Perovskites for Solar Thermoelectric Applications: A First Principle

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Article

Perovskites for Solar Thermoelectric Applications: a First Principle Study of CHNHAI (A=Pb and Sn) 3

3

3

Yuping He, and Giulia Galli Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/cm5026766 • Publication Date (Web): 21 Aug 2014 Downloaded from http://pubs.acs.org on August 25, 2014

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Chemistry of Materials

Perovskites for Solar Thermoelectric Applications: a First Principle Study of CH3 NH3 AI3 (A=Pb and Sn) Yuping He† and Giulia Galli∗,‡ Department of Chemistry, University of California, Davis, CA 95616, and The Institute for Molecular Engineering, The University of Chicago, IL 60637 E-mail: [email protected]

Abstract Hybrid organic/inorganic CH3 NH3 AI3 (A=Pb and Sn) perovskites have been recognized as promising photovoltaic materials. Using ab initio calculations, we showed that these systems may also be promising materials for solar thermoelectric applications. We found that their large carrier mobilities mainly originate from a combination of the small effective masses of electrons and holes, and a relatively weak carrier-phonon interaction. We propose that by tuning the carrier concentration to values of the order of ∼ 1018 cm−3 , the thermoelectric figure of merit of Sn and Pb based perovskites may reach values ranging from 1 to 2, which could possibly be further increased by optimizing the lattice thermal conductivity through engineering perovskite superlattices.

∗

To whom correspondence should be addressed Department of Chemistry, University of California, Davis, CA 95616 ‡ The Institute for Molecular Engineering, The University of Chicago, IL 60637 †

1 ACS Paragon Plus Environment


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INTRODUCTION Solar thermoelectric generators have recently attracted increasing attention 1–3 as an alternative to thermoelectric devices: 4 these generators convert the heat generated by sunlight into electricity using the Seebeck effect. The performance of solar thermoelectric devices depends on the efficiency of both light obsorption and thermoelectric energy conversion. Materials with a large optical absorption coefficient may be used to efficiently collect sunlight and transform it into heat, and if they also exhibit a large thermoelectric figure of merit (ZT), they can then convert the heat into electricity. The figure of merit ZT = S 2 T /ρ(κe + κL ), where ρ is the electrical resistivity, S the Seebeck coefficient, T the temperature, κe and κL are the electronic and ionic contributions to the thermal conductivity, respectively. To be competitive compared with conventional power generators, the ZT of thermoelectric (TE) materials must be larger than at least 2 or, preferably 3. 5,6 However, for solar thermoelectric generators, values of ZT moderately larger than 1 may already be advantageous. 1 It has been a challenging task to find materials with ZT > 2 due to the competing interplay between S, ρ, κe and κL ; for example decreasing ρ usually leads to a decrease of S and increase of κe in a semiconductor. In five decades ZT of bulk semiconductors has increased only from ∼0.6 to ∼1. 6 Over the past few years, significant progress 7–12 has been made in enhancing ZT, up to ∼3, using nanocomposites. Recently organic/inorganic lead and tin halide perovskites (CH3 NH3 PbI3 and CH3 NH3 SnI3 ) have been identified as promising photovoltaic (PV) materials, due to their large absorption coefficient, high charge carrier mobility and diffusion length. 13–18 In addition, it has been found that both CH3 NH3 PbI3 and CH3 NH3 SnI3 may present a large Seebeck coefficient (depending on the doping level), 19,20 indicating that these materials might be potential candidates for thermoelectric applications. In this paper, we investigated the electronic thermal transport properties of lead and tin based perovskite CH3 NH3 AI3 (A=Pb and Sn) using ab initio electronic structure calculations based on Density Functional Theory (DFT), 21 many body perturbation theory (MBPT) 22 2 ACS Paragon Plus Environment

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(a)

(b)

(c)

Figure 1: Ball and stick representation of the pseudo-cubic crystal structure of CH3 NH3 AI3 (A=Pb or Sn) perovskites (a); the optimized values of the lattice constants a, b and c are given in Table S1. Green, red and gray spheres represent Pb (Sn), I atoms and the molecular ion CH3 NH+ 3 , respectively. Isosurfaces of the square modulus of the conduction band minimum (b) and valence band maximum (c) single particle states in a 2x2x2 supercell. and approximate models to describe carrier mobilities. 23,24 We computed mobilitity and Seebeck coefficients, providing an interpretation of recent experiments and we predicted the material figure of merit ZT by treating the lattice thermal conductivity as a parameter. We found that the large carrier mobilities originate mainly from small carrier effective masses, in addition to a relatively weak electron-phonon (and hole-phonon) coupling, while the high values of Seebeck coefficients are mainly due to the multiply degenerate conduction and valence bands. We propose that for carrier concentrations of the order of 1018 cm−3 , one may reach values of ZT between 1 and 2, depending on the value of the ionic thermal conductivity, indicating that the perovskites CH3 NH3 AI3 (A=Pb and Sn) are promising materials not only for photovoltaic applications but also for solar thermoelectric applications.

COMPUTATIONAL METHODS We carried out ab initio electronic structure calculations using DFT and the generalized gradient approximation (GGA) proposed by Perdew-Burke-Ernzerhof (PBE). 25,26 We included 5d10 6s2 6p2 and 4d10 5s2 5p2 as valence electrons for Pb and Sn, respectively. We used plane



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wave basis sets and pseudopotentials, and the system Brillouin zone was sampled with a 4x4x4 Monkhorst-Pack grid. We first optimized the Pm¯3m structure of both CH3 NH3 PbI3 and CH3 NH3 SnI3 to determine the equilibrium volume using norm-conserving psedopotentials, 27 inclusive of scalar-relativistic effects for Pb, Sn and I atoms, and an energy cutoff of 160 Ry. We then further optmized these structures with respect to the atomic positions using ultrasoft psedopotential 28 with energy cutoff of 60 Ry, and including full-relativistic effects for Pb, Sn and I atoms. Starting from a perfect cubic structure, we found a non centro-symmetric optimzed geometry (see Fig. 1a), as discussed below. The importance of including full-relativistic effects to accurately describe the spin-orbit coupling contributions to the electronic structuture of Pb and Sn, has been pointed out in several previous theoretical studies. 22,29–31 In addition, we found that it is necessary to include spin-orbit coupling for the iodine atom as well, in order to obtain accurate valence band structures. The electronic thermal transport properties were evaluated using the Kane single band model 24 where all input quantities were obtained from ab initio calculations for both MAPbI3 and MASnI3 with MA along the < 100 > direction. As we show below, our calculated band structures and recent studies 22,31 show that the bands of both MAPbI3 and MASnI3 have shapes close to parabolic near the band edges, indicating that the Kane band model is a reasonably good approximation to compute the transport properties of these materials. The Rashba coupling 32,33 found in the case of the Pb based compound with MA along ¡100¿ and ¡111¿ is in principle responsible for some deviation from perfect parabolic bands; however such deviation was not considered in the present work. Within the Kane model, one adopts a k.p approximation of the Hamiltonian that is then used to evaluate the carrier lifetime within the semi-classical Boltzmann transport theory; 34 only the contribution of acoustic phonons is taken into account in evaluating lifetimes. Within such model, the transport coefficients are approximated as 23 :

S=

1 kB 1 F−2 [ 0 1 − ξ] e F−2


(1)

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ρ = 1/neµ

n=

∫ Flm

=

(4)

κe = LT /ρ

(5)

∞

(− 0

(3)

1 30 F−2 2π¯ h4 eB µ= ∗ mI (2m∗b kB T )3/2 Ξ2 0 F03/2

L=(

n

(2m∗ kB T )3/2 0 3/2 F0 3π 2 h ¯3

(2)

1 1 1 F 2 kB 2 2 F−2 ) [ 0 1 − ( 0 −2 )] 1 e F−2 F−2

∂f n )ζ (ζ + αζ 2 )m [(1 + 2αζ)2 + 2]l/2 dζ ∂ζ

(6)

(7)

where ξ is the reduced chemical potential with respect to kB T , kB the Boltzmann constant, e the electronic elementary charge, T the temperature, h ¯ the planck constant, m∗ the density of state effective mass, m∗I the conductivity effective mass, m∗b the band effective mass, B the bulk modulus, Ξ the electron-phonon (or hole-phonon) coupling energy, n, m and l power integer indices, α = kB T /Eg where Eg is the electronic gap, f =

1 eζ−ξ +1

is the Fermi-Dirac distribution function and ζ the reduced carrier energy with

respect to kB T . The functions n Flm are derived from approximate forms of the integrals ∫∞ τ vk vk (ζk − ξ)n (−∂f0,k /∂ζk )d3 k defining the transport coefficients, where τ is the car0 rier lifetime, vk the carrier velocity at vector k and f0,k is the Fermi-Dirac function. The derivation of the n Flm functions assumes that the contribution of charge carriers to transport properties is limited within ∼10 KB T around the Fermi level, which corresponds to a range of carrier concentration from 1x1016 to 5x1019 cm−3 for the Pb and Sn perovskites considered



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in this work.

RESULTS AND DISCUSSION We first investigated three configurations of CH3 NH3 PbI3 with the dipole of CH3 NH+ 3 (MA) along the < 100 >, < 110 > and < 111 > directions, respectively, to mimic the possible disorder created by the orientations of the organic cations at finite T. We found that the difference of total energy between these configurations is rather small, within 0.04 eV, indicating that the experimental samples may contain different orientations of the organic cations, consistent with recent studies. 31,35 In addition, by comparing the calculated electronic band structures of Pb and Sn based materials with MA along different directions, we found that the orientation of the organic cations does not significantly affect the electronic structure of these perovskites. However, the orientation of the MA has noticeable effects on the computed lattice constants. In our optimization procedures, we started from perfect cubic structures, and the final geometries turned out to be non centro-symmetric, pseudo-cubic structures, i.e. orthorombic lattices with lattice constants that are different in the x, y and z directions, although similar in magnitude. Irrespective of the orientation of the organic molecule within the perovskite lattice, we found that two of the lattice constants are almost identical, with the third one being slightly different, except for MA along the ¡111¿ direction, in which case all three lattice constants are almost identical (see Table SI). Our findings are consistent with experimental observations. 19 We expect synthesized samples to contain MA with several different orientations, and the refined experimental lattice constants are likely to correpond to values averaged over these multiple orientations. The comparison between optimized lattice constants with experimental values is thus not straightforward. Here we compare the average value of all three lattice constants computed for different orientations with experimental results. The calculated averaged lattice constants of MAPbI3 with MA along the < 100 >, < 110 > and < 111 > directions are 6.43, 6.40 and 6.41 ˚ A, respectively,


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5

(a)

(b)

4 3

Energy (eV)

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2 TDoS Pb-p I-p Pb-s + CH3NH3

1 0 -1

Γ

X

M

Γ

R

M

X

R

DoS (State/eV/cell)

Figure 2: (a) Band structure of CH3 NH3 PbI3 with the dipole of CH3 NH+ 3 along the < 100 > direction, as obtained using DFT-PBE calculations (see text). (b) Total ( TDoS, black) and partial electronic density of states (DoS) with contributions from Pb p-orbital (red), I p-orbtial (green), Pb s-orbital (blue) and the organic cation (purple). in satisfactory agreement (within 1-2%) with experimental data at ∼400 K ( 6.31(3) ˚ A). 19 As a representative structure for our transport properties calculations for the lead based perovskite, we chose the < 100 > configuration as it has the smallest total energy of all the orientations considered here. The calculated averaged lattice constant of the Sn provskite (MASnI3 ) with MA along the < 100 > direction is 6.35 ˚ A, 2% larger than the experimental value (6.24 ˚ A) at ∼300 K. We studied separately n-type and p-type perovskites and we considered one carrier type at a time. The conductivity effective mass m∗I = 3(2/m∗⊥ + 1/m∗|| )−1 , the band effective mass ∗ 1/3 m∗b = (m∗2 and the density of state effective mass m∗ = N 2/3 m∗b (N the number of ⊥ m|| )

degeneracies induced by the lattice symmetry) were determined by computing the longitudinal effective mass m∗|| and transverse effective mass m∗⊥ from quadratic fits of the electronic bands at the conduction band minimum (CBM) for electrons and at the valence band maximum (VBM) for holes. The electron-phonon and hole-phonon couplings were estimated using the deformation potenital (Ξ), which approximately accounts for the coupling of the



(a)

4

(b)

3

Energy (eV)

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2 1 TDoS Sn-p I-p Sn-s + CH3H3

0 -1 -2 Γ

X

M

Γ

R

M

X

R

DoS (State/eV/cell)

Figure 3: (a) Band structure of CH3 NH3 SnI3 with the dipole of CH3 NH+ 3 along the < 100 > direction,as obtained using DFT-PBE calculations (see text). (b) Total (TDoS, black) and partial electronic density of states (DoS) with contributions from Sn p-orbital (red), I porbtial (green), Sn s-orbital (blue) and the organic cation (purple). charge carriers with the acoustic phonons: Ξ = V0 (∆ECBM /∆V ) and Ξ = V0 (∆EV BM /∆V ), where V0 is the equilibrium volume of the system, ∆V is the volume change caused by the lattice vibrations, ∆ECBM the corresponding change of the energy of the CBM, and ∆EV BM that of the VBM. The bulk modulus B = V0 (∂ 2 E/∂V 2 ), where E is the total energy of the system. Eq. 1-7 have been recently employed to investigate the transport properties of type-I clathrate K8 Al8 Si8 , and yielded results in good agreement with experimental data. 36 Fig.2 and 3 show the calculated electronic band structures and partial density of states for MAPbI3 and MASnI3 with MA along the < 100 > direction, respectively, obtained by DFT-PBE calculations including spin-orbit coupling. Both materials have quasi-direct band gaps in proximity of the R point, with a noticeable Rashba splitting in the case of Pb with MA along the ¡100¿ and ¡111¿ directions. Our estimated Rashba coupling at R is of the order of 1 eV.˚ A, consistent with that reported in ref. 33,37 The calculated band gap of MAPbI3 is 0.44 eV, and that of MASnI3 is 0.33 eV, and as expected they are smaller than the respective experimental values (1.50∼1.61 eV and 1.20eV). 19,38 After using the G0 W0


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Table 1: Longitudinal (m∗|| ), transverse (m∗⊥ ), conductivity (m∗I ), band (m∗b ), and density of state effective mass (m∗ ) of electrons (e− ) and holes (h+ ) at two splitted conduction edges (LUMO1 and LUMO2) and two splitted valence band edges (HOMO1 and HOMO2) at the R point in the Brillouin Zone (see Fig. 2a and 3a). All effective masses were obtained within the G0 W0 approximation (Ref.28), and are in units of the electron mass (me ). Results obtained at the DFT-PBE level of theory are reported in Table SII. The term AVE represents the averaged value over the two splitted bands; and the effective mass m∗ was obtained by summing over two bands and it is indicated by the bold figures. DFT-PBE calculated bulk modulus (B) and electron-phonon (or hole-phonon) coupling energy ( Ξ).

m∗|| m∗⊥ m∗I m∗b m∗ Ξ (eV) B (GPa)

MAPbI3 LUMO1 0.2780 0.0938 0.1204 0.1347 0.1347

(e− ) LUMO2 0.1410 0.0825 0.0957 0.0986 0.0986 7.2 21

AVE. 0.2095 0.0881 0.1081 0.1166 0.2333

MAPbI3 (h+ ) HOMO1 HOMO2 AVE. 0.3091 0.3029 0.3060 0.0911 0.0769 0.0840 0.1191 0.1023 0.1107 0.1369 0.1214 0.1291 0.1369 0.1214 0.2583 9.5

MASnI3 LUMO1 0.3221 0.1066 0.1372 0.1541 0.1541

(e− ) LUMO2 0.3444 0.0989 0.1297 0.1499 0.1499 6.8 19

AVE. 0.3332 0.1027 0.1334 0.1520 0.3040

MASnI3 HOMO1 0.1610 0.0763 0.0925 0.0978 0.0978 10.9

(h+ ) HOMO2 0.1471 0.0737 0.0884 0.0928 0.0928

AVE. 0.1540 0.0750 0.0904 0.953 0.1906

0 W0 corrections reported in recent studies, 22,31 we obtained a G0 W0 band gap (EG ) of MAPbI3 g 0 W0 (MASnI3 )of 1.23 (1.17) eV. The value of EG for MAPbI3 is very close to that reported in g

Ref. 31 (1.27 eV), and about 0.2 ∼ 0.3 eV smaller than experiment. 19,38 This discrepancy is most likely due to having considered, for computational simplicity, a pseudo-cubic structure (stable at ∼400K) in our calculations, while experiments were conducted on the tetragonal 0 W0 phase stable at room temperature. The EG of MASnI3 is instead in good agreement with g

experiments (∼1.20eV) 19 and indeed at room temperature, the stable phase of MASnI3 is cubic. For both perovskites materials, we found that the electronic states associated with MA are deep inside the conduction and valence bands (See Fig. 2b and 3b), consistent with recent studies; 22,31 hence the organic cation plays an indirect role in determining the observed electronic and transport properties, in that it affects the lattice structure and, when placed in certain directions, it leads to a non centro-symmetric lattice. The calculated partial density of states (See Fig 2b and 3b) show that the CBM is mainly composed of Pb (Sn) p-orbitals, while the VBM is formed by I p-orbitals and Pb (Sn) s-orbitals. This finding is consistent



4000

4000

3500

2

2

µ (cm /V/s)

3000

µ (cm /V/s)

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2000

3000 2500 2000

1000 1500 0 1e+16

1e+17

1e+18

1e+19

1e+17

1e+16

-3

1e+18

1e+19 -3

Carrier Concentration (cm )


(a)

(b)

Figure 4: Calculated electron (black) and hole (red) mobilities (µ) as a function of carrier concentration at 400 K in pseudo-cubic CH3 NH3 PbI3 (a) and at 300 K in pseudo-cubic CH3 NH3 SnI3 (b), by using the Kane model with G0 W0 band gaps and effective masses. with that of recent studies. 22,31,39 In addition, we found that the contribution of s-orbitals to the VBM of MASnI3 is much more substantial than in the case of Pb in MAPbI3 . Our results show that the 6s-orbitals of Pb are strongly mixed with its 5d-orbitals, while the 5s-orbitals of Sn are only weakly interacting with its 4d-orbitals. These findings are consistent with those of previous studies reported in Ref., 40 where the authors found that the interaction of the anion p states with the cation s states is reduced significantly for heavier ions, and a divalent state is increasingly favored in going from Ge to Sn and to Pb. These different hybridization and oxidation states may impact the measured electronic resistivities of Sn and Pb perovskites, showing a metal-like and a semiconductor-like behavior, respectively. 19,20 We now turn to the discussion of transport coefficients. Recent studies 22,31 showed that DFT-PBE calculations not only underestimate the electronic band gaps but also yield slightly different effective masses, with respect to G0 W0 calculations. 22 For example, in MAPbI3 , DFT-PBE underestimated the electron effective mass by 10%, while overestimated the hole effective mass by 10% compared to G0 W0 calculations; in MASnI3 , DFT-PBE underestimated (overestimated) the electron (hole) effective mass by 14%. Therefore, to obtain accurate predictions of the thermal transport properties, we evaluated the carrier effective masses


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1

800 600

0.1

ρ (mΩ.cm)

S(µV/K)

400 200 0 -200 -400

0.01

0.001

-600 -800 1e+17

1e+16

1e+18

1e+19

1e+16

-3

1e+17

1e+18

1e+19 -3



(a)

(b) 2.5

10

2.0 3 W/mK 2 W/mK

1

κL =1 W/mK

1.5 2 W/mK

1.0

κL = 1 W/mK

3 W/mK

0.5

ZT

κtotal (W/mK)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.5 κL =1 W/mK

10 1.0 3 W/mK

2 W/mK

2 W/mK

1

0.5

κL = 1 W/mK

1e+16

3 W/mK

1e+17

1e+18

1e+19

1e+16

-3

1e+17

1e+18

1e+19 -3



(c)

(d)

Figure 5: (a) Seebeck coefficients (S), (b) electronic resistivities (ρ), (c) total thermal conductivities (κtotal ), and (d) the predicted values of the material figure of meritz (ZT) as a function of carrier concentration with κL =1, 2 and 3 W/mK, at 400 K for n-type (black) and p-type (red) doped, pseudo-cubic CH3 NH3 PbI3 , obtained from the Kane model with G0 W0 band gaps and effective masses. At the carrier concentration for which ZT is maximum, κe varies between 0.47 and 0.78 W/mK for n-type, and between 0.74 and 1.16 W/mK for p-type.



1

800 600

0.1

ρ (mΩ.cm)

S(µV/K)

400 200 0 -200 -400

0.01

0.001

-600 -800 1e+17

1e+16

1e+18

1e+19

1e+16

-3

1e+17

1e+18

1e+19 -3



(a)

(b) 2.0

10

1.5 3 W/mK

1.0

2 W/mK

1

κL =1 W/mK

κL = 1 W/mK

2 W/mK

0.5

3 W/mK

ZT

κtotal (W/mK)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1.5

10 1.0

κL =1 W/mK

3 W/mK 2 W/mK

1

1e+16

2 W/mK

0.5

κL = 1 W/mK

3 W/mK

1e+17

1e+18

1e+19

1e+16

-3

1e+17

1e+18

1e+19 -3



(c)

(d)

Figure 6: (a) Seebeck coefficients (S), (b) electronic resistivities (ρ), (c) total thermal conductivities (κtotal ), and (d) the predicted values of the material figure of meritz (ZT) as a function of carrier concentration with κL =1, 2 and 3 W/mK, at 300 K for n-type (black) and p-type (red) doped, pseudo-cubic CH3 NH3 SnI3 , obtained from the Kane model with G0 W0 band gaps and effective masses. At the carrier concentration for which ZT is maximum, κe varies between 0.35 and 0.59 W/mK for n-type, and between 0.26 and 0.4 W/mK for p-type.


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using G0 W0 resutls. 22 (For comparison, we give results obtained at the DFT-PBE level in Table SII). Table I summaries the input parameters of the Kane model for both MAPbI3 and MASnI3 . The longitudinal (m∗|| ) and transverse (m∗⊥ ) effective masses were estimated from quadratic fits of the bands along the directions R to M and R to Γ, respectively. There are two split conduction and valence bands at the R point for both Pb and Sn perovskites. The final conductivity (m∗I ) and band (m∗b ) effective mass were obtained by averaging the values obtained for two bands, and the final density of state effective masses were summed over two bands to take into account the band degeneracies. Fig.4 shows the calculated electron and hole mobilities in Pb (400 K) and Sn (300K) pseudo-cubic perovskites as a function of carrier concentration. We found that the carrier mobilities decrease as the concentration increases for both materials due to an increased carrier scatterings. For the Pb perovskite, the mobility of electrons (µe ) is in the range of 3100 ∼ 1500 cm2 /V /s, and that of holes (µh ) is 1500 ∼ 800 cm2 /V /s for concentration varying from 1016 to 1019 cm−3 . For the Sn perovskite, µe and µh are 2700 ∼ 1300 cm2 /V /s and 3100 ∼ 1400 cm2 /V /s, respectively, in the same concentration range. Interestingly we found that the electron mobility of MASnI3 is smaller than that of MAPbI3 , while the hole mobility of MASnI3 is much larger than that of MAPbI3 . These high carrier mobilities are comparable to those of typical semicondutors (i.e. in Si µe = 1500 ∼ 100 cm2 /V /s and µh =500 ∼ 50 cm2 /V /s; 41 in GaAs µe = 4000 ∼ 500 cm2 /V /s 42 and µh = 400 ∼ 40 cm2 /V /s 43 in a similar range of carrier concentrations), and they are likely responsible, at least in part, for the observed high energy conversion efficiency of Pb and Sn based organic/inorganic pervoskite solar cells. Our results indicate that the large values of carrier mobilities in these perovskites are mainly due to the small carrier effective masses, in addition to the relatively weak electron-phonon and hole-phonon coupling (See Table I). In addition, since the electron and hole diffusion lengths are proportional to the respective mobilities, our calculated carrier mobilities indicate that the holes may have smaller diffusion lengths than electrons in both Pb and Sn provskites (See Fig. 4). To further understand the large carrier diffusion length reported experimentally in these



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organic/inorganic pervoskites, 17 we analyzed the localization of the wavefunctions at the CBM and VBM for both Pb and Sn perovskites. Consistent with the results of Ref., 31,39 we found that the CBM is mainly localized around Pb (Sn) atoms and has a metal p-orbital character ( see Fig. 1b), while the VBM is largely localized around I atoms, with a I-p orbital character and a minor component on Pb (Sn) atoms with metal s-orbital character(see Fig. 1c). The limited spatial overlap between CBM and VBM is consistent with a low probability of charge recombination and thus long carrier lifetimes. We also note that the exciton binding energy (Eb ) is rather moderate in both perovskites; based on the computed optical dielectric constant (∼ 5, in agreement with Ref. 31 ), and computed effective masses, we estimated Eb to be of the order of 60 meV. Large carrier mobilities and diffusion lengths are key properties for thermoelectric application. Furthermore, recent studies showed that both MAPbI3 and MASnI3 present high Seebeck coefficients, 19,20 indicating that these perovskite materials could be promising candidates for thermoelectric energy conversion. To probe their performance for thermoelectric applications, we calculated S, ρ and κe as a function of carrier concentration (n) for n-type and p-type Pb(Sn) perovskites(Fig. 5 and 6 ), We then predicted the material figure of merit ZT by treating the lattice thermal conductivity (κL ) as a parameter (See Fig 5d and 6d). The thermal conductivity of semiconducting materials is generally dominated by lattice vibrations. Low κL is usually found in materials with complex structures, composed of elements with large mass differences, and exhibiting strong phonon-phonon scattering (e.g. strong anharmonicity). The structures of both MAPbI3 and MASnI3 are complex, with five different elements with significantly different masses (i.e. mass of Pb : mass of H = 207). In addition, our calculations and recent theoretical studies 44 showed that both materials have small values of the speed of sound vs (Pb perovskites: 1620 ∼ 2228 m/s and Sn perovskites : 2057 ∼ 2348 m/s, similar to that found in recent nanostructured clathrates 36,45 ). Furthermore the organics inside the perovskite network would probably act as rattling centers as found for Cs atoms in CsSnI3 39 and for K atoms in K8 Al8 Si38 clathrates. 45 For all these


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reasons one may expect Pb and Sn perovskites to have low lattice thermal conductivity of the order of few W/mK. Of course this assumption will have to be verified by further experimental and theoretical studies. For Pb and Sn perovskites, we computed ZT by varying κL between 1 and 3 W/mK. κtotal was then obtained as κtotal = κe + κL based on our calculated values of κe (See Fig. 5c and 6c). We found that as the carrier concentration increases, the S decreases, ρ decreases and κtotal increases for both n-type and p-type materials, leading to a peak of ZT at ∼ 1x1018 cm−3 (See Fig.5d and 6d). Experimentally, it has so far been difficult to measure the carrier concentrations of Pb and Sn organic/inorganic perovskites, 19,20,46 and to the best of our knowledge, there are no available experimental data for the thermal transport properties of doped MAPbI3 directly comparable to the conditions considered here. Most measurements have been performed for lower carrier concentrations. For example Stoumpos et al.

19

measured the resistivities and Seebeck coefficients of in-

trinsic semiconducting Pb and Sn perovskites. At room temperature, with estimated carrier concentration (n) ∼ 109 cm−3 , the measured value of S (∼ 106 µV /K) and ρ (∼ 1010 mΩ.cm) for MAPbI3 are much larger than our calculated values (See Fig. 5). Similarly, for MASnI3 with ∼ 1014 cm−3 (i.e. instrinsic perovskites), the measured ρ (∼ 104 mΩ.cm) is larger than our calculated values, as expected, while surprisingly the measured S (100 µV /K ) is slightly smaller than that of our doped perovskites (See Fig. 6). The transport properties of MASnI3 has also been investigated by Takahashi et al.

46

In 2011, they found that at room

temperature, with n ∼ 1022 cm−3 , the measured S and ρ of Sn perovskites are ∼ 90µV /K and 50 mΩ.cm, respectively. Later the same authors claimed that the carrier concentration of these perovskites should be instead ∼ 9x1017 cm−3 , 20 indicating that the experimental determination of carrier concentrations remains a difficult task. For a given value of the total thermal conductivity, we found that the ZT of Pb perovskites is always larger than that of Sn perovskite, regardless of the type of doping, and the ZT of n-type perovskites is always larger than that of p-type for either MAPbI3 or MASnI3 . For our smallest value of the lattice thermal conductivity i.e. κL = 1W/mK, one obtains



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ZT=1.7 (ZT=1.1) for n-type (p-type) MAPbI3 , and ZT=1.2 (ZT=0.8) for n-type (p-type) MASnI3 , which are promising values for solar thermal applications.

CONCLUSION We carried out a series of ab initio calcuations to evaluate the thermal transport properties of both CH3 NH3 PbI3 and CH3 NH3 SnI3 perovskites using the Kane single band model. We found that these materials exhibit small carrier effective masses and weak electron-phonon and hole phonon couplings, leading to large values of carrier mobilities. We also found that large values of the Seebeck coefficients for carrier concentrations of the order ∼ 1018 cm−3 , stem from multi-degenerate conduction and valence bands. We computed the thermoelectric figure of merit and found values in the range of 1 to 2, depending on the value of the ionic thermal conductivity, which could be possibly decreased further by engineering superlattices of perovskites. 47–49 Overall CH3 NH3 PbI3 and CH3 NH3 SnI3 appear to be promising systems not only for photovoltaic applications but also for solar thermoelectrics, for which ZT ∼ 1 is already an advantageous value of the figure of merit. 1 Work is in progress to refine our transport property calculations by including the effect of optical phonons and non-parabolic effects of the band structures arising from the Rashba effect.

SUPPORTING INFORMATION Additional information including the DFT-PBE calculated carrier effective masses, thermal transport properties and optimized lattice constants for all samples. This information is available free of charge via the Internet at http://pubs.acs.org.


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ACKNOWLEDGMENTS We thank Filippo De Angelis for interesting discussions. We gratefully acknowledge use of the computational facilities at NERSC at LBNL, and funding from DOE/BES grant No. DE-FG02-06ER46262.

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Figure 7: TOC


Perovskites for Solar Thermoelectric Applications: A First Principle

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