transport to enable highly efficient charge collection (12, 16). Entirely removing the mesoporous alumina to create a thin-film planar heterojunction has resulted in solution-processed devices with close to 100% internal quantum efficiency for charge collection, but with lower η of 5% (16). Very recently, we have demonstrated that if an extremely uniform solid perovskite absorber film can be prepared—for example, through vapor deposition—then the highest efficiencies can be achieved in solid thin-film planar heterojunction architectures (19).

Despite the rapid increase in efficiency associated with the evolution of this technology, most of the fundamental questions concerning the photophysics and device operation remain unanswered. Arguably, the most critical question concerning whether mesostructured or planar heterojunction perovskite solar cells will eventually dominate is what the exciton or the electron and hole diffusion lengths are in these materials. We performed photoluminescence (PL)–quenching measurements in order to extract the electron-hole diffusion lengths in triiodide (CH3NH3PbI3) and mixed halide (CH3NH3PbI3-xClx) perovskite thin films. We show that both electron and hole diffusion lengths are >1 μm for the mixed halide perovskite—a factor of ~5 to 10 greater than the absorption depth. In contrast, the diffusion lengths in the triiodide perovskite are only on the order of or slightly shorter than the absorption depth (~100 nm). The larger diffusion length in the mixed halide perovskite results from a much longer recombination lifetime and is consistent with far superior performance in MSSCs and planar heterojunction solar cells, as we demonstrate here.

PL quenching has been previously used successfully with organic semiconductors in order to determine the diffusion length of the photoexcited bound electron-hole pair, the exciton (22). By simply fabricating solid thin films in the presence or absence of an exciton-quenching layer, and modeling the PL decay to a diffusion equation, it is possible to accurately determine the exciton lifetime, diffusion rate, and diffusion length (22). However, for the organolead trihalide perovskites studied here, there is relatively little literature on probing the fundamental photophysics, and even the most basic question of whether PL occurs via free carrier recombination from the conduction and valence band electrons, or is preceded by exciton formation, remains unknown. Exciton binding energies for CH3NH3PbI3 have been reported in the range of 37 to 50 meV in the orthorhombic phase (2325). In principle, at ambient temperature these values are comparable to thermal energies (kBT ~ 26 meV, where kB is the Boltzmann constant and T is the temperature); thus, both free carriers and weakly bound excitons should coexist with interchange being possible between the two populations. However, provided all species (bound or free charges) decay with the same rate or through the same channel, the PL decay should still be representative of recombination or depopulation of electrons and holes from the perovskite film.

The CH3NH3PbI3 and CH3NH3PbI3-xClx perovskite precursor solutions were spin-coated on plasma-etched glass at room temperature in air, followed by annealing in air at 100°C for 45 min for the mixed halide and 150°C for 15 min for the triiodide (these temperatures and times correspond to the optimized conditions for best performance in the solar cells processed in air). Obtaining uniform and continuous perovskite films is essential for the subsequent PL-quenching measurements. As we have shown elsewhere, this is possible through precise control of processing conditions (26). In order to obtain air- and moisture-insensitive samples, the neat perovskite films (nonquenching samples) were sealed by spin-coating a layer of the insulating polymer poly(methylmethacrylate) (PMMA) on top. Full experimental details are given in the supplementary materials.

In Fig. 1A, we show the ultraviolet-visible absorption and PL spectra for a CH3NH3PbI3-xClx thin film. The PL is right at the band edge, with very little Stokes-shift. This indicates little vibronic relaxation of the perovskite crystal, unlike organic semiconductors, which typically show large Stokes-shifts (27). The nanosecond–transient absorption (TA) spectra of a CH3NH3PbI3-xClx film is shown in Fig. 1B. We observed a sharp negative band peaking at 750 nm together with a broad positive band at shorter wavelengths, peaking around 550 nm. We assign the negative band to the photobleaching (PB) of the band gap or exciton transition, whereas the positive band represents a photoinduced absorption (PA). From biexponential data fitting, we retrieved the dominant time constant of both the PB and PA to be ~280 ns, followed by a long-lived tail (>1 μs). As we show in Fig. 1C, the PA band decay (288 ± 12 ns) mirrors the PB recovery dynamics (283 ± 6 ns), suggesting that the spectra arise from the same population. If we compare the transient absorption decays with the transient PL decay (τe = 273 ± 7 ns, where τe is the time taken for the PL to fall to 1/e of its initial intensity), there is a strikingly close match. This indicates that the decay of the radiative species we are monitoring with the PL represents the decay of all absorbing species (free carriers or weakly bound excitons) in the perovskite film. We can therefore use PL-quenching measurements to determine a relevant diffusion constant and length in the perovskite films. We cannot, however, categorically determine whether this corresponds to the diffusion of free charge or excitons, but in either case, it will represent the relevant diffusion length for charge extraction in the solar cell. Additionally, we can safely exclude any contribution to the PL from trap states, which would be at lower energy and whose presence would otherwise complicate the subsequent PL-quenching analysis.

Fig. 1 Optical characterization of the mixed halide perovskite CH3NH3PbI3-xClx.

(A) Absorption (red squares) and PL (black circles) spectra of a 270-nm-thick layer of CH3NH3PbI3-xClx, coated with PMMA. (B) Transient absorption spectra of CH3NH3PbI3-xClx upon excitation at 500 nm (40 μJ/cm2 pulses). Each gated spectrum has been integrated for 200 ns, and the PL was removed. (C) Normalized photobleaching (PB) (red squares, left axis) and PL dynamics (black circles, right axis) probed at 750 and 770 nm, respectively. Biexponential fitting of the PB data (dark red line) leads to a dominant time constant of τ1 = 283 ± 6 ns, matching the dynamics of the PL (τe = 273 ± 7 ns), followed by a long-lived tail. (Inset) The photoinduced absorption (PA) dynamics at 550 nm (blue squares) with a biexponential fit (dark blue line; dominant time constant of τ1 = 288 ± 12 ns), also matching the dynamics of the PL and the dominant component of the PB.

The quenching samples were prepared by means of spin-coating layers of either a hole-acceptor (Spiro-OMeTAD) or an electron-accepting fullerene [phenyl-C61-butyric acid methyl ester (PCBM)] on top of the perovskite films. In Fig. 2A, we show a scanning electron microscopy (SEM) image of a ~270-nm-thick CH3NH3PbI3-xClx absorber layer with a ~100-nm-thick Spiro-OMeTAD hole-quenching layer. We show SEM images of all sample configurations in figs. S1 and S2 and absorption spectra in fig. S3, which indicate that the mixed halide and triiodide perovskites have very similar bandgaps.

Fig. 2 PL measurements and fits to the diffusion model for the mixed halide and triiodide perovskites in the presence of quenchers.

(A) Cross-sectional SEM image of a 270-nm-thick mixed halide absorber layer with a top hole-quenching layer of Spiro-OMeTAD. (B and C) Time-resolved PL measurements taken at the peak emission wavelength of the (B) mixed halide perovskite and (C) triiodide perovskite with an electron (PCBM; blue triangles) or hole (Spiro-OMeTAD; red circles) quencher layer, along with stretched exponential fits to the PMMA data (black squares) and fits to the quenching samples by using the diffusion model described in the text (details are available in the supplementary materials). A pulsed (0.3 to 10 MHz) excitation source at 507 nm with a fluence of 30 nJ/cm2 impinged on the glass substrate side. (Inset) Comparison of the PL decay of the two perovskites (with PMMA) on a longer time scale, with lifetimes τe quoted as the time taken to reach 1/e of the initial intensity.

We present the time-resolved PL decays, measuring the peak emission at ~770 nm, for the mixed halide and triiodide perovskite absorbers in Fig. 2, B and C, respectively. The excitation fluence was kept to 0.03 μJ cm−2/pulse so as to ensure that nonlinear effects, such as exciton-charge annihilation, are unlikely to occur. The thickness of the CH3NH3PbI3-xClx films was 270 ± 40 nm, and the thickness of the CH3NH3PbI3 films was 180 ± 35 nm, which is comparable with optimum device thicknesses. The corresponding steady-state spectra are shown in fig. S4. The PL decay of the neat CH3NH3PbI3-xClx film exhibits a time-constant of τe = 273 ± 7 ns. The addition of the PCBM and Spiro-OMeTAD electron and hole-quenching layers accelerates the PL decay, with observed time constants τe of 6.1 ± 0.1 ns and 5.1 ± 0.1 ns, respectively. In contrast, the lifetime for the neat CH3NH3PbI3 film is only τe = 9.6 ± 0.3 ns, and this is quenched further, but not by such a large fraction, to 3.17 ± 0.03 ns for electrons and 4.2 ± 0.1 ns for holes.

The PL decay dynamics were modeled by calculating the number and distribution of excitations in the film n(x,t) according to the one-dimensional diffusion equationEmbedded Image (1)where D is the diffusion coefficient and k(t) is the PL decay rate in the absence of any quencher material (further details are available in the supplementary materials) (22). The total decay rate k was determined by fitting a stretched exponential decay to the PL data measured from perovskite layers with PMMA. The effect of the quencher-layer was included by assuming that all photogenerated carriers that reach the interface are quenched, giving the boundary condition n(L,t) = 0, where x = 0 at the glass/perovskite interface and L is the perovskite film thickness. Because the samples were photo-excited from the glass substrate side of the samples, the initial distribution of photoexcitations was given by n(x,0) = n0exp(αx), where α is the absorption coefficient. The average diffusion length LD of the species was then determined from Embedded Image, where τe is the recombination lifetime in the absence of a quencher. If free charges are predominantly created upon photoexcitation, the PL decay represents the depopulation of charge carriers, and we estimated the diffusion coefficients for holes or electrons depending on which quenching layer is used. The results from the diffusion model fits are shown in Fig. 2, B and C, and the parameters summarized in Table 1. The diffusion lengths for both electrons and holes in the mixed halide perovskite are greater than 1 μm, which is much longer than the absorption depth of 100 to 200 nm. This indicates that there should be no requirement for meso- or nanostructure with this specific perovskite absorber. In contrast, the triiodide perovskite CH3NH3PbI3 films have over one order of magnitude shorter diffusion length of ~100 nm for both electrons and holes, which is too short with respect to the absorption depth for this material to perform at the highest efficiencies in the thin-film configuration. The close similarity of the derived electron and hole diffusion coefficients and lengths in each of these perovskites either indicates very similar mobility for both electrons and holes, or it indicates that the predominant diffusion species is the weakly bound exciton. We can unfortunately not discriminate between the two from these results.

Table 1 Values for diffusion constants (D) and diffusion lengths (LD) from fits to PL decays using the diffusion model described in the text.

The errors quoted predominantly arise from perovskite film thickness variations, which are ± 35 nm for the triiodide perovskite films and ± 40 nm for the mixed halide perovskite films.

View this table:

To confirm the importance of the determined diffusion length in full solar cells, and to test whether the measurement correlates well with device results, we fabricated solution-processed thin-film planar heterojunction solar cells with both the mixed halide and triiodide perovskites. We formed solid perovskite films on fluorine-doped tin oxide (FTO)–coated glass substrates, coated with an n-type TiO2 compact layer so as to ensure selective collection of electrons at the FTO substrate. Subsequently, p-type spiro-OMeTAD was deposited as a hole-transporting layer so as to form a planar p-i-n heterojunction architecture. Current-voltage characteristics for the best devices fabricated are shown in Fig. 3. The CH3NH3Pb I3-xClx planar heterojunction solar cells reach power conversion efficiencies in excess of 12%, which is the highest solution-processed planar heterojunction perovskite efficiency reported to date. In contrast, we were only able to attain η of ~4% with the CH3NH3PbI3. Upon optimization of devices to obtain the highest efficiencies, we found that a thick layer of CH3NH3Pb I3-xClx was preferable (~500 nm). However, the best CH3NH3PbI3 cells had a perovskite layer thickness of only 140 nm. This observation is consistent with the diffusion-length calculations, in which the triiodide films are limited by the ~100-nm diffusion length, so that photogenerated charge in thicker films cannot be efficiently extracted before recombining. A full set of device results and average performances is given in table S1.

Fig. 3 Current-voltage curves for optimized planar heterojunction perovskite solar cells.

CH3NH3PbI3-xClx (red line, circle symbols) and CH3NH3PbI3 (black line, square symbols) cells were both measured under 100 mW cm−2 AM1.5 simulated sunlight. JSC is the short-circuit current, VOC is the open-circuit voltage, FF is the fill factor, and η is the power conversion efficiency.

This work indicates that with correct tuning of the perovskite absorber, nano- or mesostructures are not necessary in order to achieve highly efficient charge generation and collection. Our results hence pave the way for further advances in planar heterojunction perovskite solar cells. Fundamentally, there still remain many open questions for the community concerning the nature of the excited state, the relative fraction of free and bound charge pairs at room temperature, and the interplay between the two species. Furthermore, this work introduces a new question as to why the small addition of chloride ions to the organolead triiodide perovskite results in such a striking increase in the electron-hole diffusion length, predominantly arising from a substantial inhibition of nonradiative electron-hole recombination. Understanding these subtleties will enable further improvement of the current family of materials.

Supplementary Materials

www.sciencemag.org/content/342/6156/341/suppl/DC1

Materials and Methods

Figs. S1 to S4

Tables S1 to S3

References and Notes

  1. Acknowledgments: This project was funded by the Engineering and Physical Sciences Research Council, the European Research Council (ERC-StG 2011 HYPER project 279881), Oxford Photovoltaics through a Nanotechnology KTN CASE award, and by a Royal Society Wolfson exchange grant. The authors thank V. D’Innocenzo for technical support and J. Alexander-Webber for atomic force microscopy supporting measurements. A.P. and H.J.S. thank “The Royal Society International Exchanges Scheme 2012/R2.” S.D.S. thanks Worcester College, Oxford, for additional financial support. Solar cells based on the perovskite materials studied in this report are being commercialized by Oxford Photovoltaics, a spin-out company from the University of Oxford.
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