Properties of Electrical Materials

Conductors have overlapping (or no) gap so the conduction band is partly filled; semiconductors have a small gap (~1 eV); insulators have a large gap (typically >5 eV) that blocks electron promotion at room temperature.

Silicon has a band gap of about 1.1 eV; gallium arsenide (GaAs) has a band gap of about 1.4 eV. Both are common semiconductors.

Rising temperature gives electrons enough thermal energy to cross the small band gap into the conduction band, generating more electron-hole pairs and raising conductivity (a negative temperature coefficient of resistance).

They are reciprocals: sigma = 1/rho. Resistivity is measured in ohm-meters (Ω·m) and conductivity in siemens per meter (S/m).

R = rho * L / A, where rho is resistivity, L is length, and A is cross-sectional area. Resistance rises with length and falls with area.