Secondary electron effect on sustaining capacitively coupled discharges: A hybrid modeling investigation of the ionization rate

A one-dimensional fluid/Monte Carlo hybrid model was used to quantitatively study the secondary electron effect on sustaining the discharge by examining the ionization induced by bulk electrons and secondary electrons under different external discharge parameters. The results indicate that as the voltage increases, secondary electrons gain more energy from the stronger electric field. Therefore, the ionization region induced by secondary electrons expands and the ionization rate becomes comparable to and even exceeds that of bulk electrons. As the pressure increases, secondary electrons collide with neutrals sufficiently, thus their contribution to the plasma generation becomes pronounced and eventually they dominate the discharge. Besides, the distribution of the secondary electron ionization rate varies from flat to saddle-shape, due to the energy loss at the discharge center at higher pressures. Finally, when the discharge gap expands, the electron density calculated in the case without secondary electrons increases linearly, whereas the value first increases and then decreases in the model with secondary electrons taken into account. The results obtained in this work are important for improving the high aspect ratio etching process by secondary electrons.