The Detailed Study Of Fluid Model For Radio-Frequency Capacitively Coupled Plasma

Radio-frequency capacitively coupled plasmas sources,which can produce high density plasmas and have simple structure,have been widely used in low-temperature plasma discharge technology.Because of its low cost and high efficiency,numerical simulation is often used to study the characteristics of plasma.The common numerical simulation methods mainly include PIC-MC(Particle in cell-Monte Carlo)model,fluid model and hybrid model.And the fluid model has the advantages of high computational efficiency,fast calculation speed and accurate calculation results,so in this paper,we focus on the fluid model under the capacitive coupled plasma discharge.Mainly(1)for the two general forms of the ion equation in the fluid model,namely the ion momentum conservation equation and the ion drift-diffusion approximation;(2)for the two different ionic transport parameters(depending on the elastic collision frequency),write the corresponding codes,debug different pressures,observe and analyze the simulation results,and study whether there are differences between the two different conditions,and also analyze the internal mechanism,to provide better application of the fluid model for the low-pressure RF plasma source with theoretical reference.The discharge gas is argon in this paper.First,in Chapter 1,we briefly introduce the concept and characteristics of low temperature plasma and CCP,and the recent advances of fluid models.In Chapter 2,the equations in the fluid model are given in detail,and the numerical algorithm and the boundary conditions of the model are introduced.In addition,we thoroughly derive the origin of the ion drift-diffusion approximation and lead out the concept of effective electric field.And then the chamber structure and the discharge reaction and its reaction coefficient to be considered in this paper are listed.In Chapter 3,we mainly study the influence of space step on the discharge simulation results and the significance of the existence of effective electric field.First,we select different space steps and carry out simulation studies under different pressures.The results show that the lower the space step,the higher the plasma density and the more obvious the density radial non-uniformity at low pressures.Because the grids are encrypted,the discharge gets more local and in order to ensure that the average body plasma densities are constant,the peak value of the densities increase.At high pressures,the phenomenon is similar to that at low pressures,but when the space step is large,the plasma densities drop sharply.This is because the real physical sheath becomes thin with pressure,and if the space step is too large,the sheath region cannot be accurately distinguished,so non-physical problems occur.So at high pressures,we should encrypt the grids,that is,select a smaller space step.In Chapter 4,firstly,we focus on the significance of the existence of the effective electric field in the ion drift-diffusion approximation.The ion drift-diffusion approximations with the effective electric field and with the non-effective electric field are compared at different pressures and the distribution of the plasma density is simulated.It is found that the plasma densities of ion drift-diffusion approximation with the effective field are slightly higher than the non-effective field,but the difference are quite small,which the relative error value of density is only 1.01%.Because of the large phase shift between the current and the corresponding electric field in the circumstance of effective electric field,the power deposition due to ohmic heating is increased.And at high pressures,the relative error values of plasma density obtained by the two are getting smaller and smaller,which is 0.033% at 1000 mTorr,so it is almost identical.This is because when the pressure increases,the momentum transfer frequency of ions and neutral particles becomes large,resulting in the e-exponential term in the analytical effective field(The term containing the difference between the two effective electric fields)decays rapidly to infinity,where the effective field is approximately equal to the electrostatic field.Analytical effective field is a model obtained by mathematical physics method,which helps us to verify that the existence of effective electric field in the ion drift diffusion approximation is meaningless.So in the subsequent use of ion drift-diffusion approximation,we will directly use the electrostatic field,instead of an effective electric field.In addition,the full solution formula of the effective electric field is given in our derivation process.Compared with the effective electric field in the conventional sense,it has more convection term and inertia term,which is equivalent to the full momentum conservation equation(derived from it).And then we compare the ion momentum conservation equation and the ion drift-diffusion approximation under different pressures in Chapter 4.The results show that the plasma densities obtained by the ion momentum conservation equation are higher than the ion drift-diffusion approximation at low pressures.Because the convection term affects the phase difference between the effective field and the electron flow,resulting in an increase in deposition power,so the plasma densities calculated by the momentum conservation equation are higher.And as the pressure increases,the differences between the two equations are getting smaller and smaller,which is consistent with our conventional understanding.And at high pressures,the inversion occurs,which is the plasma densities obtained by the drift-diffusion approximation are significantly higher than the momentum conservation equation in the entire discharge regions,and the differences increase with the pressure.This is because the inertia term,as a deceleration term of Newton's law,greatly reduces the effective field amplitude as the pressure increases,so that the plasma densities of full momentum conservation equation is much lower than the drift-diffusion approximation.And then,about the study of the momentum transfer frequency of ions and neutral particles in the ion momentum conservation equation,we find that if the plasma collision frequency associated with the ionic orientation velocity is used,the simulated plasma densities increase with the pressure,which is determined by the mechanism that the collision damping term(monotonic change with the orientation velocity)becomes weak,so that the transport from the ionization zone to the body zone in the edge of the sheath gets faster;correspondingly,if the mobility determined by the polarizability is used,the weakening of the collision damping term is relatively inconspicuous with the increase of the pressure,so that the transport is relatively slow,so the growth of plasma densities slow down with the pressure.