In this paper we report on the fabrication of all-epitaxial ultrathin germanium-on-crystalline lanthanum–yttrium-oxide field effect transistors. The oxide is lattice matched to Si (1 1 1) and has a dielectric constant of ∼18. The transistors show ambipolar behaviour, both N- and P-channel operations on the same device at any temperature. The transistor characteristics have an ON/OFF ratio of 102 at room temperature, while at cryogenic temperatures negative differential resistance (NDR) is observed in the channel. The NDR effect, which is stronger for lower temperatures, can be attributed to a number of reasons from intervalley or intersubband electron transfer to a heavy transport effective mass (low mobility) band or to charge trapping. A germanium-on-insulator technology, provided the material (Ge and oxide) quality improves, may be useful for building circuits that combine conventional FETs with unconventional ambipolar or NDR devices all on the same substrate.