“…In the steady state, the governing equations for linear n-type piezoelectric semiconductors without body force and free of electric charge are given by Hu et al [21] The constitutive equations for a two-dimensional n-type piezoelectric semiconductor with the polarization direction along the y-direction can be given in the form [3,4] where u, v, φ, and n are elastic displacements in the x-and y-directions, electric potential, and carrier density, respectively, which are sometimes called extended displacements; ij c , ij e , and ij ε are the elastic, piezoelectric and dielectric constants, respectively; q and 0 n are the electric charge of an electron and the initial carrier density, respectively; ij µ and ij d are the electron mobility and carrier diffusion, respectively.…”