Are solution processed CsPbI3 perovskite nanocrystalline lms similar to traditional crystalline semiconductors?

: We use ultrafast photocurrent spectroscopy with a sub-25 picosecond resolution to address a long-standing question in emergent perovskite materials: are solution-processed CsPbI 3 perovskites nanocrystal films similar to their counterparts semiconductors including GaAs and Si? Prior to carrier trapping, all semiconductors show similar transition of transport mechanism from the band-like transport due to the longitudinal optical (LO)


Introduction
Despite exhibiting superior device performance in photonics, electronics, and optoelectronics, it remains unclear why emergent perovskite semiconductors, which are typically solution-processed at low temperatures, are similar in nature to those of benchmark semiconductors such as GaAs or Si. In particular, the fundamental understanding of how the electrical transport properties of nanoand micro-crystalline perovskites differ from those of bulk crystalline semiconductors is still unclear. For example, perovskite solar cells have achieved more than 25% power conversion efficiency (1), while the efficiency of the current dominant silicon photovoltaic technology is ~22 %. Perovskite nanocrystal X-ray detectors acquire the same imagery with more than two orders of magnitude lower radiation dosage than the traditional silicon-based photodiode (2). Perovskite nanocrystal light emitting diodes (LEDs) generate purer colors than their III-V and alloy-dominant semiconductor counterparts due to narrowband emission in the range of <50 nm (3). Such insights into their transport properties will therefore enable the engineering of perovskite-based devices with superior device performance and efficiency. Furthermore, these insights could expedite the predictive discovery of future-generation technologies beyond current perovskite materials.
Typical solution synthesized and processed perovskites have an ABX3 chemical composition, wherein A=Methylammonium (MA), Formamidinium (FA), Cs, etc.; B=Pb, Sn, etc.; and X=Cl, Br, I. Due to their low-temperature synthesis and processing, perovskites have the advantage of low-cost processing and flexibility on substrates but suffer from high defect densities. Common defects include grain boundaries and dislocations, while shallow point defects of both acceptor and donor type vacancies have also been reported (4,5). In addition to reducing device performance and stability, these defects often overshadow our understanding of the carrier transport property, and most transport studies are dominated by carrier hopping transport in the energetic landscape of defect states. Typical trapping events occur in a wide temporal range from ~picoseconds (ps) to microseconds (s), as demonstrated in our previous work (6). Because of their ultrafast time resolution range from sub-ps to 10s of ps, time-resolved optical laser spectroscopies seem be able to unravel pre-trapping carrier dynamics. Two approaches categorize these spectroscopies. The first is based on the photon emission mechanism, which includes time-resolved photoluminescence (TRPL) and the streak camera technique (7). The second is the pump-probe mechanism, which includes transient absorption (8), THz-time domain spectroscopy (THz-TDS) (9)(10)(11), and other pump-probe approaches (12,13). As schematically indicated in Fig. 1a, in the absence of an electrical field to 'push' the carriers, they spatially diffuse in a short-range domain confined to a couple of nanometers (14). As a result, these photon-in and photon-out techniques characterize carrier diffusion dynamics, in spite of that they have uncovered many novel ultrafast phenomena such as slow hot carrier cooling (8), efficient many-body interactions (15), and large polaron effects (16). However, for solar cells, LEDs, and photodetectors, the carrier drift dynamics (parameters including mobility, lifetime, and drift length, etc.) is the backbone of transport mechanism, in particular, when devices are at work, i.e., in operando conditions. The electrical field in operando devices exerts a force or 'push' the carriers, enabling an understanding of carrier drift dynamics, in particular, in a long-range transport. For example, in a photoconductive device, the time-resolved photoconductivity techniques such as the time-of-flight photocurrent (17) and photo-CELIV (charge extraction by linearly increasing voltage) characterize the carrier drift properties including carrier mobility, lifetime, and drift length (18) (Fig. 1b). However, their time resolution is rather slow (~ 10s ns) (19) and is much longer than the trapping events in most solution-processed perovskites. Thus, most measurements are influenced by defect states. Although ultrafast THz-TDS can derive carrier properties including mobility and lifetime at the same time based on the classic Drude model, the carriers are still confined to nanoscale domain, as demonstrated in the early studies with CdSe nanocrystals as well as perovskites (10,20). In the end, there are scarce studies that shed light on the drift dynamics in devices before carrier trapping, as well as long-range transport features. (d) The UPCS with sub-25 ps time resolution is comprised of a high-speed co-planar waveguide, gold (Au) electrodes, and a nanocrystal thin film that is illuminated by an ultrafast laser pulse to a generate photocurrent that is collected by a sampling oscilloscope. The laser beam covers the entire device including the nanocrystal film and the Au electrodes.
In this work, we uses ultrafast photocurrent spectroscopy (UPCS) with a sub-25 ps time resolution to unravel the ultrafast carrier drift dynamics in perovskite nanocrystal photoconductive devices to address whether the underlying mechanisms present in solution processed CsPbI3 perovskite nanocrystal films are similar to those present in classic crystalline semiconductors. We aim to bridge two gaps in knowledge: 1) The similarity between solution-processed perovskite and classic crystalline semiconductors with respect to their transport properties, and 2) the relationship between ultrafast carrier dynamics and in operando devices. We use inorganic CsPbI3 nanocrystal arrays as a model system (Lattice structure and SEM image are shown in Fig. 1c). Unlike bulk perovskites, they have a wider tunability in terms of nanocrystal size, structure (quantum dots, layered materials, nanotube), surface chemistry, in addition to composition tunability. We discover that before defect states trap carriers, the CsPbI3 nanocrystal thin films exhibit similar carrier transport properties as GaAs and Si. In the ultrafast temporal region, carriers undergo band-like transport due to the interaction of carriers with longitudinal optical (LO) phonons that dominate the higher temperature region (>240 K). In the lower temperature region (>240 K), carrier 'hopping' due to defect scattering dominates transport. These regions are delineated by a transition temperature that is unique to CsPbI3. Although all three semiconductors exhibit carrier-LO phonon interactions, CsPbI3 nanocrystal thin films demonstrate the strongest interaction compared to among these semicondcutors. In CsPbI3 nanocrystals, carriers preserve band-like transport, leading to a drift length larger than 125 nm with mobility >25 cm 2 /Vs.

Results
As shown in Fig. 1d, by integrating a CsPbI 3 nanocrystal thin film photoconductor into transmission line architecture as a high-speed waveguide, the carrier drift dynamics can be investigated in photoconductors in operando with a sub-25 ps time resolution by the UPCS. The UPCS is superior to the Auston photoconductive switch technique since it has a much higher temporal resolution and can characterize various materials systems (21)(22)(23). A detailed nanocrystal film morphology and experimental configuration can be found in Supplementary Methods and Supplementary Fig. 1. Fig. 2a shows the various temperature-dependent ultrafast photocurrent curves for CsPbI3 nanocrystal film. Its typical photocurrent can be characterized by a fast rise to ~25 ps followed by a rapid decay up to 125 ps, and then a slow tail extending beyond 600 ps (zero time is at 10 % of the peak photocurrent). These three temporal regions are denoted by dashed vertical lines in Fig. 2a. In the first temporal region I, during the initial rise to ~25 ps, the peak photocurrent (Ipeak) decreases with increasing temperature from 240 to 400 K, as shown in Fig. 2b, and can be described as ~ − (1), where n is an index and T is the temperature. This classic power-law relation is the signature of band-like transport due to carrier-phonon scattering. At the same time, the n value indicates the strength of the carrier-phonon interaction, as discussed further below. Supplementary Fig. 2 depicts a complete photocurrent decay with an average carrier lifetime in the temperature range from 80 K to 400 K (see Supplementary Table 1). In region II, two competing transport mechanisms govern the photocurrent response between ~25 to ~125 ps. On the one hand, the photocurrent dependence continues to decrease with increasing temperature, indicating the presence of phonon scattering. On the other hand, the time decay ( Supplementary Fig. 3) shows an opposite trend; it increases with increasing temperature, which is a signature of hopping transport due to defect scattering. An Arrhenius relation for decay time with temperature can be written as where E is the activation energy, kB is the Boltzmann constant, and is the decay time constant.
The thermal activation energy of ~1.8 meV is derived in Supplementary Note 1 and Supplementary  Fig. 3. In region III, i.e., beyond ~125 ps, the slow decay tail can be attributed to a hopping transport mechanism with an activation energy of ~4.5 meV. Fig. 2: Ultrafast photocurrent dependence on temperature. (a, c, e) Temperaturedependent ultrafast photocurrents for CsPbI3 nanocrystal films, doped-GaAs, and lightly doped-Si, respectively. The corresponding temperature-dependent photocurrent peak on a log-log scale is shown in panels b, d, and f .
To demonstrate the significance of events before trapping (based on the data we consider initial trapping occurs in region I as depicted in Fig. 2a), we compare the ultrafast photocurrents of CsPbI3 nanocrystal films with the traditional bulk semiconductors under the same electrical field and the photon density in the range of 10 16 cm -3 (Figs. 2c and e). For doped-GaAs with a defect density >10 15 cm -3 , the temperature-dependent photocurrent decay trend is similar to the CsPbI3 nanocrystal films, i.e., a fast rise followed by a rapid decay. Similarly, the photocurrent peak decreases with increasing temperature in the range from 300 to 500 K as illustrated in Fig. 2d. This can be attributed to carrier-phonon scattering. Moreover, the decay constant also increases as a result of defect scattering. In contrast, for slightly doped-Si with a defect density < 10 15 cm -3 , the photocurrent exhibits a fast rise, followed by a plateau up to a couple of ns, as shown in Fig. 2e. Like the CsPbI3 nanocrystal films and GaAs, the photocurrent peak is attributed to phonon scattering since its amplitude decreases with increasing temperature (from 400 K to 500 K), as illustrated in Fig. 2f. In addition to the temporal evolution of the photocurrent as seen in Figs. 2a, 2c, and 2e, the evolution of the peak photocurrent with temperature (Figs. 2b, 2d, and 2f) is also an indication of the carrier transport mechanism. All three semiconductors exhibit a similar transition of the transport mechanism in the low temperature and high temperature regimes. For instance, the photocurrent peak of CsPbI3 nanocrystal films exhibits a weak temperature dependence below 240 K. For doped-GaAs and slightly doped-Si, the transition temperature is 300 K and 380 K, respectively. We attribute these transitions to a combination of defect scattering and acoustic phonon scattering at lower temperatures, which exhibit a temperature dependence opposite to that observed above the transition temperatures.
The mobility, which is a critical parameter to evaluate the carrier transport property, can be derived from the peak photocurrent as follows (24): where µp and µe are the hole and electron mobilities, respectively, µ = (µp + µe) is the total carrier mobility, e is the electron charge, η is the product of quantum efficiency of carrier photogeneration and carrier collection, N is the effective photon number, E is the electric field, and L is the electrode spacing. For CsPbI3 nanocrystal thin films, conservatively calculated carrier mobility at room temperature is ~2.5 cm 2 /Vs. (assuming that the quantum efficiency is 100 % so  = ) (See Supplementary note for calculations). Similarly, for GaAs and Si, the calculated carrier mobilities at room temperature are ~ 177 cm 2 /Vs and ~ 264 cm 2 /Vs, respectively. We note that these values are much lower than previously reported mobility values. For instance, the electron mobility is ~ 3000 cm 2 /Vs for GaAs (25) and ~ 1500 cm 2 /Vs for Si (26). The is due to the assumption that the quantum efficiency (QE) of carrier photogeneration and collection is 100%. For a 10% QE, the mobility for CsPbI3 nanocrystal thin films is ~25 cm 2 /Vs, which is in the same range as that characterized by the THz TDS (11). Moreover, this high mobility value (>10 cm 2 /Vs) at room temperature is consistent with the phonon scattering mechanism in CsPbI3 films, leading to bandlike transport. The linear dependence on electric-field and laser-intensity at 80 K for CsPbI3 nanocrystal thin films ( Supplementary Figs. 5-8), as well the GaAs and Si (Supplementary Fig. 9), suggest that all three semiconductors exhibit the same photogeneration mechanism resulting from the free carrier generation or weak exciton with <6.9 meV (80 K) binding energy, rather than an exciton model.

Carrier Phonon Interaction
Since the hopping transport mechanism is well documented by the carrier trapping model in perovskite bulk films (6,27,28) and nanocrystals (29,30), here, we focus on pre-trapping dynamics to gain insights into the carrier-phonon interactions. The strength of the carrier-phonon interaction is related to the temperature-dependent carrier mobility (µ= µp + µe) as: ~ − , (4) As shown in Fig. 3, for CsPbI3, in the temperature range of 240 K to 380 K, n = 2.7. At low temperatures (< 240 K), n = 0.1, which is attributed to a combination of defect scattering and acoustic phonon scattering (Supplementary Fig. 10). However, a striking feature is that the n value of CsPbI3 is the highest compared to that of 1) traditional semiconductors, viz., n = 1.77 and n = 2.56 for Si and GaAs, respectively; and 2) low-temperature solution-processed emerging perovskites such as MAPbI3 (n = 1.53) (31) and FAPbI3 (n = 1.64) (32). Apart from the above experimentally obtained n values, first principle calculations starting from the Hamiltonian describing the relevant electronic bands and their interaction with phonons, computed using density functional theory (DFT) on CsPbBr3 by Motta and Sanvito(33) shows n = 1.47. Moreover, some of the above have an n index value much greater than 1.5, which is the benchmark for acoustic phonon scattering. Therefore, they all share a similar optical phonon-carrier scattering mechanism. Although the origin of this carrier-phonon scattering mechanism is still under debate, microscopic insight and quantitative analysis from first-principles calculations are still missing. Below we discuss reasons for the varying n values and their relationship to the carrier-phonon scattering process. In solution-processed emerging perovskites, the carrier-phonon coupling is due to the bond characteristics of the halide anion (in this case I -) and the central organic (MA + , FA + ) or inorganic (Cs + ) cation. Two specific parameters determine the strength of the phonon scattering. They are i) the carrier-phonon coupling constant determined by the bond length d of the cation(A)-halogen(X) bond (MA-I, FA-I, Cs-I) and the coordination number a defining the number of bonds that connect X to A; and ii) symmetric nature of the lattice. In CsPbI3, A is Cs + , which has a smaller radius but heavier ion (with respect to MA + ), and its bonding with I-(X) preserves PbI6 4symmetry as depicted in Supplementary Fig. 11 and Supplementary note 3. The large Cs-I bond length (d ~ 4.5 Å) and weak dodeca-coordination with Ilead to a strong carrier phonon coupling. In comparison, MAPbI3, has the much lighter organic MA + cation, which interacts with I − by forming linear I−...H3N, halidehydrogen bonding perpendicular to the Pb 2+ -I − -Pb 2+ cubic frame. This anisotropic perpendicular hydrogen bonding breaks the symmetry of the PbI6 4lattice. In contrast, the smaller bonding length (d ~ 2.75 Å) and tri-coordination effectively suppress lattice vibrations leading to weaker carrier phonon coupling. Hence, when the organic cation MA + is replaced by Cs + an increased carrier-phonon scattering (increased n index) is observed due to the enhanced PbI3−LO phonon mode coupling resulting from Cs + -I bonding and the strong vibration of the symmetric PbI6 4lattice (Pb-I cage).
Unlike the perovskites, both GaAs and Si have face-centered cubic structures (zinc blend for GaAs and diamond for Si) with bond lengths of ~2.5 Å and ~3.8 Å, respectively. They are tetracoordinated and have a free vibrational structure (ions not confined to a cage). The symmetric nature of the bonding and strong ionic repulsion of Ga-Ga and Si-Si enhances LO lattice vibrations, resulting in a stronger carrier-phonon coupling than that of the anti-symmetric organic metal halide perovskites. Larger n values indicate this coupling, but it is weaker (due to lower d and a) when compared with PbI3-LO lattice vibrations in the symmetric CsPbI3. Hence, the n values are smaller than that of CsPbI3. Additionally, the relationship between the n value and the LO phonon mode is defined by Fivaz and Mooser(34) as, where ħ is the reduced Planck's constant and ωpolar is the polar optical frequency. The LO phonon energy (Epolar = ħωpolar) obtained from the above equation is E polar ~90 meV (Supplementary note 3 and Supplementary Fig. 12). Although this value is larger than the 60 meV as determined by temperature-dependent steady-state photoluminescence ( Supplementary Fig. S13), the discrepancy may attribute to the nonequilibrium ultrafast timescale. Similarly, the derived LO phonon energy is ~ 66 meV for Si, and ~85 meV for GaAs, respectively, and these values are consistent with the previous reports (35,36).

Carrier Transport Mechanism
In Fig. 4, we identify the subtle ultrafast evolution of carrier drift length along an array of nanocrystals under an electrical field. We compare our results to the carrier diffusion length reported previously using ultrafast optical spectroscopies (37). The photogenerated carriers with excess energy typically thermalize to the band edge on a sub-ps timescale upon ultrafast laser excitation. At room temperature, from the sub-ps to sub-25 ps region, the calculated minimum drift length of the carrier under a moderate electrical field of 2×10 4 V/cm with minimum mobility of ~25 cm 2 /Vs is ~120 nm, which is equivalent to around ten nanocrystal width (each nanocrystal length is ~12 nm and the separation is ~0.6 nm as shown in Fig. 2c). Assuming that the band-like transport indicated by the temperature-dependent carrier mobility power law relation (T -n , n = 2.7) is maintained evenly throughout the entire drift length, the LO-carrier scattering period within each nanocrystal is ~ 2.4 ps. The inter-nanocrystal carrier transport is tunneling transport mechanism, indicated by n = 0, and the tunneling time is ~ 0.1 ps. For reference, Zhang et al. reported a scattering time in CsPbI3 of ~0.02 ps, characterized by THz-TDS (11). As a result, more than 100 scattering events in one nanocrystal can be reduced by further increasing the electric field, leading to a longer drift length. The scattering time found above is comparable to LO-carrier scattering times reported for GaAs (38) and Si (39), which corresponds well to similarities in the transport dynamics between CsPbI3 nanocrystal films and Si, GaAs that was discussed previously.

Conclusion
This ultrafast photophysics work has a profound implication for the photonic, optoelectronic, and electronic devices because perovskite devices such as solar cells, LEDs, X-ray, or photodetectors operate under the nonequilibrium conditions, where the carriers resides the excited state of band edges. By elucidating the nature of carrier drift dynamics and carrier-phonon interactions using the UPCS in operando photoconductive devices, our work establishes a foundation of the intrinsic electrical transport property in solution-processed perovskite and traditional semiconductors. The insights of intrinsic carrier transport mechanism will lead to a predictive discovery of emergent novel materials beyond perovskites through rational design of compositions, lattice structures, and Fig. 4: The temporal and spatial evolution of the transport mechanism before carrier trapping. In the initial ~25 ps, carrier transport is due to LO-carrier scattering mechanism within each nanocrystal, and tunneling among nanocrystals, resulting in a larger than 120 nm drift length. Ec and Ev are the conduction and valence band edges, respectively. atomic bonds. Our work also directly bridge the gap between carrier dynamics and the figure-ofmerit of devices including carrier mobility, lifetime, and drift length, etc. resulted from the in-situ characterization nature of the UPCS.

Data and materials availability:
All data are available in the main text or supplementary materials.