Interband Tunneling

  • E. O. Kane
  • E. I. Blount


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
$$E\left( k \right)={{E}_{c}}+{{E}_{1}}$$
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
$$\psi \left( x \right)={{e}^{ikx}}{{u}_{c,k}}\left( x \right)$$
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
$$E\left( ix \right)={{E}_{c}}+{{E}_{2}}$$
where E 2 is negative. In this forbidden region k is pure imaginary (in the simplest cases) and the eigenfunctions have the form
$$\psi \left( x \right)={{e}^{-\varkappa x}}{{u}_{c,\varkappa }}\left( x \right)$$


Branch Point Dirac Equation Bloch Function Weber Function Tunneling Problem 
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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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