Simulation Study Of Nonlinear Harmonics And Resonance Effects In Very High Frequency Capacitively Coupled Plasmas

Very high frequency capacitively coupled plasmas（VHF-CCPs）are widely used in dry etching and film deposition for silicon wafer and flat panel processing.In CCPs,higher driving frequencies produce higher ion fluxes with reduced ion bombarding energy at the wafer target,which is desirable for integrated circuit processing with smaller critical dimensions,reduced substrate damage,and increased etching and deposition rates.Moreover,large area sources are also required since the wafer size increases.As the increases of driving frequency and chamber size,the electromagnetic（EM）effects,such as the standing wave effect and skin effect,negatively affect the plasma spatial uniformity.Besides,the standing wave effect can also be enhanced by the nonlinear harmonics excited by sheath motion.Since the plasma spatial nonuniformity caused by these EM effects can significantly limit plasma processing,EM effects in CCPs have attracted much interest from researchers and semiconductor equipment manufacturers.Therefore,in this thesis,different numerical models are developed to study the physical mechanisms of EM effects and their influence on plasma spatial nonuniformity.The thesis is arranged as follows:In Chapter 1,the applications of low temperature plasmas are overviewed.Then,the CCPs and the physical mechanisms of EM effects in VHF-CCPs are introduced.Finally,a review of the research progresses,and the challenging issues for EM effects are given.In Chapter 2,the influence of axial plasma density profile on EM effects in large area geometrically symmetric VHF-CCPs is studied by solving the Maxwell equations in the frequency domain numerically.Simulation results show that the spatially uniform plasma density profile underestimates the standing wave effect and overestimates the skin effect.As the increase of driving frequency and the decrease of sheath width,the surface wavelength becomes shorter,giving rise to the enhanced standing wave effect,and the electron absorption power density exhibits center-high or even bimodal profiles.When the electron elastic collision frequency（gas pressure）increases,the radial damping of surface waves becomes prominent.Moreover,the skin depth decreases at higher plasma density,leading to a significant skin effect.In Chapter 3,the Maxwell equations solved in the frequency domain are coupled with a radially localized global model and an analytical sheath model to study the standing wave effect,stop band effect,and skin effect in large area geometrically symmetric VHF-CCPs.Simulation results indicate that as the driving frequency increases,the surface wavelength decreases,so the standing wave effect becomes pronounced.Therefore,the radial profiles of the electron density shift from uniform over center-high to multiple-node.When the driving frequency is close to or higher than the series resonance frequency,the surface waves show significant radial damping and cannot propagate to the center.Hence,the stop band effect dominates the discharge,and the electron density at the center becomes nearly zero.As the electron power increases,the skin depth decreases with the increase of electron density.Thus,the skin effect plays a dominant role,and the density peak shifts from the center to the radial edge.In Chapter 4,the nonlinear EM capacitive discharge model is developed to study the nonlinear harmonic excitations in geometrically asymmetric VHF-CCPs.In this model,a nonlinear transmission line（NTL）model is used to determine the spatiotemporal distribution of EM fields and the nonlinearly excited harmonics.The spatial profiles of the electron density and electron temperature are determined by a two-dimensional（2D）plasma fluid model.Moreover,a collisionless or collisional（ion）analytical sheath model is employed to give the nonlinear dependence of sheath voltage on sheath charge,as well as the stochastic and ohmic sheath heating.Simulation results show that at 20 m Torr,the higher harmonics excited by nonlinear sheath motion,which can be enhanced by the plasma series resonance effect,significantly increase the electron power deposited near the center and lead to a sharp electron density peak there.By comparing with the results obtained by the collisionless sheath model,the collisional sheath model gives a smaller sheath width,leading to the lower series and spatial resonance frequencies,as well as the lower source voltage.Therefore,lower harmonics with decreased magnitudes are excited,reducing the center-high profile of plasma density.Besides,as the pressure increases from 20 m Torr to 100 m Torr,the collisional damping of nonlinear harmonics becomes more pronounced,so the enhancement of electron power deposition near the center becomes negligible.Moreover,more power is deposited near the powered electrode edge due to decreased skin depth and weakened energy diffusion.As a result,the density peak shifts from the center to the powered electrode edge.In Chapter 5,the nonlinear EM capacitive discharge model is further generalized to study the antisymmetric and symmetric mode spatial resonances in geometrically asymmetric VHF-CCPs.In this generalized NTL model,the radial variation of plasma density is considered,and a variable-sized spacer between the powered and grounded electrode edges is included.Simulation results indicate that the first antisymmetric mode resonance frequency f_a1 is in the range between 80 MHz and 90 MHz,and the first symmetric mode resonance frequency f_s1is about 100 MHz.As the driving frequency reaches f_a1,the powered electrode sheath becomes smaller than the grounded electrode sheath.When the driving frequency reaches f_s1,the source voltage reaches a minimum value.Besides,the standing wave effect and the nonlinearly excited harmonics can be further enhanced by spatial or series resonances,leading to a sharp center peak of the electron density.Moreover,as the driving frequency increases to 120 MHz,which is higher than f_a1and f_s1,a second density peak appears in the chamber.