Dynamic disorder, phonon lifetimes, and the assignment of modes to the vibrational spectra of methylammonium lead halide perovskites

TLDR: Comparison of experimental spectra and calculated vibrational modes enables confident assignment of most of the vibrational features between 50 and 3500 cm-1, and it is found that MAPbI3 shows exceptionally short phonon lifetimes, which can be linked to low lattice thermal conductivity.

Abstract: We present Raman and terahertz absorbance spectra of methylammonium lead halide single crystals (MAPbX3, X = I, Br, Cl) at temperatures between 80 and 370 K. These results show good agreement with density-functional-theory phonon calculations.1 Comparison of experimental spectra and calculated vibrational modes enables confident assignment of most of the vibrational features between 50 and 3500 cm-1. Reorientation of the methylammonium cations, unlocked in their cavities at the orthorhombic-to-tetragonal phase transition, plays a key role in shaping the vibrational spectra of the different compounds. Calculations show that these dynamics effects split Raman peaks and create more structure than predicted from the independent harmonic modes. This explains the presence of extra peaks in the experimental spectra that have been a source of confusion in earlier studies. We discuss singular features, in particular the torsional vibration of the C-N axis, which is the only molecular mode that is strongly influenced by the size of the lattice. From analysis of the spectral linewidths, we find that MAPbI3 shows exceptionally short phonon lifetimes, which can be linked to low lattice thermal conductivity. We show that optical rather than acoustic phonon scattering is likely to prevail at room temperature in these materials.

Figures

Figure 1 Summary of the crystal systems and space groups adopted by MAPbI3, 19-23

Figure 7 Effect of disorder on the frequency of the MA torsional mode (19 in Figure 3 and Table 3) of MAPbI3 .The histograms show the distribution of frequencies of mode 19, extracted from 248 individual calculations in which the MA cation was randomly orientated and partially relaxed (see supplementary information). The solid line is the kernel density estimation of these sampled data.

Figure 4 Decomposition of the 36 gamma-point eigenmodes of cubic MAPbI3 (a), MAPbBr3 (b) and MAPbCl3 (c) into relative energetic contribution of each atom. The

Figure 3 Phonon dispersions of the 18 low frequency (inorganic cage) modes within the

Figure 9 Temperature dependence of the estimated phonon lifetimes for MAPbI3 (a.),

Figure 10 Electron-phonon scattering rate factor for optical and acoustic phonons as a function of electron energy. This approximate quantity is synthesised from a superposition of estimated contributions from each phonon. These are derived from the energy of each mode at the Γ point, scaled by its relative IR activity (considered a proxy for its piezoelectric coupling), convolved with a parabolic density of electronic

Frequently asked questions

Q1. What are the contributions in "Dynamic disorder, phonon lifetimes, and the assignment of modes to the vibrational spectra of methylammonium lead halide perovskites" ?

The authors present Raman and terahertz absorbance spectra of methylammonium lead halide single crystals ( MAPbX3, X = I, Br, Cl ) at temperatures between 80 and 370 K. The authors discuss singular features, in particular the torsional vibration of the C-N axis, which is the only molecular mode that is strongly influenced by the size of the lattice. From analysis of the spectral linewidths, the authors find that MAPbI3 shows exceptionally short phonon lifetimes, which can be linked to low lattice thermal conductivity. The authors show that optical rather than acoustic phonon scattering is likely to prevail at room temperature in these materials. Furthermore, the assignment of spectral peaks to particular vibrations which could be influenced by chemical changes will allow the stability of the materials exposed to different operating environments to be monitored using vibrational spectroscopy. 

Q2. What is the force constant used to construct a dynamical matrix?

The force constants, which define the change in force on a reference atom in response to the displacement of another, are used to construct a dynamical matrix, which is then diagonalised to give the eigenvalues (vibrational frequencies) and associated eigenvectors (normal modes of the motion). 

Q3. How can the authors obtain the scattering rate at a temperature T?

The scattering rate per electron of a given energy at a temperature T can be obtained by convolution of the scattering factor with a Bose-Einstein distribution function. 

Q4. What can be done to characterize the chemical environments in materials in situ?

Raman spectroscopy can characterize the chemical environments in materials in situ, as well as revealing the nature of the lattice vibrations (phonons). 

Q5. What is the effect of the laser light on the vibrational spectra of MAPb?

Heating by laser light directly absorbed by MAPbI3 has been shown to lead to rapid degradation of the material, resulting in PbI2 Raman signatures. 

Q6. What is the way to resolve the molecular modes at Raman shifts?

Short wavelength excitation allows the molecular modes at Raman shifts above ~ 200 cm -1 to be clearly resolved, but is less suitable for resolving the cage modes at lower energies. 

Q7. What is the role of phonons in the lattice?

In these materials, optical phonons contribute considerably to the lattice thermal conductivity and serve as important scattering channels for acoustic phonons. 

Q8. What is the sensitivity of the MA torsional vibration to the halide cage?

The sensitivity of the MA torsional movements to steric hindrance by the surrounding lattice cages suggests that the spectral peak corresponding to this vibration could be used to probe variation of lattice structure in spatially-resolved studies, or in mixed-halide systems. 

Q9. What is the pronounced peak broadening in MAPbI3?

The peak broadening occurring at the orthorhombic-to-tetragonal phase change in MAPbI3 is the most pronounced and corresponds to a step-like decrease of the lifetimes of most of the low frequency modes. 

Q10. What is the cause of the inhomogeneous broadening of the Raman ?

This is known as inhomogeneous broadening and is likely to be due to the appearance of a distribution of bond lengths resulting from spatial disorder in the orientation and/or position of the MA molecules within the perovskite cages. 

Q11. What is the effect of the coupling between organic and inorganic sub-lattices?

For all three compounds, the coupling between both organic and inorganic sub-lattices leads to an increase in the existing Raman peak widths rather than creating a distribution of new mode frequencies. 

Q12. What is the effect of the small size of the voids on the dynamic coupling?

On the other hand, the small size of the voids enhances a lot steric hindrance and consequently the dynamic coupling is enhanced as well. 

Q13. What is the reason for the lack of resolution of these molecular features?

The other reason for the lack of resolution of these molecular features is dynamic broadening, which is discussed in detail below. 

Q14. Why do the authors think the Raman peaks are preserved at room temperature?

The authors therefore propose that the unhindered rotations in the more cubic cavity might preserve the width of the Raman peaks, even at room temperature. 

Q15. What are the modes that have no spectroscopic activity?

These necessarily have zero frequency atthe gamma point and, by their translational symmetry, no associated spectroscopic activity. 

Q16. What is the corresponding abrupt broadening of the peaks in MAPbBr?

The Raman features associated with cage vibrations merge across the phase change around 160 K, and the corresponding abrupt broadening of the peaks can be seen in Figure S17a in the supplementary information.