Charge carrier mobility in hybrid halide perovskites
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Charge carrier mobility in hybrid
halide perovskites
Carlo Motta1, Fedwa El-Mellouhi2 & Stefano Sanvito1
received: 23 December 2014
accepted: 09 June 2015
Published: 03 August 2015
The charge transport properties of hybrid halide perovskites are investigated with a combination
of density functional theory including van der Waals interaction and the Boltzmann theory for
diffusive transport in the relaxation time approximation. We find the mobility of electrons to be
in the range 5–10 cm2V−1s−1 and that for holes within 1–5 cm2V−1s−1, where the variations depend
on the crystal structure investigated and the level of doping. Such results, in good agreement with
recent experiments, set the relaxation time to about 1 ps, which is the time-scale for the molecular
rotation at room temperature. For the room temperature tetragonal phase we explore two possible
orientations of the organic cations and find that the mobility has a significant asymmetry depending
on the direction of the current with respect to the molecular axis. This is due mostly to the way the
PbI3 octahedral symmetry is broken. Interestingly we find that substituting I with Cl has minor effects
on the mobilities. Our analysis suggests that the carrier mobility is probably not a key factor in
determining the high solar-harvesting efficiency of this class of materials.
Hybrid halide perovskites have made a breakthrough in the field of organic solar cells1. Their unique
energy-harvesting efficiency, combined with the low manufacturing costs position them as an ideal materials class to focus research. The conversion of sunlight into electrical power has recently surpassed the
outstanding efficiency of 15% for both mesoporous metal-oxide scaffolds and in planar heterojunction
architectures2–4 and the latest studies report a value exceeding 20%5. A unique property of these materials
is the ability to both act as light-harvesting medium and as charge carrier transporter. However, despite
the intense research carried out in the past two years, some questions remain open regarding the nature
of the material’s working principles. For instance, it is still under debate whether the photo-generated
charges have an excitonic or a free-carrier character, with results pointing towards contrasting conclusions6–8. Also, the origin of the high efficiencies of perovskite-based solar cell devices still needs to
be unraveled, and it is not completely clear how the mobility of the active layer influences the overall
performance.
Savenije et al.8 have recently performed microwave photo-conductance and photo-luminescence
experiments, measuring a mobility of 6.2 cm2/Vs at 300 K. They found a band-like dependence of the
mobility with temperature with a slope of T−1.6. At the same time, using transient THz spectroscopy,
Wehrenfennig and coworkers have shown that CH3NH3PbI3 exhibits long charge-carrier diffusion
lengths, exceeding 1 μm, and a high-frequency mobility of 8 cm2/Vs, an indeed remarkable result for a
solution-processed material7. They inferred that the low bimolecular recombination rate arises from a
spatial separation of electrons and holes in the system. Finally, early dielectric measurements9 suggest a
picosecond relaxation process at room temperature.
To our knowledge, to date no theoretical calculations have addressed the problem of evaluating the
conductivity and charge mobility in hybrid perovskites. Motivated by this gap in the knowledge and
by the intriguing rôle that the charge transport is expected to play, here we present a first-principles
analysis of the transport properties of organolead halide perovskites. In particular we consider the
methyl-ammonium lead-iodide perovskite, CH3NH3PBI3, which is the archetype of this class of materials. The cubic, tetragonal, and orthorhombic phases are explored. We show that, depending on the phase
of the material and the doping level, the mobility spans a range between 5 and 12 cm2/Vs for holes and
1
School of Physics, AMBER and CRANN Institute, Trinity College, Dublin 2, Ireland. 2Qatar Environment and
Energy Research Institute, Doha, Qatar. Correspondence and requests for materials should be addressed to
C.M. (email: ) or F.E.-M. (email: )
Scientific Reports | 5:12746 | DOI: 10.1038/srep12746
1
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2.5 and 10 cm2/Vs for electrons. Furthermore, our results suggest that Cl doping has little impact on the
transport properties.
The electronic structure of CH3NH3PBI3 has been calculated with the all-electron fhi-aims code at the
level of the generalised gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE)10 parameterization. Long-range van der Waals interactions are included via the Tkatchenko and Scheffler (TS)
scheme11, which is constructed over a GGA and a pairwise dispersive potential. In order to verify the
goodness of the bandstructure, additional calculations with the HSE12 and HSE0613 functional have been
performed. Since these give us rather similar mobilities than those obtained with GGA, the results are
not presented here. The reciprocal space integration was performed over an 8 × 8 × 8 Monkhorst-Pack
grid14 in the case of the cubic cell, and a 6 × 6 × 4 one for both the tetragonal and the orthorhombic. A pre-constructed high-accuracy all-electron basis set of numerical atomic orbitals was employed,
as provided by the fhi-aims “tight” default option. Structural optimization was performed with the
Broyden-Fletcher-Goldfarb-Shanno algorithm15, with the crystal geometry determined by optimizing
both the internal coordinates and the supercell lattice vectors with a tolerance of 10−3 eV/Å and with the
constraint of orthogonal cell vectors.
The charge mobility has been determined by mean of the semiclassical Boltzmann theory within the
constant relaxation time approximation, as implemented in the BoltzTrap code16. The code has been
interfaced with fhi-aims and uses the fhi-aims-calculated wave-functions and eigenvalues. A very dense
k-point sampling of 32 × 32 × 32 (32768 k-points over the full Brillouin zone) has been employed for the
cubic cell, while for the tetragonal and orthorhombic cells it was reduced to 18 × 18 × 12.
We now briefly summarize the key steps of the scheme. From the first-principles bandstructure, εi,k,
the α component of the group velocity for a charge carrier in the i-th band is obtained as
v α ( i , k) =
1 ∂εi,k
,
∂k α
(1 )
and used to compute the conductivity tensor
σ α,β (i, k) = e 2τ i,k v α (i , k) v β (i , k),
(2 )
where e is the electronic charge and τi,k is the relaxation time. By integrating σα,β(i, k), one can extract
the conductivity as a function of the temperature, T, and the chemical potential, ν,
dk
∫ 8π 3 −
i
σ α , β (T , ν ) = ∑
∂ f (T , ν )
σ α,β (i , k),
∂ε
(3)
where f is the Fermi-Dirac distribution function. Note that ν is determined by the number of free carriers or, equivalently, by their concentration. On (...truncated)
