The Phenomenon of parametric interaction of compiled wave exhibits a vital role in nonlinear optics. Using the straight forward compiled mode theory, the lattice displacement plays the great role in the parametric amplification is analytically investigated in magnetized piezoelectric as well as non piezoelectric semiconductors. The origin of nonlinear interaction is taken to be in the second order optical susceptibility arising from the nonlinear induced current density and polarization through lattice displacement. The threshold value of the pump electric field (E_0th), lattice displacement (u), effective non linear polarization (P_EN) and efficiency of crystal cell are obtained for different situation of practical interest, i.e. (i) for piezoelectric coupling only (ii) for deformation potential coupling only, (iii) for both the couplings.

The analytical investigations reveal that piezoelectric and deformation potential coupling, wave number, scattering angle, carrier concentration and magnetic field strongly affect the polarization and cell efficiency and also lattice displacement. This study provides new means for construction of crystal cell and for diagnostics of semiconductors devices.