Abstract: First-principle complex band structures have been computed for rutile TiO2 and tetragonal ZrO2 insulating materials that are of current technological relevance to dynamic random accessmemorymetal-insulator-metal (MIM) capacitors. From the magnitude of the complex wave vectors in different orientations, the most penetrating orientations have been identified. Tunneling effective masses m(tunnel) have been extracted, are shown to be a crucial parameter for the intrinsic leakage, and are identified to be an important parameter in further scaling of MIM capacitors.