Composite of layers which comprises a dielectric layer and a layer which comprises pyrogenic zinc oxide and is bonded to the dielectric layer. Process for producing the composite of layers, in which the pyrogenic zinc oxide is applied to the dielectric layer in the form of a dispersion in which the zinc oxide particles are present with a mean aggregate diameter of less than 200 nm, and the zinc oxide layer is dried and then treated at temperatures of less than 200° C. Process for producing the composite of layers, in which the pyrogenic zinc oxide is applied to a substrate layer or a composite of substrate layers in the form of a dispersion in which the zinc oxide particles are present with a mean aggregate diameter of less than 200 nm to form a zinc oxide layer, and then the zinc oxide layer and the substrate layer are treated at temperatures of less than 200° C., and then a dielectric layer is applied to the zinc oxide layer. Field-effect transistor which has the composite of layers.