The present invention is notably directed to a method of fabrication of a microfluidic chip (1), comprising: providing (S10-S20) a wafer (10, 12) of semiconductor material having a diamond cubic crystal structure, exhibiting two opposite main surfaces (S1, S2), one on each side of the wafer, and having, each, a normal in the or direction; and performing (S30) self-limited, anisotropic wet etching steps on each of the two main surfaces on each side of the wafer, to create a via (20, 20a) extending transversely through the thickness of the wafer, at a location such that the resulting via connects an in-plane microchannel (31) on a first one (S1) of the two main surfaces to a second one (S2) of the two main surfaces, the via exhibiting slanted sidewalls (20s) as a result of the self-limited wet etching. The invention further concerns microfluidic chips accordingly obtained.