Terahertz (THz) plasma oscillation in n⁺nn⁺ InGaAs vertical diodes is studied by using a numerical approach based on the hydrodynamic (HD) equations. The 1D HD model is coupled to 1D Poisson equation. We simulate the diode response to the optical excitation of plasma waves at room temperature. Our results clearly show the presence of 3D plasma resonances in the THz frequency domain. The selection of appropriately shaped optical excitation pulses helps in the realization of the detected frequency. The investigation is completed by introducing stochastic perturbations according to the Langevin equation.