Understanding charge transport in lead iodide perovskite thin-film field-effect transistors.

Fundamental understanding of the charge transport physics of hybrid lead halide perovskite semiconductors is important for advancing their use in high-performance optoelectronics. We use field-effect transistors (FETs) to probe the charge transport mechanism in thin films of methylammonium lead iodide (MAPbI3). We show that through optimization of thin-film microstructure and source-drain contact modifications, it is possible to significantly minimize instability and hysteresis in FET characteristics and demonstrate an electron field-effect mobility (μFET) of 0.5 cm2/Vs at room temperature. Temperature-dependent transport studies revealed a negative coefficient of mobility with three different temperature regimes. On the basis of electrical and spectroscopic studies, we attribute the three different regimes to transport limited by ion migration due to point defects associated with grain boundaries, polarization disorder of the MA+ cations, and thermal vibrations of the lead halide inorganic cages.

INTRODUCTION

Hybrid organic-inorganic perovskites, such as methylammonium lead iodide (CH3NH3PbI3; hereafter MAPbI3), represent a previously unknown class of semiconductors for a wide range of optoelectronic applications. These materials exhibit interesting properties such as high absorption coefficient (), tunable bandgap (), and high photoluminescence quantum yield (). Despite low-temperature (≤100°C) solution processing, the density of electronic defect states is surprisingly low, hence it has been possible to realize solar cells with efficiencies of more than 20% (), color-pure light-emitting diodes (, ), and optically pumped lasing (, ). On the basis of impressive device performance and superior optoelectronic properties, such as clean band structure (, ), high degree of crystallinity (), and low effective mass of charge carriers comparable to inorganic semiconductors such as GaAs and Si (), the charge mobility of these materials is generally regarded as “high.” Measurements of the carrier mobilities on single crystals using terahertz (THz) techniques have yielded values of up to 100 cm2/Vs (), which are higher than conventional organic semiconductors but modest compared with inorganic semiconductors that exhibit similar high performance in solar cells (). However, many aspects of the charge transport, such as the mechanism of carrier scattering and trapping, the role of ion migration, the origin of hysteresis in the device characteristics, and the electronic structure of grain boundaries in these hybrid perovskites, particularly for polycrystalline thin films, remain unexplored.

Field-effect transistors (FETs) provide a versatile platform to study the charge transport mechanism of semiconductors in a controlled manner. In addition to determining field-effect mobility (μFET), FETs allow precise electrical control of the charge density and have yielded valuable insight into the transport physics of organic (, ) and inorganic semiconductors (), including tin-based two-dimensional (2D) perovskites () with a μFET of ~0.6 cm2/Vs. However, the fabrication of FETs with the 3D perovskites, such as MAPbI3, has remained challenging (–). A major difficulty has been ion migration, which causes a partial screening of the applied gate field, yielding a very low room temperature μFET of 10−4 cm2/Vs in thin films of MAPbI3 (). Li et al. () reported perovskite phototransistors that owed their high photoresponsivity to a very poor transistor performance in the dark, which substantially improved upon light illumination. Furthermore, the reported perovskite FETs are prone to degradation during operation over multiple cycles and exhibit significant hysteresis in their current-voltage characteristics (). Even in single-crystal devices, strong hysteresis and moderate mobilities of <10−3 cm2/Vs were reported at room temperature (). This low device performance, at room temperature and in the absence of light, has limited the fundamental insight into the transport physics that could be gained from FET studies and relate it to the observed excellent solar cell performance. To make progress with perovskite FETs, we need to better understand the instabilities in their device characteristics associated with hysteresis and their degradation upon repeated cycling and to develop techniques to reduce their effect and allow sufficiently stable operation not only at low temperatures but also at room temperature. Through the optimization of processing conditions to control thin-film microstructure and the modification of source-drain (S-D) contacts, we are able to fabricate MAPbI3 FETs that exhibit clean electron transport under dark conditions, with significantly reduced instability and hysteresis. This allows us to meaningfully evaluate charge transport across a wide temperature range, from 100 K to room temperature. As a result, we are able to identify different temperature regimes in which different scattering mechanisms and transport-limiting factors manifest themselves.

RESULTS AND DISCUSSION

The choice of the perovskite precursor materials and the technique for their solution deposition controls the polycrystalline microstructure and charge transport properties of MAPbI3 FET thin films (). Here, we use a precursor mixture based on Pb(Ac)2 () that results in compact thin films with uniform coverage, a root mean square (RMS) roughness of ~5.4 nm, and a grain size of 38 nm (Fig. 1A). In contrast, films grown from the more conventional PbI2-based precursor mixtures exhibit a higher RMS surface roughness of ~114 nm and poorer film coverage for similar grain size and film thickness (fig. S1) (). In addition, a comparison of the x-ray diffraction (XRD) of perovskite films prepared using both methods suggests a lower degree of precursor conversion for the latter with a more intense peak due to residual PbI2 (2θ = 12.5°) (figs. S2 to S4) (), compared with a near-complete conversion in Pb(Ac)2-based films.

Fig. 1

Effect of grain size on the characteristics of FET devices with gold S-D contacts.

(A) Scanning electron microscopy (SEM) images of MAPbI3 films fabricated from 0.25, 0.5, and 0.75 M precursor solutions. Scale bars, 200 nm. (B) Grain size as a function of concentration of the precursor solution. (C) Transfer characteristics at 100 and 270 K for MAPbI3 FETs with channel length (L) = 10 μm and width (W) = 1 mm deposited with different precursor concentrations. (D) μFET as a function of precursor concentration measured from perovskite FETs at 100 and 270 K.

We fabricated bottom-contact, top-gate field-effect transistors with gold S-D contacts and a fluoropolymer gate dielectric (Cytop) using 0.25 M solutions of both PbI2 and Pb(Ac)2 precursors, which result in perovskite films with a thickness of ~100 nm (). Devices fabricated from the PbI2 precursor mixtures exhibit very poor, leakage-dominated characteristics, which makes it difficult to estimate the μFET even at 100 K (fig. S5). In contrast, devices fabricated from the Pb(Ac)2 precursor exhibit much better n-type transport characteristics (Fig. 1C and fig. S6). Despite significant “clockwise” hysteresis in the device characteristics, we can identify linear and saturation regimes in the output characteristics and reliably extract a saturation electron μFET of ~0.2 ± 0.08 cm2/Vs and an on/off ratio of ~105 (for a detailed discussion of the method of mobility extraction, see section S4). However, upon increasing the temperature to 250 K, μFET decreases strongly to 0.02 ± 0.01 cm2/Vs, and the output characteristics exhibit a complex, nonideal behavior without a clean saturation regime (fig. S6B). This behavior bears the signature of ion migration under the action of the applied gate and S-D electric fields (for a detailed discussion, see section S5). No field-induced transport could be observed at room temperature in these perovskite FETs.

To optimize device performance, we investigated the role of the grain size in MAPbI3 thin films by varying the grain size from 38 nm (for our initial devices fabricated from 0.25 M solutions) to 150 nm, with increasing concentration of the Pb(Ac)2 precursor from 0.25 to 1.00 M (Fig. 1B) (details in Materials and Methods). SEM images (Fig. 1A) show the grain size for films prepared with different precursor concentrations. Upon increasing the grain size, the transfer characteristics exhibit an increase in S-D current (Ids) by up to an order of magnitude, resulting in a μFET of ~0.6 ± 0.2 cm2/Vs at 100 K and 0.05 ± 0.01 cm2/Vs at 270 K for a film grown from the 0.75 M concentration (Fig. 1C). As the grain size increases, field-effect transport was observed at room temperature. Typical transfer characteristics of a perovskite FET fabricated from 0.75 M Pb(Ac)2 precursor operating at room temperature is shown in fig. S6F. For devices with large grain size, it was also possible to observe comparatively clean output curves from 100 to 270 K (figs. S6 and S7), with channel currents at least one order of magnitude higher than in devices with smaller grain size. This tendency of increasing μFET and device stability with grain size suggests that film microstructure plays an important role in device instabilities.

To better understand the enhancement in charge transport with increasing grain size, we performed XRD crystallography analysis on the samples. In fig. S4, we compare grazing incidence wide-angle x-ray scattering (GIWAXS) images of thin films prepared with different precursor concentrations. Perovskite films with smaller grain size exhibit a preferential orientation of crystallites with the (110) direction oriented out of plane. A smaller population of randomly oriented crystallites also exists, evidenced by powder-like diffraction rings. In contrast, films of larger grains (0.75 M) exhibit two different populations of preferentially oriented crystallites, one with the (110) direction oriented out of plane and another with the (110) direction oriented at 45° to the substrate plane. This observation suggests that for the different precursor concentrations, there are different growth modes that lead to films with different crystallite orientations. Furthermore, it is evident from the XRD that films with larger grain size exhibit significantly sharper diffraction spots than those with small grain size (inset, fig. S2). Detailed structural analysis of the 0.25 M films by high-resolution XRD (fig. S3) showed strong perovskite peaks at 2θ = 14.1°, 28.4°, and 43.2° assigned to (110)/(002), (220)/(004), and (330)/(006), respectively, in the out-of-plane direction, confirming the well-known tetragonal (I4/mcm) phase with lattice parameters a = b = 8.86 Å and c = 12.57 Å, as determined by a full Rietveld refinement. This agrees with the literature for perovskite thin films ().

The absence of certain predicted reflections indicates a strong degree of preferential orientation of the crystallites, in agreement with our GIWAXS findings. The Bragg peak at 12.5°, which corresponds to unconverted PbI2, is more intense by a factor of 5 in the 0.25 M film compared with the 0.75 M one (fig. S2). This correlates well with the decrease in grain size (or increase in the area of grain boundaries) by a factor of approximately 4, which may suggest that the unconverted PbI2 is predominantly phase-segregated from the perovskite and is instead located at or near grain boundaries (). A confirmation of the phase segregation between perovskite and PbI2 is obtained by fitting the peak assigned to the impurity of PbI2 (Pm1) with the published lattice parameters a = b = 4.575 Å and c = 7.0357 Å. This clear correlation between microstructure and device performance suggests that the improved transport characteristics in the 0.75 M films at room temperature may at least partly be attributed to a lower concentration of PbI2 located between grains, resulting in reduced migration of ions arising from point defects at grain boundaries that screen the applied gate voltage. This will be discussed in more detail below.

To further improve room temperature FET characteristics, we modified the gold S-D contacts with the self-assembled monolayer (SAM) pentafluorobenzenethiol (PFBT; ~1 nm thick) and the polymer surface modification layer polyethylenimine ethoxylated (PEIE; ~2 nm thick) (), which increase and decrease the gold work function, respectively. In Fig. 2A, we compare the transfer characteristics of perovskite devices fabricated with bare gold electrodes with those modified with different SAM layers. The introduction of these interlayers results in an increase of the Ids in both cases, and correspondingly, a μFET of 1 to 2.5 cm2/Vs is observed at 100 K. Specifically, the PEIE contact modifications reduced the hysteresis in the transfer characteristics measured in pulsed gate voltage mode at room temperature to a much smaller level (Fig. 2B) that allowed reliable extraction of transport parameters at room temperature.

Fig. 2

Electrical characterization of MAPbI3 FETs with different S-D contact modifications.

Transfer characteristics at (A) 100 K for different S-D contact modification and (B) 300 K for PEIE-treated Au contacts. Also shown is the square root of Ids and the linear fit over a large positive Vg range. Output characteristics of FETs with PEIE-treated Au S-D contacts at (C) 100 K and (D) 300 K (L = 20 μm and W = 1 mm). (E) Transfer characteristics measured at 100 K upon thermal cycling. (F) Effect of the base voltage variation on the transconductance plots for the same FET. The inset shows a schematic diagram of the pulse voltage. For all devices, we used a 0.75 M precursor concentration.

The room temperature μFET increases from 0.02 ± 0.01 cm2/Vs for bare gold contacts to 0.1 to 0.5 cm2/Vs for PEIE-treated electrodes (fig. S8 shows the mobility distribution statistics). In champion PEIE-treated devices, μFET values as high as 5 cm2/Vs at 100 K and 3 cm2/Vs at room temperature were observed, which approach, within an order of magnitude, the local mobility estimates from THz () and microwave conductivity () measurements. Furthermore, upon PEIE treatment of contacts, it became possible to obtain an output curve at room temperature (Fig. 2D). Generally, a mismatch in the magnitude of Ids is observed between the output and transfer characteristics under the same S-D (Vd) and gate (Vg) potentials, which reflects an instability of the device current depending on the different measurement sequences. We define the Ids mismatch parameter (ξ) under the same voltage condition (here, Vd = Vg = 60 V); for a perfectly stable FET, ξ is expected to be 1. In 0.75 M perovskite FETs with bare gold contacts, ξ increases from ≈ 2 to 100 as the temperature is raised from 100 to 270 K. However, for devices with treated contacts, the mismatch is comparatively small, increasing from ξ ≈ 1.2 to 2 for PEIE and from ξ ≈ 1.5 to 10 for PFBT between 100 and 300 K, thus indicating that a moderately thick interlayer is needed to maximize device stability (fig. S13E). Devices with PEIE-modified electrodes exhibit significantly enhanced and more stable operational characteristics near room temperature compared to those with unmodified contacts (section S8).

To understand the mechanism for the observed enhancement in transport properties with different interlayers, we first note that the observed improvement in room temperature operation with contact modification cannot be explained by work function/electron injection barrier arguments because both PFBT- and PEIE-modified contacts exhibit this improvement (fig. S13). To investigate the role of the microstructure, we performed SEM imaging of the channel region (figs. S14 to S15). These measurements indicate further increase in the grain size of the perovskite thin films inside the channel region from 150 nm for bare gold contacts to <200 nm for treated electrodes. This is possibly driven by the contact-induced enhanced nucleation of the perovskite and its crystallization into confined channel regions, which could be attributed to the enhanced halogen-halogen or amine-amine interaction from PFBT- and PEIE-treated electrodes, respectively; similar effects have previously been observed for organic FETs (, ). Thus, although there may well be effects of interfacial electronic structure or electrochemical reactions that contribute to the improved performance by contact modification, the effects of contact-induced changes in film microstructure and grain size in the channel are likely to be an important contributing factor.

The optimized devices exhibit stable operation and can be measured over multiple cycles and bias stressed for periods of 30 min without significant changes in current or hysteresis behavior (figs. S17 to S19). These rather reproducible characteristics allowed us to more systematically investigate the origin of the residual hysteresis, which depends strongly on temperature and measurement conditions. The output curves (Fig. 2, C and D) display hysteresis over the complete temperature range, showing that hysteresis increases with increasing gate voltage and temperature. However, the transfer characteristics exhibit significant hysteresis only at low temperature, which decreases at room temperature (Fig. 2, A and B).

The difference in hysteresis behavior between the output and transfer characteristics arises from the difference in the transfer and output characteristic measurement sequences (details in Materials and Methods). In the transfer scans, Vg is pulsed, whereas Vd is held constant; in the output scans, Vd is pulsed, whereas Vg is maintained at a constant bias. A comparison between Figs. 2B and 2D shows that when near room temperature (T > 240 K, as shown in a later section), the hysteresis is primarily induced by the applied gate voltage. This becomes evident when the transfer curves were measured by applying both Vd and Vg in a continuous mode where a large hysteresis is observed, particularly near room temperature (fig. S20). This suggests that at T > 240 K, the observed clockwise hysteresis between forward and reverse characteristics can be ascribed to the gate voltage–induced migration of ions or charged point defects in the perovskite. When negatively (positively) charged point defects drift toward (away from) the interface under application of a positive gate voltage, they screen the applied gate electric field and reduce the concentration of mobile electrons in the accumulation layer of the FET. Further evidence of the ionic defect migration affecting the field-effect behavior is obtained from the measurements on a dual gate transistor with a Cytop top gate and Si/SiO2 bottom electrodes as the control gate. It was possible to regulate the defect screening of gate potential by varying the bias at the back gate, and consequently, a clear tunability of transport from a bulk space charge limited behavior to a clean field modulated saturated behavior is obtained (for detailed discussion, see section S5).

However, at low temperatures, the origin of hysteresis behavior must be different; even when measured in pulsed gate voltage mode, the transfer characteristics retain hysteresis at 100 K. This would not be expected from ion migration because ion migration is expected to slow down at low temperature, which should make it easier, not harder, to avoid hysteresis effects by gate voltage pulsing. Furthermore, the transfer curves at low temperatures exhibit a similar degree of hysteresis independent of the grain size (Fig. 1C), whereas, as discussed above, the room temperature device performance clearly indicated more pronounced ion migration in films with small grain size. It is expected that ion migration is becoming increasingly less important for temperatures below 240 K (also shown by the impedance spectroscopy below) because the diffusion of charged point defects is a strongly temperature-activated process. Typical activation energies of 0.58, 0.84, and 2.31 eV have been calculated for iodide (, methylammonium (), and lead () vacancies, respectively (, ). Considering a typical Boltzmann probability, the diffusion coefficient of the most mobile iodine vacancies would be expected to decrease by a factor of 105 between room temperature and 100 K. This suggests that at low temperature, the hysteresis might have a different origin and is not dominated by ion migration.

To better understand the origin of the low-temperature hysteresis, we analyzed possible sources for hysteresis such as ferroelectricity (–). Ferroelectric polarization measurements performed on perovskite thin films at different temperatures and frequencies (fig. S21) did not show any evidence of a clear ferroelectric loop. We also performed transfer characteristic measurements with varying base gate voltage (Vb) to which the gate voltage was switched in between the pulsed measurements (inset, Fig. 2F). It was possible to significantly reduce the hysteresis by choosing Vb = 40 V while only decreasing the on current at Vg = 60 V by less than 30%. This is not expected for a hysteresis mechanism based on ion migration because a positive applied Vb is expected to significantly increase the amount of gate voltage screening. The dependence on Vb and particularly the strongly negative onset voltages for negative Vb can be more readily explained by an electronic mechanism based on injection and trapping of holes in the perovskite under negative Vg followed by recombination with electrons that are injected into the channel as the gate voltage is swept to positive voltages. The ensuing hysteresis is expected to be less severe if Vb is kept positive and hole injection is minimized. In addition, we also observe that the low-temperature hysteresis in the transfer plot increases with high-k dielectrics like polymethyl methacrylate (PMMA), indicating a possible trap-dominated electronic mechanism for the hysteresis (fig. S22).

One further interesting aspect of the electrical characteristics of our perovskite FETs is an observed enhancement in device performance upon thermal cycling. On the second cooling-heating cycle, the temperature-dependent device characteristics were significantly improved (by up to two orders of magnitude) compared to the first cycle (Fig. 2E and section S12). All transistor characteristics presented here, except when stated otherwise, are from the second cooling cycle after the device has undergone one complete cycle of cooling to 100 K and warming up. Corresponding enhancement in the output characteristics on thermal cycling is shown in fig. S24.

To isolate the effects of applied bias and thermal cycling, we performed transfer measurements independently under the effect of bias and thermal cycling (section S12). We attribute the observed enhancement to a combination of thermal cycling and electrical biasing, with thermal cycling being the more important factor. In capacitance measurements performed during thermal cycling, we observe evidence for increased polarization order of the MA+ cations (fig. S28) and the structural analysis. Correspondingly, the energetic disorder quantified by the Urbach energy (Eu; estimated from the tail state absorption) was observed to decrease by around 1 meV (fig. S29). Furthermore, structural analysis of the thin films upon thermal cycling indicates a relative decrease of the unconverted PbI2 peak (fig. S30). From this analysis, it is evident that both polarization order as well as the decrease in point defect densities improve during thermal cycling.

The device instabilities discussed above clearly complicate the understanding of the underlying transport physics of the perovskite. However, we have mitigated these instabilities to a level where a meaningful investigation of the μFET(T) behavior of perovskite FETs fabricated from films with varied grain size and different interlayers at the S-D electrodes is possible (Fig. 3). We extracted μFET(T) from the saturated transfer characteristics and compared values obtained from the forward and reverse sweeps. As shown earlier, fig. S7 shows examples of mobility extraction from the transfer characteristics at different temperatures. Mobilities extracted from the forward and reverse characteristics differed by no more than 9% at low temperatures, where transconductance plots have larger hysteresis, and up to a maximum of 0.02 cm2/Vs for room temperature operation. For the plots in Fig. 3, we used the values from the forward characteristics, which tend to be more conservative. In contrast to most other thin-film FETs based on, for example, organic semiconductors or amorphous silicon, where disorder usually leads to a temperature-activated behavior, μFET(T) exhibits a clear negative temperature coefficient, that is, an increase in μFET with decreasing temperature, over the complete temperature range from 100 to 300 K. This is remarkable given the polycrystalline morphology of our thin films and their relatively low mobility compared to theoretically expected values and suggests that either there are very few electronic traps states in the density of states or, more likely, there are strongly temperature-dependent scattering mechanisms that counteract the effect of residual electronic trap states.

Fig. 3

Temperature-dependent transport measurements on MAPbI3 FETs.

(A) μFET(T) with different interlayers at the S-D contacts depicting three different regimes of charge transport with a power law behavior: μ ~ μ0T−γ. Region I: inorganic cage vibrational disorder (γ ~0.2 to 0.4); region II: dominated by the polarization fluctuation of MA+; region III: dominated by ion migration (γ ~4.1 to 5.3). (B) μFET(T) from FETs fabricated with different precursor concentration of perovskite solutions and PEIE-modified S-D electrodes. (C) Schematic of top-gate bottom-contact perovskite FETs summarizing the different sources of disorder mechanisms prevalent in a perovskite FETs corresponding to different regimes in the μFET(T) (left: vibrations of inorganic cage; middle: defect migration; right: MA+ polarization disorder).

We observe three temperature regimes identified from the distinct slopes in the μFET versus T plots (Fig. 3, A and B), which are analyzed by fitting a typical power law behavior to μFET ~ μ0T−γ. The exponent γ was found to be ranging from 0.2 to 0.4 in the low-temperature regime I (100 K < T < 160 K), from 2.6 to 3.2 in the intermediate-temperature regime II (160 K < T < 250 K), and from 4.1 to 5.3 in the high-temperature regime III (250 K < T < 300 K) (Fig. 3 and fig. S33). The values of the extracted exponent should be considered as indicative only because the individual temperature regimes are too narrow to allow an accurate determination, particularly in regime II. In regime III, there is a clear correlation between the mobility exponent and the film quality, that is, films with smaller grain size exhibit a larger mobility exponent (Fig. 3B).

To obtain insights into the mechanisms that govern the different transport regimes, we performed electrical and optical spectroscopy on our perovskite thin films. Impedance spectroscopy measurements were performed on films sandwiched between two metal gold contacts to probe the sources of polarization (electronic versus ionic) and dielectric relaxation (details in Materials and Methods). Hence, we measured both bulk capacitance (C) (Fig. 4A) and dielectric loss (ε″) (Fig. 4B) as a function of frequency and temperature; all measurements were performed in the dark to avoid the large photocapacitance effects that have previously been reported for these materials (, ). The C(f) measurements are shown over a frequency range of 1 kHz to 10 MHz to avoid the superlinear capacitive behavior at low frequency due to the ionic contribution (Fig. 4A and fig. S34) (, ).

Fig. 4

Spectroscopic investigation of the sources of disorder in MAPbI3 thin films.

(A) Capacitance of 250-nm-thick perovskite thin films measured on an Au/perovskite/Au sandwich device (schematically shown in the inset) as a function of temperature in steps of 40 K with an applied ac voltage of 30 mV. (B) Corresponding dielectric loss measurement as a function of frequency and temperature. (C) Raman spectra for 0.75 and 0.25 M perovskite thin films as well as reference single crystals measured at room temperature with a 532-nm laser excitation. The inset shows the Lorentzian fits to the different peaks of the spectrum. a.u., arbitrary units. (D) Plot of the shift in peak position corresponding to the vibration mode of MA+ and the Pb-I octahedron with temperature. The insets show a schematic representation of the corresponding molecular vibrations.

The dielectric loss spectroscopy results provide clear evidence that in regime III, transport mainly reflects the temperature dependence of ion migration and the associated screening of the gate electric field by negatively charged iodide ions. At 300 K, the dielectric loss spectra exhibit two characteristic relaxation frequencies, a low-frequency component at frequencies of <104 Hz attributed to ionic relaxation and a high-frequency component (~105 to 106 Hz), which can be ascribed to an electronic conduction and trapping mechanism in MAPbI3 (Fig. 4B and fig. S34) (, ). Upon cooling the perovskite devices to T = 240 K, we observed that the low-frequency component, which we attribute to the ionic relaxation, disappeared, and only the high-frequency electronic relaxation remained. This suggests that at T ≤ 240 K, ion migration is effectively suppressed. This is fully consistent with the observation in Fig. 3B that the strong dependence of mobility on microstructure and grain size, which we interpret in terms of different concentrations of charged point defects in the films, only sets in around this temperature; that is, the screening effect of the gate field associated with ion migration can be effectively neglected for T < 240 K, which is consistent with the previous reports of perovskite FETs demonstrated over a temperature range of 77 to 220 K (, ).

The dielectric constant εr = Cd/εoA (where C is the capacitance, d is the film thickness, A is the area of the capacitance, and εo is the vacuum permittivity) calculated from the capacitance data in Fig. 4A at room temperature is relatively high (εr ~ 21 to 23 at 100 kHz) and increases further to values of ~27 to 33 (at 100 kHz) upon cooling to 100 K. We model the dielectric behavior using the standard Kirkwood-Fröhlich equation for polar, orientationally disordered solids. At room temperature where the entropy associated with the MA+ orientations is high, we can assume that the Kirkwood correlation factor g ~ 1, indicating no specific interaction among the MA+ cations (). Assuming that the optical dielectric constant of perovskite ε∞ ~ 6.5 () and the molar volume (, ) is 3.95 × 1027 m−3, we obtain a dipole moment of 1.94 D, which is of comparable magnitude to the dipole moment estimated from ab initio electronic structure calculations (2.1 D).

This reasonable agreement between experiment and theory points to the fact that the dielectric constant measurement reflects mainly the polarization of the MA+ cation dipole moments (, , ). They are disordered near room temperature, but upon lowering the temperature, the thermal disorder in the dipole orientation decreases, which gets reflected as an increase in the dielectric constant (), in agreement with ultrafast vibrational spectroscopy results (). This interpretation is also consistent with measurements of the bulk energetic disorder in our films, obtained from external quantum efficiency measurements in the sub-bandgap region on a perovskite solar cell (with a power conversion efficiency η ~ 11%) at different temperatures. As shown in fig. S35, we observe a clear decrease in Eu from 14 meV at 300 K to 9.5 meV at 100 K. This decrease in energetic disorder is consistent with the dielectric spectroscopy and with the negative coefficient of μFET(T) (fig. S35E and Fig. 3).

To obtain further spectroscopic signatures of the polarization disorder from MA+ cations and to better understand the potential contribution of inorganic cage (PbI6) distortion to the disorder, Raman spectroscopy measurements were performed on perovskite thin films with different grain sizes as well as single crystals. Figure 4C shows typical room temperature Raman spectra with Lorentzian fits to the peaks of the 0.75 M sample shown as an inset. Characteristic peaks corresponding to the PbI6 cage modes (I-Pb-I bending ~70 cm−1 and Pb-I stretching ~90 cm−1) and peaks due to MA+ motion (libration ~160 cm−1 and torsional motion in the range of ~220 to 250 cm−1) were observed (, ). Additionally, a strong band centered at ~110 cm−1 has been assigned to a coupled mode of cage and MA+ libration (). Upon increasing the grain size, the Raman peaks assigned to the inorganic cage motion increase in intensity and the peak at 110 cm−1 exhibits a relative reduction, indicating, respectively, a higher degree of order and a decrease in the coupling between the inorganic cage and MA+. These differences are qualitatively similar to those observed previously between “disordered” MAPbI3 films grown on mesoporous substrates and “ordered” MAPbI3 films grown on flat substrates (). Furthermore, upon increasing the grain size, the peak corresponding to the torsional motion of the MA+ cation undergoes an increase in frequency by around 10 cm−1 at room temperature, indicating a stiffening of the MA+ cation vibration with increased grain size of the perovskite films (, ). From both structural analysis and Raman measurements, we conclude that the 0.25 M films not only exhibit a smaller grain size but are generally more disordered structurally and also exhibit a higher degree of MA+-induced polarization disorder than the 0.75 M films. Temperature-dependent Raman measurements were performed on both 0.25 and 0.75 M films (fig. S36). Interesting trends are observed upon tracking the peak positions of 90 and 220 cm−1 with temperature. Figure 4D shows the shift in the peak position corresponding to the torsional motion of MA+ for the 0.25 and 0.75 M samples with temperature. As shown in Fig. 4D, both samples show significant softening of the peak position with temperature; however, the degree of softening is more pronounced in the 0.25 M sample. Peak softening of 14 cm−1 was observed for films with small grain size (0.25 M) compared to a softening of 6 cm−1 for the films with larger crystallites (0.75 M). This observed pronounced softening of the peak with temperature is also consistent with a higher degree of MA+ polarization disorder for perovskite samples with smaller grain size compared to films with larger grains (–). In the same temperature range, the peak position corresponding to the Pb-I does not exhibit significant shifts. This suggests that vibrations of the Pb-I cages may become the most important source of thermal disorder below ~165 ± 10 K in the orthorhombic phase where the MA+ dipole moments become ordered ().

Because the most significant reduction in the disorder of the MA+ dipole moments occurs at temperatures above 160 K (Fig. 4A) (, ), we propose that in regime II, the observed μFET temperature dependence is governed by the decrease in the MA+ polarization disorder with decreasing temperature. The transition into regime I reflects a different carrier scattering mechanism with the weaker temperature dependence becoming dominant. We define the transition temperature TI-II between the two regimes, which is estimated from the intersection of the power-law fitting, in regime I and II. TI-II closely corresponds to the crystal phase transition in our perovskite films. The phase transition temperature was directly observed in our films to be 165 ± 10 K for all perovskite films, irrespective of the grain size, using temperature-dependent optical absorption spectroscopy (fig. S37). In the orthorhombic phase, the MA+ dipoles are ordered (, , ), and one might expect carrier scattering to become dominated by the vibrations of the Pb-I cages to which electrons in the Pb 6p-like conduction band are expected to couple strongly (). We emphasize that in contrast to the work of Duan et al. (), we do not observe an abrupt step change in mobility that indicates the phase transition (). This could possibly be attributed to the polycrystalline nature of thin films exhibiting broader phase transition temperatures in contrast to the well-defined phase transition temperature expected for single crystals (section S17).

In conclusion, with systematic control of grain size and contact interface engineering, it was possible to demonstrate high-performance perovskite FETs that exhibit clearly defined linear and saturation regime of the charge transport with μFET of ~0.5 cm2/Vs at 300 K and >2 cm2/Vs at 100 K, which approach, within an order of magnitude, local mobility values reported previously from THz and microwave conductivity measurements. A combination of structural and spectroscopic investigations were performed to probe the different sources of disorder prevalent in the perovskite field-effect transport. From the analysis, we attribute the enhanced charge transport and observation of room temperature field-effect transport to the combination of factors originating from the minimization of charged point defects located at grain boundaries, a decrease in the polarization fluctuation of the MA+ cations with larger grain size, and appropriate contact engineering to induce crystalline order as well as isolate the S-D electrode from the perovskite. These strategies have not only allowed us to gain an insight into the different scattering mechanisms that govern the temperature-dependent transport physics of these materials but are also likely to be important for achieving further improvements in device performance and extending FET charge transport studies to related classes of hybrid materials, such as 2D perovskites.

MATERIALS AND METHODS

Perovskite preparation

CH3NH3I was synthesized according to previously reported procedure (). Absolute ethanol (100 ml) was used to dilute 24 ml of methylamine solution (33% in ethanol) in a 250-ml round bottom flask, followed by the addition of 10 ml of aqueous solution of hydriodic acid (57 weight %) under constant stirring. After 1 hour of reaction time at room temperature, a rotary evaporator was used to remove the solvents from the reaction mixture. The white solid residual was then washed using dry diethyl ether and recrystallized from ethanol to get methylammonium iodide crystals (CH3NH3I). Lead(II) acetate trihydrate (99.999%) was purchased from Sigma-Aldrich Inc. The precursor solution for fabricating thin films of perovskites was prepared by adding a 3:1 molar ratio of methylammonium iodide and lead acetate in N,N′-dimethylformamide to get 0.25, 0.50, and 0.75 M concentrations of perovskite precursor solutions, respectively. The perovskite films were spin-coated at 2000, 3000, and 5000 rpm for 0.25, 0.5, and 0.75 M, respectively, and annealed at 100°C for 5 min. Preparation of the perovskite thin films at different concentrations and spin speeds allowed the tuning of the crystallite size of the perovskite thin films as shown in the SEM images (Fig. 1A).

Device fabrication

The transport measurements were performed on a bottom-contact top-gate field-effect transistor. For the fabrication of the FETs Cr/Au (2 nm:20 nm), electrodes were evaporated and patterned by photolithography onto precleaned plasma-treated glass substrates onto which the perovskite layer was deposited as described above. A Cytop dielectric layer of thickness ~500 nm was spin-coated over the perovskite film and annealed at 90°C for 20 min. This was followed by the evaporation of the Au gate electrode (25 nm) through a shadow mask to complete the device. For the dual-gated devices, the perovskite layer is coated on lithographically patterned S-D electrodes over the Si/SiO2 (300 nm) substrates. This was followed by spin-coating a Cytop layer and further coating the gate electrode in the same way as described earlier. All the devices, except the ones specified as continuous mode, were characterized using an Agilent 4155B parameter analyzer operated in pulsed mode. In the pulsed mode of operation, for the transfer (output) measurement Vg, (Vd) was applied over a short impulse of 0.5 ms. When the continuous mode of operation was used, the voltages were applied continuously in between measurements during the scan. The temperature-dependent transport measurements were performed using a Desert Cryogenics low-temperature probe station.

Impedance measurement

Sandwich devices were fabricated with patterned Au bottom electrode and shadow mask–patterned top Au electrode. To minimize leakage and obtain reliable devices, thicker perovskite films (>0.25 μm) were used. The spin-coated films were annealed at 100°C for 5 min. Impedance measurements were performed using a standard HP 4912A Impedance Analyzer over a frequency of 100 Hz to 10 MHz. The sample temperature was varied using a Desert Cryogenics low-temperature probe station.

Raman measurements

Raman spectroscopy measurements were performed on perovskite films fabricated on a quartz substrate. The Raman spectra were collected using a HORIBA T64000 Raman spectrometer attached to a confocal microscope with a 100× objective and a 532-nm laser for the excitation. Laser power was minimized to ensure that no degradation of the sample was induced. The spectra were recorded from 50 to 300 cm−1 and averaged over several accumulations. The samples were mounted on an Oxford Instruments MicrostatHiResII cryostat for temperature-dependent studies in the range of 10 to 300 K. The samples were cooled using a liquid helium cryostat while maintained at a vacuum of 10−6 mbar. Achieving significant signal-to-noise ratio while maintaining a sufficiently small laser intensity to avoid degradation of the sample was difficult at intermediate temperatures; hence, we only show here measurements at room temperature and low temperatures (100 K), where degradation induced peaks are not present ().

SEM measurements

The surface of the perovskite films were imaged using an LEO Variable SEM. It was ensured that the voltage levels did not affect the integrity of the perovskite thin films.

Photothermal deflection spectroscopy

Samples were prepared in an identical fashion as used for the device fabrication on spectrosil quartz slides (which were cleaned with deionized water, acetone, and isopropanol followed by 10 min of oxygen plasma etch). The samples were kept in an airtight-sealed quartz cuvette filled with an inert liquid, Fluorinert FC-72 from 3M Corporation, which acts as the deflection medium with a large temperature-dependent refractive index. The perovskite thin films were excited with a modulated monochromatic light beam perpendicular to the plane of the sample obtained by a combination of a Light Support MKII 100W Xenon arc source and a CVI DK240 monochromator. The transverse probe beam was produced with a Qioptiq 670-nm fiber-coupled diode laser and passed as close as possible to the perovskite film surface. Beam deflection was measured using a differentially amplified quadrant photodiode and a Stanford Research SR830 lock-in amplifier, which is proportional to the absorption in the sample.