Sustainable materials modelling for a sustainable future
Jarvist Moore Frost
Humanity needs new materials for power generation without reliance on fossil fuels, and for everyone (the earth's population is predicted to be nearly 10 billion by 2050) to enjoy a high standard of living. Ideally these materials would be made out of earth-abundant elements, would be non-toxic in extraction, use and disposal, and would not require much energy to process. Materials modelling is essential for the design of these materials, both in a purely predictive manner (suggesting a material to make), and more subtly in enabling the correct interpretation of measurements, and thereby the correct empirical design rules.
We also need sustainability both in our calculations, and in our careers. State of the art materials calculations require increasingly highfalutin physics, and eye watering amounts of computer time. Long gone are the prospects of a comfortable research career built on the application of standard density functional theory methods. As community codes have become more reliable, and computers have got bigger, large automated computational sifts of all materials have taken place.
But all is not lost! It is a much better application of our human brains to be dreaming up new models and interpretable explanations of observed behaviour, than debugging FORTRAN run-time errors. Many material properties of actual technical interest are phenomenological in nature: they are not direct observables.
I will take some examples from recent work on halide perovskite materials, to show how calculations with standard electronic structure theory codes can feed into modest (but bespoke) computational models to explain new data.
Halide perovskites are soft, polar, semiconductors [1]. As well as being materials of potential technological use, they are scientifically interesting in being a high performance yet solution processed semiconductor, and being a semiconductor composed of heavy (e.g. Pb Z=82) elements.
Anharmonicity in the phonon modes leads to extremely low thermal conductivity [2]. This anharmonicity has been observed by x-ray scattering [3] and neutron spectroscopy [4].
Strong dielectric electron-phonon coupling leads to correlated electron and phonon degrees of freedom, the formation of a polaron. We can describe this interacting system with path integrals, integrating out the (infinite) degrees of freedom associated with the phonon quantum field. We have recently implemented codes to calculate the finite-temperature Feynman polaron state, based on a Fröhlich electron-phonon Hamiltonian [5,6]. For a polar material, the long-range dielectric coupling can be expected to dominate the electron-phonon interaction. This model provides temperature dependent charge carrier mobility, with no free parameters. For halide perovskite systems, the predictions agree well with experiment, indicating that we are capturing the essential physics.
From a characterisation of this finite-temperature polaron state, we have proposed a model for the observed slow carrier cooling in halide perovskites [7]. The polaron state is stable at high temperature, and results in a limited density of states which the hot-electron is in thermal contact with. The very low lattice thermal conductivity retains the localisation of this transient hot-spot. This model explains cation and halide trends in observed cooling rates [8].
The fundamental enigma of the halide perovskite semiconductor is how a solution processed (and thus defective) semiconductor has such a slow minority carrier recombination rate. I propose this is due to a combination of the heavy elements leading to relativistic effects in the band-structure [9] (which persist when thermal disorder is present [10]), and the underlying device physics of polarons. Most device physics models (such as those used to fit experimental data) assume electrons scatter as plane waves, extending the models to include the Gaussian wavepacket localisation of a polaron changes the result considerably.
I will discuss the design principles which can be derived from studying the behaviour of the halide perovskite material, both for new defect tolerant semiconductors, and new solar cell device architectures.
[1] JM Frost et al. Acc.Chem.Res. 49 (3) pp 528–535 (2016).
[2] LD Whalley et al. "Phonon anharmonicity, lifetimes, and thermal transport in CH3NH3.PbI3 from many-body perturbation theory" Phys. Rev. B 94, 220301(R) (2016).
[3] AN Beecher et al. "Direct observation of dynamic symmetry breaking above room temperature in methylammonium lead iodide perovskite" ACS Energy Letters 1 (4), 880-887 (2016)
[4] A Gold-Parker et al. "Acoustic phonon lifetimes limit thermal transport in methylammonium lead iodide" Proceedings of the National Academy of Sciences 115 (47), 11905-1191 (2018)
[5] JM Frost. "Calculating polaron mobility in halide perovskites" Phys. Rev. B 96, 195202 (2017)
[6] https://github.com/jarvist/PolaronMobility.jl
[7] JM Frost et al. "Slow cooling of hot polarons in halide perovskite solar cells" ACS Energy Lett., 2017, 2 (12), pp 2647–2652
[8] T Hopper et al. "Ultrafast Intraband Spectroscopy of Hot-Carrier Cooling in Lead-Halide Perovskites" ACS Energy Lett., 2018, 3 (9), pp 2199–2205
[9] P Azarhoosh et al. "Research Update: Relativistic origin of slow electron-hole recombination in hybrid halide perovskite solar cells" APL Materials 4 (9), 091501 (2017)
[10] S McKechnie et al. "Dynamic symmetry breaking and spin splitting in metal halide perovskites" Phys. Rev. B 98 (8), 085108
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