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Interband Tunneling

  • E. O. Kane
  • E. I. Blount

Abstract

We will begin our discussion of interband tunneling by considering the square barrier problem for a solid as shown in Fig. 1. Here c and v represent the edges of the conduction band and valence band, respectively, with the forbidden band between them. The straight line represents the constant energy of the electron. In region 1 the electron has band energy
$$E\left( k \right)={{E}_{c}}+{{E}_{1}}$$
(1)
where E c represents the conduction band edge and E 1 is positive. This equation determines a real value of k and corresponds to an eigenfunction of the Bloch form
$$\psi \left( x \right)={{e}^{ikx}}{{u}_{c,k}}\left( x \right)$$
(2)
where u c (x) is the cell periodic part of the conduction-band wave function. The solution is analogous to a plane wave which propagates without attenuation. In the barrier region the band energy of the electron is given by
$$E\left( ix \right)={{E}_{c}}+{{E}_{2}}$$
(3)
where E 2 is negative. In this forbidden region k is pure imaginary (in the simplest cases) and the eigenfunctions have the form
$$\psi \left( x \right)={{e}^{-\varkappa x}}{{u}_{c,\varkappa }}\left( x \right)$$
(4)
.

Keywords

Branch Point Dirac Equation Bloch Function Weber Function Tunneling Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press 1969

Authors and Affiliations

  • E. O. Kane
    • 1
  • E. I. Blount
    • 1
  1. 1.Bell Telephone LaboratoriesMurray HillUSA

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