The dependence of the tunneling current on density of states in non-superconducting junctions

Abstract

The theory that the tunneling current in a non-superconducting tunnel junction depends on the densities of states of the electrodes has been known for sometime although Harrison has suggested that it is in fact not correct. In this paper Harrison's suggestion is critically discussed and the expression for the tunneling current is written in a way that emphasizes its dependence on the surface densities of states of the electrodes and takes into account the band structure of the oxide barrier. We find ▪ where ƒ L, ƒ R are the Fermi function of the left and right hand electrodes, D is the probability that an electron tunnels from a point r L in the barrier near the left hand electrode to a point r R in the barrier near the right hand electrode. ξ depends on the oxide and is a slowly varying function of ω and k ∥, the electron momentum parallel to the epectrode surfaces. ϱ ⊥ L ( r L, ω, k ∥) is the one dimensional density of states of the left hand electrode in the direction normal to the electrode at a position r L in the barrier for electrons of energy ω and momentum k ∥ and ϱ ⊥ R has a similar meaning. This expression for J reduces to that previously derived by Harrison if the electrodes as well as the oxide barrier are treated in a WKB approximation. In this limit J has no dependence on the densities of states due to cancellations from the factor ξ. Recent field emission experiments and theory have shown that the tunneling current is dependent on the electrode density of states so the expression for J given above must be used. It is suggested that the failure to observe such effects in tunnel junctions is due to imperfections in the junction and that tunneling in metal-vacuum-metal junctions or in perfected tunnel junctions will give density of states information.