Appealing Perspectives of Hybrid LeadâIodide Perovskites as

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On the Appealing Perspectives of Hybrid LeadIodide Perovskites as Thermoelectric Materials Alessio Filippetti, Claudia Caddeo, Pietro Davide Delugas, and Alessandro Mattoni J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b10278 • Publication Date (Web): 02 Dec 2016 Downloaded from http://pubs.acs.org on December 3, 2016

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The Journal of Physical Chemistry

On the Appealing Perspectives of Hybrid LeadIodide Perovskites as Thermoelectric Materials A. Filippetti,*1,2 C. Caddeo,2 P. Delugas,3 and A. Mattoni2

ABSTRACT

The fundamental properties of lead halide perovskites, rivaling those of conventional semiconductors, makes these systems attractive not just for solar cells, but for a broader playground of energy and nanotechnology applications. The recently measured ultra-low thermal conductivity of the perovskites suggests the possibility of high thermoelectric efficiency and the possible use of the perovskites for solar-thermoelectric generation capable to capture both abovegap and below-gap sun illumination. Here we explores this possibility presenting a theoretical analysis of the thermoelectric behavior of CH3NH3PbI3 for a wide range of temperatures and carrier concentrations. For electron doping, we find optimal carrier density n∼1019 cm-3, at which this material displays room-T power factor σS2∼0.8× 10-3 W/mK2, derived by moderate electrical conductivity σ and robust thermopower, with Seebeck coefficient S∼ hundreds µV/K, typical of

1

Dipartimento di Fisica, Università di Cagliari, Cittadella Universitaria, Monserrato 09042-I (CA), Italy

2

Istituto Officina dei Materiali, CNR-IOM SLACS Cagliari, Cittadella Universitaria, Monserrato 09042-I (CA), Italy

3

Scuola Internazionale di Studi Superiori Avanzati - Via Bonomea 265, 34136 - Trieste, Italy.

ACS Paragon Plus Environment

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polar insulating perovskites. In combination with a measured thermal conductivity ∼0.3-0.5 W/mK, this delivers figure of merits Z∼1-3×10-3 K-1, thus in the league of the best performing thermoelectric tellurides and skutterudites. For hole doping, on the other hand, the figure of merit is sensitively reduced by a factor 2 to 3, due to the isotropic nature of the valence band edge. These results can be a stimulus and a guideline to the search of strategies for chemical doping, which has been scarcely investigated so far, for these materials.

1. INTRODUCTION The solid-solution processed CH3NH3PbI3 (MAPI) perovskite1-3 behaves, from several standpoints, as the most efficient inorganic semiconductors,4-12 and has the potential to be a landmark material not only for solar cells, but also for a variety of energy applications. In particular, recent measurements13,14 show that bulk MAPI is characterized by an ultra-low thermal conductivity of ∼0.5 W/mK for mm-size single-crystals (SC), and an even lower 0.3 W/mK for poly-crystals (PC); (in contrast, high conductivity is reported in Ref.15.) Consistently, several molecular dynamics calculations for bulk at room-T16-19 report values lower than 1 W/mK. These values are exceptionally small even in comparison to the best 3D thermoelectric materials,20 especially considering that they are 'native' of the system, i.e. obtained before any process of nanostructurization,21-23 and represent a strong encouragement to investigate the possibility of an additional exciting playground for MAPI: that of thermoelectric applications.


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This perspective has two more stimulating aspects on its side: first, the low-cost processing of hybrid perovskites is a fundamental added value for thermoelectrics since, ultimately, the material cost to the produced Watt ratio is the parameter which matters the most.24 A second aspect concerns the solar thermoelectric generation (STGE) design,25-27 where IR, below bandgap solar irradiance is converted to heat and naturally exploited to generate a large thermal gradient across a slab of thermoelectric material. Recently, solar thermoelectric generators based on nanostructured Bi2Te3 were realized with ∼5% efficiency under AM1.5G conditions.27 Since efficient solar to heat conversion requires strong absorbance and small emittance, hybrid perovskites are potentially suited to the aim. However, there are also important drawbacks, as the well known tendency of MAPI to thermal degradation28,29 and ionic diffusion.30-32 In particular, thermal instability may be a severe limitation, since the peak of thermoelectric efficiency is typically reached several hundred Kelvins above room-T. Thermogravimetric analysis show that MAPI sublimates at about 200 o

C,28 although perovskite degradation can be shifted above 300 oC through viable atomic or

molecule substitutions (e.g. in formamidinium lead iodide FAPbI3,33 and in mixed (FAPbI3)1x(MaPbBr3)x,

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and Cs1-xFaxPbI335 perovskites). Another non-trivial aspect concerns doping:

most transport measurements are for the undoped dark perovskite, thus with an undefined fraction of 'native' carriers; while ambipolar charge manipulation by field-effect was demonstrated,36 explicit chemical doping has not been widely explored, so far. In Ref.37 an abysmally low ZT was estimated for undoped MAPI, but measurements for doped MASnI3 brought authors to envisage possible ZT nearing unity upon suited chemical doping. Leaving aside these operative difficulties, here we use theory to draw a complete account of the thermoelectric properties of MAPI for a wide range of electron and hole charge concentration


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and temperature. Our scope is stimulating the practical design of chemical-doped MAPI with the highest possible thermoelectric efficiency.

2. MODELS AND METHODS The thermoelectric efficiency is related to a single material-dependent parameter, the adimensional figure of merit:

ܼܶ =

ߪܵ ଶ ܶ ݇௘௟ + ݇௅

The determination of Z is an hard challenge which requires the evaluation of electrical conductivity (σ), thermopower (i.e. Seebeck coefficient (S)), electronic thermal conductivity (kel), and lattice thermal conductivity (kL). Here we calculate σ, S, and kel, using an innovative combination of ab-initio band structures and scattering rate modeling, integrated according to the Bloch Boltzmann Theory (BBT),38,39 while for kL we rely on the experimental data of Ref.13. Since measurements are for the insulating perovskites in the dark, they do not contain any electronic contribution, thus the total thermal conductivity can be simply obtained by adding measured and calculated electronic thermal conductivity. This approach was used in the past to calculate the thermoelectric properties of a series of oxides,40-44 and the electric mobility of MAPI.45 For the latter we obtained results in agreement with the experiments46 assuming the room-T mobility limited by the electron scattering with polar optical phonons. This interpretation is confirmed by recent analysis of the photoemission broadening with temperature.47 We remark that several transport calculations for MAPI are present in literature,48-51 however they assumed either constant scattering rate (i.e. relaxation time) or mobility only limited by acoustic phonon scattering, which is clearly insufficient to describe MAPI in the broad temperature range. A brief


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outline of BBT can be found in the SI, while the complete description of the electron-phonon scattering model used for these calculations is given Ref.45, and will not be reported here again. The band structures used as input for the BBT calculations are obtained by Density Functional Theory within Local Density Approximation. For these calculations we employed the PWSIC code, implemented in plane-wave plus ultrasoft pseudopotentials,52 with 35 Ry cut-off energy and dense k-point grid for self-consistency. The cell parameters are taken from the experiments of Ref.53. Spin-orbit coupling was not included in the calculation. The same band structures were previously applied to the study the electron mobility in MAPI.45 Notice that the same bulk results are juxtaposed to the measured thermal conductivities for SC and PC MAPI. This is a reasonable approximation, since electronic transport is much less sensible to nanostructurization than thermal transport.

3. RESULTS AND DISCUSSION 3.1 Overview of MAPI Thermoelectric Performance. The overall MAPI thermoelectric performance is sketched in Fig.1, in comparison with various tellurides, skutterudites, and clathrates.54 Fig.1a reports power factor (PF=σS2) vs. total thermal conductivity k=kel + kL. For SC and PC MAPI we consider our calculated values at room-T, for an hypothetical n=1019 cm-3 electron charge concentration, which, as explained later, optimizes the thermoelectric performance of the perovskite, while the other compounds are evaluated at their best-performing temperature.


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Fig. 1: Thermoelectric properties of n-doped SC and PC MAPI, in comparison with other best-performing families of thermoelectric materials. a: power factor vs. thermal conductivity, adapted from Beekman et al.;[54] straight lines are guide to the eye to visualize reference values for the figure of merit Z (corresponding to the slope of the line). b: ZT vs. T, adapted from Ref.26; all the systems are 3D bulk materials, i.e. before any nanostructurization or layering.

For MAPI we obtain σS2∼0.8× 10-3 W/mK2, which is not particularly striking if compared with the five- or six-time larger value of some tellurides and skutterudites; however, k is small enough to push MAPI in the ballpark of potentially promising thermoelectrics. In terms of Z=PF/k ratio, we see that SC-MAPI is well above the Z=1×10-3 K-1 border, which is the minimal requirement for high-T applications, while PC-MAPI is just on top of the Z=3×10-3 K-1 slope, thus approaching the top-performing thermoelectric tellurides. In Fig.1b we report the ZT vs. T behavior of MAPI (again at

n=1019 cm-3) in comparison with other thermoelectric bulk

materials.26 The thermoelectric quality of MAPI is apparent, with ZT near unity for T=400 K, a viable temperature for STGE applications.25,26 It is remarkable that the ultra-low thermal conductivity of MAPI derive by intrinsic single-crystal properties, specifically the low sound velocity associated to the PbI3 inorganic sublattice;18,19 and the rotations16 and internal modes19 of the methylammonium (MA) molecules, which function as centers of incoherent inelastic scattering for the long-wavelength phonons of the inorganic


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sublattice (i.e. MA's behave similarly to the 'rattling' atoms in skutterudites and clathrates). This suggests that k could be further reduced in MAPI films or wires (paramount examples are Bi2Te3/Sb2Te3 superlattices21 with k=0.6 W/mK against 1.45 W/mK in bulk, and PbTe1-xSex films22 with k=0.6 W/mK against 2.5 W/mK of bulk). From Fig.1a we infer that a moderate 30% reduction in thermal conductivity is sufficient to shift PC-MAPI right above the Z=4×10-3 K-1 slope, which is a threshold of excellence for thermoelectric applications. 3.2 Thermoelectric Properties of MAPI as a Function of Carrier Concentration. In Figs.2 and 3 we report the thermoelectric properties of electron-doped MAPI as a function of carrier concentration. Here doping is treated at level of rigid-band approximation, which is justified by the low carrier densities considered in this work. However, we should be aware on the fact that in presence of polaronic behavior55 the results based on a rigid band scenario could be altered. The band structure used for the calculation corresponds to the lowest-energy tetragonal structure,56,57 with band-gap of 1.61 eV. Hereafter all the reported properties are 3D-averaged in space. The electrical conductivity σ (Fig. 2a) is markedly linear in the density across the whole carrier concentration range, coherently with a shallow-doped semiconducting behavior. At roomT its amplitude (corresponding to mobility µ∼50-60 cm2/Vs) is substantially smaller than in conventional semiconductors like Si, Ge, or GaAs; indeed, it was recently understood that at room-T, σ and µ are governed by polar optical phonon scattering,45,47 and not by acoustic phonon scattering, as in conventional semiconductors. Thermopower (Fig.2b) is obviously negative for electrons, and decreases in magnitude for increasing carrier density with a less-than-linear dependence. Its magnitude is fairly large (240 µV/K at n=1019 cm-3 and T=300 K, 362 µV/K at 600 K) and of the same order found for oxide perovskites (e.g. ∼500 µV/K for SrTiO3);40 S


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remains sizeable up to n=1021 cm-3 and then quickly fades for n>1021 cm-3. The combination of moderate electrical conductivity and large Seebeck reflects the character of MAPI as a polar perovskite with large ionic permittivity ( ε 0 ∼60 at room-T)58, low-frequency PbI3 phonon modes,59-62 sizeable LO-TO splitting ( hω LO ∼80 cm-1=10 meV),59 and moderate electronic screening ( ε ∞ ∼6.5).63-65

Fig. 2: Calculated transport and thermoelectric properties of n-doped MAPI vs. carrier concentration at two temperatures (indicated with different colors in the legend). a): electrical conductivity (σ); b) Seebeck (S); c) the power factor PF=S2 σ; d) electronic thermal conductivity kel.

As seen in Fig.2c, the resulting PF increases almost linearly with n, since the σ growth overcomes the corresponding decay of S. The PF peak occurs at n=1021 cm-3, while PF = 0.84×10-3 W/mK2 at the optimal density n=1019 cm-3 (i.e. the density at which ZT is peaked, see Fig.3b and Fig.3d). In Fig.2d we see that kel grows linearly with n, and up to n=1018 cm-3 is totally discardable with respect to the lattice contribution kL ∼ 0.3-0.5 W/mK; then at n=1019 cm-3


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kel ∼ 0.1 W/mK, and at n=1020 cm-3 kel ∼ 1.5 W/mK, thus large enough to abundantly overcome kL. In practice the optimal charge density n=1019 cm-3 corresponds to the highest possible density for which the fast rising kel is not yet comparable or preponderant over its lattice counterpart. As an indication of temperature effects, we report calculations at 300 K and 600 K (the detailed T-dependence is discussed in the SI). At the optimal density n=1019 cm-3 the net effect of temperature on PF is a 20% increment, from 0.84×10-3 W/mK2 at T=300 K to 1.05×10-3 W/mK2 at T=600 K; for the same temperature change, kel increases from 0.1 W/mK to 0.145 W/mK.

Fig. 3: Total thermal conductivity k = kel + kL (panels a, c) and the adimensional figure of merit ZT (panels b, d) vs. charge concentration for electron-doped MAPI, calculated at two different temperatures; kL is extrapolated from the experimental data of Ref.13: black dots and red squares corresponds to the experimental kL values for SC-MAPI and PC-MAPI, respectively; the other symbols are for rescaled kL values (indicated in the legend), mimicking eventual thermal conductivity suppression occurring in 2D wells of thickness L=40 nm (green diamonds), 20 nm (blue circles), and 10 nm (orange squares).

In Fig.3 we display k=kel +kL and ZT=PF×T/k. For kL we adopt the experimental values for SCMAPI and PC-MAPI reported up to 300 K in Ref.13; the high-T behavior is extrapolated from the experimental data assuming linear decay beyond T=300 K, which is typical for


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thermoelectric materials at high T. In addition to the experimental values, we include in the analysis some scaled-down values of kL (see the legend) to monitor the effect of kL suppression obtained in a hypothetical 2D well. In the simple kinetic approximation, k L = 1 / 3 CVυ L and

∆kL / kL = ∆L / λ , where L is the well thickness, ν the sound velocity, CV the heat capacity and λ the phonon mean free path. Assuming λ = 100 nm (which is in the error bar of the experimental14 and theoretical19 estimates), we extracted kL relative to wells of thickness L=40 nm (green diamonds), 20 nm (blue circles), and 10 nm (orange squares). We see that, between n=1014 cm-3 and n=1018 cm-3, k is essentially pinched to the kL value which is substantially n-independent, whereas above n=1018 cm-3 kel becomes quickly dominant over kL. The resulting ZT is then peaked at n=1019 cm-3 for any kL value, and for both T=300 K and 600 K. At T=300 K and n=1019 cm-3 we obtain ZT=0.41 and 0.61 for SC- and PC-MAPI respectively, which are robust values for room-T. Also, at T=600 K we have ZT=1.13 and 1.61 for SC- and PC-MAPI, respectively, which compare well with ZT=1.1 and 1.7 found for bulk PbTe at T=800 K before and after the inclusion of SrTe nanocrystals, respectively.23 According to our modeling, for 20-nm films kL ∼ 0.1 W/mK and ZT >1 at room-T, while for 40-nm films kL ∼ 0.16 W/mK and ZT>2 at 600 K. Table 1: Values of electric conductivity (s), Seebeck (S), power factor (σS2), electronic thermal conductivity (κel) and adimensional figure of merit (ΖΤ) calculated for electron-doped and hole-doped MAPI at the diagnostic optimal charge n=1019 cm-3 and various temperatures. ZT is obtained using the experimental values for single-crystal (SC) and poly-crystal (PC) MAPI reported in Ref.13.

σ (Ωcm)-1

S (µV/K)

σS2 (10-4 W/mK2)

κel (W/mK)

ΖΤ (SC)

ΖΤ (PC)

n-type

160

-238

8.4

0.1

0.38

0.61

p-type

94

181

3.1

0.06

0.15

0.25

300 K

600 K


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n-type

89

-362

10.5

0.145

1.06

1.61

p-type

41

295

3.6

0.06

0.43

0.71

n-type

68

-428

11.3

0.151

1.74

2.56

p-type

25

358

3.3

0.04

0.64

1.08

800 K

The properties of MAPI at optimal density are summarized in Table 1, for both electron and hole doping. Even for the holes, the calculated optimal density is around n=1019 cm-3. However, it is apparent that the thermoelectric performance for the hole charge is remarkably less brilliant: at room-T σ and S amplitudes are 40% and 25% lower, respectively, than for electron charge. Table 2: Conductivity (σ) and Seebeck (S) at n=1019 cm-3 and T=300 K for electrons and holes along the Cartesian axes of the tetragonal cell. The previously analyzed 3D-average values are also rewritten, for clarity. Fermi energies EF, calculated with respect to the corresponding band edges, are reported as well. electrons

σ (Ωcm)-1

S (µV/K)

a

56

-236

b

33

-252

c

391

-227

3D-av

160

-238

14.1

holes

σ (Ωcm)-1

S (µV/K)

EF (meV)

a

79

181

b

72

183

c

131

180

3D-av

94

181

EF (meV)

40.7

The combined decrease of σ and S produces PF, ZT, and kel which are 2-3 times lower for holes than for electrons, see Tab.1. This neat breaking of ambipolar behavior contrasts with the similarity of electron and hole transport.66 Naively, the lower Seebeck for holes may be


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counterintuitive since S usually increases with the effective masses; in fact, S is primarily governed by the Fermi energy (EF), not by the masses: the lower EF, the higher S. At the valence band top (VBT) the bands are predominantly derived by isotropic Pb(6s) orbitals, thus EF is essentially set by a single effective mass value. At the conduction band bottom (CBB), on the other hand, there is a predominance of highly anisotropic Pb(6p) states: now σ is dominated by its contribution along the lightest mass direction (the c axis of the tetragonal cell), while EF is determined by the whole 3D effective mass tensor, thus the Pb(6p) masses in the heavy-mass direction contribute to keep EF low and close to the CBB edge. In Table 2 we report σ, S, and EF for electrons and holes along the Cartesian axes of the tetragonal cell, and their 3D average. We see that S is rather isotropic, in particular for holes, since primarily determined by EF, while σ is extremely sensitive to the anisotropy. The larger S for the electrons is then easily explained by the lower EF at same carrier concentration and temperature. The beneficial effect of band anisotropy in the simultaneous optimization of conductivity and thermopower was previously discussed in literature.67,68 3.3 Dependence of thermoelectric properties on the atomic structure. Thermopower is usually quite sensitive to some characteristics of the electronic structure at the band edge, such as band curvature, degeneracy, and anisotropy, which in MAPI are mainly governed by the octahedral tilting, in turn ruled by molecular orientation and structural symmetry. Now we analyze the effect of different symmetry and molecular orientations on the thermoelectric properties of MAPI, so far described on the basis of a specific tetragonal phase (labeled I0). In Tab.3 we compare I0 with two more structures: an higher-energy tetragonal phase (I1) with smaller octahedral tilting, effective masses and band gap, and the ground-state orthogonal


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structure (P0) (the structures are described in detail in Ref.57). All values are for T=300 K and n=1019 cm-3. Table 3: Comparison of several thermoelectric properties calculated for T=300 K and n=1019 cm-3 among the tetragonal ground-state (I0), a tetragonal structurally-excited state (I1), and the orthorhombic ground-state (P0), for electron and hole charge; EF are calculated with respect to the band edges. S (µV/K)

σS2 (10-4 W/mK2)

(W/mK)

160

-238

8.4

37.9

228

-195

1.584

12.7

181

I0

1.614

40.7

I1

1.510

P0

1.584

Egap (eV)

EF (meV)

(Ωcm)

I0

1.614

14.1

I1

1.510

P0

ΖΤ (SC)

ΖΤ (PC)

0.10

0.38

0.61

8.7

0.15

0.39

0.57

-255

11.0

0.12

0.52

0.77

94

181

3.1

0.06

0.15

0.25

54.3

121

158

3.1

0.075

0.15

0.24

48.7

116

168

3.3

0.073

0.16

0.25

σ -1

κel

electrons

holes

The comparison between I0 and I1 is immediately understood in terms of the smaller octahedral tilting of I1, which means smaller effective masses (thus higher σ), but also smaller c/a anisotropy, thus higher EF (smaller S); the change in σ and S largely compensate in the power factor, which is very similar in I0 and I1, for both electrons and holes. On the other hand, the difference in kel substantially reflects the difference in electrical conductivity. For SC-MAPI kel is discardable with respect to kL, thus ZT is substantially the same for the two tetragonal structures; for SC-MAPI a slightly larger ZT is obtained for I0, as a consequence of the smaller kel. Consider now the comparison between orthorhombic P0 and tetragonal I0 phases for electron doping: they are rather similar in terms of band gap and EF, and nevertheless the small changes in σ and S both favors P0, and combined, give a 22% increment in PF and ZT for the


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orthorhombic phase. For hole doping, on the other hand, EF is slightly higher in P0, thus σ and S compensate almost perfectly in PF and ZT. In summary, our analysis reveals that the effect of different molecular orientation and/or structural symmetry is marginal: i) in case of large difference in octahedral tilting, the effects on conductivity and Seebeck are always opposite (σ decreases and S increases with larger tilting), then they compensate in PF and ZT; ii) when tilting is similar, the difference in band structure is minor or residual; in this case small, univocal changes may occur in σ and S, giving rise to change in ZT by 20% or so.

4. CONCLUSIONS In conclusion, we provided a theoretical assessment on the thermoelectric properties of MAPI, drawing actual limitations and future perspectives. According to our calculations combined with the recently measured ultra-low lattice thermal transport, hybrid perovskites appear promising materials for low-cost thermoelectric and solar-thermoelectric applications. The character of fairly ionic, polar material with large dielectric constant, and the remarkable conduction band anisotropy conveys robust thermopower and moderate room-T electrical conductivity, which combine in power factors ∼10-3 W/mK2 for electron carriers at the optimal density n=1019 cm-3. On the basis of the measured thermal conductivity, we predict adimensional figure of merits that approach unity for electron-doped poly-crystal MAPI at 400 K, and potentially place the perovskites in the league of the most promising thermoelectric families, provided that the known difficulties related to thermal and electrical stability could be overcome. For hole carriers the thermoelectric performance is severely reduced, primarily due to the smaller band anisotropy of the holes. Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: ??? Thermoelectric properties of MAPI vs. temperature (doc)


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AUTHOR INFORMATION Corresponding Author E-mail: [email protected] Notes: The authors declare no competing financial interest. Acknowledgements We acknowledge financial support under Project PON-NETERGIT and computational funding by CINECA, Italy, through ISCRA Projects VIPER and THESTA.

References (1) Kojima, A.; Teshima, K.; Shirai, Y.; T. Miyasaka, T. Organometal Halide Perovskites as Visible-Light Sensitizers for Photovoltaic Cells. J. Am. Chem. Soc. 2009, 131, 6050−6051. (2) Lee, M. M.; Teuscher, J.; Miyasaka, T.; Murakami, T. N.; Snaith, H. J. Efficient Hybrid Solar Cells Based on Meso-Superstructured Organometal Halide Perovskites. Science 2012, 338, 643-647. (3) Burschka, J.; Pellet, N.; Moon, S.-J.; Humphry-Baker, R.; Gao, P.; Nazeeruddin, M. K.; Grätzel, M. Sequential Deposition as a Route to High-Performance Perovskite-Sensitized Solar Cells. Nature 2013, 499, 316−319. (4) Stranks, S. D. ; Eperon, G. E.; Grancini, G. ; Menelaou, C. ; Alcocer, M. J. P.; Leijtens, T.; Herz, L. M.; Petrozza, A.; Snaith, H. J. Electron-Hole Diffusion Lengths Exceeding 1 Micrometer in an Organometal Trihalide Perovskite Absorber. Science 2013, 342, 341-344. (5) Xing, G.; Mathews, N.; Sun, S.; Lim, S. S.; Lam, Y. M.; Grätzel, M.; Mhaisalkar, S.; Sum, T. C. Long-Range Balanced Electron- and Hole-Transport Lengths in Organic-Inorganic CH3NH3PbI3. Science 2013, 342, 344-347. (6) Saba, M. ; Cadelano, M.; Marongiu, D.; Chen, F. ; Sarritzu, V.; Sestu, N.; Figus, C.; Aresti, M.; Piras, R.; Geddo Lehmann, A.; et al. Correlated Electron-Hole Plasma in Organometal Perovskites. Nature Commun. 2014, 5, 5049. (7) D’Innocenzo, V.; Kandada, A. R. S.; De Bastiani, M.; Gandini, M.; Petrozza, A. Tuning the light emission properties by band gap engineering in hybrid lead halide perovskite. J. Am. Chem. Soc. 2014, 136, 17730−17733. (8) Gonzalez-Pedro, V.; Juarez-Perez, E. J.; Arsyad, W.-S.; Barea, E. M.; Fabregat-Santiago, F.; Mora-Sero, I. ; Bisquert, J. General Working Principles of CH3NH3PbX3 Perovskite Solar Cells. Nano Lett. 2014, 14, 888-893. (9) Shi, D.; Adinolfi, V. ; Comin, R.; Yuan, M.; Alarousu, E.; Buin, A.; Chen, Y.; Hoogland, S.; Rothenberger, A. ; Katsiev, K.; et al. Low Trap-State Density and Long Carrier Diffusion in Organolead Trihalide Perovskite Single Crystals. Science 2015, 347, 519-522. (10) Dong, Q. ; Fang, Y. ; Shao, Y.; Mulligan, P.; Qiu, J.; Cao, L.; Huang, J. Electron-Hole Diffusion Lengths >175 µm in Solution-Grown CH3NH3PbI3 Single Crystals. Science 2015, 347, 967-970. (11) Stoumpos, C. C.; Malliakas, C. D.; Kanatzidis, M. G. Semiconducting Tin and Lead Iodide Perovskites with Organic Cations: Phase Transitions, High Mobilities, and Near-Infrared Photoluminescent Properties. Inorg. Chem. 2013, 52, 9019−9038.


15


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

Page 16 of 20

(12) Takahashi, Y.; Hasegawa, H.; Takahashi. Y.; Inabe, T. Hall Mobility in Tin Iodide Perovskite CH3NH3SnI3: Evidence for a Doped Semiconductor. J. Solid State Chem. 2013, 205, 39–43. (13) Pisoni, A.; Jaćimović, J.; Barišić, O. S.; Spina, M.; Gaál, R.; Forró, La.; Horváth, E. Ultra-Low Thermal Conductivity in Organic−Inorganic Hybrid Perovskite CH3NH3PbI3. J. Phys. Chem. Lett. 2014, 5, 2488–2492. (14) Guo, Z.; Yoon, S. J.; Manser, J. S.; Kamat P. V.; Luo, T. Structural Phase- and Degradation-Dependent Thermal Conductivity of CH3NH3PbI3 Perovskite Thin Films. J. Phys. Chem. C 2016, 120, 6394–6401. (15) Chen, Q.; Zhang, C.; Zhu, M.; Liu, S.; Siemens, M. E.; Gu, S.; Zhu, J.; Shen, J.; Wu, X.; Liao, C.; Zhang, J.; Wang, X.; Xiao, M. Efficient Thermal Conductance in Organometallic Perovskite CH3NH3PbI3 Films. Appl. Phys. Lett. 2016, 108, 081902. (16) Hata, T.; Giorgi G.; Yamashita, K. The Effects of the Organic−Inorganic Interactions on the Thermal Transport Properties of CH3NH3PbI3; Nano Letters 2016, 16, 2749–2753. (17) Qian, X.; Gu, X.; Yang, R. Lattice Thermal Conductivity of Organic-Inorganic Hybrid Perovskite CH3NH3PbI3. Appl. Phys. Lett. 2016, 108, 063902. (18) Wang, M.; S. Lin, S.; Anisotropic and Ultralow Phonon Thermal Transport in Organic–Inorganic Hybrid Perovskites: Atomistic Insights into Solar Cell Thermal Management and Thermoelectric Energy Conversion Efficiency. Adv. Funct. Mater. 2016, 26, 5297–5306. (19) Caddeo, C.; Melis, C.; Saba, M. I.; Filippetti, A.; Colombo, L.; Mattoni, A. Tuning the Thermal Conductivity of Methylammonium Lead Halide by the Molecular Substructure. Phys. Chem. Chem. Phys. 2016, 18, 24318-24324. (20) Cahill, D. G.; Braun, P. V.; Chen, G.; Clarke, D. R.; Fan, S. ; Goodson, K. E.; Keblinski, P.; King, W. P.; Mahan, G. D.; Majumdar, A.; Maris, H. J.; Phillpot, S. R.; Pop, E. ; Shi, L. Nanoscale Thermal Transport. II. 2003– 2012; Appl. Phys. Rev. 2014, 1, 011305. (21) Venkatasubramanian, R.; Siivola, E.; Colpitts T.; O'Quinn, B. Thin-film Thermoelectric Devices with High Room-Temperature Figures of Merit. Nature 2001, 413, 597-602. (22) Harman, T. C.; Taylor, P. J.; Walsh, M. P.; LaForge, B. E. Quantum Dot Superlattice Thermoelectric Materials and Devices; Science 2002, 297, 2229-2232. (23) Biswas, K.; He, J.; Blum, I. D.; Wu, C.-I.; Hogan, T. P.; Seidman, D. N.; Dravid, V. P.; Kanatzidis, M. G. High-Performance Bulk Thermoelectrics with All-Scale Hierarchical Architectures; Nature 2012, 489, 414-418. (24) Yee, S. K.; LeBlanc, S.; Goodsonb, K. E.; Dames, C. $ per W Metrics for Thermoelectric Power Generation: Beyond ZT; Energy Environ. Sci. 2013, 6, 2561-2571. (25) Tritt, T. M.; Böttner, H .; Chen, L. Thermoelectrics: Direct Solar Thermal Energy Conversion; MRS Bulletin 2008, 33, 366-368. (26) Jarman, J. T.; Khalil, E. E.; Khalaf, E. Energy Analyses of Thermoelectric Renewable Energy Sources; Open Journal of Energy Efficiency 2013, 2, 143-153. (27) Kraemer, D.; Poudel, B.; Feng, H.-P.; Caylor, J. C.; Yu, B.; Yan, X.; Ma, Yi.; Wang, X.; Wang, D.; Muto, A.; McEnaney, K.; Chiesa, M.; Ren, Z.; Chen, G. High-Performance Flat-Panel Solar Thermoelectric Generators with High Thermal Concentration. Nat. Mater. 2011, 10, 532-538. (28) Dualeh, A.; Gao, P.; Il Seok, S.; Nazeeruddin, M. K.; Grätzel, M. Thermal Behavior of Methylammonium Lead-Trihalide Perovskite Photovoltaic Light Harvesters. Chem. Mater. 2014, 26, 6160−6164. (29) Yang, J.; Siempelkamp, B. D.; Mosconi, E.; De Angelis, F.; Kelly, T. L. Origin of the Thermal Instability in CH3NH3PbI3 Thin Films Deposited on ZnO. Chem. Mater. 2015, 27, 4229−4236.


16

Page 17 of 20

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


(30) Meloni, S.; Moehl, T.; Tress, W.; Franckevičius, M.; Saliba, M.; Lee, Y. H.; Gao, P.; Nazeeruddin, M. K.; Zakeeruddin, S. M.; Rothlisberger, U.; et al. Ionic Polarization-Induced Current-Voltage Hysteresis in CH3NH3PbX3 Perovskite Solar Cells. Nat. Commun. 2016, 7, 10334. (31) Snaith, H. J.; Abate, A.; Ball, J. M.; Eperon, G. E.; Leijtens, T.; Noel, N. K.; Stranks, S. D.; Wang, J. T.-W.; Wojciechowski, K.; Zhang, W. Anomalous Hysteresis in Perovskite Solar Cells. J. Phys. Chem. Lett. 2014, 5, 1511−1515. (32) Delugas, P.; Caddeo, C.; Filippetti, A.; Mattoni, A. Thermally Activated Point Defect Diffusion in Methylammonium Lead Trihalide: Anisotropic and Ultrahigh Mobility of Iodine. J. Phys. Chem. Lett. 2016, 7, 2356−2361. (33) Eperon, G. E.; Stranks, S. D.; Menelaou, C.; Johnston, M. B.; Herz, L. M.; Snaith, H. J.; Formamidinium Lead Trihalide: a Broadly Tunable Perovskite for Efficient Planar Heterojunction Solar Cells. Energy Environ. Sci. 2014, 7, 982-988. (34) Jeon, N. J.; Noh, J. H.; Yang, W. S.; Kim, Y. C.; Ryu, S.; Seo, J.; Il Seok, S. Compositional Engineering of Perovskite Materials for High-Performance Solar Cells. Nature 2015, 517, 476-481. (35) Yi, C.; Luo, J.; Meloni, S.; Boziki, A.; Ashari-Astani, N.; Grätzel, C.; Zakeeruddin, S. M.; Rothlisberger, U.; Grätzel, M. Entropic Stabilization of Mixed A-cation ABX3 Metal Halide Perovskites for High Performance Perovskite Solar Cells; Energy Environ. Sci. 2016, 9, 656-662. (36) Chin, X. Y.; Cortecchia, D.; Yin, J.; Bruno, A.; Soci, C. Lead Iodide Perovskite Light-Emitting Field-Effect transistor. Nat. Commun. 2015, 6, 7383. (37) Mettan, X.; Pisoni, R.; Matus, Pe.; Pisoni, A.; Jaćimović, J.; Náfrádi, Ba.; Spina, M.; Pavuna, D.; Forró, La.; Horváth, E. Tuning of the Thermoelectric Figure of Merit of CH3NH3MI3 (M=Pb,Sn) Photovoltaic Perovskites. J. Phys. Chem. C 2015, 119, 11506−11510. (38) Allen, P. B. Boltzmann Theory and Resistivity of Metals, in: J.R. Chelikowsky, S.G. Louie (Eds.), Quantum Theory of Real Materials, Kluwer, Boston, 1996, pp. 219–250. (39) Madsen, G.; Singh, D. BoltzTraP. A Code for Calculating Band-Structure Dependent Quantities. Computer Physics Communications 2006, 175, 67-71. (40) Filippetti, A.; Delugas, P.; Verstraete, M. J.; Pallecchi, I.; Gadaleta, A.; Marré, D.; Li, D. F.; Gariglio, S.; Fiorentini, V. Thermopower in Oxide Heterostructures: the Importance of Being Multiple-Band Conductors, Phys. Rev. B 2012, 86, 195301. (41) Puggioni, D.; Filippetti, A.; Fiorentini, V. Ordering and Multiple Phase Transitions in Ultra-Thin Nickelate Superlattices, Phys. Rev. B 2012, 86, 195132. (42) Delugas, P.; Filippetti, A.; Verstraete, M.; Pallecchi, I.; Marrè, D.; Fiorentini, V. Doping-Induced Dimensional Crossover and Thermopower Burst in Nb-doped SrTiO3 Superlattices. Phys. Rev. B 2013, 88, 045310. (43) Delugas, P.; Filippetti, A.; Gadaleta, A.; Pallecchi, I.; Marré, D.; Fiorentini, V. Large Band Offset as Driving Force of 2-Dimensional Electron Confinement: the Case of SrTiO3/SrZrO3 interface. Phys. Rev. B 2013, 88, 115304. (44) Delugas, P.; Fiorentini, V.; Mattoni, A.; Filippetti, A. Intrinsic Origin of the 2D Electron Gas at the (001) Surface of SrTiO3. Phys. Rev. B 2015, 91, 115315. (45) Filippetti, A.; Mattoni, A.; Caddeo, C.; Saba, M. I.; Delugas, P. Low Electron-Polar Optical Phonon Scattering as a Fundamental Aspect of Carrier Mobility in Methylammonium Lead Halide CH3NH3PbI3 Perovskites. Phys. Chem. Chem. Phys. 2016, 18, 15352-15362.


17


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

Page 18 of 20

(46) Wehrenfennig , C.; Eperon, G. E.; Johnston , M. B.; Snaith, H. J.; Herz, L. M. High Charge Carrier Mobilities and Lifetimes in Organolead Trihalide Perovskites. Adv. Mater. 2014, 26, 1584–1589. (47) Wright, A. D.; Verdi, C.; Milot, R. L.; Eperon, G. E.; Pérez-Osorio, M. A.; Snaith, H. J.; Giustino, F.; Johnston, M. B.; Herz, L. M. Electron–Phonon Coupling in Hybrid Lead Halide Perovskites. Nat. Commun. 2016, 7, 11755. (48) Lee, C.; Hong, J.; Stroppa, A.; Whangbo, M.-H.; Shim, J. H. Organic–Inorganic Hybrid Perovskites ABI3 (A=CH3NH3, NH2CHNH2; B = Sn, Pb) as Potential Thermoelectric Materials: a Density Functional Evaluation. RSC Adv. 2015, 5, 78701–78707. (49) Motta, C.; El-Mellouhi, F.; Sanvito, S. Charge Carrier Mobility in Hybrid Halide Perovskites. Sci. Rep. 2015, 5, 12746. (50) He, Y.; Galli, G. Perovskites for Solar Thermoelectric Applications: A First Principle Study of CH3NH3AI3 (A = Pb and Sn). Chem. Mater. 2014, 26, 5394−5400. (51) Zhao, T.; Shi, W.; Xi, J.; Wang, D.; Shuai, Z. Intrinsic and Extrinsic Charge Transport in CH3NH3PbI3 Perovskites Predicted from First-Principles. Sci. Rep. 2016, 6, 19968. (52) Vanderbilt, D. Soft Self-Consistent Pseudopotentials in a Generalized Eigenvalue Formalism. Phys. Rev. B, 1990, 41, 7892-7895. (53) Baikie, T.; Fang, Y.; Kadro, J. M.; Schreyer, M.; Wei, F.; Mhaisalkar, S. G.; Graetzel, M.; White, T. J. Synthesis and Crystal Chemistry of the Hybrid Perovskite (CH3NH3)PbI3 for Solid-State Sensitised Solar Cell Applications. J. Mater. Chem. A 2013, 1, 5628-5641. (54) Beekman, M.; Morelli D. T.; Nolas, G. S. Better Thermoelectrics Through Glass-Like Crystals. Nat. Mater. 2015, 14, 1182-1185. (55) Brenner, T. M.; Egger, D. A.; Rappe, A. M.; Kronik, L.; Hodes, G.; Cahen, D. Are Mobilities in Hybrid Organic−Inorganic Halide Perovskites Actually “High”? J. Phys. Chem. Lett. 2015, 6, 4754−4757. (56) Filippetti, A.; Mattoni, A. Hybrid Perovskites for Photovoltaics: Insights from First Principles. Phys. Rev. B 2014, 89, 125203. (57) Filippetti, A.; Delugas, P.; Mattoni, A. Radiative Recombination and Photoconversion of Methylammonium Lead Iodide Perovskite by First Principles: Properties of an Inorganic Semiconductor within a Hybrid Body. J. Phys. Chem. C 2014, 118, 24843-24853. (58) Onoda-Yamamuro, N.; Matsuo, T.; Suga, H. Dielectric Study of CH3NH3PbX3 (X = Cl, Br, I). J. Phys. Chem. Solids 1992, 53, 935-939. (59) Pérez-Osorio, M. A.; Milot, R. L.; Filip, M. R.; Patel, J. B.; Herz, L. M.; Johnston, M. B.; Giustino, F. Vibrational Properties of the Organic−Inorganic Halide Perovskite CH3NH3PbI3 from Theory and Experiment: Factor Group Analysis, First-Principles Calculations, and Low Temperature Infrared Spectra. J. Phys. Chem. C 2015, 119, 25703−25718. (60) Quarti, C.; Grancini, G.; Mosconi, E.; Bruno, P.; Ball, J. M.; Lee, M. M.; Snaith, H. J.; Petrozza, A.; De Angelis, F. The Raman Spectrum of the CH3NH3PbI3 Hybrid Perovskite: Interplay of Theory and Experiment. J. Phys. Chem. Lett. 2014, 5, 279−284. (61) Mattoni, A.; Filippetti, A.; Saba, M. I.; Delugas, P. Methylammonium Rotational Dynamics in Lead Halide Perovskite by Classical Molecular Dynamics: The Role of Temperature. J. Phys. Chem. C 2015, 119, 17421-17428.


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Page 19 of 20

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


(62) Mattoni, A.; Filippetti, A.; Saba, M. I.; Caddeo, C.; Delugas, P. Temperature Evolution of Methylammonium Trihalide Vibrations at the Atomic Scale. J. Phys. Chem. Lett. 2016, 7, 529−535. (63) Umari, P.; Mosconi, E.; De Angelis, F. Relativistic GW Calculations on CH3NH3PbI3 and CH3NH3SnI3 Perovskites for Solar Cell Applications. Sci. Rep. 2014, 4, 4476. (64) Bokdam, M.; Sander, T.; Stroppa, A.; Picozzi, S.; Sarma, D. D.; Franchini, C.; Kresse, G. Role of Polar Phonons in the Photo Excited State of Metal Halide Perovskites. Sci. Rep. 2016, 6, 28618. (65) Juarez-Perez, E. J.; Sanchez, R. S.; Badia, L.; Garcia-Belmonte, G.; Kang, Y. S.; Mora-Sero, I.; Bisquert, J. Photoinduced Giant Dielectric Constant in Lead Halide Perovskite Solar Cells. J. Phys. Chem. Lett. 2014, 5, 2390−2394. (66) Giorgi, G.; Fujisawa, J.-I.; Segawa, H.; Yamashita, K. Small Photocarrier Effective Masses Featuring Ambipolar Transport in Methylammonium Lead Iodide Perovskite: A Density Functional Analysis. J. Phys. Chem. Lett. 2013, 4, 4213−4216. (67) Heremans, J. P.; Jovovic, V.; Toberer, E. S.; Saramat, A.; Kurosaki, K.; Charoenphakdee, A.; Yamanaka, S.; Snyder, G. J. Enhancement of Thermoelectric Efficiency in PbTe by Distortion of the Electronic Density of States; Science 2008, 321, 554-557. (68) Chen, X.; Parker, D.; Singh, D. J. Importance of Non-Parabolic Band Effects in the Thermoelectric Properties of Semiconductors. Sci. Rep. 2013, 3, 3168.


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Table of Contents Graphic


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