Abstract <p>This work investigates the influence of relativistic effects on infrared (IR) parametric generation in semiconductor magnetoplasmas, highlighting departures from conventional phase-matching constraints. Using a hydrodynamic model and coupled-mode theory, we analyze parametric generation in a homogeneous, doped semiconductor plasma of infinite extent. The process originates from second-order optical susceptibility induced by nonlinear current density in a piezoelectric medium. From the plasma equations, expressions for the induced polarization, threshold pump intensity, and transmitted intensity beyond phase matching are derived. Comparative analysis reveals that relativistic electron mass variation significantly modifies the generation dynamics, underscoring its critical role in extending parametric processes beyond traditional limits. Numerical validation of the proposed model is performed using n-InSb crystal irradiated by a 1.06&#xa0;μm Nd: YAG laser at 77&#xa0;K, with photon energy well below the band gap and damage threshold. Results indicate that the non-relativistic regime offers lower threshold requirements, while the relativistic regime enhances transmission characteristics. These findings hold significance for cost-effective, large-scale fabrication of integrated optoelectronic chips and advance the fundamental understanding of nonlinear optical phenomena in plasma media.</p> Graphical abstract <p></p>