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How does replacing lanthanum ions with calcium ions increase conductivity in lanthanum chromite?

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Figure 1: Schematic diagram of a zirconia oxygen sensor used to monitor automobile exhaust gases. The sensor, approximately the size of a spark plug, is fitted into the exhaust manifold of an automobile engine. The thimble-shaped zirconia sensor, sandwiched between thin layers of porous platinum, is exposed on its interior to outside air and on its exterior to exhaust gas passing through slits in the sensor shield. The two platinum surfaces serve as electrodes, conducting a voltage across the zirconia that varies according to the difference in oxygen content between the exhaust gas and the outside air.
conductive ceramics Figure 1: Schematic diagram of a zirconia oxygen sensor used to monitor automobile exhaust gases. The sensor, approximately the size of a spark plug, is fitted into the exhaust manifold of an automobile engine. The thimble-shaped zirconia sensor, sandwiched between thin layers of porous platinum, is exposed on its interior to outside air and on its exterior to exhaust gas passing through slits in the sensor shield. The two platinum surfaces serve as electrodes, conducting a voltage across the zirconia that varies according to the difference in oxygen content between the exhaust gas and the outside air.

In the context of conductive ceramics, lanthanum chromite acts as a small polaron conductor. When calcium ions (Ca²⁺) are substituted for lanthanum ions (La³⁺) in the crystal lattice, an equal proportion of chromium ions (Cr³⁺) is converted to Cr⁴⁺ to maintain charge neutrality. This process facilitates the hopping of electrons between the two states of chromium ions (Cr³⁺ and Cr⁴⁺), which results in high electrical conductivity, particularly at elevated temperatures.1