Energy Spectrum of Electrons in Heavily Doped Semiconductors

  • Victor I. Fistul’
Part of the Monographs in Semiconductor Physics book series (MOSEPH, volume 1)


Schrödinger’s Equation. In an isolated atom, such as hydrogen, only the valence electron and the nucleus interact. Therefore, Schrödinger’s equation, which expresses essentially the law of conservation of energy, has the following simple form:
$$\frac{{\hbar ^2 }}{{2m}}\frac{{d^2 \psi \left( r \right)}}{{dr^2 }} + V_0 \left( r \right)\psi \left( r \right) = E\psi \left( r \right).$$
The first term on the left-hand side of this equation represents the kinetic energy of the interaction between the electron and the nucleus and the second term represents the potential energy. The sum of these energies is equal to the total energy of the system Eψ(r). The solution of Eq. (1.1.1) yields plane waves of the type
$$\psi \left( r \right) = e^{ \pm ikr} $$
where k is the wave vector of the electron, equal to k = p/h, where p is the electron momentum.


Conduction Band Energy Spectrum Valence Band Band Structure Brillouin Zone 


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Copyright information

© Plenum Press 1969

Authors and Affiliations

  • Victor I. Fistul’
    • 1
  1. 1.Institute for Fine Chemical TechnologyAcademy of Sciences of the USSRMoscowUSSR

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