Charge transfer and coherent charge propagation in metal-insulator junctions

In a metal-insulator-metal junction, electron transfer from the inside of the barrier to one metal side, or vice versa, due to the change in height and shape of the potential barrier is calculated by means of the linear-response theory. A step-type potential model with a single interface is used as an electron potential in the junction. One of the results shows that without any external field in the metal region, the electrons pushed out into the metal from the barrier propagate through the metal as a coherent pulse of electric current accompanied by some amount of extra electrons, while the scattering by lattice defects does not occur. This transport differs from the ballistic transport in a semiconductor caused by the hot electrons, which is the flow along a part of some closed circuit with an external driving force field. It can be shown that each of these electrons has the Fermi energy, and the wave front of the pulse moves with the Fermi velocity through the free-electron sea at rest. The behavior of incoherent electrons resulting from coherent ones after the scattering is also considered. These incoherent electrons flow backward and do not contribute appreciably to the electric current. The conservation among the charges calculated here, i.e., the charge pushed out of the barrier, the coherent and incoherent charges in the metal, and surface charge remaining at the interface, is satisfied. The energy conservation associated with the above four types of charges is also verified. The electric field, potential, and Coulomb energy associated with coherent charge propagation are calculated in detail and the stability of this propagation with respect to the Coulomb force is considered. The coherent waves in response to oscillating input voltage are also considered for the experimental observations.