Substrate-free silicon nitride films for metamaterial absorbers designed with Lorentz quadratic model

4-inch wafer-level substrate-free low-stress silicon nitride (SiN_x) thin films are demonstrated in this paper for fabrication of terahertz (THz) metadevices. The chemical compositions, surface roughness, and THz properties of the SiN_x film are investigated. Narrowband metamaterial absorbers designed with a Lorentz quadratic model are fabricated to evaluate the performance of the SiN_x films. The new model reveals the quantitative relationship between the parameters of the model and the geometric parameters of the absorber. The performance of the absorber agrees well with the model which exhibits a full-width at half-maximum (FWHM) ≈ 0.11 THz and near-unity absorption (≈ 94%) at f_c = 1.13 THz. Our results show that the wafer-level SiN_x films will facilitate the development of large-scale, sophisticated-substrate-free THz metadevices. Moreover, the employed Lorentz model as well as its quadratic model can be a novel and practical method for the design of THz metadevices.