Thin films of bismuth‐germanium have been fabricated by the method of codeposit vapor quenching onto liquid nitrogen or water‐cooled substrates. Structural, electrical, optical, and photoelectrical characterizations of these films have been accomplished. In this paper, Paper I of a two‐paper series, the structural and electrical characterization results are reported. X‐ray diffraction measurements indicate that a stable amorphous phase exists for the BixGe1−xthin‐film system for 0 ≤x≤ 0.12. Low‐field dc resistivity as a function of temperature from room temperature to liquid‐nitrogen temperature and relative thermopower measurements show that in the amorphous range the BixGe1−xthin films aren‐type semiconductors with a continuously decreasing thermal activation energy asxincreases. The resistivity of amorphous bismuth‐germanium films decreases with an increase in bismuth concentration. Current‐voltage data taken on several films at 300 and 162°K indicate Ohmic behavior with no evidence of Poole‐Frenkel, Schottky‐barrier, or switching effects. A structural model for the amorphous bismuth‐germanium system is proposed with covalent hybrid bonding of monoatomic bismuth to a Polk‐Turnbull amorphous germanium random network. An energy‐band density‐of‐states model is proposed based on the Weaire‐Thorpe interpretation of the Polk‐Turnbull network and considerations from the theory of heavily doped semiconductors. The proposed structural and energy‐band models are utilized to explain the observed electrical and optical properties.