In this paper, we studied the electronic properties, effective masses, and carrier mobility of monolayer $$\hbox {MoS}_2$$
using density functional theory calculations. The carrier mobility was considered by means of ab initio calculations using the Boltzmann transport equation coupled with deformation potential theory. The effects of mechanical biaxial strain on the electronic properties, effective mass, and carrier mobility of monolayer $$\hbox {MoS}_2$$
were also investigated. It is demonstrated that the electronic properties, such as band structure and density of state, of monolayer $$\hbox {MoS}_2$$
are very sensitive to biaxial strain, leading to a direct–indirect transition in semiconductor monolayer $$\hbox {MoS}_2$$
. Moreover, we found that the carrier mobility and effective mass can be enhanced significantly by biaxial strain and by lowering temperature. The electron mobility increases over 12 times with a biaxial strain of 10%, while the carrier mobility gradually decreases with increasing temperature. These results are very useful for the future nanotechnology, and they make monolayer $$\hbox {MoS}_2$$
a promising candidate for application in nanoelectronic and optoelectronic devices.