Ion-energy-distribution functions (IEDFs) are numerically investigated in capacitively coupled (cc) radio frequency (rf) ${\mathrm{A}\mathrm{r}/\mathrm{C}\mathrm{F}}_4/{\mathrm{N}}_2$ discharges by a one-dimensional particle-in-cell/Monte Carlo model. The simulation considers electron-neutral collisions, various kinds of collisions of ions $({\mathrm{Ar}}^{+},$ ${\mathrm{CF}}_3^{+},$ ${\mathrm{N}}_2^{+},$ ${\mathrm{F}}^{-},$ and ${\mathrm{CF}}_3^{-})$ with neutral, positive-negative ion, and electron-ion recombination. The influence of pressure, applied voltage amplitude, and applied frequency on the ${\mathrm{Ar}}^{+},$ ${\mathrm{CF}}_3^{+},$ and ${\mathrm{N}}_2^{+}$ IEDFs is presented. The dependence on the frequency regime is investigated by simulations of the ${\mathrm{A}\mathrm{r}/\mathrm{C}\mathrm{F}}_4/{\mathrm{N}}_2$ mixture in single (13.56 MHz) and dual frequency $(2+27\mathrm{}\mathrm{MHz}$ or $1+27\mathrm{MHz})$ cc reactors. A comparison of the simulation results with analytical calculations in a collisionless rf sheath is discussed. The results show that the IEDFs shift toward the low energies with increasing pressure or decreasing applied voltage amplitude. The ${\mathrm{Ar}}^{+}$ and ${\mathrm{N}}_2^{+}$ IEDFs exhibit secondary maxima due to the charge transfer collisions. The ${\mathrm{CF}}_3^{+}$ IEDF has a peak at high energies in consistency with the average sheath potential drop. The IEDFs in the dual frequency regime are broad and bimodal.

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