Failure to dope halide perovskites: insufficient optimization or a physically-mandated bottleneck?

Intentional chemical doping of halide perovskites (HP) produce very low carriers concentration, not exceeding 10¹⁴cm^-3. One wonders if this represents a temporary setback due to insufficient optimization of the synthesis process, or an intrinsic, physically-mandated bottleneck. To elucidate this we use 3 Design Principles (DP), needed to be satisfied for ideal doping that are also supported by density functional theory calculations. These are DP(i): The impurities or structural defect should have shallow thermodynamic transition levels, lying close to the conduction band (CB) for n-type, or valence band (VB) for p-type; DP(ii): The Fermi level (E_F) pinning energy representing the maximum and minimum position of E_F, should be closed to VBM for p-type or CBM for n-type; and DP(iii): The shift in the doping-induced equilibrium Fermi energy should be sufficiently large to have, after doping, E_F close to VBM for p-type or CBM for n-type. For inorganic HP, we find that 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 and p-type doping in systems based on I, Br and Cl.