This work illustrates the feasibility of ultra-high-frequency operation in a vertical three-terminal electronic device by exploiting the advantages of two-dimensional (2D) crystal heterostructures. The proposed device utilizes a gapped 2D material as the tunnel barrier between a graphene base and a metallic emitter, while the Schottky contact with an n-type substrate forms the base-collector junction. The ultrathin active region formed by the 2D insulating and semimetallic layers ensure the required subnanometer-scale control in the thickness and the lateral uniformity, overcoming the major limitations of conventional 3D materials. Atomistic simulations based on the coupled density functional theory and nonequilibrium Green's function method, in combination with an equivalent device model, clearly reveal well-defined transistor characteristics with a good current drive. The analysis also points out the prominence of emitter material selection for superior performance. With proper optimization, the device is capable of reaching the intrinsic cutoff frequencies over a few THz even under realistic constraints, indicating a technological pathway beyond the current limit.