Tunneling through Impure Barriers

We consider the influence of the presence of a nonmagnetic impurity inside a tunneling barrier on the wave function of a tunneling particle. We can thus evaluate the relevant cross sections and transmission coefficient for the particle. We then compute the tunneling current when the barrier contains many impurities. It is shown that when the impurities are distributed randomly inside the barrier, the tunneling characteristic displays the same features as if no impurities were present. On the other hand, when the impurities are not distributed randomly inside the barrier, an asymmetric tunneling characteristic and a strong rectifying effect may be obtained under certain conditions.