Effects of image force and tunneling on current transport in metal-semiconductor (Schottky barrier) contacts

Abstract

Image force lowering of the potential energy barrier is included in a theoretical calculation of current transport in metal-semiconductor (Schottky barrier) contacts. Thermionic and thermionic-field (tunnel) emission are analyzed in a normalized formulation to yield the current ( I) vs. voltage ( V) relationship. Quantum-mechanical reflection of carriers near the top of the image force rounded barrier is included in the theory by the use of Kemble's transmission probability which incorporates the one-dimensional WKB-type tunneling approximation into a transmission probability applicable both above and below the top of the barrier. Carrier distributions in the semiconductor and in the metal are described by Maxwell-Boltzmann statistics. For any given combination of three dimensionless input parameters E b kT , kT E 00 , and E 00 E 11 , which correspond to bias, temperature and donor concentration respectively, two dimensionless output parameters I f I m (current) and the diode n value (inverse slope of the semilog I vs. V relationship) are determined. Computer solutions are presented in both graphical and tabular form. The results permit a straightforward calculation of the barrier height and the semiconductor donor concentration from experimental I− V data. In comparison with the predictions of current transport models that neglect image force lowering, the present work shows that inclusion of image force leads to a significant increase in the predicted magnitude of the current density and to minor changes in the magnitude of the diode n value. Corrections to the predictions of models that neglect image force arise primarily from enhanced thermionic emission over the image force lowered barrier rather than from enhanced tunnel emission through the image force narrowed barrier. The Kemble transmission probability may be defined in terms of a characteristic transmission energy, E t , which is useful when thermionic emission dominates the conduction process to the extent that quantum-mechanical tunneling and reflection may be considered as a perturbation on thermionic emission. When this occurs E t can be used to estimate the magnitude of the perturbation.