  Experimentally synthesized $\mathrm{MoSi_2N_4}$
(\textcolor[rgb]{0.00,0.00,1.00}{Science 369, 670-674 (2020)}) is a
piezoelectric semiconductor. Here, we systematically study the large biaxial
(isotropic) strain effects (0.90 to 1.10) on electronic structures and
transport coefficients of monolayer $\mathrm{MoSi_2N_4}$ by density functional
theory (DFT). With $a/a_0$ from 0.90 to 1.10, the energy band gap firstly
increases, and then decreases, which is due to transformation of conduction
band minimum (CBM). Calculated results show that the $\mathrm{MoSi_2N_4}$
monolayer is mechanically stable in considered strain range. It is found that
the spin-orbital coupling (SOC) effects on Seebeck coefficient depend on the
strain. In unstrained $\mathrm{MoSi_2N_4}$, the SOC has neglected influence on
Seebeck coefficient. However, the SOC can produce important influence on
Seebeck coefficient, when the strain is applied, for example 0.96 strain. The
compressive strain can change relative position and numbers of conduction band
extrema (CBE), and then the strength of conduction bands convergence can be
enhanced, to the benefit of n-type $ZT_e$. Only about 0.96 strain can
effectively improve n-type $ZT_e$. Our works imply that strain can effectively
tune the electronic structures and transport coefficients of monolayer
$\mathrm{MoSi_2N_4}$, and can motivate farther experimental exploration.

Materials Science