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Why do germanium transistors have more leakage current than silicon transistors?

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NMOS transistorNegative-channel metal-oxide semiconductors (NMOS) employ a positive secondary voltage to switch a shallow layer of p-type semiconductor material below the gate into n-type. For positive-channel metal-oxide semiconductors (PMOS), all these polarities are reversed. NMOS transistors are more expensive, but faster, than PMOS transistors. — transistor NMOS transistor
Negative-channel metal-oxide semiconductors (NMOS) employ a positive secondary voltage to switch a shallow layer of p-type semiconductor material below the gate into n-type. For positive-channel metal-oxide semiconductors (PMOS), all these polarities are reversed. NMOS transistors are more expensive, but faster, than PMOS transistors.

Germanium transistors exhibit higher leakage current than silicon transistors primarily due to the difference in their band gap energies.1

In semiconductor materials, electrons must gain enough thermal energy to cross the band gap from the valence band to the conduction band to become free charge carriers. The band gap for silicon is approximately 1.1 eV, whereas the band gap for germanium is significantly smaller, at about 0.7 eV.1

Because germanium has a narrower band gap, it is much easier for thermal energy at ordinary temperatures to excite electrons across the gap. This results in a higher concentration of thermally generated charge carriers, which manifests as increased leakage current in the device. This sensitivity to temperature is also why germanium devices cannot be operated at the higher temperatures that silicon components can withstand.12