A tunneling transistor is implemented in silicon, using a FinFET device architecture. The tunneling FinFET has a non-planar, vertical, structure that extends out from the surface of a doped drain formed in a silicon substrate. The vertical structure includes a lightly doped fin defined by a subtractive etch process, and a heavily-doped source formed on top of the fin by epitaxial growth. The drain and channel have similar polarity, which is opposite that of the source. A gate abuts the channel region, capacitively controlling current flow through the channel from opposite sides. Source, drain, and gate terminals are all electrically accessible via front side contacts formed after completion of the device. Fabrication of the tunneling FinFET is compatible with conventional CMOS manufacturing processes, including replacement metal gate and self-aligned contact processes. Low-power operation allows the tunneling FinFET to provide a high current density compared with conventional planar devices.