How it works
Electrons in a solid occupy discrete energy bands rather than single energy levels because of periodic crystal potential, explained by Bloch's theorem. The valence band holds bound electrons at 0 K; the conduction band is where free electrons live. In silicon at room temperature, thermal energy (~0.026 eV) is enough to kick a small number of electrons across the 1.1 eV gap, generating electron-hole pairs. Germanium's gap is only 0.67 eV, so it conducts more easily but leaks more at high temperatures. The Fermi level sits at mid-gap for intrinsic semiconductors.
Key points to remember
The forbidden gap, also called the band gap, is 1.1 eV for silicon and 0.67 eV for germanium — these numbers appear directly in exam problems. Conductors have zero or overlapping band gaps, insulators exceed 5 eV, and semiconductors fall between 0.5 eV and 3 eV. At absolute zero, a perfect semiconductor behaves as an insulator. Increasing temperature narrows the band gap slightly and dramatically increases carrier concentration. The Fermi level position — mid-gap for intrinsic material — shifts toward the conduction band for n-type and toward the valence band for p-type doping.
Exam tip
The examiner always asks you to compare the band gaps of Si and Ge and explain why Ge devices fail at higher temperatures — keep those values 1.1 eV and 0.67 eV locked in memory.