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The compounds exhibit piezoelectricity, which demands to break inversionsymmetry, and then to be a semiconductor. For $\mathrm{Ga_2O_3}$, theorthorhombic case ($\epsilon$-$\mathrm{Ga_2O_3}$) of common five phases breaksinversion symmetry. Here, the piezoelectric tensor of$\epsilon$-$\mathrm{Ga_2O_3}$ is reported by using density functionalperturbation theory (DFPT). To confirm semiconducting properties of$\epsilon$-$\mathrm{Ga_2O_3}$, its electronic structures are studied by usinggeneralized gradient approximation (GGA) and Tran and Blaha's modified Beckeand Johnson (mBJ) exchange potential. The gap value of 4.66 eV is predictedwith mBJ method, along with the the effective mass tensor for electrons at theconduction band minimum (CBM) [about 0.24 $m_0$]. The mBJ gap is very close tothe available experimental value. The elastic tensor $C_{ij}$ and piezoelectricstress tensor $e_{ij}$ are attained by DFPT, and then piezoelectric straintensor $d_{ij}$ are calculated from $C_{ij}$ and $e_{ij}$. In this process,average mechanical properties of $\epsilon$-$\mathrm{Ga_2O_3}$ are estimated,such as bulk modulus, Shear modulus, Young's modulus and so on. The calculated$d_{ij}$ are comparable and even higher than commonly used piezoelectricmaterials such as $\alpha$-quartz, ZnO, AlN and GaN.

Piezoelectric properties of $\mathrm{Ga_2O_3}$: a first-principle study