Theoretical And Numerical Simulation Of Electromagnetic Effects And Related Issues In Capacitively Coupled Plasmas

Capacitively coupled plasma(CCP)sources are widely used in the semiconductor industry for etching of materials and deposition of thin films.Higher frequency driven CCPs can provide higher plasma densities and lower ion energy bombing the electrodes.Therefore,very high frequency(VHF)CCPs have attracted increasing academic and industrial interests in recent years.However,there exist great challenges those have to be overcome before VHF discharges could be used to optimize the plasma technique.For instance,at higher driving frequency,electromagnetic effects(EM),i.e.,the standing wave effects and the skin effects,will negatively affect the plasma uniformity especially when the electromagnetic wave length is comparable to the size of the chamber,and these has been observed experimentally.Furthermore,recent experimental measurements also show nonlinearly excited higher harmonics,which induce an enhanced central-high profile of plasma density,and this also indicates the negative influence of EM effects on plasma processing of materials.In addition,for pulsed CCPs,the phase shift between the pulse signal and rf signal has an important influence on the plasma characteristics over the pulse period,and this consequenctly affects the plasma processing.Thus,the pulsed CCP related issues have also been under hot discussions recently.In Chapter 1,the author briefly introduces several commonly used plasma sources and corresponding applications in the semiconductor industry.Subsequently,the author emphatically focus on the research progresses of EM effects and the challenging issues in very high frequency CCPs.In Chapter 2,a Child law sheath model driven by a voltage source is derived and coupled to an EM transmission line model for a single sheath.Furthermore,the interaction between nonlinear series resonance dynamics and standing wave effects is investigated.The results show that at the discharge center,the nonlinearly excited higher harmonics consist of series resonance oscillations and the first resonance surface wave;however,at the edge,the excited higher harmonics only include the series resonance oscillation induced by the sheath collapse.After the nonlinear series resonance is excitated,the corresponding current density amplitude can be calculated by an analytical expression.Finally,by introducing an adiabatic quantity,the dynamics of the current density and charge density are described by the Hamiltonian theory.In Chapter 3,based on the EM transmission line model in Chapter 2,an improved EM transmission line model is developed for a powered-electrode/plasma/grounded-electrode system,incorporating both symmetric and anti-symmetric surface wave modes,as well as the nonlinear series resonance excitation.At low driving frequency(30 MHz),the nonlinear series resonance excitation is captured,and the sheath at every point over the driven electrode oscillate in phase,implying that the results obtained by the EM model are similar to those in the electrostatic case.At higher driving frequency(60 MHz),the nonlinear higher harmonics couple with standing waves,and this gives rise to a central-high profile for the electron power deposition.In addition,it is found that the anti-symmetric mode surface wave plays a more important role when the frequency is higher.In Chapter 4,the symmetric and anti-symmetric EM wave dispersion relationship is solved,and the corresponding results justify the use of two-dimensional electrostatic Particle-in-Cell/Monte Carlo(PIC/MCC)simulation to capture both the symmetric and anti-symmetric mode wave propagation in the frequency range of interest.The simulations indicate the existence of standing waves and wave-induced hysteresis of the plasma density,i.e.,two different steady states(low and high plasma density)are obtained for the same driving rf voltage amplitude,when the voltage increases from a low voltage or decreases from a high value.To understand the propagation of symmetric and anti-symmetric waves under two different states,the PIC/MCC results are compared with those calculated by the nonlinear EM transmission line model in Chapter 3,and a good agreement is achieved,showing central-low and central-high profile of the anti-symmetric mode voltage at low density and high density.In addition,a lumped circuit model of two wave modes is developed to analyse the hysteresis phenomenon,and the results show a similar trend of the hysteresis with the pressure and driving frequency.In Chapter 5,an one-dimensional electrostatic PIC/MCC model is employed to investigate the characteristics of pulsed dual-frequency CCPs by examining the plasma density,ionization rate and current etc.The results demonstrate that higher pulse frequency leads to higher plasma density with fixed phase shift at the high frequency modulation.This is because when the pulse frequency is lower,more charged particles are lost during the longer afterglow period,due to the ambipolar diffusion and the absence of the electron heating.By adjusting the phase shift between the pulse signal and the high frequency signal,the plasma density shows a peak value ad ?=?/2,where the excited higher harmonics are the strongest and enhance electron heating.When the low frequency signal is modulated,the plasma density shows a similar trend as that in the case of high frequency signal modulation.In addition,different ion energy distribution(IED)functions are obtained at various phase shifts,and the number of high-energy ions is smaller at ???/2.Finally,in Chapter 6.a hybrid model,i.e.,global model bidirectional coupled with ion fluid sheath model is developed to study the effects of the capacitive sheath on inductively coupled plasmas.Comparing with the traditional fluid simulations,the hybrid model is more time-saving and can reveal plasma density and IED at various external parameters,such as pressure,coil power,bias voltage amplitude,as well as chamber size.To validate the hybrid model,the calculated plasma densities and IEDs are compared with those measured in experiments,and good agreements are obtained.Furthermore,the hybrid model for argon discharges is extended to weak electronegative O2/Ar discharges,and the calculated IEDs also agree well with the experimental measurements in previous references.