Effect of low frequency voltage waveform on plasma uniformity in a dual-frequency capacitively coupled plasma

In a dual-frequency capacitively coupled plasma (CCP) with disparate frequencies, the low frequency (LF) voltage usually has a strong influence on the ion energy distribution function (IEDF) but contributes less to plasma generation. It is well-known that rectangular LF voltage waveform with a small positive period yields a narrow, nearly monoenergetic IEDF. This paper focuses on the effect of the LF voltage waveform on plasma uniformity in a low-pressure dual-frequency (40 + 0.8 MHz) CCP. A two-dimensional particle-in-cell model is used for this investigation, and the effect of LF voltage amplitude on plasma uniformity is investigated for sinusoidal and rectangular voltage waveforms. When the LF voltage is low, the peak in plasma density is at the chamber center due to ample diffusion at the low pressure considered (20 mTorr) and higher losses to the chamber walls. As the LF voltage is increased, the sheath gets thicker at the powered electrode and charged species densities decrease for a constant 40 MHz voltage. The plasma profile, however, evolves differently for the two LF voltage waveforms. With sinusoidal LF voltage, the plasma spreads out between the electrodes. On the other hand, with rectangular LF voltage waveform, the plasma splits into two regions: a density peak at the chamber center and another peak near the electrode edge. This double-peaked density profile with a rectangular wave can be attributed to the location and timing of plasma generation. 40 MHz produces plasma most efficiently when the LF rectangular wave is positive and the sheath at the powered electrode is thin (frequency coupling). This plasma is produced uniformly between the electrodes, but only for a short period. When the LF voltage becomes negative, the sheath expands at the powered electrode and the plasma is produced near the electrode edge where the sheath is thinner and the electric field is stronger.