Theory of tunneling into interface states

TLDR: In this paper, a theory of electron tunneling from the metal through the insulator and into the semiconductor of a MIS-structure is developed using a square well model, the interface states are represented by a distribution of δ-function potentials, and their wave functions calculated.

Abstract: A theory of electron tunneling from the metal through the insulator and into the semiconductor of a MIS-structure is developed. Using a square well model, the interface states are represented by a distribution of δ-function potentials, and their wave functions calculated. Following the method of Bardeen, the tunneling matrix element and current are found and used with an extension of Shockley-Read recombination theory to determine a tunnelling time constant, τ To , similar to the surface recombination time constant, τ. Small signal solutions are calculated and presented in the form of equivalent circuits. For a single level state the equivalent circuit consists of the thick insulator, non-tunneling MIS-capacitor plus a tunneling current, j 1 , injected from the metal into the midpoint of the recombination RC circuit. j 1 is made up of three terms caused by modulation of the effective barrier height, and by modulation of the metal and trap occupancy functions. For τ To ⪡ τ , the case of an ideal Schottky barrier, the tunneling current is controlled by the recombination time, τ. If τ To > τ , the tunneling limited case, j 1 is controlled by τ To . This case is discussed in detail. The model's current and conductance characteristics are numerically calculated and graphically presented as a function of interface state density and distribution, interface potential, insulator thickness, and a.c. frequency.