Lattice parameter formula.

In this study, zinc-oxide (ZnO) nanoparticles (NPs) doped with cobalt (Co) were synthesized using a simple coprecipitation technique. The concentration of Co was varied to investigate its effect on the structural, morphological, optical, and dielectric properties of the NPs. X-ray diffraction (XRD) analysis confirmed the hexagonal wurtzite structure of both undoped and Co-doped ZnO-NPs. Scanning electron microscopy (SEM) was used to examine the morphology of the synthesized NPs, while energy-dispersive X-ray spectroscopy (EDX) was used to verify their purity. The band gap of the NPs was evaluated using UV-visible spectroscopy, which revealed a decrease in the energy gap as the concentration of Co2+ increased in the ZnO matrix. The dielectric constants and AC conductivity of the NPs were measured using an LCR meter. The dielectric constant of the Co-doped ZnO-NPs continuously increased from 4.0 × 10−9 to 2.25 × 10−8, while the dielectric loss decreased from 4.0 × 10−8 to 1.7 × 10−7 as the Co content increased from 0.01 to 0.07%. The a.c. conductivity also increased with increasing applied frequency. The findings suggest that the synthesized Co-doped ZnO-NPs possess enhanced dielectric properties and reduced energy gap, making them promising candidates for low-frequency devices such as UV photodetectors, optoelectronics, and spintronics applications. The use of a cost-effective and scalable synthesis method, coupled with detailed material characterization, makes this work significant in the field of nanomaterials and device engineering.