Dielectric breakdown has been studied in several materials intended for high-dielectric DRAMs (dynamic random access memories), emphasizing lead zirconate-titanate (PZT) and barium strontium titanate (BST) ceramics. In this paper we present our results on PZT. A second paper will deal with BST. In order to distinguish among impulse thermal breakdown, de thermal breakdown, and avalanche breakdown mechanisms, studies have been carried out as functions of temperature, electrode material and shape, frequency and duration of applied fields, and specimen size and shape. Notable in the results is the fact that maximum breakdown field varies directly with electrode work function but is uncorrelated with electrode thermal conductivity; this militates against a purely thermal breakdown interpretation and instead favors an avalanche mechanism in which the iniation step is impact ionization of Ti ions from electrons emitted from the electrodes, followed by thermal run-away. Thickness dependence also favors avalanche mechanisms, but dependence upon applied field ramp rate favors an impulse thermal mechanism. Taken altogether, the data indicate characteristics of mixed impulse-thermal and avalanche mechanisms: i.e., electron-initiation followed by thermal run-away.