Electron Energy Bands of Semiconductors

In cases in which both the upper edge level of the valence band and the lower edge level of the conduction band are at the same wave vector of electrons (GaAs, etc.), the band gap is called the direct band gap-, while it is called the indirect band gap in cases in which the two band edge levels are at difierent wave vectors (Si, etc.). The band gap is e, = 1.1 eV for silicon and e, = 1.4 eV for gallium arsenide. 

Since the band gap is relatively narrow in semiconductors, a few electrons in the fully occupied valence band are thermally excited up to the conduction band leaving positive holes (vacant electrons) in the valence band. The concentration, ni, of thermally exdted electron-hole pairs is given, to a first approximation, by the Boltzmann function as shown in Eqn. 2-6  

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