The epitaxial growth of oxides on silicon presents opportunities to harness the full spectrum of electronic, optical, and magnetic behavior available in oxides, while simultaneously exploiting the properties of the underlying semiconductor. One key application for epitaxial oxides on silicon, which will be the focus of this talk, is to produce a viable gate dielectric alternative to SiO@sub 2@ for silicon MOSFETs with higher dielectric constant (K). As a first step in the identification of such an alternative gate dielectric, we used tabulated thermodynamic data to comprehensively assess the thermodynamic stability of binary oxides and nitrides in contact with silicon at temperatures from 300 to 1600 K. Sufficient data exist to conclude that the vast majority of binary oxides and nitrides are thermodynamically unstable in contact with silicon. The dielectrics that remain are candidate materials for alternative gate dielectrics. Of these remaining candidates, the oxides have significantly higher K than the nitrides. We then extended this thermodynamic approach to multicomponent oxides comprised of candidate binary oxides. The result is 13 silicon-compatible gate dielectric materials with K > 20, of which at least six have an optical bandgap @>=@ 5 eV. Having identified promising candidate materials with high K, high optical bandgap, and the likelihood for thermodynamic stability in contact with silicon, we have been using MBE to epitaxially integrate the candidate materials having the best lattice match with silicon. High-resolution cross-sectional TEM analysis of the epitaxial interface between silicon and epitaxial oxides will be shown. Some of these interfaces were formed by growing silicon on the dielectric; others were formed by growing the dielectric on silicon. Achieving the former interface is easier as it involves the deposition of a single component material (Si) in a vacuum environment. In contrast, the latter involves multiple components, and as one of these components is oxygen, the possibility of oxidizing the silicon surface and not only losing the epitaxial template, but also forming an undesired SiO@sub 2@ layer. Over the last two decades, three strategies have been used to grow epitaxial oxides on silicon: (1) to grow with no excess oxidant, (2) to grow with excess oxidant at high substrate temperatures, and (3) to grow with excess oxidant at low substrate temperatures. The overarching goal of all three strategies is to avoid the formation of an amorphous SiO@sub 2@ layer that would result in the loss of the substrate's crystalline template before the oxide has a chance to nucleate on it. Most reports of the epitaxial growth of oxides on silicon fall into the high temperature / excess oxidant regime. Although successful for the nucleation of an epitaxial oxide layer, these growth conditions typically lead to the growth of an SiO@sub 2@ layer at the silicon interface. To avoid this layer, whose replacement is the purpose of the alternative gate dielectric, we have studied the last of the three regimes-the low temperature / excess oxidant regime. In this regime the oxidation of silicon by the oxidant is limited by kinetics. However, kinetic barriers to the oxidation of the constituents of the desired oxide at these low temperatures can also occur. We have performed in situ oxidation studies to assess the low temperature oxidation of various elements. Examples illustrating oxides that can be grown epitaxially on silicon in the low temperature / excess oxidant regime will be presented, as well as epitaxial oxide / silicon heterostructures that make use of the integration of the overlying epitaxial oxide layers and the underlying silicon.