Upheaval of Negative\nDielectric Permittivity and Semiconductor\nto Metallic Transition in a Thermally Induced Sn-Doped β‑Ga<sub>2</sub>O<sub>3</sub> (−201) Single Crystal

Thermally induced dielectric and conductivity properties\nof an\nSn-doped β-Ga<sub>2</sub>O<sub>3</sub> (−201) single\ncrystal were investigated by frequency-domain impedance spectroscopy\nin the frequency window from 100 Hz to 1 MHz with temperatures between\n293 and 873 K. The (−201) plane-orientated single crystalline\nnature and the presence of an Sn dopant in β-Ga<sub>2</sub>O<sub>3</sub> were confirmed by X-ray diffraction (XRD) and X-ray photoelectron\n(XPS) spectroscopy. Two different trends of impedance spectra have\nbeen discussed by the modulation of relaxation times and semiconductor\nto metallic transition after ∼723 K due to activation of a\nsignificant number of Sn dopants and their movements with temperature.\nThe negative impedance values were encountered in the Nyquist plots\n(<i>Z</i>′ vs <i>Z</i>″) after 573\nK and constitute a reverse movement after 723 K with temperature.\nThe average normalized change (Δ<i>Z</i>′/Δ<i>f</i>)/<i>Z</i><sub>0</sub> of impedance exhibits\na broad downward relaxation plateau near 723 K, indicating a weak\nelectrical transition. The increases in the positive value of the\ndielectric constant (<i>ε</i><sub>r</sub>′)\nbelow a percolating threshold temperature 573 K is attributed to the\ninterfacial and dipolar polarizations, and the plasma oscillation\nof delocalized electrons governed by the Drude theory is responsible\nfor the negative dielectric constant above 573 K. The 3D projections\nof the real dielectric constant create a sharp downward sinkhole near\n723 K, indicating the existence of negative dielectric permittivity.\nThe electrical conductivity dramatically changes its trends after\n523 K and confirms a transition from hopping conduction (dielectric\nor semiconductor) following Jonscher’s power law to metallic\nconduction by Drude theory. Below the percolating threshold temperature,\na nonoverlapping small polaron tunneling conduction mechanism was\nunveiled with defect-induced activation energy of 0.21 eV. The Sn-doped\nβ-Ga<sub>2</sub>O<sub>3</sub> exhibits unique and tailored electromagnetic\nresponses with temperatures that can be associated with a variety\nof applications in electromagnetic wave manipulations, cloaking devices,\nantennas, sensors, medical imaging, seismic wave propagation, etc.