Energy Transfer Processes Of Electrons In Radio Frequency Inductively Coupled Plasma

Inductively coupled plasma(ICP)sources are widely used in the microelectronics industry,such as plasma etching and thin film deposition in semiconductors,etc.,where the heating mechanism of the electrons has an important influence on the properties of the generated plasma,especially at low pressure,and collisionless electron heating has been a hot topic of research in recent years.For collisionless electron heating in inductively coupled plasmas,kinetic and single-particle models are widely used to describe the energy transfer between electrons and the radio frequency(RF)field.In an inductively coupled discharge,the electrons will experience a bouncing motion because of the formation of sheaths at the ends of the device.Self-consistent kinetic theroy has shown that collisionless electron heating is caused by the interaction of Landau and bounce resonances.Although both resonance mechanisms have been intensively studied,the effects on the energy transfer between electrons and electric fields are not discussed in detail until now when both resonances are present.In addition,although kinetic models can self-consistently describe collisionless electron heating in RF discharges,the mathematical treatment is more complicated and the dependence on the parameters is difficult to obtain analytical expressions.In order to obtain an analytical formulation of electron heating,the single-particle model is used to describe the physical picture of electron heating,and the results show that the heating mechanism of electron heating is caused by non-resonant interactions,which are different from the resonant interactions of the kinetics,so how to unify the physical picture in the two models in different parameter regions is the biggest challenge to understand the electron heating mechanism in the low temperature plasma discharges process.Therefore,the single-particle method can be used in certain parameter regions to obtain analytical expressions for electron heating.The single-particle approach describes the collisionless electron heating well within certain parameters,but resonant interactions are not represented in the singleparticle approach and it is still unclear how to unite the physical picture in two models.In the paper,we study the energy transfer between electrons and electric fields in inductively coupled plasmas,which includes the energy transfer between electrons with bouncing motion and electrostatic waves,and the energy transfer between electrons and a spatially exponentially decaying electric field and a series of plane wave superposition fields,respectively,in order to reveal the contribution of the non-resonant and resonant parts of energy transfer.First,this paper systematically investigates the synergy effect of bounce resonance and Landau damping on collisionless electron heating by combining analytical theoretical models and test particle simulation methods,and discusses the energy transfer process between the electron and the wave when both resonances are present and resonance overlap occurs.The results show that bounce resonance heating mainly occurs in the first few harmonics of the bounce frequency(nωb,n=1,2,3,…,ωb represents the bounce resonance frequency.).In the parameter regimes in which bounce resonance overlaps with Landau resonance,the higher harmonic bounce resonance may accelerate electrons at the velocity much lower than the wave phase velocity to Landau resonance region,enhancing Landau damping of the wave.Meanwhile,Landau resonance can increase the number of electrons in the lower harmonic bounce resonance region.Thus electrons can be efficiently heated.Second,the equivalence of the kinetic and single-particle approaches in certain parameter ranges has now been demonstrated,with the kinetic results showing that collisionless electron heating arises from resonance interactions,while the single-particle model results indicate that the heating is mainly caused by non-resonance interactions.In our thesis work,we first refine the theory of the Vahedi’s single-particle model[1]by considering the effect of different positions of the electron initial during the discharge process,and obtain an analytical expression for the electron absorbed power per unit area.In order to understand the similarities and difference between the physical picture of electron heating given by the Vahedi’s single-particle model and Shaing’s kinetic model[2]for a given discharge parameter,we carried our test particle simulations for two scenarios,the spatial exponentially decaying electric field and the plane-wave superposition electric field,respectively.The simulation results show that when the resonance interaction between the electrons and the electric field is weak,the imaginary part of the plasma surface impedance is small,and in this case the electric field can be approximated by an exponential function of the spatial decay,and the electron heating is mainly dominated by the non-resonance interaction,in which case the electron heating can be described by the Vahedi’s single-particle model.When the resonance interaction between the electron and the electric field is strong,the imaginary part of the plasma surface impedance becomes important,and then the resonance interaction dominates the electron heating,and the electric field can no longer be approximated by the exponential function of the spatial decay,and then the Vahedi’s single-particle model is no longer applicable.Finally,although the single-particle approach successfully explains the nonresonant interactions,it neglects the bouncing motion of the electron.Based on the single-particle model,the energy transfer between electrons and fields is derived analytically by considering the bouncing motion of electrons,and then test particle simulations are carried out to study the interaction between electrons and waves,showing in detail the evolution of the total kinetic energy of electrons.When the real part of the surface impedance is relatively small,both the exponential function electric field and the superposition field of a series of plane waves demonstrate well the bounce resonance interaction,and the bounce motion can enhance collisionless electron heating.When it is shown that the real part of the surface impedance cannot be neglected,the bounce resonance effect is also weaker due to the fact that the electron’s length of motion L in the plasma also becomes larger,when the electron is still interacting with the wave through the Landau damping,and this resonant heating is dominant.