Excellent capacitor-voltage characteristics with near-ideal hysteresis are realized in a capacitive-like structure that uses an electrode substrate-type material with a high-k dielectric layer having a thickness of a few-to-several Angstroms capacitance-based SiO2 equivalent (“TOx, Eq”). According to one particular example embodiment, a semiconductor device structure has an electrode substrate-type material having a Germanium-rich surface material. The electrode substrate-type material is processed to provide this particular electrode surface material in a form that is thermodynamically stable with a high-k dielectric material. A dielectric layer is then formed over the electrode surface material with the high-k dielectric material at a surface that faces, lies against and is thermodynamically stable with the electrode surface material.