The Schottky-Mott rule is not entirely incorrect since, in practice, metals with high work functions form the best contacts to p-type semiconductors, while those with low work functions form the best contacts to n-type semiconductors. Unfortunately experiments have shown that the predictive power of the model doesn't extend much beyond this statement. Under realistic conditions, contact metals may react with semiconductor surfaces to form a compound with new electronic properties. A contamination layer at the interface may effectively widen the barrier. The surface of the semiconductor may reconstruct leading to a new electronic state. The dependence of contact resistance on the details of the interfacial chemistry is what makes the reproducible fabrication of ohmic contacts such a manufacturing challenge.