Using first-principles calculations, we studied the electronic properties of quasi-2D MoS2/MX2 (MX2 = WS2, MoSe2 and WSe2) heterobilayers, focusing on engineering the band gap via application of in-plane biaxial strain and out-of-plane normal compressive strain (NCS). All heterobilayers show semiconducting characteristics with an indirect band gap except for the MoS2/WSe2 system which exhibits direct band gap character. The band gaps can all be widely tuned through strain and semiconductor–metal transitions can occur. In particular the direct band gap can be tuned and an appropriate compressive strain can tune the direct band gap of MoS2/WSe2 and MoS2/MoSe2, but MoS2/WS2 does not exhibit a direct band gap under any circumstances.
