  Exploration of new dielectrics with large capacitive coupling is an essential
topic in modern electronics when conventional dielectrics suffer from the
leakage issue near breakdown limit. To address this looming challenge, we
demonstrate that rare-earth-metal fluorides with extremely-low ion migration
barriers can generally exhibit an excellent capacitive coupling over 20 $\mu$F
cm$^{-2}$ (with an equivalent oxide thickness of ~0.15 nm and a large effective
dielectric constant near 30) and great compatibility with scalable device
manufacturing processes. Such static dielectric capability of superionic
fluorides is exemplified by MoS$_2$ transistors exhibiting high on/off current
ratios over 10$^8$, ultralow subthreshold swing of 65 mV dec$^{-1}$, and
ultralow leakage current density of ~10$^{-6}$ A cm$^{-2}$. Therefore, the
fluoride-gated logic inverters can achieve significantly higher static voltage
gain values, surpassing ~167, compared to conventional dielectric. Furthermore,
the application of fluoride gating enables the demonstration of NAND, NOR, AND,
and OR logic circuits with low static energy consumption. Notably, the
superconductor-to-insulator transition at the clean-limit
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ can also be realized through fluoride
gating. Our findings highlight fluoride dielectrics as a pioneering platform
for advanced electronics applications and for tailoring emergent electronic
states in condensed matters.
