We investigate the highly efficient terahertz nonlinearity exhibited by n-type GaAs crystals under metallic metamaterials. An intense THz field applied to the metamaterials leads to impact ionization in the GaAs substrate, which emits electroluminescence in the near-infrared region. Even for a similar THz field strength, n-type GaAs emits near-infrared photons more efficiently than semi-insulating GaAs. We analyzed the luminescence lineshapes and intensity as a function of the excitation field strength, using Fermi-Dirac statistics and the density of states in the conduction band to quantify electron density and locate the Fermi level after the relaxation of excited hot electrons.