Determination of Ultimate Leakage Through Rutile $\hbox {TiO}_{2}$ and Tetragonal $\hbox {ZrO}_{2}$

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 access memory metal-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.