Modelling hot carrier cooling in halide perovsite solar cells

Jupyter notebooks outlining theory and calculations for hot polaron cooling in halide perovskites including CH3NH3PbI3 and CsPbI3.

Static renders of the notebooks are available here, but simply download the repository and open using jupyter notebook for interactive versions.

Files

Polaron_effective_mass_theories.ipynb contains Julia codes to evaluate effective-mass theories (in the asymptotic variational limit, as presented by Feynman in the original 1955 paper). You can express Frohlich α values, mass renormalisations, Schultz polaron radius and volumes, exciton effective mass theory radius and spectra; summations with Bose-Einstein statistics over phonon modes to get specific heat capacities; Franck-Condon overtone spectrum from polaron variational solution; overlaid plots of polaron wavefunction and Schultz's definition of radius; some notes on the derivations in Schultz.

Additionally the codes used to generate data for Figure 2 using the PolaronMobility.jl package are available. Here is a specific (October 2017) point in history, which reproduces the data for the publication figure: ThermalPathways.jl.

Diffusion_eqn_for_hot_sphere.ipynb outlines the derivation of the analytical expression for heat diffusion for a hot sphere. This was used for calculating the final stage of cooling to equilibrium.

Polaron_cooling_via_heat_diffusion.ipynb contains Python codes to generate the polaron Temperature-Radius (Figure 3) and Energy-Time (Figure 4) plots.

Publication

"Slow cooling of hot polarons in halide perovskite solar cells" by Jarvist M. Frost, Lucy D. Whalley and Aron Walsh (2017) [arXiv]

License

The notebooks are made available under the GNU General Public Licence (GPL) v3. See the LICENSE file for the full text.