Revisiting Jonscher's universal power law: a modified formalism with Cole-Cole-type non-Debye dielectric relaxation...

The present work expounds the high-temperature dielectric response and conduction mechanism in ultrawide bandgap α-quartz-type GeO₂ through a combined experimental and density functional theory (DFT) study. The Rietveld refinement of X-ray diffraction (XRD) analysis revealed the single-phase α-quartz-type GeO₂ with high crystallinity, confirming phase purity and structural integrity. The distinctive lattice dynamics and bonding characteristics of the tetragonal α-quartz-type phase structure were further confirmed by its signature A_1g and E_g modes of Raman spectroscopy. The development of a dense microstructure with uniform grain growth in the sub-micrometer range and elemental composition (Ge and O) was supported by field-emission scanning electron microscopy (FESEM) and energy-dispersive X-ray spectroscopy (EDS). The UV-vis spectroscopic optical measurements revealed a broad experimental bandgap of ∼5.8 eV, in line with the electronic structure and density of states determined by DFT. The metal-oxide (M-O, O-M-O) and hydroxyl stretching (M-OH) vibrational modes of GeO₂ are further reinforced by Fourier transform infrared (FTIR) spectroscopy. The dielectric permittivity (ε _r) increased significantly from 7.2 to 33.5 between 573 K and 773 K, an effect attributed to defect-assisted processes and thermally activated space-charge polarization. The obtained Cole-Cole parameter (α) lies between 0.2 and 0.8, which recommends the non-Debye type dielectric relaxation process. The frequency-dependent ac conductivity followed a modified Jonscher's power law, , and the variation of frequency exponent (n) with temperature indicates correlated barrier hopping conduction between localized states. The dc activation energy (E _dc) was estimated to be ∼0.98 eV using the Arrhenius equation. The impedance and complementary modulus spectroscopy reveal non-Debye-type dielectric relaxation, negative temperature coefficient of resistance (NTCR), and activation energy (E _a) for grain ∼0.48 eV and grain boundary conduction ∼0.81 eV, respectively. The density functional theory (DFT) calculations supported the experimentally reported polaronic transport behavior by providing a microscopic understanding of the density of states (DOS), theoretical dielectric constants, charge localization, and a theoretical band gap of ∼4.59 eV. This study provides important insights into the dielectric response, conduction kinetics, and electrical transport of tetragonal α-quartz-type GeO₂, highlighting it as a promising candidate for next-generation high-temperature power electronics, dielectric devices, and harsh-environment functional systems.