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At present, explicit expressions for the electron g factor in crystals are known only for the following two cases: when the Fermi energy eF of the electrons lies at the edge of the electron energy band, e(kex), or when the electron energy spectrum of a crystal can be approximated by the two-band model. Here we obtain explicit formulas for the g factor in situations when the Fermi level eF is close to but does not coincide with the band edge and when the two-band model of the spectrum includes small corrections from other electron energy bands. In particular, we derive expressions that describe the dependences of the g factor on eF−e(kex) and on the magnetic field direction for doped semiconductors. The results are applied to III–V semiconductors and to bismuth.

The electron g factor for one-band and two-band extended models of the electron energy spectrum