Phonon Mode Transformation Across the OrthohombicâTetragonal

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Letter

Phonon Mode Transformation across the OrthohombicTetragonal Phase Transition in a Lead-Iodide Perovskite CHNHPbI: A Terahertz Time-Domain Spectroscopy Approach 3

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Chan La-o-vorakiat, Jeannette Medina Kadro, Teddy Salim, Daming Zhao, Towfiq Ahmed, Yeng Ming Lam, Jian-Xin Zhu, Rudolph A Marcus, Maria-Elisabeth Michel-Beyerle, and Elbert E.M. Chia J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.5b02223 • Publication Date (Web): 03 Dec 2015 Downloaded from http://pubs.acs.org on December 5, 2015

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The Journal of Physical Chemistry Letters

Phonon Mode Transformation Across the Orthohombic-Tetragonal Phase Transition in a Lead-Iodide Perovskite CH3NH3PbI3: a Terahertz Time-Domain Spectroscopy Approach Chan La-o-vorakiat,∗,† Jeannette Kadro,¶ Teddy Salim,§ Daming Zhao,¶ Towfiq Ahmed,k Yeng Ming Lam,§ Jian-Xin Zhu,k,# Rudy A. Marcus,⊥,@ Maria-Elisabeth Michel-Beyerle,¶ and Elbert E. M. Chia∗,¶ Nanoscience and Nanotechnology Graduate Program, King Mongkut’s University of Technology Thonburi, 10140 Thailand, Theoretical and Computational Science Center (TaCS), Faculty of Science, King Mongkut’s University of Technology Thonburi, 10140 Thailand, Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore, School of Materials Science and Engineering, Nanyang Technological University, 639798 Singapore, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA, and Noyes Laboratory, California Institute of Technology, Pasadena, California 91125, USA. E-mail: [email protected]; [email protected]

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During the past few years, the organometallic lead halide perovskite CH3 NH3 PbI3 and its relatives have been subjected to intense research as next-generation photovoltaic materials. 1–4 The material demonstrates a progressively rising efficiency of solar energy conversion reaching 20% 5–7 resulting from the advantages of long charge diffusion length, high carrier mobility and broadband absorption across the solar radiation spectrum. The simple solution-based fabrication procedure offers the promise of low-cost large-scale fabrication. The huge promise of the perovskites motivated the characterizations of the perovskites using many experimental and theoretical techniques such as optical spectroscopy, X-ray diffraction 8–11 and electronic-structure calculations. 12–21 However, there are only few studies of the lowest-lying phonon modes in the terahertz (1 THz = 1012 Hz) range, and how these phonon modes evolve with temperature. The study of phonon modes in the THz range is important because these phonons contribute to the photoconductivity in the same frequency range as the free carriers. It is important to disentangle these free-carrier and phonon contributions, in order to isolate the behavior of the free carriers generated upon irradiation with visible light. Recent THz investigations have revealed that phonon-mode signals superimpose onto the photoconductivity of free carriers, 17,22–24 and a mechanism of strong phonon coupling with charge carriers explains the homogeneous broadening of photoluminescence linewidth with temperature. 25 The ability to identify the vibrational modes, and how they evolve with temperature in the different crystal phases, will help with the development of quantitative models for the generation, transport and recombination of photogenerated carriers in perovskite-based solar cells. 26 The investigation of phonon modes must be performed over a large temperature range. A single-crystal CH3 NH3 PbI3 exhibits structural phase transitions: 10 162.2 K Orthorhombic

⇐⇒

327.4 K Tetragonal

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⇐⇒


Cubic


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We have reported the strong influence of the crystal phase on the performance of solar cells, as the diffusion length is reduced in the orthorhombic phase. 23 – The perovskite structure of CH3 NH3 PbI3 consists of a CH3 NH+ 3 cation with 12 I ions

forming a cuboctahedral geometry at temperatures above 327.4 K, while Pb2+ ion defines the crystal structure. At room temperature, the perovskite has a tetragonal crystal structure. The phase transition should directly influence the vibration modes involving the Pb and I ions as the b- and c- axes of the unit cell are distorted. 10,27 In addition, upon cooling down to the orthorhombic phase, the lattice distortion constrains the position of the cation such that it becomes ordered, in contrast to the disordered and fluctuating orientation 10 in the tetragonal and cubic phases. Such an enhancement of the orientational order influences the vibration modes, 28 NMR 29 and crystallography. 11 However, the vibrational frequencies of the cations are in the infrared region, 28 which is not covered by our THz spectrometer. In this paper, we study the temperature evolution of the phonon modes of the organometallic lead halide perovskite CH3 NH3 PbI3 thin film, in the terahertz region (0.5–3 THz) and temperature range 20–300 K. These modes are related to the vibration of the Pb−I bonds of the perovskite. 14 We found that two phonon modes in the tetragonal phase at room temperature split into four modes in the low-temperature orthorhombic phase. By use of Lorentz model fitting to the phonon modes, we analyze the critical behavior of this phase transition. We also observe the coexistence of orthorhombic and tetragonal phases near the transition temperature as evidenced by the smearing of transition temperature. The perovskite sample is prepared by a conventional solution-based protocol. First, z cut quartz substrates (10 x 10 x 1 mm) were cleaned and deposited with the perovskite precursor solution. Then the substrates were subjected to an air plasma treatment for 5 minutes, and subsequently transferred to a nitrogen glove box. The CH3 NH3 I and PbI2 components were dissolved in stoichiometric ratio to form the precursor solution (30 wt% in dimethylformamide) for spin coating, followed by heating on a hotplate at 373 K. The thickness of our final polycrystalline CH3 NH3 PbI3 film is about 200 nm. 4


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We measure the phonon modes embedded in the complex optical conductivity (˜ σ ) in the THz range. Our setup 30,31 consists of a Teraview TPS3000 spectrometer coupled to a Janis ST-100-FTIR continuous flow cryostat, a homemade three-axis alignment stage, and a Cryo Industries cryocooler to control the sample temperature from 20 K – 320 K. 31 We keep the sample under vacuum (∼10−7 mbar) during the entire duration of experiment with minimum exposure to air during the sample mounting to avoid sample degradation. The raw data taken from the spectrometer are the THz waveform in the time domain (a typical waveform is shown in the inset of Fig 1a). Next, we calculate the THz transmission function T˜(ω) =

Eperovsikie Equartz

(Fig 1b) defined as

the ratio of electric field amplitudes of two successive measurements of a CH3 NH3 PbI3 sample on a z -cut quartz substrate, and on a bare z -cut quartz substrate as reference. As shown in Fig 1a, the perovskite is quite transparent to THz beams as the transmission amplitude ranges from 0.82 to 1.0 (completely transparent). With only the knowledge of the sample and substrate thicknesses, we calculate the THz conductivity (˜ σ (ω) = σ1 (ω) + iσ2 (ω)) using an analytical form of the THz transmission function: 31 (b)

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Transmission Function

Time Domain

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Time (ps)

z-cut quartz Perovskite + z-cut quartz

0

0.5

1

1.5

2

2.5

Frequency (THz)

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(c) 8

1

Real Refractive Index

(a) THz Spectral Amplitude (a.u.)

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0.98 0.96 0.94 20 K 50 K 75 K 100 K 130 K 150 K 160 K 300 K

0.92 0.9

0.5

1

1.5

2

2.5

3

Frequency (THz)

6 4 20 K 50 K 75 K 100 K 130 K 150 K 160 K 300 K

2 0 0.5

1

1.5

2

2.5

3

Frequency (THz)

Figure 1: (a) THz waveforms in time-domain (inset) obtained from our THz spectrometer after transmitting through the perovskite sample (blue) and the z -cut quartz reference (red). Fourier transformations result in transmitted THz spectra. (b) The complex amplitude of E . The perovskite is quite transmissive in transmission function defined as T˜(ω) = perovskite Equartz ˜ the THz range. The features inside T (ω) are due to phonon modes. (c) The calculated real refractive index n.

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T˜(ω) =

nsub −1) 2˜ n(˜ nsub + 1) exp[ iωd(˜cn−1) ] exp[ −iω∆L(˜ ] c , n ] (1 + n ˜ )(˜ n+n ˜ sub ) + (˜ n − 1)(˜ nsub − n ˜ ) exp [ 2iωd˜ c

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(1)

where n ˜ is the (complex) refractive index of the perovskite film, n ˜ sub is the refractive index of the z -cut quartz substrate obtained from a separate measurement, d is the film thickness, c is the speed of light in vacuum, and ∆L is the difference in thickness of sample and reference √ substrates. σ ˜ (ω) are then obtained from the sample refractive index n ˜ = n + ik = ǫ1 + iǫ2 and σ ˜ (ω) = iωǫ0 (1 − n ˜ 2 ). Note that we solve Eqn. 1 exactly without the help of a thinfilm approximation that assumes that the factor iωd˜ n/c is small. As a cross-check, we compare the low-frequency limit of our refractive index (˜ n) to those measured by a standard dielectric measurement at low frequencies of ω/2π = 100 Hz – 100 kHz. 10,32 The reported lower frequency limits of ǫ1 ∼ 36 agree well with our present measurement of n ∼ 6 and k ∼ 0, where ǫ˜ = n2 − k 2 (Fig 1c). The contribution of the phonon modes to the optical conductivity follows the Lorentzian behavior — the real part σ1 peaks at the phonon mode (resonant) frequencies, and the imaginary part σ2 crosses zero at the resonance frequencies. At room temperature (300 K), two main phonon modes are observed at ∼1 and 2 THz (Fig 2 red). The two modes agree well with a recent DFT density-functional theory (DFT) calculation of infrared-active modes where the peaks due to the Pb−I vibrations are near 1.0 and 2.0 THz. 17,26,33 In addition, Brivio et al. attributed the 1-THz phonon modes to the buckling of the Pb–I–Pb angles, and the 2-THz phonon modes to Pb–I length vibrations. Since the orientational randomness of the methylammonium molecule and distortions in the lattice break the space-group symmetry of the lattice, the above phonon modes contain an admixture of longitudinal optical (LO) and transverse optical (TO) characters. 26 As the temperature is reduced, the two phonon modes evolved to four modes (Fig 2) right below 160 K — near the expected tetragonal-to-orthorhombic transition temperature. Clearly we have observed the onset of the structural phase transition. The branching of the phonon modes also appears in the infrared spectra involving the modes from cations 6


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20000

5HDO &RQGXFWLYLW\ k1 (1-1m-1)

(a)

1 3

4

20000

2

20 K

15000

,PDJLQDU\ &RQGXFWLYLW\ k2 (1-1m-1)

(b)

15000 20 K

50 K

50 K

75 K

10000

75 K

10000

100 K

100 K

120 K

120 K

130 K

5000

130 K

5000

150 K

150 K

160 K

160 K

300 K

0

0

0.5

1

1.5

2

2.5

3

300 K

0.5

1

1.5

2

2.5

3

Frequency (THz)

Frequency (THz)

Figure 2: Temperature dependent THz (a) real and (b) imaginary conductivities (˜ σ = σ1 + iσ2 ) of the pervoskite sample CH3 NH3 PbI3 : two phonon modes are visible at 1 and 2 THz at temperatures above 150 K. Two additional phonon peaks develop below 150 K due to the structural phase transition (arrows). Lorentz model fits are performed on both real and imaginary part (dashed lines). The Lorentz contributions are plotted for the real conductivity at 20 and 300 K. Data are shifted for clarity by horizontal dotted lines.

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−1 28 (CH3 NH+ and a vibrational peak at 50 cm−1 in 3 ) located near 30 THz (∼1000 cm ),

DFT spectra splits into two when the crystal structure is orthorhombic. 14 This splitting at the tetragonal-to-orthorhombic transition is also found in a iron-pnictide superconductor Ba(Fe1-x Cox )2 As2 .

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We focus on the phase-transition behavior by quantitatively analyzing these phonon modes, at each sample temperature, using the Lorentz model:

σ(ω) = −iǫ0 ω(ǫ∞ − 1) +

2 ǫ0 ωp,m ω , 2 2 i(ω − ω ) + ωΓ m 0,m m=1−4

X

(2)

where ωp,m , ω0,m = 2πfm , and Γi are plasma frequencies, phonon resonance frequencies, and the scattering rate of oscillator m, respectively. The high-frequency dielectric constant ǫ∞ accounts for dielectric contributions beyond our experimental frequency window. We need two Lorentzian oscillators to fit the high-temperature data (T >165 K), but require two additional ones at low temperatures (T

Phonon Mode Transformation Across the OrthohombicâTetragonal

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Phonon Mode Transformation Across the OrthohombicâTetragonal