K+ doping and sintering synergistically tune defects, size, and non-Debye dielectric relaxation in ZnO nanoparticles for electronic applications

This study presents a comparative investigation of undoped and potassium-doped zinc oxide (K:ZnO) nanoparticles with varying particle sizes, synthesized via a sol–gel method and sintered at 500 °C for 3 and 5 h. The structural properties were characterized using X-ray diffraction (XRD), which confirmed the formation of single-phase hexagonal wurtzite structures. Crystallite size analysis via the Debye–Scherrer equation revealed a decrease in size (43.6 and 51.7 nm), reduced to 37.6 and 36.0 nm for (ZnO–3 h), (ZnO–5 h), (K:ZnO–3 h), and (K:ZnO–5 h), respectively, upon K⁺ incorporation. Scanning electron microscopy (SEM) confirmed quasi-spherical grains with average particle sizes of − 48 nm (ZnO–3 h), − 63 nm (ZnO–5 h), − 52 nm (K:ZnO–3 h), and − 70 nm (K:ZnO–5 h), and energy-dispersive X-ray spectroscopy (EDX) validated the morphological uniformity and successful K⁺ doping. Dielectric spectroscopy showed enhanced dielectric constant (ε′) with temperature and longer sintering. AC conductivity increased with K-doping, especially at low frequencies and high temperatures, due to increased charge carrier density and interfacial polarization. Conversely, dielectric loss and impedance were reduced, reflecting improved electrical stability. Impedance spectroscopy and complex modulus analysis revealed thermally activated non-Debye relaxation behavior, with shorter relaxation times in doped and long-sintered samples. By combining controlled K⁺ incorporation with optimized sintering time, we demonstrate a simple processing route to tune crystallite size, defect chemistry, and non-Debye dielectric relaxation in ZnO nanoparticles. The joint structural and impedance analysis shows that K⁺ doping together with longer sintering strongly reduces grain boundary resistance while suppressing crystallite growth, providing a synergistic strategy to engineer ZnO-based dielectrics for low-loss and varistor-type electronic applications.