Enhanced Ballistic Transport of Charge Carriers in Alloyed and K-Passivated Alloyed Perovskite Thin Films.

Hybrid organic-inorganic perovskites show remarkable charge transport properties despite their deposition via low-temperature solution phase methods. It has recently been shown that this includes the ballistic transport of charges following photoexcitation, with ballistic transport lengths as large as 150 nm measured in MAPI3 films, which is almost twice the value reported for GaAs. Here we explore the ballistic transport regime in high-performance triple-cation and K-passivated triple-cation perovskite films, using femtosecond transient absorption microscopy, which allows us to image carrier motion with 10 fs temporal resolution and 10 nm spatial precision. We observe ballistic transport lengths of 160 and 220 nm in triple-cation and K-passivated triple-cation perovskite films, respectively. We propose that the ballistic transport is limited by nanoscale trap clusters at grain boundaries and interfaces, which can be passivated via chemical treatments to enhance the ballistic transport length, which implies that further enhancements are possible as passivation methods are improved.

Hybrid organic–inorganic halide perovskites are of great interest for various high-performance optoelectronic applications.[1] They possess a number of favorable intrinsic properties such as strong absorption coefficients (104 cm–1),[2] sharp band edges with low trap state densities,[3] and excellent charge transport properties, with charge diffusion lengths on the order of micrometers.[4−6] These charge transport properties are of particular importance in photovoltaic (PV) applications and hence, the fundamental factors governing charge transport and how it is affected by chemical composition, disorder, and trapping are areas of intense investigation.

While many investigations have focused on steady state or quasi-steady state charge transport properties, it has recently been recognized that hybrid perovskites show unusual non-equilibrium charge transport at early times after light absorption and charge generation. For instance, it was shown that in methylammonium lead iodide (MAPI3) films, carriers traveled 230 nm within the initial 300 fs after photoexcitation.[7] Using a recently developed femtosecond transient absorption microscopy (fs-TAM) technique, with 10 fs temporal resolution and 10 nm spatial precision, we were able to show that this initial non-equilibrium carrier motion occurs ballistically in MAPI3 films, i.e., before electron–electron scattering takes place, and can transport carriers over a distance of 150 nm in the thin films within 30 fs.[8] This transport length was found to be limited by energetic disorder in the films. For comparison, ballistic transport lengths in molecular beam epitaxy-grown GaAs have been reported to be on the order of 85 nm,[9] which shows the remarkable performance hybrid perovskites can achieve despite their low-temperature solution processed deposition. A long ballistic transport length not only helps to move carriers quickly and efficiently toward the charge collection layers but could also open up new possibilities such as the extraction of non-equilibrium carriers in hot carrier devices. This is therefore an exciting and important area of charge transport to study.

While MAPI3 does show excellent optoelectronic properties, there has been an intense effort to develop new materials with improved performance and stability.[10] For instance, via replacement of the volatile methylammonium (MA) cations with a combination of organic and inorganic cations such as cesium cation (Cs+), formamidinium (FA), and MA, enhancements in crystallinity, phase stability, and therefore optoelectronic properties of perovskites have been achieved.[11−14] State-of-the-art alloyed perovskites such as (Cs0.06MA0.15FA0.79)Pb(I0.85Br0.15)3 (triple cation or Tc) exhibit good moisture, thermal, and phase stability and excellent PV performance. In addition, there have been great strides made in studying and passivating trap sites and suppressing energetic disorder in such materials. One successful strategy has been the addition of potassium (K) or rubidium (Rb) halides to triple-cation perovskites, resulting in higher luminescence yields and enhanced charge carrier transport.[15−17]

It is thus clear that triple-cation films and passivation treatments can enhance optoelectronic performance, but their effect on early time charge transport dynamics has not yet been explored. Here we explore the relationship between chemical composition and passivation methods with the ultrafast ballistic transport regime in these materials. We study both Tc and K-passivated Tc (K-Tc) films (see Materials and Methods in the Supporting Information for sample preparation), using fs-TAM. We find that the Tc film shows a ballistic transport length of 160 nm, comparable to that of MAPI3 films, while the K-Tc film shows longer ballistic transport lengths of ∼220 nm. Our results suggest that it is possible to tune the ballistic transport lengths in hybrid perovskites via chemical passivation techniques.

To gain an understanding of the ultrafast non-equilibrium carrier motion in alloyed perovskites and the effect of passivation, we performed fs-TAM measurement on Tc and K-Tc perovskite thin films. While a full description of the instrument can be found elsewhere, we briefly explain the working principle of TAM.[8,18] The setup delivers a near diffraction-limited [a width (σ) of 107 ± 7.5 nm] and transform-limited (9.2 fs) pump pulse to the films, creating a Gaussian-shaped profile of carriers at time zero as shown in Figure a. A loosely focused [a width (σ) of 6.4 μm] and transform-limited (6.8 fs) probe pulse arrives after the pump pulse to image the spatial distribution of carriers. The delay between the pump and probe is controlled by a mechanical delay stage, just as in a normal ensemble level pump–probe setup. Imaging the spatial carrier distribution as a function of time after photoexcitation by the pump pulse enables us to monitor the spatial carrier dynamics right after the initial photoexcitation (Figure b). As explained in detail elsewhere,[8,18−20] although all pulses are limited by diffraction, by subtracting images of the carrier distribution at different times from each other, we can monitor changes in the shape of the distributions and hence track carrier motion with a precision better than 10 nm.

Figure 1

(a) Concepts of fs-TAM. A near diffraction-limited and transform-limited pump pulse (green) was delivered to the sample with a counter propagating and loosely focused probe pulse (orange). (b) Schematic representations of fs-TAM images at two different pump–probe time delay, describing the expansion of carrier distribution over time.

Figure presents representative fs-TAM images of Tc and K-Tc films. We note that both Tc and K-Tc films have similar band gap of ∼760 nm (Figure S1).[21−23] Tc and K-Tc were photoexcited at a center wavelength of 580 nm to create non-equilibrium carriers at the initial mean carrier density of ∼1017 cm–3, where the hot phonon effect is negligible. Initially generated carriers assume a non-equilibrium distribution around the pump energy.[24] The concomitant phase-space and band-filling effects create a strong photobleaching band and a broad high-energy tail as generally seen in transient absorption spectra of perovskite films.[25−27] Accordingly, we expect to obtain ultrafast spatial carrier motion of non-equilibrium carriers by probing at the high-energy tail of the photobleaching band (∼720 nm). fs-TAM images obtained in the initial tens of femtoseconds following photoexcitation will provide a clear picture of the spatial motion of non-equilibrium carriers. This is a time regime before electron–electron scattering causes thermalization (normally on 50–100 fs time scales) and before electron–phonon scattering causes cooling with a phonon (>100 fs).

Figure 2

Representative fs-TAM images (top) and corresponding carrier distribution functions fitted with isotropic two-dimensional Gaussian functions (bottom) of (a) Tc and (b) K-Tc at 720 nm (1.72 eV) recorded as a function of pump–probe delay upon excitation at a λc of 580 nm. The scale bar is 500 nm.

As shown in Figure , carrier distributions for Tc and K-Tc at the pump–probe delay of 2 fs show initially generated carrier distributions with widths (σ) of 214 ± 16 and 215 ± 10 nm, respectively, which are slightly larger than the carrier distribution at time zero (∼176 ± 23, the distribution width obtained by convoluting diffraction-limited pump and probe beams). Over time, the carrier distributions of Tc and K-Tc reveal clear spatial expansions over a few tens of femtoseconds. This spatial expansion suggests the carriers move rapidly at the earliest time after photoexcitation for both Tc and K-Tc thin films. To quantitatively analyze the spatial carrier dynamics, we fitted fs-TAM images with an isotropic two-dimensional Gaussian functions and extracted the corresponding σ.[7,19] The carrier transport is described by calculation of the mean-square displacement (MSD = σ2 – σ02) as plotted in Figure a. The MSD profile of K-Tc within 20 fs is described well by the power law fit (σ2 – σ02 = Dtα), giving a diffusion index (α) of 2.0 ± 0.3 (where D is the diffusion coefficient).[8] The fitted α value of 2.0 ± 0.3 is consistent with ballistic propagation of non-equilibrium carriers in K-Tc. Although the MSD profile of Tc is not well-fitted due to the poor signal-to-noise ratio of the Tc case and its short duration, the initial ultrafast feature in the MSD profile of Tc implies that the non-equilibrium carriers in Tc can propagate in a ballistic manner.

Figure 3

(a) Time evolution of the MSD = σ2 – σ02 profiles of Tc (gray) and K-Tc (red), where σ02 is the width of the spatial carrier distribution obtained at a zero pump–probe delay. (b) Time evolution of the relative changes in the ballistic transport length, = vt, in the ballistic transport region, The gray solid lines represent the resultant fit, while the red dotted lines highlight the well-fitted region.

With a given diffusion index of 2, the MSD profiles can be converted into ballistic transport length profiles (lt) through the relationship , where v is the transport velocity. In other words, the linear region of the relative changes in the width of the carrier distribution plotted as a function of time can be described as the ballistic transport limit of carriers. Figure b compares the ballistic transport lengths between Tc and K-Tc. We note that the fs-TAM images were obtained by averaging the images taken over 50 runs on several different spots across Tc and K-Tc films. As highlighted by the red dotted line in Figure b, the well-fitted linear region of this plot provides the ballistic transport length. Interestingly, the ballistic transport length of Tc is measured to be 160 ± 20 nm, which is slightly larger than the ballistic transport length previously measured for MAPI3 films (153 ± 6 nm).[8] A ballistic transport length of 225 ± 6 nm is obtained for K-Tc. These observations demonstrate that ballistic transport of non-equilibrium carriers is a universal phenomenon in hybrid organic–inorganic perovskite films and not limited to MAPI3.

We note that the carrier densities used here are similar to those in the pervious study of MAPI3 films. This allows us to compare across the different films and find that the intrinsic ballistic transport lengths increase in the following order: MAPI3 < Tc < K-Tc (i.e., 153 ± 6 nm < 160 ± 20 nm < 225 ± 6 nm) as plotted in Figure . Because it is generally believed that the alloyed perovskite promotes enhanced crystallinity and phase stability, the small increment in the intrinsic ballistic transport length of Tc is a somewhat surprising result. Recently, the deep trap distribution in Tc films was mapped by performing photoemission electron microscopy (PEEM).[14] The direct correlation of PEEM images with compositional intensity maps reveals that nanoscale trap clusters appear at the interfaces between crystallographically and compositionally distinct grains. Furthermore, the trap-to-trap distance is found to be approximately 150 nm in Tc films. This value matches well with the ballistic transport distance measured here. Consequently, we propose that after photoexcitation the non-equilibrium carriers ballistically propagate across the grain before being scattered by these deep trap clusters. In other words, the intrinsic ballistic transport length of alloyed perovskite films is dictated by the distance between deep trap clusters and therefore is not greatly increased despite the enhanced crystallinity of Tc films.

Figure 4

Ballistic transport length plot of perovskite thin films, MAPI3 (black), alloyed perovskite (Tc, red), and K-passivated alloyed perovskite (K-Tc, blue).

In contrast, longer-range ballistic propagation of non-equilibrium carriers is observed for K-Tc. The large increment in the intrinsic ballistic transport length of K-Tc is likely to stem from the passivation by K at the grain boundaries and interfaces of perovskite films,[15,17,28] although further work will be required to explain how deep trap clusters can be healed by the addition of K+ cations. Indeed, it has previously been proposed that upon its addition to the precursor solution, the K+ cation selectively draws out Br from the perovskite lattice, which leads to a reduced defect density within the bulk material and aids in passivating halide vacancy defects at grain boundaries.[10,17,29] The beneficial effects of Br in the seeding of high-quality grain growth persist. Consequently, the K passivation results in reduction of traps at interfaces, enhancing crystallinity and phase stability and hence improving the intrinsic ballistic transport length.

In conclusion, we have directly imaged non-equilibrium charge carrier dynamics in alloyed and K-passivated alloyed perovskite thin films via fs-TAM. We observed ballistic propagation of non-equilibrium carriers for both Tc and K-Tc, suggesting that the ultrafast ballistic transport is a universal phenomenon in hybrid organic–inorganic perovskite films. The intrinsic ballistic transport lengths increase in the order MAPI3 < Tc < K-Tc (153 ± 6 nm < 160 ± 20 nm < 225 ± 6 nm), which demonstrates the effect of cation alloying and K passivation on the early time dynamics of charge carriers. We propose that nanoscale trap clusters in the alloyed perovskite film dictate the non-equilibrium carrier behavior, resulting in similar ballistic transport lengths for Tc and MAPI3. On the other hand, because of the beneficial effect of K passivation, i.e., the healing of defects at the film surface and grain interfaces, the K-passivated alloyed perovskite film shows an enhanced ballistic transport length. This increase in the ballistic transport length, to values 3 times that of GaAs, via simple chemical passivation strategies is very encouraging and suggests that further enhancements are possible as passivation methods are improved, leading to enhanced device performance as well as opening new possibilities for device architectures and applications.