The Schottky Barrier

Abstract

The classical Schottky barrier is introduced. The Schottky approximation is initially used with parameters listed and F (x) and Ψ (x) are given. The zero current solution for n(x). Diffusion potential and junction field is given. The De-bye length and barrier width are defined. The accuracy of the Schottky approximation is discussed. n(x) for non vanishing currents are evaluated. The Dobson integral is given. The Boltzmann term is shown to be independent of the current. Current voltage characteristics are calculated. A modified Schottky barrier is introduced. Schottky barrier with current dependent Interface density is identified. Metal/semiconductor boundary conditions are given. Richardson-Dushman emission is identified. Current voltage characteristic in modified Schottky barriers are computed. The ideal diode equation is given. The shape factor is given. DRO and DO ranges are identified. A modified Boltzmann range is shown. Electrostatic and electrochemical potential in the Schottky barrier are identified. A metal of sufficiently high work function causes the electron density of an n-type semiconductor to be much lower than determined by its doping in the bulk, causing a space charge near the electrode. The bias-induced shift and deformation of this space charge determines the corresponding changes in the current. An understanding of this interrelation is the key for deriving the current-voltage characteristics of such a Schottky barrier device. In this chapter, we will analyze the space charge induced by the metal-semiconductor boundary and its deformation by an applied bias, yielding the typical diode characteristics. We analyze the mathematical relations given by the transport and Poisson equations which yield as approximative solutions the diode equation. We will approach this problem by starting from a rather simple model, and will later introduce more realistic modifications that yield results more in tune with experimental observation. 26.1 The Classical Schottky Barrier When an n-type semiconductor is connected to a metal of a sufficiently high work function, electrons from the semiconductor leak out into the adjacent