A process is provided to fabricate a finFET device having a semiconductor layer of a two-dimensional “2D” semiconductor material. The semiconductor layer of the 2D semiconductor material is a thin film layer formed over a dielectric fin-shaped structure. The 2D semiconductor layer extends over at least three surfaces of the dielectric fin structure, e.g., the upper surface and two sidewall surfaces. A vertical protrusion metal structure, referred to as “metal fin structure”, is formed about an edge of the dielectric fin structure and is used as a seed to grow the 2D semiconductor material.