Zitterbewegung and its effects on electrons in semiconductors

An analogy between the band structure of narrow gap semiconductors and the Dirac equation for relativistic electrons in vacuum is used to demonstrate that semiconductor electrons experience a Zitterbewegung (trembling motion). Its frequency is ωZ≈Eg∕ and its amplitude is λZ, where λZ=∕m₀*u corresponds to the Compton wavelength in vacuum (Eg is the energy gap, m₀* is the effective mass, and u≈1.3×10⁸0.3em0excm∕s). Once the electrons are described by a two-component spinor for a specific energy band there is no Zitterbewegung but the electrons should be treated as extended objects of size λZ. The magnitude of λZ in narrow gap semiconductors can be as large as 700.3em0ex. Possible consequences of the above predictions are indicated.