Effects of Hydrostatic Pressure and Biaxial Strains on the Elastic and Electronic Properties of β-Si₃N₄

First principles calculations have been performed to investigate the effects of hydrostatic pressure and biaxial strains (ϵ_xx) on the electronic and elastic properties of β-Si₃N₄. Both bulk modulus and Vickers hardness enhance (decrease) with pressure and compressive (tensile) ϵ_xx. The evolution of B_H/G_H ratio indicates that β-Si₃N₄ has a better (worse) ductile behavior under pressure and compressive (tensile) ϵ_xx. The 3D plots of Young's modulus show huge difference in mechanical properties between [0001] direction and a-b plane and the anisotropy becomes larger by using strain engineering. The sound velocities and Debye temperature are also discussed. The energy gap increases monotonically with pressure, however, strain-induced changes in band gap are asymmetric and nonlinear. β-Si₃N₄ undergoes an indirect to direct band gap transition at biaxial strain of 5%, while β-Si₃N₄ is always an indirect band gap semiconductor under pressure and compressive strains.