New achievement of the global sheath-bulk model for the collisionless radio-frequency using in scale industries

Plasma processing is extensively utilized in enormous industries products like semiconductor devices, textile fabrics, modifying polymers, and seed treatments. One of the most significant enhancements to this technology is the low pressure of capacitively coupled plasma (CCPs). Contrary to other plasma processes like atmospheric pressure plasma jet, low-pressure plasma under vacuum is the best choice for scale industrial applications, including etching, semiconductor IC fabrication, and seed processing for agricultural use. This is due to its full soft control and complete ionization chamber. It is quite difficult to analyze the dynamics of the plasma sheath theory. Despite being among the most relevant models, the step approximation model does not fully account for all nonlinear dynamics, particularly high harmonic effects, the particle density singularity between the sheath and bulk regions, and the absence of an ambipolar field in the bulk zone. We provide a significant solution to this issue in this study. The numerical fluid model for collisionless self-consistency is solved. As a result, the sheath charge distribution V(Q), which is considered as the main factor of control all nonlinear dynamics of the sheath, is estimated. Strong agreement between experimental data from the Ziegler et al. [7] study and our cubic fitting formula for the V(Q) distribution. Additionally, by compared the results of step approximation with the non step model, theoretical advancements like handling the particle density singularity and the merging of the sheath-bulk zone are further illustrated. Moreover, the most simple but effective solution at a minimal computing cost, the global model, is solved. By applying accurate sheath charge distribution, which controls all nonlinear dynamics, the global model's accuracy is established. As a result, more nonlinear dynamics are achieved, including distributions of currents, densities, charges, and power. Finally, excellent calculations of average power and sheath distance in case of collisionless region are calculated. Our study can find a more accurate physical and engineering approach which may help in industry applications.