Assessing Temperature Dependence of Drift Mobility in

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Cite This: J. Phys. Chem. C 2018, 122, 5935−5939

Assessing Temperature Dependence of Drift Mobility in Methylammonium Lead Iodide Perovskite Single Crystals Shreetu Shrestha,†,‡ Gebhard J. Matt,†,* Andres Osvet,† Daniel Niesner,§ Rainer Hock,∥ and Christoph J. Brabec†,‡ †

Institute of Materials for Electronics and Energy Technology (i-MEET), Friedrich-Alexander-University Erlangen−Nürnberg (FAU), Martensstrasse 7, 91058 Erlangen, Germany ‡ Erlangen Graduate School of Advanced Optical Technologies (SAOT), Friedrich-Alexander-University Erlangen−Nürnberg (FAU), Paul-Gordan-Strasse 6, 91052 Erlangen, Germany § Institute of Solid State Physics, Friedrich-Alexander-Universität Erlangen−Nürnberg (FAU), Staudtstrasse 7, 91058 Erlangen, Germany ∥ Institute for Crystallography and Structural Physics, Friedrich-Alexander-University Erlangen−Nürnberg (FAU), Staudtstrasse 3, 91058 Erlangen, Germany S Supporting Information *

ABSTRACT: Hybrid organic−inorganic perovskites have emerged as costeffective and high-performance semiconductors for optoelectronic applications. Precise knowledge of charge carrier mobility and especially the temperature dependence of mobility is therefore of utmost relevance for advancing highperformance materials. Here, the charge carrier mobility in methylammonium lead iodide single crystals is investigated with time of flight technique from 290 to 100 K. A nondispersive transport with an electron mobility of 135 (±20) cm2/V s and a hole mobility of 90 (±20) cm2/V s is obtained at room temperature. A power-law temperature dependence of mobility, μ ∝ Tm, with an exponent m = −2.8 and −2.0, is measured for electrons and holes in the tetragonal phase. The highest electron and hole mobilities measured are 635 (±70) and 415 (±20) cm2/V s, respectively. Our results indicate that the scattering of charge carriers with phonons is the limiting factor for carrier mobilities at room temperature. 164 cm2/V s.2−5 This rather wide-spread reported mobility values could, in part, be explained by the differences in the quality of single crystals used because crystals grown under different conditions might not have the same quality even though they are single crystals.6 Another factor which has been pointed out is that different measurement techniques probe different time scales, spatial resolutions, carrier densities, and have different systematic errors.7,8 Hence, studying charge transport dynamics with different techniques could give complementary information to make a complete picture. Time of flight (TOF) is a transient photocurrent technique, where the time required for charge carriers to drift through a known distance under the influence of an electric field is measured to calculate the drift mobility. There are three main advantages of this technique: (i) mobility is measured directly (as opposed to measuring another parameter which scales with mobility such as conductivity), (ii) both electron and hole mobilities can be determined independently, and (iii) information about the nature of charge transport can be

1. INTRODUCTION Hybrid organic−inorganic perovskites (HOIPs) have emerged as promising materials for optoelectronic applications. HOIP light-absorbing layers fabricated by simple and low-cost solution processing techniques have led to solar cells with more than 22% power conversion efficiency.1 Besides solar cells, HOIP-based photodetectors, light-emitting diodes, and lasers have also generated significant interest. Regardless of the specific application, a precise knowledge of charge transport is necessary to further advance high-performance device concepts. Charge carrier mobility is arguably the most important transport parameter. For solar cells and photodetectors, the mobility sets an upper limit to the thickness of the active layer. Besides device optimization, the mobility is interesting also from a fundamental point of view. The mobility is limited primarily by charge carriers scattering off impurities and lattice vibrations (phonons). Since different scattering mechanisms have different temperature dependence, the nature of interaction of charge carriers with impurities and phonons can be inferred from the temperature dependence of mobility. Methylammonium lead iodide (MAPbI3) is the most widely investigated HOIP prototype. The charge carrier mobility in MAPbI3 single crystals reported in literature ranged from 2.5 to © 2018 American Chemical Society

Received: January 11, 2018 Revised: January 24, 2018 Published: February 1, 2018 5935

DOI: 10.1021/acs.jpcc.8b00341 J. Phys. Chem. C 2018, 122, 5935−5939

Article

The Journal of Physical Chemistry C

Figure 1. Schematic of TOF measurement setup.

obtained from the shape of the TOF transient. Moreover, because TOF is a direct measurement, the analysis is simple. Here, we measure electron and hole drift mobilities of MAPbI3 single crystals with the TOF method. We observe nondispersive transport for electrons and holes with a mobility of 135 (±20) and 90 (±20) cm2/V s, respectively, at room temperature. At low temperatures, the mobility increases significantly. This strong temperature dependence indicates that scattering of carriers with phonons limits the mobility of MAPbI3 at higher temperatures.

μ=

d2 V × t tr

(1)

where, d is the crystal thickness and V is the applied voltage. By reversing the polarity of the applied field, the mobility of the opposite charge carrier species can be calculated from the corresponding transit time. Accumulation of charge at electrodes because of possible ion diffusion or other slow transient effects, for example, can disrupt the field. To prevent charge buildup during the measurement, a modulated bias at 500 Hz was used. Another factor which can disturb the applied electric field is the photoexcited charge itself. Therefore, the laser intensity was reduced to a low level of 0.6 ms) with respect to the onset of the voltage pulse to ensure a stable electric field in the bulk. The transient current was measured as the voltage drops over a load resistor amplified with a voltage amplifier (FEMTO HVA 200M 40F) and recorded with a digital oscilloscope (Tektronix DPO3034). A cryostat with a liquid nitrogen cooling system was used to cool the samples under nitrogen atmosphere.

2. METHODS 2.1. Single Crystal Growth. One to three millimeters thick MAPbI3 single crystals were grown by the bottom seed solution growth method, as reported in literature3 (Figure S1). In short, the solution of methyl-ammonium iodide and lead iodide in equimolar ratio in gamma-butyrolactone was prepared. The precursor was heated at 100 °C for 3 h which produced small MAPbI3 crystals. One carefully selected MAPbI3 small crystal was used as a seed in a fresh precursor solution and allowed to grow overnight at 100 °C. 2.2. Device Fabrication. The crystals [(100) facets] were contacted by gold on one side and semitransparent silver on the other side. A one micron thick poly(methyl methacrylate) (PMMA) blocking layer was used between the crystal and the semitransparent silver electrode to reduce the injection of carriers. The PMMA layer was deposited by drop-casting (20 mg/mL PMMA in chlorobenzene). The gold (70 nm) and the semitransparent silver (40 nm) electrodes were thermally evaporated. 2.3. TOF Measurement. The schematic of the measurement setup is shown in Figure 1. The crystal was illuminated through the semitransparent silver electrode by a 1.3 ns pulsed, frequency-doubled Nd:YAG laser (from CryLaS GmbH) emitting at 532 nm. Because 532 nm is strongly absorbed by MAPbI3 (attenuation length < 100 nm), a sheet of charge carriers is generated close to the illuminated surface. A bias voltage was applied on the sample using a function generator (Agilent 33500B) and a voltage amplifier (Falco Systems WMA-300). Depending on the polarity of the applied bias, either electrons or holes drift through the bulk to the opposite electrode. As the carriers drift, they give rise to an instantaneous displacement current which is seen as a plateau in the transient photocurrent signal. When the carriers reach the gold electrode, the current decays resulting in a tail in the transient signal. The transition from the plateau to the tail is marked by a characteristic “kink”. The position of this kink is considered the transit time (ttr), that is, the time taken by the carriers to travel through the bulk of the crystal. Once ttr is known, the mobility (μ) can be calculated using the equation

3. RESULTS AND DISCUSSION Figure 2 shows the TOF transients from holes for different electric fields at room temperature. The characteristic plateau and tail can be clearly seen in the transients. The flat plateau region indicates nondispersive transport meaning that the velocity and number of carriers remain constant as the charge carriers transverse the sample. Similarly, a well-defined transit time and nondispersive transport is also measured for electrons (Figure S2). The electron and hole mobilities at room temperature calculated from eq 1 using the transit time obtained are 135 (±20) and 90 (±20) cm2/V s, respectively. The electron mobility measured is approximately 1.5 to 2 times higher than the hole mobility. These values are within the range of previously reported values.2−5 Upon cooling the crystals, the carrier mobility increases. Figure 3 shows a normalized hole transient photocurrent signal at 1100 V/cm from 260 to 100 K. At lower temperatures, the kink indicating the transit time (shown by a black arrow) moves to the left. This means that at lower temperature, the transit time is shorter and the mobility is higher. Because there is lower phonon scattering of carriers at lower temperatures, such higher mobility values are expected. Interestingly, at longer time scales, the current gives the impression of a second plateau, indicating an additional low mobility feature. This feature became more distinct at low 5936


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mobility feature at higher temperature (Figure S3). Another possibility is the thermally activated detrapping of carriers at higher temperatures. Further experimental evidence is required to clarify the origin of the low-mobility feature. TOF transients at high temperatures in Figure 3 show an overshoot (current rises over time instead of a flat plateau). This indicates a nonuniform field distribution which is typically attributed to field perturbation because of photoexcited charges.11−14 Depending on the degree of perturbation, the peak position of the overshoot has been theoretically predicted to range from 78 to 100% of the transit time.11,12 Figure 4 shows the temperature dependence of mobility in a double logarithmic scale. A straight line that describes the

Figure 4. Temperature dependence of electron and hole mobility of MAPbI3 single crystals. m indicates the slope of the linear fit (red line).

Figure 2. Electric filed dependence of the hole transient photocurrent in (a) linear scale and (b) in double logarithmic scale at room temperature. The MAPbI3 crystal was 1.48 mm thick.

power law dependence μ ∝ Tm shows a good fit with the measured data. The error bars are calculated from the standard deviation of measurements at different electric fields after including the uncertainty due to field perturbation. For the tetragonal phase, we determine m = −2.8 and −2.0 for electrons and holes, respectively. These values are significantly higher than those reported in literature for mobilities obtained by time-resolved terahertz spectroscopy (TRTS)15,16 and timeresolved microwave photoconductivity (TRMC).17 As mentioned earlier, variations are to be expected because of different samples and different measurement techniques. TOF measures the drift mobility with generally lower excitation intensity over a longer time span (microseconds), whereas “ultrafast” techniques such as TRMC and TRTS measure a local or microscopic mobility over a shorter time span. Moreover, because TOF measurements are sensitive to traps, mobilities obtained from TOF are typically lower than those obtained from ultrafast techniques, especially at low temperatures where detrapping can be slow. However, this would result in a smaller temperature dependence of mobility from TOF which is the opposite of what we observe. Hence, another explanation is required to account for this discrepancy. Below 170 K in the orthorhombic phase, the electron and hole mobilities increase but not as rapidly. This indicates that as phonons start to freeze out at very low temperatures, other scattering mechanisms start to dominate. Similar behavior is also observed in inorganic semiconductors. At 100 K, electron and hole mobilities measured are 635 (±20) and 415 (±20) cm2/V s, respectively. Although the temperature coefficient in the orthorhombic phase is lower than in the tetragonal phase, no significant discontinuities at the phase transition temperatures can be seen. Subsequently, warming slightly decreases

Figure 3. Temperature dependence of hole transient photocurrent at 1100 V/cm electric field. The MAPbI3 crystal was 1.48 mm thick.

temperature, and its position did not show temperature dependence. Initially, we considered the presence of two different domains in the crystal, which has also been reported in literature,9 yielding different mobility values. However, considering that the carriers have to drift through typically 2 mm thick crystals, it appears very unlikely to assume isolated domains which would be large enough to form a continuous path extending up to 2 mm. Transport via an indirect local maximum with a smaller curvature in the valence band could also be responsible for the low mobility feature, as was reported for Br-based crystals because of a giant Rashba splitting.10 The spillover of carriers from the main band to an indirect local minimum could explain the higher photocurrent from the low 5937


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(kT ≫ phonon energy, h̵ω) and μ ∝ exp(−h̵ω/kT) in the low temperature limit (kT ≪ h̵ω).31 The reported energy of polar optical phonons in MAPbI3 (16 meV,28 ≈186 K) is in the intermediate range where the temperature dependence of mobility requires rigorous mathematical calculations. In Figure S6, we attempt to fit the mobility of MAPbI3 in the tetragonal phase to a simplified version19,30 of the equation developed by Callen to describe the temperature dependence of the momentum relaxation time limited by polar optical phonon scattering.32 The fit is reasonable and gives a phonon energy of 20 meV, which is also close to the reported value.28 Future studies on the electronic band structure of MAPbI3 could help quantitatively analyze the experimental data better.

the hole mobility (Figure S4). Significant hysteresis, however, is not observed. The mobility value at each temperature, as shown in Figure 4, is an average of six to nine measurements at different electric fields (Figure S5). Although there were slight variations from crystal to crystal, the data shown in Figure 4 are representative for all samples measured. The most important result of this work is our observation of nondispersive charge transport in MAPbI3. Although MAPbI3 consists of both organic and inorganic parts, theoretical studies suggest that states from the organic cation are energetically far from band edges, and MA does not directly contribute to the electronic band structure relevant for transport but primarily stabilizes the perovskite structure.18 As such, it is not surprising that the charge transport in MAPbI3 single crystals is nondispersive, similar to the one reported for other inorganic semiconductors. Table 1 compares the temperature dependence of the mobility from our studies on MAPbI3 single crystals with

4. CONCLUSIONS In summary, we measure the electron and hole drift mobilities in MAPbI3 single crystals with the TOF method from 290 to 100 K. We believe that reliable mobility data over a wide temperature and electrical field regime are essential for the community to verify and validate theoretical models describing transport and scattering in perovskites. In this study, we measure nondispersive electron and hole mobilities of 135 (±20) and 90 (±20) cm2/V s at room temperature. A powerlaw temperature dependence of the mobility, μ ∝ Tm, with exponents m = −2.8 and −2.0 for electrons and holes, respectively, is obtained in the high-temperature tetragonal phase. In the low-temperature orthorhombic phase, the exponent decreases and the highest electron and hole mobilities measured are 635 (±70) and 415 (±20) cm2/V s, respectively. Our results indicate that scattering between charge carriers and phonons at high temperatures limits the carrier mobility.

Table 1. Temperature Dependence of Mobility of MAPbI3 and Some Common Semiconductors in the Room Temperature Rangea material Si GaAs MAPbI3 MAPbI3 MAPbI3 MAPbI3 a

polycrystalline film polycrystalline film polycrystalline film single crystal (this work)

Method

electron

hole

TOF Hall TRMC TRTS TRTS TOF

−2.5 −2.323 −1.617 −1.516 −1.515 −2.8

−2.722 −2.323

22

−2.0

■

The numbers show the value of the exponent m for μ ∝ T . m

previous studies as well as with other inorganic semiconductors. It is noteworthy that our measurements on single crystals report a stronger temperature dependence of the mobility than in the previous microscopic studies on MAPbI3 polycrystalline thin films. The values observed in our studies, however, compare well with conventional semiconductors. In the covalent semiconductor (nonpolar) Si, a combination of acoustic deformation potential scattering and intervalley scattering is used to explain strong dependence.19,20 Whereas in the heteropolar semiconductor GaAs, the strong dependence is attributed to polar optical phonon scattering,19−21 where the oppositely charged ions vibrate in opposite directions. Because the mobility limited by impurity scattering has positive temperature dependence, there is a general agreement that this mechanism is not dominant at room temperature in MAPbI3.15,24 Considering the low-trap density, 109 to 1010 per cubic centimeter in MAPbI3 single crystals,6 and the “defecttolerant” nature,25 this seems reasonable. The question then is which phonon scattering mechanism is dominant in the high-temperature range in MAPbI3? Different mechanisms: acoustic deformation potential scattering,15 piezoelectric scattering,26 polar optical phonon scattering,24 and large polaron formation27−29 have been proposed to play a significant role. Considering the ionic nature of MAPbI3, it seems likely that scattering due to polar modes and polar optical modes in particular, which are efficiently scattering, plays a vital role. Polar optical phonon scattering is also predominant at room temperature in II−VI and III−V semiconductors.20,30 For scattering by polar optical phonons, μ scales theoretically with T−0.5 in the high temperature limit

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b00341. X-ray diffraction, picture of MAPbI3 single crystal, electron TOF transients, field dependence of low mobility feature, TOF transients measured during cooling and warming of the samples, field dependence of mobility, fit to polar optical scattering, mobility lifetime product, current overshoot, and temperature dependence of electron TOF transients (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +49 9131 85 27726. ORCID

Shreetu Shrestha: 0000-0002-3606-7624 Daniel Niesner: 0000-0001-7810-6823 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support via DFG-funded Cluster of Excellence “Engineering of Advanced Materials” and the doctoral program GRK 1896 “In situ Microscopy with Electrons, X-rays and Scanning Probes” is gratefully acknowledged. The authors thank Prof. Lothar Ley for the valuable comments on the manuscript. 5938


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(20) Rode, D. L. Low-Field Electron Transport. In Semiconductors and Semimetals; Willardson, P. K., Beer, A. C., Eds.; Academic Press: New York, 1975; Vol. 10, pp 1−89. (21) Stillman, G. E.; Wolfe, C. M.; Dimmock, J. O. Hall Coefficient Factor for Polar Mode Scattering in N-Type GaAs. J. Phys. Chem. Solids 1970, 31, 1199−1204. (22) Ludwig, G. W.; Watters, R. L. Drift and Conductivity Mobility in Silicon. Phys. Rev. 1956, 101, 1699−1701. (23) Blakemore, J. S. Semiconducting and Other Major Properties of Gallium Arsenide. J. Appl. Phys. 1982, 53, R123−R181. (24) Wright, A. D.; Verdi, C.; Milot, R. L.; Eperon, G. E.; PérezOsorio, M. A.; Snaith, H. J.; Giustino, F.; Johnston, M. B.; Herz, L. M. Electron-Phonon Coupling in Hybrid Lead Halide Perovskites. Nat. Commun. 2016, 7, 11755. (25) Steirer, K. X.; Schulz, P.; Teeter, G.; Stevanovic, V.; Yang, M.; Zhu, K.; Berry, J. J. Defect Tolerance in Methylammonium Lead Triiodide Perovskite. ACS Energy Lett. 2016, 1, 360−366. (26) Lu, Y.-B.; Kong, X.; Chen, X.; Cooke, D. G.; Guo, H. Piezoelectric Scattering Limited Mobility of Hybrid Organic-Inorganic Perovskites CH3NH3PbI3. Sci. Rep. 2017, 7, 41860. (27) Zhu, X.-Y.; Podzorov, V. Charge Carriers in Hybrid OrganicInorganic Lead Halide Perovskites Might Be Protected as Large Polarons. J. Phys. Chem. Lett. 2015, 6, 4758−4761. (28) Sendner, M.; Nayak, P. K.; Egger, D. A.; Beck, S.; Müller, C.; Epding, B.; Kowalsky, W.; Kronik, L.; Snaith, H. J.; Pucci, A.; et al. Optical Phonons in Methylammonium Lead Halide Perovskites and Implications for Charge Transport. Mater. Horiz. 2016, 3, 613−620. (29) Frost, J. M. Calculating Polaron Mobility in Halide Perovskites. Phys. Rev. B 2017, 96, 195202. (30) Ridley, B. K. Quantum Processes in Semiconductors, 4th ed.; Oxford University Press: Oxford, 1999. (31) Rose, A. Electron Phonon Interactions; World Scientific Publication: Singapore, 1989. (32) Callen, H. B. Electric Breakdown in Ionic Crystals. Phys. Rev. 1949, 76, 1394−1402.

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Assessing Temperature Dependence of Drift Mobility in

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