Hybrid simulation of the energy cost of O($^1$D) and O($^3$P) generation in a capacitive Ar/O$_2$ discharge driven by sawtooth-type voltage waveforms

Abstract

Low-pressure radio-frequency capacitively coupled plasmas operated in Ar/O$_2$ gas mixtures are widely adopted in critical semiconductor manufacturing processes. O($^3$P) and O($^1$D) are key highly reactive species for oxidation or as oxygen sources for deposited thin films. Optimizing external parameters to realize efficient generation of these species under limited energy deposition is essential for improving process yield.Based on a one-dimensional (1D) fluid/electron Monte Carlo (EMC) hybrid model, this study investigates the energy cost of O($^1$D) and O($^3$P) generation driven by sawtooth up-type voltage waveforms at a fixed peak-to-peak voltage, focusing on the effects of the harmonic number ($N$) and the O$_2$ ratio. The results show that O($^3$P) generation is consistently more efficient than that of O($^1$D). The generation energy cost decreases with increasing O$_2$ ratio, yet increases as $N$ increases. However, in the specific scenario of 10% O$_2$, an inflection point can be observed at $N = 2$. As $N$ increases from 1 to 2, the discharge mode shifts from the DA mode to the $\alpha$-DA hybrid mode, expanding the effective spatio-temporal range of the ionization rate and enhancing its peak, which increases electron density. Consequently, the generation rates are significantly enhanced, leading to a reduction in the generation energy cost.Moreover, as discussed above, monotonically increasing the harmonic number $N$ does not reduce the generation energy cost of O($^1$D) and O($^3$P) associated with medium-energy (8-20 eV) electrons. Only by selecting the appropriate $N$ to sustain the discharge in the hybrid $\alpha$-DA mode, thereby increasing the electron density and promoting the generation of these species, can the generation energy cost be reduced.