We present a new analytical potential fluctuations model for the interpretation of current/voltage and capacitance/voltage measurements on spatially inhomogeneous Schottky contacts. A new evaluation schema of current and capacitance barriers permits a quantitative analysis of spatially distributed Schottky barriers. In addition, our analysis shows also that the ideality coefficient n of abrupt Schottky contacts reflects the deformation of the barrier distribution under applied bias; a general temperature dependence for the ideality n is predicted. Our model offers a solution for the so-called T0 problem. Not only our own measurements on PtSi/Si diodes, but also previously published ideality data for Schottky diodes on Si, GaAs, and InP agree with our theory.