Halide Perovskites: Thermal Transport and Prospects for Thermoelectricity

Abstract

The recent re-emergence of halide perovskites has received escalating interest for optoelectronic applications. In addition to photovoltaics, the multifunctional nature of halide perovskites has led to diverse applications. The ultralow thermal conductivity coupled with decent mobility and charge carrier tunability led to the prediction of halide perovskites as a possible contender for future thermoelectrics. Herein, recent advances in thermal transport of halide perovskites and their potentials and challenges for thermoelectrics are reviewed. An overview of the phonon behavior in halide perovskites, as well as the compositional dependency is analyzed. Understanding thermal transport and knowing the thermal conductivity value is crucial for creating effective heat dissipation schemes and determining other thermal-related properties like thermo-optic coefficients, hot-carrier cooling, and thermoelectric efficiency. Recent works on halide perovskite-based thermoelectrics together with theoretical predictions for their future viability are highlighted. Also, progress on modulating halide perovskite-based thermoelectric properties using light and chemical doping is discussed. Finally, strategies to overcome the limiting factors in halide perovskite thermoelectrics and their prospects are emphasized.

Keywords: halide perovskites; hybrids; perovskites; phonons; thermal transport; thermoelectrics.

Figure 1

Schematic illustration of tradeoffs between various thermoelectric parameters.

Figure 2

Structure of hybrid and inorganic perovskites. a) Illustration of the 3D hybrid perovskite structure ABX₃, showing the corner‐sharing [BX₆]⁴⁻ octahedra. A is an organic cation, B is a metal cation, and X is a halide. b) Illustration of the structures of low‐dimensional perovskites with different numbers of perovskite layers (n). The pure 2D perovskite (n = 1) has a R₂BX₄ structure, where R is a bulky organic cation. For n > 1, the quasi‐2D perovskites arrange into a R₂A_{n −1}B_nX_{3 n +1} structure. Reproduced with permission.^{[ 61 ]} Copyright 2018, Nature Publishing Group.

Figure 3

a) Temperature dependence of κ of single crystal (black) and polycrystal (red) MAPbI₃ samples. Blue lines are obtained from the theoretical model. The inset shows the detail around the structural transition at 160 K. b) Resistivity as a function of temperature for single (black curve) and polycrystalline (red curve) samples. Reproduced with permission.^{[ 20 ]} Copyright 2014, American Chemical Society. c) Equilibrium molecular dynamics predicted anisotropic κ along various axes (κ_x, κ_y, and κ_z) as a function of temperature. The phonon dispersion curves of d) orthorhombic, e) tetragonal, and f) cubic MAPbI₃ in the low‐frequency domain. Reproduced with permission.^{[ 32 ]} Copyright 2016, Wiley‐VCH.

Figure 4

Room temperature experimental and theoretical κ for halide perovskites.^{[ 20} , ³² , ⁷⁰ , ⁷¹ , ⁷⁸ , ⁷⁹ , ⁸⁰ , ⁸¹ , ⁸² , ⁸⁴ , ⁸⁵ , ⁸⁶ , ⁸⁷ , ⁸⁸ , ⁸⁹ , ⁹⁰ , ⁹¹ , ⁹² , ⁹³ , ^{94 ]}

Figure 5

Thermal measurement of perovskite nanowires. a) False‐color SEM image of typical microbridge device with a perovskite nanowire bridging between two suspended pads. The heat flow is defined from heating membrane (red) to sensing membrane (blue) through the nanowire (green). (Inset) High‐magnified SEM image of typical measured nanowire. b) κ of corresponding MAPbI₃ nanowire. The dip around 160 K coincides with the orthorhombic‐to‐tetragonal phase transition. κ of CsPbBr₃, MAPbBr₃, and MAPbI₃ nanowires. c) κ comparison between MAPbBr₃ and MAPbI₃ reveals the role of accelerated cation dynamics in suppressing κ (green arrow in c) at low temperature. d) κ comparison between CsPbBr₃ and MAPbBr₃ reveals the role of cation dynamic in suppressing κ (green arrow in d). Insets in (c,d) are the simplified schematic diagrams of MAPbI₃, MAPbBr₃, and CsPbBr₃ unit cell with indication of cation dynamic motion in hybrid perovskite (red arrow in the unit cell). Scattered data points are the measurement results and the solid lines are the model fitting curves. Reproduced with permission.^{[ 85 ]} Copyright 2018, American Chemical Society.

Figure 6

a) Schematic of the FDTR measurement on an Au‐coated perovskite single crystal. A pump laser (blue) heats the crystal while a probe laser (green) measures the temperature‐dependent reflectance of Au to determine the κ of the crystal. b) Common phase transitions of the perovskite lattice, shown for MAPbX₃. In the tetragonal and cubic phases, the MA cations are under constant motion within the lattice and are therefore shown in random orientations. The purple arrows in these phases illustrate some of the many possible octahedron motions of the system under dynamic disorder. c) Optical microscope image of a CsPbBr₃ crystal with an Au transducer layer evaporated on top. Scale bar is 50 µm. d) κ as a function of sound speed (v̅_s). e) κ as a function of C_a‑cubic v̅_s/3, where C_a‑cubic is the volumetric heat capacity of acoustic phonons based on a cubic unit cell. Reproduced with permission.^{[ 86 ]} Copyright 2017, American Chemical Society.

Figure 7

a–c) Spectral energy density of dynamical modes in MAPbI₃ at different temperatures from ab initio molecular dynamics. The dotted white line for T = 1 K shows the lattice dynamics result for comparison. The band line‐widths broaden as temperature increases. At T = 300 K, the vibrational modes between 3–4 THz that are well‐defined at low temperatures are now heavily blurred. d) The modal relaxation time extracted from SED compared to recent experimental measurements. The relaxation time is close to the wave period for each thermal carrier, suggesting the conventional phonon picture is not an adequate description of the carriers. e) Freezing the rotations of the MA molecules recovers the well‐defined lattice dynamical modes, which suggests that interactions between the inorganic framework and sublattice MA orientational disorder are responsible for the loss of wave nature in (c). f) κ calculated via Green–Kubo formalism using classical molecular dynamics, with MA fixed and unfixed, compared with experiments. Reproduced with permission.^{[ 97 ]} Copyright 2018, Royal Society of Chemistry.

Figure 8

Total κ = κ_el + κ_l (a,c) and the dimensional figure of merit ZT (b,d) versus charge concentration for electron‐doped MAPbI₃, calculated at two different temperatures; κ_l is extrapolated from the experimental data published elsewhere. Black dots and red squares correspond to the experimental κ_l values for single crystal MAPbI₃ and poly crystal MAPbI₃, respectively; the other symbols are for rescaled κ_l values (indicated in the legend), mimicking eventual κ suppression occurring in 2D wells of thickness L = 40 nm (green diamonds), 20 nm (blue circles), and 10 nm (orange squares). Reproduced with permission.^{[ 131 ]} Copyright 2014, American Chemical Society.

Figure 9

Anomalous Seebeck effect. Potential difference as a function of temperature difference for a) Au/SC/Ag sample and b) Ag1/SC/Ag2 sample at 313 K. c) Temperature‐dependent potential difference when ΔT = 0 K. d) Temperature‐dependent Seebeck coefficients for Au/SC/Ag sample when using Au/SC and Ag/SC surfaces as HT terminal, respectively. e) Temperature‐dependent Seebeck coefficients for Ag1/SC/Ag2 sample when using Ag1/SC and Ag2/SC surfaces as HT terminal, respectively. f) Temperature‐dependent carrier density. Schematic diagram of g) metal/ion interactions at metal/MAPbI₃ interfaces, h) metal/ion interactions induced p‐i‐n junction across a MAPbI₃ single crystal. i) Dark current density‐electrical field (J‐E) characteristics of Au/SC/Ag sample. j) Diagram of negative Seebeck effect due to electron‐dominant diffusion. k) Diagram of positive Seebeck effect due to hole‐dominant diffusion assisted by built‐in field caused by the p‐i‐n junction. Reproduced with permission.^{[ 132 ]} Copyright 2014, American Chemical Society.

Figure 10

Individual AIHP NW is suspended between two membranes. The transport measurement direction is along the growth direction of the NWs. a) SEM image of the individual AIHP NW. Experimental data of thermoelectric properties in CsSnI₃. b) Temperature‐dependent electrical conductivity (σ, black squares) and Seebeck coefficient (S, blue circles) of a single CsSnI₃ NW. The positive sign of S indicates p‐type behavior, and CsSnI₃ exhibits a relatively high electrical conductivity despite its ultralow κ. c) Figure of merit ZT (black dots) and power factor (blue squares) of single CsSnI₃ NW. Power factor and ZT of as‐synthesized CsSnI₃ before any attempts at optimization are 186 µW·m⁻¹·K⁻² and 0.11 at 320 K, respectively. Reproduced with permission.^{[ 88 ]} Copyright 2017, National Academy of Sciences. d–g) From top to bottom: thermoelectric power, S, electrical resistivity, ρ, thermal conductivity, κ, and figure of merit, ZT, of MAPbI₃ (left panel) and MASnI₃ (right panel) for light (photoelectron) and impurity doping. The three curves of MAPbI₃, red, orange, and yellow correspond to light intensities of 80, 165, and 220 mW cm⁻². The vertical dashed lines denote a structural phase transition observed in both MAPbI₃ and MASnI₃. Left inset: Optical image of a MAPbI₃ crystal. Right inset: Scanning electron microscope image of a MASnI₃ crystallite. Reproduced with permission.^{[ 89 ]} Copyright 2015, American Chemical Society.

Figure 11

Crystal structure of MASnI₃ at a) 295 K and b) 140 K. Sn is represented by the gray spheres and I by the pink spheres. MA cations are disordered and are not included. c) Change in the electrical resistivity and thermoelectric power caused by intentional doping. Reproduced with permission.^{[ 145 ]} Copyright 2011, Royal Society of Chemistry. d) X‐band electron paramagnetic resonance (EPR) of solid crystalline samples of 1‐as, 1‐N₂, 1‐O₂, and 1‐I₂ at 77 K. e) The experimental setup used for single crystal electrical conductivity measurements and representation of the layered hybrid perovskites orientation showing the direction of conductivity measurements. f) Microphotograph showing a device made with a single crystal of 1‐ as; scale bar: 4 mm. g) Averaged values and standard uncertainties for in‐plane conductivity of [OA]₂PbBr₄, 1‐as, 1‐N₂, 1‐O₂, 1‐I₂, and 1‐N₂/I₂ at 423 K. Reproduced with permission.^{[ 146 ]} Copyright 2018, Wiley‐VCH. h) Device architecture of perovskite photovoltaic‐Thermoelectric (PV‐TE) hybrid device with carbon top electrode. Reproduced with permission.^{[ 147 ]} Copyright 2018, Wiley‐VCH. i) Schematic device architecture of PV‐TE hybrid device with gold top electrode. Also shown is the simulated heat variation in the vertical direction of the PV‐TE hybrid system. Reproduced with permission.^{[ 148 ]} Copyright 2019, Elsevier.