We present the structural, morphological, and electrical analysis of the copper-doped (wt 3%) ZnO (CZO) thin film grown with the RF sputtering system. CZO thin films were deposited on both soda–lime silicate glass and n-type (100)-oriented GaAs substrates. Following CZO thin-film deposition, samples were annealed at various temperatures ranging from 300 to 600 °C (by step 100 °C). Structural properties of the as-deposited CZO thin films grown on soda–lime silicate substrate and annealed at different temperatures (300 °C, 400 °C, 500 °C, 600 °C) were characterized by X-ray diffraction (XRD) measurements. It was seen that CZO thin film with 600 °C annealed temperature has the best peak compared to other annealed samples. Surface morphology of the CZO thin film with 600 °C annealed temperature was investigated by utilizing atomic force microscopy (AFM) and scanning electron microscopy (SEM) measurements. AFM and SEM results have shown that CZO with 600 °C annealed temperature has low surface roughness and good homogeneity. CZO thin film with 600 °C annealed temperature deposited on the n-GaAs substrate was used for electrical characterizations. C–V and G/ω–V forward and reverse bias measurements between − 2 and 4 V of Au/CZO/n-GaAs MOS structure with an annealing temperature of 600 °C were performed in the temperature range from 200 to 380 K (by step 30 K) at 1 MHz. It was observed to exhibit negative capacitance (NC) behavior for high-temperature region (320–380 K) from C–V measurements at forward bias voltage.