Assessing Temperature Dependence of Drift Mobility in

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Assessing Temperature Dependence of Drift Mobility in Methylammonium Lead Iodide Perovskite Single Crystals Shreetu Shrestha, Gebhard Josef Matt, Andres Osvet, Daniel Niesner, Rainer Hock, and Christoph J. Brabec J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b00341 • Publication Date (Web): 01 Feb 2018 Downloaded from http://pubs.acs.org on February 1, 2018

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The Journal of Physical Chemistry

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†‡

†Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Institute of Materials for Electronics and Energy Technology (i-MEET), Martensstrasse 7, 91058 Erlangen, Germany. ‡Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Erlangen Graduate School of Advanced Optical Technologies (SAOT), Paul-Gordan-Strasse 6, 91052 Erlangen, Germany. §Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Institute of Solid State Physics, Staudtstrasse 7, 91058 Erlangen, Germany. #

Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Institute for Crystallography and

Structural Physics, Staudtstrasse 3, 91058 Erlangen, Germany.

*G.J.M. [email protected], Tel. +49 9131 85 27726

ACS Paragon Plus Environment

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ABSTRACT

Hybrid organic inorganic perovskites (HOIPs) have emerged as cost effective 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 high performance materials. Here, charge carrier mobility in MAPbI3 single crystals is investigated with Time of Flight (TOF) technique from 290 K to 100 K. A nondispersive transport with electron mobility of 135 (±20) cm2/Vs and hole mobility of 90 (±20) cm2/Vs is obtained at room temperature. A power law temperature dependence of mobility, µ α 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) cm2/Vs and 415 (±20) cm2/Vs, respectively. Our results indicate that scattering of charge carriers with phonons is the limiting factor for carrier mobilities at room temperature.


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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, HOIPs 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 mobility sets an upper limit to the thickness of the active layer. Besides device optimization, mobility is interesting also from a fundamental point of view. 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. Charge carrier mobility in MAPbI3 single crystals reported in literature range from 2.5 -164 cm2/Vs.2-5 This rather wide spread in reported mobility values could, in part, be explained by the differences in the quality of single crystals used, since 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


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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 obtained from the shape of TOF transient. Moreover, since TOF is a direct measurement, analysis is simple. Here, we measure electron and hole drift mobilities of MAPbI3 single crystals with the TOF method. We observe non-dispersive transport for electrons and holes with a mobility of 135 (±20) cm2/Vs and 90 (±20) cm2/Vs, 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.

2. METHODS

2.1. Single crystal growth. One to three millimeters thick MAPbI3 single crystals were grown by bottom seed solution growth method as reported in literature3 (Figure S1). In short, solution of MAI and PbI in equimolar ratio in GBL was prepared. The precursor was heated at 100 °C for 3 hours 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.


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2.2. Device fabrication. (100) facets of the crystals were contacted by gold on one side and semi-transparent silver on the opposite side. A one micron thick Poly(methyl methacrylate) (PMMA) blocking layer was used between the crystal and the semi-transparent silver electrode to reduce injection of carriers. The PMMA layer was deposited by drop casting (20 mg/ml PMMA in Chlorobenzene). The gold (70 nm) and semi-transparent 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 semi-transparent silver electrode by a 1.3 ns pulsed, frequency doubled Nd:YAG laser (from CryLaS GmbH) emitting at 532 nm. Since 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 plateau to 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 ݀ଶ ߤ= ܸ ∗ ‫ݐ‬௧௥ (1)


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where, d is crystal thickness and V the applied voltage. By reversing the polarity of the applied field, the mobility of opposite charge carrier species can be calculated from the corresponding transit time.

Figure 1. Schematic of time of flight measurement setup. Accumulation of charge at electrodes, due to possible ion diffusion or other slow transient effects for example, can disrupt the field. To prevent charge build-up during the measurement, a modulated bias at 500 Hz was used. Another factor which can disturb the applied electric field is the photo-excited 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 voltage drop over a load-resistor amplified with a voltage amplifier (FEMTO HVA 200M 40F) and recorded with a digital oscilloscope (Tektronix DPO 3034). A cryostat with liquid nitrogen cooling system was used to cool the samples under nitrogen atmosphere.


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3. RESULTS AND DISCUSSION

Figure 2 shows 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 non-dispersive 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 non-dispersive transport is also measured for electrons (Figure S2).

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


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Electron and hole mobilities at room temperature calculated from Equation 1 using the transit time obtained are 135 (±20) cm2/Vs and 90 (±20) cm2/Vs, respectively. The electron mobility measured is approximately 1.5 to 2 times higher than the hole mobility. These values are within the range of the previously reported values.2-5 Upon cooling the crystals, the carrier mobility increases. Figure 3 shows normalized hole transient photocurrent signal at 1100 V/cm from 260 K 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. Since there is lower phonon scattering of carriers at lower temperatures, such higher mobility values are expected.

Figure 3. Temperature dependence of hole transient photocurrent at 1100 V/cm electric field. MAPbI3 crystal was 1.48 mm thick. 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 temperature and its position did not show a temperature dependence. Initially we considered the presence of two different domains in the crystal which has also been reported in literature9


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yielding different mobility values. However, considering that the carriers have to drift through a typically 2 mm thick crystals, it appears very unlikely to assume isolated domains which would be large enough to form a continuous path extending 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 due to 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 mobility feature at higher temperature (Figure S3). Another possibility is the thermally activated de-trapping 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 non-uniform field distribution which is typically attributed to field perturbation due to photo-excited 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 which describes the 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 time resolved microwave photoconductivity (TRMC).17 As mentioned earlier, variations are to be expected due to different samples and different


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measurement techniques. TOF measures the drift mobility with generally lower excitation intensity over a longer time span (microseconds) while “ultrafast” techniques like TRMC and TRTS measure a local or microscopic mobility over a shorter time span. Moreover, since TOF measurements are sensitive to traps, mobilities obtained from TOF are typically lower than those obtained from ultrafast techniques, especially at low temperatures where de-trapping 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.

Figure 4. Temperature dependence of electron and hole mobility of MAPbI3 single crystals. m indicates the slope of the linear fit (red line). 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) cm2/Vs and 415 (±20) cm2/Vs, respectively. While the temperature coefficient in the orthorhombic phase is lower


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than in the tetragonal phase, no significant discontinuities at the phase transition temperatures can be seen. Subsequently warming slightly decreases the hole mobility (Figure S4). Significant hysteresis, however, is not observed. The mobility value at each temperature shown in Figure 4 is an average of 6 to 9 measurements at different electric fields (Figure S5). While there were slight variations from crystal to crystal, the data shown in Figure 4 is representative for all samples measured. The most important result of this work is our observation of non-dispersive 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 charge transport in MAPbI3 single crystals is non-dispersive, similar to one reported for other inorganic semiconductors. Table 1 compares the temperature dependence of the mobility from our studies on MAPbI3 single crystals with 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 previous microscopic studies on MAPbI3 polycrystalline thin films. The values observed in our studies, however, compare well with conventional semiconductors. In the covalent semiconductor (non-polar) Si, a combination of acoustic deformation potential scattering and inter-valley scattering is used to explain the strong dependence.19,20 Whereas in the hetero-polar semiconductor GaAs, the strong dependence is attributed to polar optical phonon scattering19-21 where the oppositely charged ions vibrate in opposite directions.


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Table 1. Temperature dependence of mobility of MAPbI3 and some common semiconductors in the room temperature range. The numbers show the value of the exponent m for µαTm.

material

method electron

hole

Si

TOF

-2.522

-2.722

GaAs

Hall

-2.323

-2.323

MAPbI3 polycrystalline film

TRMC

-1.617


TRTS

-1.516


TRTS

-1.515

MAPbI3 single crystal (this work)

TOF

-2.8

-2.0

Since 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 crystals6 and the “defect tolerant” nature25 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 scattering24 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


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Assessing Temperature Dependence of Drift Mobility in

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