  We report density functional theory (DFT) investigation of $B$-site doped
CaFeO$_3$, a prototypical charge-ordered perovskite. At 290 K, CaFeO$_3$
undergoes a metal-insulator transition and a charge disproportionation reaction
2Fe$^{4+}$$\rightarrow$Fe$^{5+}$+Fe$^{3+}$. We observe that when Zr dopants
occupy a (001) layer, the band gap of the resulting solid solution increases to
0.93 eV due to a 2D Jahn-Teller type distortion, where FeO$_6$ cages on the
$xy$ plane elongate along $x$ and $y$ alternatively between neighboring Fe
sites. Furthermore, we show that the rock-salt ordering of the Fe$^{5+}$ and
Fe$^{3+}$ cations can be enhanced when the $B$-site dopants are arranged in a
(111) plane due to a collective steric effect that facilitates the size
discrepancy between the Fe$^{5+}$O$_6$ and Fe$^{3+}$O$_6$ octahedra and
therefore gives rise to a larger band gap. The enhanced charge
disproportionation in these solid solutions is verified by rigorously
calculating the oxidation states of the Fe cations with different octahedral
cage sizes. We therefore predict that the corresponding transition temperature
will increase due to the enhanced charge ordering and larger band gap. The
compositional, structural and electrical relationships exploited in this paper
can be extended to a variety of perovskites and non-perovskite oxides providing
guidance in structurally manipulating electrical properties of functional
materials.
