Charged particle dynamics and distribution functions in low pressure dual-frequency capacitively coupled plasmas operated at low frequencies and high voltages

In high aspect ratio (HAR) dielectric plasma etching, dual-frequency capacitively coupled radio-frequency plasmas operated at low pressures of 1 Pa or less are used. Such plasma sources are often driven by a voltage waveform that includes a low-frequency component in the range of hundreds of kHz with a voltage amplitude of 10 kV and more to generate highly energetic vertical ion bombardment at the wafer. In such discharges, the energetic positive ions can overcome the repelling potential created by positive wall charges inside the etch features, which allows high aspect ratios to be reached. In order to increase the plasma density a high-frequency driving component at several 10 MHz is typically applied simultaneously. Under such discharge conditions, the boundary surfaces are bombarded by extremely energetic particles, of which the consequences are poorly understood. We investigate the charged particle dynamics and distribution functions in this strongly non-local regime in argon discharges by particle-in-cell simulations. By including a complex implementation of plasma-surface interactions, electron induced secondary electron emission (δ-electrons) is found to have a strong effect on the ionization dynamics and the plasma density. Due to the high ion energies at the electrodes, very high yields of the ion induced secondary electron emission (γ-electrons) are found. However, unlike in classical capacitive plasmas, these γ-electrons do not cause significant ionization directly, since upon acceleration in the high voltage sheaths, these electrons are too energetic to ionize the neutral gas efficiently. These γ- and δ-electrons as well as electrons created in the plasma bulk and accelerated towards the electrodes to high energies by reversed electric fields during the local sheath collapse are found to induce the emission of a high number of δ-electrons, when they hit boundary surfaces. This regime is understood fundamentally based on the following approach: first, dual-frequency discharges with identical electrode materials are studied at different pressures and high-frequency driving voltages. Second, the effects of using electrodes made of different materials and characterized by different secondary electron emission coefficients are studied. The electron dynamics and charged particle distribution functions at boundary surfaces are determined including discharge asymmetries generated by using different materials at the powered and grounded electrodes. (paper)