The spatial variations of the three charged gold states in the transition region of silicon p+n and n+p step junctions are calculated. The exact solution is obtained at thermal equilibrium. Under reverse applied bias, exact solution is not possible and approximate solutions using staircased charge distributions are obtained. Under reverse bias, most of the gold atoms in the transition region are in the negative or acceptor charge state for both p+n and n+p junctions. This is due to the dominance of the hole emission process at the neutral gold centers over all other electron and hole emission processes of the three charge states at 300°K. Since the shallow-level impurities in these two types of junctions are of opposite charge and the deep-level gold impurity is mainly in the negative charge state, quite different electrical behaviors are expected from these two junction types. In work to be described elsewhere, some of these differences have been demonstrated experimentally, such as the breakdown voltage and the impedance, and quantitatively correlated with theory using the spatial variations obtained in this paper.