The time‐dependent dielectric breakdown (TDDB) characteristics of thin oxide–nitride–oxide (ONO) films containing 4 nm of Si3N4were found to be exclusively determined by statistical thickness fluctuations of the Si3N4layer. A two‐parameter statistical model describes this roughness and explains experimental TDDB data. A simple growth model combined with the statistical model reduces the number of parameters to one. It is consistent with TDDB data and is in quantitative agreement with transmission electron microscopy and x‐ray photoelectron spectroscopy data and is able to explain the origin of the roughness. On an ONO with a 4 nm Si3N4layer and an area of 8 cm2—corresponding to the total storage area of a 256 Mbit dynamic random access memory—the thinnest point in the Si3N4can be expected to be below 10 A˚. So eliminating the Si3N4roughness would bring a drastic improvement in reliability. ©1996 American Institute of Physics.