Fig. 5.

Shortening of disorder potential and band-edge distributions in CsPbBr₃. a Autocorrelation function of the disorder potential corresponding to three scenarios, where the configurations of Pb atoms were always chosen from the MD simulation (T = 425 K), and: (i) Cs and Br atoms were fixed to their ideal lattice positions (blue curve); (ii) configurations of Br atoms were also chosen from the MD trajectory, but Cs atoms were fixed to their ideal lattice positions (green curve); and (iii) configurations of Cs atoms were also chosen from the MD trajectory, but Br atoms were fixed to their ideal lattice positions (orange curve). The thin curves show sample snapshots taken along the MD trajectory (T = 425 K), and the thick curves their averages. The longer correlation length in the disorder potential induced by the Pb displacements is dynamically shortened by the Cs and especially the Br displacements. b Normalized histograms of the instantaneous energies, E_i, of the valence band maximum (VBM) and conduction band minimum (CBM), calculated along two relevant MD scenarios: constrained configurations for which Pb atoms were chosen from the MD simulation (T = 425 K), but all other atoms were fixed to their ideal lattice positions (blue curve with dots); and configurations for which all atoms are displaced according to the MD calculation at T = 425 K (red curve with stars). $E_{\mathrm{VBM}∕\mathrm{CBM}}^{*}$ denotes the VBM/CBM energy with the highest occurrence, $n_{\max }$, which is given by $n_{\max }=n\left(E_{\mathrm{VBM}∕\mathrm{CBM}}^{*}\right)$, and $E_{\mathrm{gap}}^{*}=E_{\mathrm{CBM}}^{*}-E_{\mathrm{VBM}}^{*}$; see Methods section for details. The spread in the CBM energy distribution due to the displaced Pb atoms is reduced by the presence of other displacements occurring in the material