## 1 Introduction
The complex dielectric constant of materials or biological and medical research was detected using THz pulses in electro-optic crystals, but the waveform distortions of THz pulses due to effects of phase mismatch, dispersive propagation, and absorption become more severe with the increase of crystal thickness. The (110)-oriented ZnTe crystal as thick as 3 mm has proven to work for the frequency below 3 THz without remarkable distortions. In view of the difficulty in the crystal growth of \(<\)110\(>\) ZnTe wafers due to the high melting point of 1568 K and structural defects, a temperature gradient solvent method under Te-rich condition with subwavelength microstructure on the ZnTe crystal surface by reactive ion etching was performed to obtain the optical level of ZnTe crystals [12]. In this case, the analysis of the bulk resistivity under a bias voltage of 1 V indicates that ZnTe:V (Zn\({}_{1-x}\)Mn\({}_{x}\)Te) shows higher resistivity of 10\({}^{8}\)-10\({}^{9}\)\(\Omega\)-cm (200-400 \(\Omega\)-cm) than intrinsic ZnTe of 50-100 \(\Omega\)-cm. The manganese-doped ZnTe crystal can enhance the THz emitter and sensor by 10-19% and 17-28%, respectively. The ZnTe:V crystal can increase the detection sensitivity by 20-30%. In applications requiring the use of the copper doping in cadmium telluride (CdTe) solar cells while limiting the diffusion of copper due to copper as interstitial defects with high mobility, the Cu-doped ZnTe film was selected for the back contacts in the CdTe photovoltaic devices [13]. The CdTe photovoltaic device with a ZnTe layer shows a better open-circuit voltage of 841 mV, a higher short-circuit current of 26.7 mA/cm\({}^{2}\), and an external quantum efficiency as high as 17.66%. On the theoretical side, a full-potential linearized augmented plane wave (FP-LAPW) and the local orbital (LO) calculations for structural, electronic, and optical properties of zinc blende and wurtzite phases of the ZnTe indicated that the zinc blende ZnTe appears to be the most stable at room temperature [14]. The reflectivity of zinc blende and wurtzite phases of the ZnTe are about 30% and 38%, respectively, which show that the zinc blend phase ZnTe has good transmittance in the visible range, better than the wurtzite one. For ultrashort coherent light sources, the production of transition metal-doped zinc chalcogenides has become very important. In the particular cases of ZnS, ZnSe, and ZnTe alloys individually doped with Cr\({}^{2+}\), Co\({}^{2+}\), Ni\({}^{2+}\), or Fe\({}^{2+}\), previous studies have shown that the transition metal ions in the II-VI compounds are susceptible to distortions of tetragonal symmetry [15]. Moreover, the tetragonal deformation leads to Jahn-Teller effects which further split the ground and excited states. For examples in Cr\({}^{2+}\) doped ZnS, ZnSe, and ZnTe alloys the wavelengths of room-temperature emission spectra are all between 1900 and 2700 nm, suggesting the emission bands from the transitions from the metastable excited state to the ground state. Furthermore, divalent chromium doped lasers of the II-VI family emitting in the mid-infrared (mid-IR) (2070-2420 nm) have been reported, such as Cr\({}^{2+}\):ZnS, Cr\({}^{2+}\):ZnSe, and Cr\({}^{2+}\):ZnTe. The emission-quantum yield is as high as 100% at 300K, but the transition in detail is less explainable [16]. In order to explain intermediate band states of substitutional transition metal defects in the II-VI compounds, we investigate the atomic structures, band structures and electronic structures of \(TM^{2+}{}_{x}Zn_{1-x}\)Te (\(TM\) = V, Cr, Mn) alloys, in which the transition metal ion \(TM^{2+}\) is distributed on the substitutional site.