Metal-air batteries continue to become attractive energy storage and conversion systems due to their high energy and power densities, safer chemistries, and economic viability. Semiconductor-air batteries - a term we first define here as metal-air batteries that use semiconductor anodes such as silicon (Si) and germanium (Ge) - have been introduced in recent years as new high-energy battery chemistries. In this paper, we describe the excellent doping-dependent discharge kinetics of p-type Ge anodes in a semiconductor-air cell employing a gelled KOH electrolyte. Owing to its Fermi level, n-type Ge is expected to have lower redox potential and better electronic conductivity, which could potentially lead to a higher operating voltage and better discharge kinetics. Nonetheless, discharge measurements demonstrated that this prediction is only valid at the low current regime and breaks down at the high current density region. The p-type Ge behaves extremely better at elevated currents, evident from the higher voltage, more power available, and larger practical energy density from a very long discharge time, possibly arising from the high overpotential for surface passivation. A primary semiconductor-air battery, powered by a flat p-type Ge as a multi-electron anode, exhibited an unprecedented full discharge capacity of 1302.5 mA h gGe(-1) (88% anode utilization efficiency), the highest among semiconductor-air cells, notably better than new metal-air cells with three-dimensional and nanostructured anodes, and at least two folds higher than commercial Zn-air and Al-air cells. We therefore suggest that this study be extended to doped-Si anodes, in order to pave the way for a deeper understanding on the discharge phenomena in alkaline metal-air conversion cells with semiconductor anodes for specific niche applications in the future.