Intrinsic doping limitations in inorganic lead halide perovskites

Abstract

Inorganic halide perovskites (HP's) of the CsPbX₃ (X = I, Br, Cl) type have reached prominence in photovoltaic solar cell efficiencies, leading to the expectation that they are a new class of semiconductors relative to the traditional ones. Peculiarly, they have shown an asymmetry in their ability to be doped by holes <i>vs.</i> electrons. Indeed, both structural defect-induced doping as well as extrinsic impurity-induced doping strangely often result in HP's 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 <i>via</i> 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 between different charge states 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 <i>E</i>(n)pin and holes <i>E</i>(p)pin (being the limiting value 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 shift in equilibrium Fermi energy Δ<i>E</i>(n)F towards the conduction band for n-type doping (shift of Δ<i>E</i>(p)F 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) fails for both holes and electrons, being the ultimate bottleneck for the n-type doping in Iodide HP's. This suggests an intrinsic mechanism for doping limitations in this class of semiconductors in terms of recognized physical mechanisms.