Since the advent of the integrated circuit in 1959 and the introduction of MOS capacitors in the early ‘60’s, electronic technology has relied on silica (SiO2) as the gate dielectric in a field effect transistor. However, silica-based transistor technology is approaching fundamental limits. Feature-size-reduction and the ever-demanding technology roadmaps have imposed scaling constraints on gate oxide thickness to the point where excessive tunneling currents make transistor design untenable; an alternative gate dielectric is needed. Crystalline oxides on silicon (COS), simply by virtue of their high dielectric constants, could fundamentally change the scaling laws for silicon-based transistor technology. More importantly, COS could provide the opportunity for an entirely new device physics based on anisotropic response of crystalline oxides grown commensurately on a semiconductor. In this paper, we report that high dielectric constant alkaline earth and perovskite oxides can be grown in perfect registry with silicon. Commensurate heteroepitaxy between the semiconductor and the oxide is established via a sequenced transition that uniquely addresses the thermodynamics of a layer-by-layer energy minimization at the interface. The perfection of the physical structure couples directly to the electrical structure, and we thus obtain the unparalleled result of an equivalent oxide thickness of less than I nm in a MOS capacitor. With this demonstration it is apparent that COS presents a functional alternative to SiO2. With COS, a transistor gate can not only exhibit a much higher dielectric response, but add entirely new capabilities such as logic-state retention with the anisotropic response of ferroelectric polarization in a ferro-gated device. COS is the basis for fundamental change in semiconductor technology.