Insight into the collective vibrational modes driving ultralow thermal conductivity of perovskite solar cells

The past few years have witnessed a rapid evolution of hybrid organic-inorganic perovskite solar cells as an unprecedented photovoltaic technology with both relatively low cost and high-power conversion. The fascinating physical and chemical properties of perovskites are benefited from their unique crystal structures represented by the general chemical formula $AM{X}_3$, where the $A$ cations occupy the hollows formed by the $M{X}_3$ octahedra and thus balance the charge of the entire network. Despite a vast amount of theoretical and experimental investigations have been dedicated to the structural stability, electrical, and optical properties of hybrid halide perovskite materials in relation to their applications in solar cells, the thermal transport property, another critical parameter to the design and optimization of relevant solar cell modules, receives less attention. In this paper, we evaluate the lattice thermal conductivity of a representative methylammonium lead triiodide perovskite $\left({\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3\right)$ with direct nonequilibrium ab initio molecular dynamics simulation. Resorting to full first-principles calculations, we illustrate the details of the mysterious vibration of the methylammonium cluster $\left({\mathrm{CH}}_3{\mathrm{NH}}_3^{+}\right)$ and present an unambiguous picture of how the organic cluster interacting with the inorganic cage and how the collective motions of the organic cluster drags the thermal transport, which provide fundamental understanding of the ultralow thermal conductivity of ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$. We also reveal the strongly localized phonons associated with the internal motions of the ${\mathrm{CH}}_3{\mathrm{NH}}_3^{+}$ cluster, which contribute little to the total thermal conductivity. The importance of the ${\mathrm{CH}}_3{\mathrm{NH}}_3^{+}$ cluster to the structural instability is also discussed in terms of the unconventional dispersion curves by freezing the partial freedoms of the organic cluster. These results provide more quantitative description of organic-inorganic interaction and coupling dynamics from accurate first-principles calculations, which are expected to underpin the development of emerging photovoltaic devices.

Figure 1

The side view (top panel), top view (middle panel), and the spatial charge density (bottom panel) of (a) pseudocubic, (b) orthorhombic, and (c) tetragonal phase of methylammonium lead triiodide perovskite structures $({\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$, MAPI).

Figure 2

NEAIMD simulation models of (a) pseudocubic and (b) tetragonal phase MAPI. (c), (d) The corresponding length-dependent thermal conductivity. The shaded area indicates the error bar of the NEAIMD simulation. The green and yellow dotted lines are thermal conductivity results from previous theoretical calculations [9, 10], and the black dashed line denotes experimental data [8].

Figure 3

(a) The full phonon dispersion curves (left panel) of pseudocubic phase MAPI and the corresponding partial phonon density of states (right panel), where the low-, middle-, and high-frequency islands are clearly identified. (b)–(d) The low-frequency phonon dispersion curves of only inorganic cages for the pseudocubic, orthorhombic, and tetragonal phases, respectively, by freezing the motions of the ${\mathrm{MA}}^{+}$ cluster (see text for details).

Figure 4

The frequency-dependent (a) phonon group velocities and (b) phonon lifetime of pseudocubic phase MAPI. In (b), the blue, red, and pink data points correspond to the low-, middle-, and high-frequency islands, respectively, which are shown in the right panel of Fig. 3.

Figure 5

Comparison of the partial vibrational density of states of Pb and I ions in the inorganic cages with and without ${\mathrm{MA}}^{+}$ cluster. The solid lines are the results of normal pseudocubic MAPI structure (with ${\mathrm{MA}}^{+})$ and the dashed-dotted lines represent the empty pseudocubic inorganic cages (without ${\mathrm{MA}}^{+})$. (Inset) The deformation charge density of pseudocubic MAPI with isosurface value 0.005. The green and yellow colors represent the negative and positive charge densities, respectively.

Figure 6

Schematic of some representative phonon modes associated with the ${\mathrm{MA}}^{+}$ cluster in the pseudocubic phase perovskite solar cell. The arrows indicate the movement of the entire cluster or atoms. For brevity, only the ${\mathrm{MA}}^{+}$ cluster is shown.

Figure 7

Analysis of phonon anharmonicity of representative rotational and translational modes in the pseudocubic phase perovskite solar cell by first-principles calculations (supercell $2\times 2\times 2)$. (a), (b) Represent the change of the potential energy of the system with respect to the rotational angle for the modes of rotations I and II, respectively. (c), (d) Illustrate the corresponding results for the modes of translations I and II, respectively. The solid lines are quadratic fitting to the energy change. (Insets) Schematic of the movement of the ${\mathrm{MA}}^{+}$ cluster.