We demonstrate the growth of crystalline strontium titanate, SrTiO3 (STO), and strontium hafnate, SrHfO3 (SHO), directly on Ge via atomic layer deposition (ALD). Both STO (a ~ 3.905 ï¿½) and SHO (a ~ 4.069 ï¿½) have good lattice match to the Ge (001) surface (a/?2 ~ 3.992 ï¿½), yielding a ~2.2% tensile and ~1.9% compressive strain in the epitaxial film, respectively. After thermal deoxidation, the Ge substrate is transferred in vacuo to the deposition chamber where a thin film of STO / SHO is deposited by ALD. Following a post-deposition anneal, the perovskite film becomes crystalline with epitaxial registry to the underlying Ge (001) substrate. The 2ï¿½1 reconstructed, clean Ge (001) surface is a necessary template to achieve crystalline films upon annealing. In situ x-ray photoelectron spectroscopy confirms stoichiometric films with no GeOx formation or carbon impurities. The STO and SHO films exhibit excellent crystallinity, as shown by x-ray diffraction and transmission electron microscopy. Capacitor structures using the crystalline STO dielectric show a high permittivity (k~90), but also high leakage current (~10 A/cm2 at +1 eV). The unfavorable conduction band offset (and high leakage current) of STO on Ge is circumvented by growing the Hf-based perovskite, SHO. The SHO films have favorable electronic properties, with satisfactory band offsets with Ge (> 2 eV), low leakage current (< 10-5 A/cm2 at an applied field of 1 MV/cm) at an equivalent oxide thickness of 1 nm, and a reasonable dielectric constant (k~15). The interface trap density (Dit) is estimated to be ~2-5 ï¿½ 1012 cm-2 eV-1 under the current growth and anneal conditions. Some interfacial reaction is observed between SHO and Ge at temperatures above ~650 ï¿½C, which may contribute to the observed Dit value. In efforts to improve electrical performance of the crystalline perovskite dielectric, including leakage current, permittivity, and Dit, we have recently studied crystalline SrHfxTi1-xO3 (SHTO) grown directly on Ge by ALD. SHTO benefits from a reduced leakage current over STO and a higher permittivity than SHO. The SHTO films crystallize at a relatively lower temperature than SHO (600 ï¿½C vs. 650 ï¿½C), which limits the formation of hafnium germanide. In addition, the lattice constant of SrHfxTi1-xO3 (x~0.5) is estimated to be 4.014 ï¿½, yielding minimal (~0.6%) compressive strain in the epitaxial film. By minimizing the epitaxial strain and maintaining an abrupt interface, the SHTO films are expected to reduce Dit at the oxide-Ge interface. We will report our recent results on the growth, characterization, and electrical performance of epitaxial SHTO films on Ge for next-generation high-k dielectric applications, and compare them against STO and SHO films grown directly on Ge(001).