A Series of Ultra-low\nPermittivity ALaP<sub>4</sub>O<sub>12</sub> (A = Li, Na, K) Metaphosphate\nMicrowave Dielectric\nCeramics for Ultra-wideband Dielectric Resonant Antenna Application

The employment of ultra-low permittivity materials in\nthe configuration\nof antennas has been demonstrated to augment the antenna bandwidth\nand diminish signal delay effectively. This study presents three ultra-low\npermittivity metaphosphate microwave dielectric ceramics (MWDCs).\nThe ALaP<sub>4</sub>O<sub>12</sub> (A = Li, Na, K) metaphosphate ceramics,\nwhich all belong to the monoclinic crystal system, exhibit extremely\nlow permittivity (ε<sub>r</sub> ≈ 5) and excellent quality\nfactor (<i>Q</i>·<i>f</i> > 10,000 GHz)\nat\na low sintering temperature (<i>T</i> < 950 °C).\nTerahertz time-domain spectroscopy indicates that the ε<sub>r</sub> of ALaP<sub>4</sub>O<sub>12</sub> at terahertz frequencies\nis comparable to that observed in the microwave band and its value\nremains stable over an extensive frequency range. Furthermore, the\nrelationship between the crystal structure and the dielectric properties\nof ALaP<sub>4</sub>O<sub>12</sub> has been analyzed through the lens\nof chemical bond theory. The highest <i>Q</i>·<i>f</i> value observed for LiLaP<sub>4</sub>O<sub>12</sub> can\nbe attributed to the high chemical bond strength and stability of\nits crystal structure. The lowest ionic polarizability per unit volume\nis exhibited by NaLaP<sub>4</sub>O<sub>12</sub>, which results in\nthe lowest pore-corrected permittivity. The thermal expansion of the\nchemical bonds within KLaP<sub>4</sub>O<sub>12</sub> is considerable,\nresulting in the highest coefficient of thermal expansion. Finally,\nthe performance of a LiLaP<sub>4</sub>O<sub>12</sub>-based dielectric\nresonator antenna (DRA) excited by slot-coupled microstrip lines was\ndesigned and optimized by using different ceramic radius-to-height\n(RH) ratios. It was found that when the RH ratio of DRA reached 1.85,\nboth the fundamental mode (HEM<sub>11δ</sub>) and the higher-order\nmode (HEM<sub>12δ</sub>) of DRA were simultaneously excited.\nThe two modes overlap significantly, resulting in an ultra-wideband\n(UWB) of 46.8% (bandwidth = 7.93 GHz). Concurrently, the maximum radiation\nefficiency and gain of the DRA, obtained from the simulation, are\n97.9% and 7.92 dBi, respectively. The findings of this study may inform\nthe investigation of ultra-low permittivity phosphorus-based MWDCs\nand UWB DRAs.