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The trends in electronic band structure are studied in the cubic ABX3 halide perovskites for A= Cs, B=Pb, Sn, Ge, Si and X=I, Br, Cl. The gaps are found to decrease from Pb to Sn and from Ge to Si, but increase from Sn to Ge. The trend is explained in terms of the atom s-levels of the group-IV element and the atomic sizes which changes the amount of hybridisation with X-p and hence the valence band width. Along the same series spin-orbit coupling also decreases and this tends to increase the gap because of the smaller splitting of the conduction band minimum. Both effects compensate each other to a certain degree. The trend with halogens is to reduce the gap from Cl to I, i.e. with decreasing electro-negativity. The role of the tolerance factor in avoiding octahedron rotations and octahedron edge-sharing is discussed. The Ge containing compounds have tolerance factor t > 1 and hence do not show the series of octahedral rotation distortions and the existence of edge-sharing octahedral phases known for Pb and Sn based compounds, but rather a rhombohedral distortion. CsGeI3 is found to have a suitable gap for photovoltaics both in its cubic (high-temperature) and rhombohedral (low-temperature) phases. The structural stability of the materials in the different phases is also discussed. We find the rhombohedral phase to have lower total energy and slightly larger gaps but to present a less significant distortion of the band structure than the edge-sharing octahedral phases, such as the yellow phase in CsSnI3. The corresponding silicon based compounds have not yet been synthesized and therefore our estimates are less certain but indicate a small gap for cubic CsSiI3 and CsSiBr3 of about 0.2±0.2 eV and 0.8±0.6 eV for CsSiCl3. The intrinsic stability of the Si compounds is discussed.

Charge transport is crucial to the performance of hybrid halide perovskite solar cells. A theoretical model based on large polarons is proposed to elucidate charge transport properties in the perovskites. Critical new physical insights are incorporated into the model, including the recognitions that acoustic phonons as opposed to optical phonons are responsible for the scattering of the polarons; these acoustic phonons are fully excited due to the "softness" of the perovskites, and the temperature-dependent dielectric function underlies the temperature dependence of charge carrier mobility. This work resolves key controversies in literature and forms a starting point for more rigorous first-principles predictions of charge transport.

The first-principles linear response method is used within the local-density approximation (LDA) to calculate the full phonon band structures and phonon density of states (DOS) of CsSnX3 (X=Cl, Br, or I) in different phases. The relations between soft phonon modes and phase transitions are investigated. We find soft phonon modes only in the cubic and tetragonal phases, not in the orthorhombic and monoclinic phases. A dispersion-less soft phonon branch spreads from the kpoint M to R in the Brillouin zone of the cubic phase. The lower symmetry tetragonal phase results from the condensation of the soft phonon mode at the k-point M . Furthermore, the condensation of the soft phonon mode at the k-point Z in the Brillouin zone of tetragonal phase results in the orthorhombic γ-phase. To facilitate comparison with experimental data, we calculate infrared spectra for the cubic phase. At this point only a limited comparison with experimental data is possible. We find that the calculated modes agree with the available experimental data when we assign the second and third calculated modes to the experimental first and second modes. The lowest calculated mode is at a frequency where the phonon DOS has a maximum value. So the strong phonon-phonon interaction results in short phonon lifetime or strong broadening which could explain why this mode has not been observed. Our first-principles calculated IR spectra show that the third observed mode in IR absorption is actually the highest LO rather than TO mode. We show furthermore that a strong LO-plasmon coupling may be expected in these materials and can explain observed Raman data for CsSnI3.

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