Interband Tunneling

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)

.