Intrinsic doping limitations in inorganic lead halide perovskites

Inorganic Halide perovskites (HP's) of the CsPbX3 (X=I, Br, Cl) type have reached prominence in photovoltaic solar cell efficiencies. Peculiarly, they have shown, however, an asymmetry in their ability to be doped by holes rather than by electrons. Indeed, both structural defect-induced doping as well as extrinsic impurity-induced doping strangely result in a unipolar doping (dominantly p-type) with low free carriers concentration. This raises the question whether such doping limitations presents just a temporary setback due to insufficient optimization of the doping process, or perhaps this represents an intrinsic, physically-mandated bottleneck. In this paper we study three fundamental Design Principles (DP's) for ideal doping, applying them via density functional doping theory to these HP's, thus identifying the violated DP that explains the doping limitations and asymmetry in these HP's. Here, the target DP are: (i) requires that the thermodynamic transition level induced by the dopants must ideally be energetically shallow both for donors (n-type) or acceptors (p-type); DP-(ii) requires that the 'Fermi level pinning energies' for electrons and holes (being the limiting values of the Fermi level before a structural defect that compensate the doping forms spontaneously) should ideally be located inside the conduction band for n-type doping and inside the valence band for p-type doping. DP-(iii) requires that the doping-induced equilibrium Fermi energy shifts towards the conduction band for n-type doping (shift towards the valence band, for p-type doping) to be sufficiently large. We find that, even though in HP's based on Br and Cl there are numerous shallow level dopants that satisfy DP-(i), in contrast DP-(ii) is satisfied only for holes and DP-(iii) fail for both holes and electrons, being the ultimate bottleneck for the n-type doping in Iodine HP's.