Dielectric breakdown decisively determines the reliability of nano- to centimeter sized electronic devices and components. Nevertheless, a systematic investigation of this phenomenon over the relevant lengths scales and materials classes is still missing. Here, the thickness and permittivity-dependence of the dielectric breakdown strength of insulating crystalline and polymer materials from the millimeter down to the nanometer scale is investigated. While the dependence of breakdown strength on permittivity was found to be thickness-independent for materials in the nm-mm range, the magnitude of the breakdown strength was found to change from a thickness-independent, intrinsic regime, to a thickness-dependent, extrinsic regime. The transition-thickness is interpreted as the characteristic length of a breakdown-initiating conducting filament. The results are in agreement with a model, where the dielectric breakdown strength is defined in terms of breakdown toughness and length of a conducting filament
