Effective frequency

Abstract: A homogeneous plasma model for dual radio-frequency (rf) discharges driven by two sinusoidal current sources has been analyzed. Under the assumptions of time-independent and collisionless ion motion and inertialess electrons, the analytic expressions for discharge parameters are obtained as a function of the effective parameters such as effective frequency, effective current, and effective voltage. Effective parameters are determined by the ratio of two currents or voltages. Two rf sources are generally coupled to each other through the plasma medium. It is also shown that the reduction of the bulk plasma length due to the sheath size has to be considered for calculating the discharge parameters since the sheath length is not always negligible compared to the bulk plasma length. Furthermore, the dependence of discharge parameters on the low frequency is presented.

Abstract: One-dimensional particle-in-cell Monte Carlo collision (PIC-MCC) simulations of low-pressure (10?mTorr) argon plasmas sustained by a triple-frequency (1, 30 and 120?MHz) source in symmetrical current-driven and voltage-driven capacitively coupled plasma reactors are carried out. We concluded that the effective current, the effective voltage and the effective frequency are helpful in explaining the physics of triple-frequency capacitively coupled plasma sources (CCPs) alike single-frequency CCPs. The rf discharge parameters such as the ion energy distribution function (IEDF), the sheath length, the plasma potential and the powers dissipated by electrons and ions can be expressed as the effective frequency and the effective current density (or effective voltage). The analytical model of the IEDF for triple-frequency CCPs in the high-frequency regime is developed. The analytical calculations of the IEDF in the high-frequency regime through the effective frequency visualized in this paper are compared with the simulation results of the IEDF calculated from the 1D PIC-MCC model. The ion energy width and the average ion energy of the IEDF are controlled by the effective frequency, which is expressed as a function of the current density (or voltage) and frequency ratios of the triple-frequency source. The evolution of the effective frequency with the current density or voltage ratio of three frequency sources is different depending on the mode of operating source, which is either voltage or current. The effective frequency in voltage-driven CCPs is 2?10 times higher than that of current-driven CCPs at the same ratio of current density and voltage. As a result, the current-driven CCPs is more desirable than the voltage-driven CCPs from the aspect of independent control of ion flux and ion bombardment energy because the ion energy width increases with decreasing effective frequency.