Hybrid perovskite materials CH₃NH₃PbI₃ (MAPI) and CH₃NH₃PbI_3-xCl_x (MAPIC) are used as optically active components in high efficiency solution processed solar cells. Despite the tremendous interest focusing on these semiconductors, a range of significantly different possible energy band diagrams have been suggested and the optical constants of the material have not yet been reported.

In this work, we solve these issues with a complementary study ellipsometry modelling and the highest level of ab initio quantum chemical calculations available for crystal structures: relativistic quasi-particle self-consistent GW simulations with no adjustable parameters.¹

Ellipsometry looks at the change of polarization state of a reflected light beam which can be modelled to yield information about the optical properties of a material. An ensemble of critical points of the joint density of states (four in this case) can be fitted to precisely derive the index of refraction and extinction coefficient of both MAPI and MAPIC.The nature of the critical points can also be used infer detailed information about the energy band structure of MAPI and MAPIC.

We show excellent agreement between the optical constants of MAPI calculated from ellipsometry and the ab initio band structure calculations, the clear first experimental validation of ab-initio calculations on this material. The very close match emphasises the superiority of the GW approximation over density-functional based approaches and the importance of accounting for spin-orbit coupling which contributes 1 eV to the band gap.

The combined results of ellipsometry modelling and quantum chemical calculations enable us to highlight the following interesting features which could have implications for device preparation:

(i)                 The bandgap edge is found to be anisotropic (2D). This means that absorption occurs only in two directions <100> and <010> but not in the third <001> around the first critical point of the joint density of states. If oriented crystals of MAPI can be grown, the active layer used in solar cells can become significantly thinner!

(ii)                The valence band maximum and conduction band minimum are non-parabolic. Their relative flatness is due to spin-orbit degeneration and suggests a high effective mass of the charge carriers. This suggests that mobilities could be further enhanced by doping the material.

1- Brivio et al. Physical Review B, vol. 89, p. 155204, 2014.