Effect of Phase Transition on Optical Properties and Photovoltaic

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Effect of Phase Transition on Optical Properties and Photovoltaic Performance in Cesium Lead Bromine Perovskite: A Theoretical Study WenXing Zhang, Zhenxu Lin, Rui Huang, and Yuzheng Guo J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b05629 • Publication Date (Web): 12 Aug 2019 Downloaded from pubs.acs.org on August 12, 2019

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The Journal of Physical Chemistry

Effect of Phase Transition on Optical Properties and Photovoltaic Performance in Cesium Lead Bromine Perovskite: A Theoretical Study WenXing Zhang1*, ZhenXu Lin1, Rui Huang1*, Yuzheng Guo2* 1School

of Materials Science and Engineering, HanShan Normal University, China 521041

2School

of Electrical Engineering and Automation, WuHan University, China 430072

Email: [email protected]; [email protected]; [email protected] Abstract CsPbBr3 perovskite is considered as a promising material for solar cell and light emitting diode. But the application is hindered by light (or heat) induced transition from cubic phase to orthorhombic phase or vice versa under ambient conditions. We utilized density functional theory and linear response theory to explore the phase transition in CsPbBr3 crystal. We studied both the energy evolution with respect to phase change and the vibration modes of negative frequencies in orthorhombic phase. It is identified that both phases are metastable intermediate structures that could interconvert easily at room temperature. Analyzing the optoelectronic transport properties, we predicted the cubic phase of CsPbBr3 has bigger short-circuit current while the orthorhombic one has bigger open-circuit voltage. Therefore, the best photovoltaic performance should be a balance of the two typical phases depending on specific application. The finding of characteristic optical spectra and photocurrent spectra is important for characterizing and improving the performance of CsPbBr3 based optoelectronic devices. 1. Introduction CsPbBr3 crystal has attracted broad research interests in many optical and electrical applications such as solar cells, light emitting diodes, photo detectors due to its advanced optoelectronic properties.1-11 In practice, humidity has intensive interference to CsPbBr3 crystal and can be suppressed effectively by coating or passivating with special molecules.9-15 However, rapid degradation after irradiation of light, 1

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heat or electron beam prevents further characterization and application.12,

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Understanding the poor

stability, i.e. phase transition of CsPbBr3 crystal when absorbing energy, is the key to device optimization. The phase transition in cesium lead halide perovskite has been reported, including structure of lattice, dielectric constant, critical temperature, etc.

17-18

Recently, effects of external pressure and strain were

also reported for CsPbBr3 crystal experimentally.2,

19

At least two phases have been confirmed for

CsPbBr3 based on X-ray diffraction (XRD),9 nuclear magnetic resonance (NMR),17 transmission electron microscope (TEM),16 photo-luminescence spectra (PL) and Raman spectra,2, 20, cubic phase (space group: 𝑃𝑚3𝑚) and orthorhombic phase (space group: 𝑃𝑏𝑛𝑚). The two phases may coexist in small CsPbBr3 crystals like nanocube, nanoplate and nanowire at room temperature due to the effect of quantum confinement.18-22 Previous theoretical studies mainly focused on electronic properties of CsPbBr3 perovskite, such as partial density of states, band structure, dependence of lattice parameters on strain or pressure, and evolution of energy gap.3-7 To the best of our knowledge, it is still lacking of theoretical study on the phase stability of CsPbBr3 crystal and in-depth insight to its effect on optoelectronic conversion. In this work, we studied the phase stability by density functional theory and linear response theory. We also proposed practical ways to characterize and improve the optoelectronic performance of CsPbBr3 in devices based on the non-equilibrium transport properties under illumination of sunlight. We found cubic CsPbBr3 has bigger short-circuit current (Isc) and orthorhombic one has bigger open-circuit voltage (Voc). The best performance of CsPbBr3 must be a balance between Isc and Voc. 2. Computational Methods In this work, electronic structure and optical properties were calculated with CASTEP package.23-27 GGA-PBE functional and OTFG norm-conserving pseudopotential were used to determine the electronic density of ground state. The cutoff energy was set to 1225eV. A 222 Monkhorst-Pack mesh was used 2


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for k point sampling. A

2 22 supercell with 20 atoms of cubic structure was used for comparison

with the unit-cell of orthorhombic structure (Fig.1a). In all calculations, 10-6 eV/atom and 10-5 eV/Å were set as convergence criteria for energy and force, respectively. To clarify the process of phase transition, the most possible path of reaction was searched out from cubic phase to orthorhombic phase with complete LST/QST transition state search method. Fifteen intermediate images are calculated and three of them are shown to illustrate the process of transition (Fig.1b). Lattice dynamics was conducted by density functional perturbation theory.27 Vibration modes were analyzed for negative frequencies (Fig.2). Vibrational energy at room temperature was calculated using the phonon spectra and Bose distribution. For effect of phase transition on optoelectronic properties, electronic structures (Fig.3) and Infrared spectra (Fig.4a) were calculated for both phases while Raman spectra (Fig.4b) were calculated by linear response theory only for orthorhombic phase because cubic phase is Raman inactive due to symmetry. The photocurrent was calculated with Qunatumwise-ATK package based on the non-equilibrium green’s function method (NEGF).28 In transport calculation, metaGGA functional was employed and the photocurrent was calculated by adding the electron-photon interaction to the device Hamiltonian using first-order perturbation theory.29 3. Results and Discussion As shown in Fig.1a, when CsPbBr3 crystal changes from cubic structure to orthorhombic structure, the PbBr6 octahedrons are distorted from square to parallelogram and rotated by a small angle from the lattice axis c. The total free energy, including static energy and vibrational energy at room temperature,

3



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Figure 1. (a) Structures of 𝑃𝑚3𝑚 (cubic) phase and 𝑃𝑏𝑛𝑚 (orthorhombic) phase. Left side is side view and right side is top view. a, b and c are lattice axes. (b) Evolution of net force on atoms and total free energy/unitcell along the reaction path. The energy of reactant Er is subtracted for comparison. Green PbBr6 octahedrons are plotted to illustrate the distortion. is decreased by only ~0.5eV/unit-cell i.e. ~25meV/atom during the transition (Fig.1b), consistent with phase transition induced by absorbing light or heat because the energy difference is comparable with average kinetic energy of thermal fluctuation at room temperature. While the orthorhombic phase is a bit more stable than cubic phase because of lower energy, but it is not stationary because net force on atoms increases with energy decreasing. Thus, metastable cubic phase is the ground state due to zero force when the temperature is higher than room temperature. Orthorhombic phase is preferred due to lower total energy when the temperature declines. In nanosacle such as quantum dot or nanowire, both phases may coexist under ambient conditions due to strong quantum confinement. To reveal the origin of phase instability in CsPbBr3, lattice dynamics was studied for both structures. 4


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Figure 2. (a) Vibration modes of the three negative-frequencies in 𝑃𝑏𝑛𝑚 phase: -62cm-1, -61cm-1, and -8cm-1. Green arrows illustrate the amplitude and direction of vibrations. (b) Evolution of total energy/unit cell along the path of vibration mode: the reactant corresponds to the most negative displacement of atoms, and the product corresponds to the most positive. Ee, the energy of equilibrium configuration (𝑃𝑏𝑛𝑚) is subtracted for comparison. There is no negative frequency in the phonon spectrum of cubic phase, but there are three negative frequencies for orthorhombic phase (-8cm-1, -61cm-1, -62cm-1). The vibrational modes of negative frequencies are shown in Fig.2a and the curves of total energy with respect to atom displacement are shown in Fig.2b where reaction paths are employed. The total energy of equilibrium configuration is set to zero for comparison. The orthorhombic configuration is found on a saddle-like point of the potential energy surface and produces anharmonic effects. These modes distort PbBr6 octahedron and the mode of -62cm-1 decreases total energy the most quickly. All these modes make the crystal transform in various configurations among which the cubic and orthorhombic ones are two metastable states. The PbBr6 octahedrons deviate easily from the orthorhombic configuration at room temperature and the cubic configuration is preferred at high temperature. So the structure of CsPbBr3 could be tuned to improve the optical or electronic device performance. We further studied energy band and partial density 5



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Figure 3. (a) Energy bands of 𝑃𝑚3𝑚 phase (blue) and 𝑃𝑏𝑛𝑚 phase (red). Valence band maximum (grey) is set to zero. (b) Partial density of states (PDOS). Red dash line is the contribution from Cs 6s orbital and blue dot line is the contribution from Pb 6p orbital. Grey dash-dot line is sum of the two orbitals. of states as shown in Fig.3. Both phases have direct gap. The energy gap of cubic phase (1.57eV) is lower than orthorhombic one (1.87eV). In general, GGA functional underestimates the energy gap, but comparisons with the hybrid functional HSE and metaGGA functional showed the PBE produced the same trends and their results agreed within 20%. Taking the computational cost into account, PBE was employed for band structure. Electrons of direct transition from valence band maximum to conduction band minimum are mainly from the 6p orbital of lead. All lead ions are surrounded by Br ions, so the energy gap changes mainly due to distortions of PbBr6 octahedron, i.e. movement of Br ions. From viewpoint of energy gap, the cubic phase is more efficient for light conversion. So the instability of CsPbBr3 crystal is the bottleneck and study on stabilizing the cubic phase is needed. The phase instability gives rise to change of property in CsPbBr3 crystal. Although all atoms are too

6


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heavy to drift far, especially lead and cesium ions, the symmetry of crystal changes dramatically when

Figure 4. (a) Infrared spectra for 𝑃𝑚3𝑚 and 𝑃𝑏𝑛𝑚 structures. (b) Raman spectra for 𝑃𝑏𝑛𝑚 structure. The inset shows the Raman peak at 130 cm-1. PbBr6 octahedrons rotate a little. Thus, vibration spectra like infrared and Raman would be very sensitive to the variance of configuration. The primitive unit cell of cubic phase is four times smaller than that of orthorhombic phase and vibration in cubic phase comes mainly from bromine ions. So the spectra of cubic phase should have much less characteristic peaks and high frequency peaks should be more visible. Fig.4a shows the results of linear response calculation, which is the same as our discussion. For the cubic phase, the infrared spectra have three characteristic peaks while for the orthorhombic one, there are much more peaks and obvious redshift for high frequency ones. Moreover, the cubic phase is Raman inactive 7



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due to the limit of symmetry while the orthorhombic phase is Raman active. Our calculation in Fig.4b showed three recognizable peaks (42cm-1, 72cm-1 and 130cm-1) for orthorhombic phase and they are in

Figure 5. (a) Dark current of CsPbBr3. (b) Photocurrent of CsPbBr3 in standard illumination of sunlight (Flux=1). (c) Total IV characteristics of CsPbBr3. (d) Photovoltaic power of CsPbBr3. consistent with experimental results.20 The calculated photocurrent verified the conclusions above and revealed an important new rule to improve the performance, the rule of balance between Voc and max-power point (MPP), i.e. balance between cubic and orthorhombic phases. As shown in Fig.5, the transport of electrons and holes are really somewhat blocked with symmetry decreasing from perovskite to non-perovskite. Both the dark current (Fig.5a) and the photocurrent (Fig.5b) own a bigger value for cubic structure than orthorhombic one. The dark current increases with bias exponentially while the photocurrent increases much more slowly. So the orthorhombic structure has a bigger Voc and a smaller Isc as shown in Fig.5c. Finally, the cubic structure captures a bigger MPP (Fig.5d). The improvement of performance depends on the real needs: 8


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higher Voc or bigger power, which is more important. The solar cell performance is influenced by many factors (impurity concentration, electrode contact, interfaces and so on). So the direct comparison between theoretical predictions here with experiments is difficult, although the energy gap and Voc in our work are rather close to previous experimental reports30-31. 4. Conclusions We used density functional theory to study the phase transition in CsPbBr3 crystal and its effect on optical and optoelectronic transport properties. The cubic phase is advantageous for light conversion but is metastable at room temperature. The orthorhombic phase is more stable under low temperature but not stable either due to anharmonic vibrations. No perfect structure appears for solar cell, because the cubic structure has bigger max-power while the orthorhombic one has higher open-circuit voltage. But both factors are crucial to conversion of solar energy. To stabilize the structure to cubic phase which is more efficient for light conversion, one possible way is introducing strain from encapsulation and constraining every atom to the cubic configuration. Thus, matching degree of lattice between CsPbBr3 and coating material is important to its performance. We will focus on optimization of coating materials. The change of vibration spectra would be used to monitor the phase transition and to characterize the quality of device experimentally. Data availability The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request. Acknowledgements This work was supported by National Natural Science Foundation of China (Nos. 61274140), Natural Science Foundation of Guangdong Province (2015A030313871). 9



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Conflict of interest The authors declare that they have no conflict of interest. Contributions W. X. Z. conceived the idea, performed the DFT calculation and analysis. W. X. Z. and R. H. supervised the work. W. X. Z., Z. X. L., R. H. and Y. Z. G contributed to the discussion of the results and the writing of the manuscript.

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Effect of Phase Transition on Optical Properties and Photovoltaic

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