Effective-mass theory of metal-semiconductor contact resistivity

We have calculated the contact resistivity for a metal-silicon interface, using an accurate application of effective-mass theory that includes tunneling and quantum reflection. We found that earlier treatments missed an increase in resistivity of a factor of ten due to the mismatch of the wavefunctions at the interface, not included in the WKB approximation. This arises in effective-mass theory for all metal-semiconductor interfaces. We carried out full numerical calculations of the interface resistivity and describe approximations which lead to explicit formulae for the current flow, allowing one to see the dependence of the resistivity on doping, Schottky-barrier height, temperature, crystal orientation, and choice of metal. Finally, we see how the number and energy distribution of transmitted carriers changes as a function of doping density.