A method of fabricating semiconductor circuits having integrated capacitors that have a dielectric or a ferroelectric material between electrodes. The materials are subjected to heat treatment at high temperatures in an oxygen atmosphere for the purpose of crystallization. The dielectric or ferroelectric is heated separately from the semiconductor substrate, is comminuted into small particles and only afterward applied in this form to the semiconductor substrate. This makes it possible to integrate substances with arbitrarily high crystallization temperature without damaging the integrated semiconductor circuit, since the semiconductor substrate itself does not have to be heated. Diffusion barriers for oxygen are unnecessary. Previous limitations on the capacitor capacitance are obviated owing to the free choice of dielectric or ferroelectric made possible, and the packing density of the capacitors is increased.