Analytical Determination of Collisionless Sheath Properties for Triple Frequency Capacitively Coupled Plasma

A triple frequency capacitively coupled plasma(TF-CCP) has been considered to investigate the behavior of the sheath parameters.A self-consistent time-independent collisionless model has been developed.The sheath width and potential are calculated using the present model and compared with those calculated using a single-frequency(SF),a dual-frequency(DF)and a triple-frequency(TF) model for time independent collisionless cases.The sheath motion and sheath potential are found to be larger compared with those of SF and DF CCPs for an inhomogeneous sheath,and that of TF CCP for a homogeneous sheath.The effects of the source parameters,i.e.,current magnitudes,frequencies and phase difference,on the sheath parameters are investigated.The sheath parameters show higher values at higher source currents whereas they decrease with the increase of excitation frequencies.It has also been found that,by the proper choice of source frequencies and phase differences,it is possible to adjust the energy of ions when they hit the electrode.     

Effects of Fast-Ion Injection on a Magnetized Sheath near a Floating Wall

A fully kinetic particle-in-cell/Monte Carlo model is employed to self-consistently study the effects of fast-ion injection on sheath potential and electric field profile in collisional magnetized plasma with a floating absorbing wall. The influences of the fast-ion injection velocity and density, the magnetic field and angle θ0 formed by the magnetic field and the x-axis on the sheath potential and electric field are discussed in detail. Numerical results show that increasing fast-ion injection density or decreasing injection velocity can enhance the potential drop and electric field in the sheath. Also, increasing the magnetic field strength can weaken the loss of charged particles to the wall and thus decrease the potential and electric field in the sheath. The time evolution of ion flux and velocity distribution on the wall is found to be significantly affected by the magnetic field.     

Frequency Matching Effects on Characteristics of Bulk Plasmas and Sheaths for Dual-Frequency Capacitively Coupled Argon Discharges： One-Dimensional Fluid Simulation

A one-dimensional fluid model is proposed to simulate the dual-frequency capacitively coupled plasma for Ar discharges. The influences of the low frequency on the plasma density, electron temperature, sheath voltage drop, and ion energy distribution at the powered electrode are investigated. The decoupling effect of the two radio-frequency sources on the plasma parameters, especially in the sheath region, is discussed in detail.     

Effect of Low-Frequency Power on Etching Characteristics of 6H-SiC in C4Fs/Ar Dual-Frequency Capacitively Coupled Plasma

Dry etching of 6H silicon carbide （6H-SiC） wafers in a C4Fs/Ar dual-frequency capacitively coupled plasma （DF-CCP） was investigated. Atomic force microscopy （AFM） and X-ray photoelectron spectroscopy （XPS） were used to measure the SiC surface structure and compositions, respectively. Optical emission spectroscopy （OES） was used to measure the relative concentration of F radicals in the plasma. It was found that the roughness of the etched SiC surface and the etching rate are directly related to the power of low-frequency （LF） source. At lower LF power, a smaller surface roughness and a lower etching rate are obtained due to weak bombardment of low energy ions on the SiC wafers. At higher LF power the etching rate can be efficiently increased, but the surface roughness increases too. Compared with other plasma dry etching methods, the DF-CCP can effectively inhibit CχFγ films＇ deposition, and reduce surface residues.     

Effect of Low-Frequency Power on Etching Characteristics of 6H-SiC in C_4F_8/Ar Dual-Frequency Capacitively Coupled Plasma

Dry etching of 6H silicon carbide(6H-SiC)wafers in a C_4Fs/Ar dual-frequency capacitively coupled plasma(DF-CCP)was investigated.Atomic force microscopy(AFM)and X-ray photoelectron spectroscopy(XPS)were used to measure the SiC surface structure and compositions,respectively.Optical emission spectroscopy(OES)was used to measure the relative concentration of F radicals in the plasma.It was found that the roughness of the etched SiC surface and the etching rate are directly related to the power of low-frequency(LF)source.At lower LF power,a smaller surface roughness and a lower etching rate are obtained due to weak bombardment of low energy ions on the SiC wafers.At higher LF power the etching rate can be efficiently increased,but the surface roughness increases too.Compared with other plasma dry etching methods,the DF-CCP can effectively inhibit C_xF_y films'deposition,and reduce surface residues.     

Characteristics of Collision, Capacitive Radio Frequency Sheath

A simple collisional radio frequency (rf) sheath fluid model, which is not restricted by the ratio of rf frequency to ion plasma frequency (β = ωrf/ωpi), was established and solved numerically. In the ion balance equation, the effect of the collision on the ion and the ion velocity is assumed to be a direct ratio to ion velocity. The ion energy distributions (IEDs) calculated in the model in comparison with the experimental data [M. A. Sobolewski, J. K. Olthoff, and Y. C. Wang, J. Appl. Phys. 85, 3966 (1999)], proved the validity of the model. And the effect of the collision on the sheath characteristic was obtained and discussed. This paper demonstrates that the collision frequency is another crucial parameter as well as the ratio β to determine the rf sheath characteristics and the shape of IEDs.     

Investigation of Capacitively Coupled Argon Plasma Driven by Dual-Frequency with Different Frequency Configurations

Low pressure argon dual-frequency （DF） capacitively coupled plasma （CCP） is generated by using different frequency configurations, such as 13.56/2, 27/2, 41/2, ...     

Study of Characteristics of the Radio-Frequency Sheath over a Substrate with a Circular Trench

Since processed substrates usually exhibit nonplanar surface structures in Micro-Electro-Mechanical-Systems (MEMS) etching, a two-dimensional (2D) fluid model is developed to simulate the characteristics of the sheath near a conductive substrate with a circular trench, which is placed in an argon discharge powered by a radio-frequency (rf) current source. The model consists of 2D time-dependent fluid equations, the Poisson equation, and a current balance equation that can self-consistently determine the instantaneous voltage on the substrate placed on a powered electrode. The effects of both the aspect ratio (depth/width) and the structure of the trench on the characteristics of the sheath are simulated. The time-averaged potential and electric field in the sheath are calculated and compared for different discharge parameters. The results show that the radial sheath profile is not uniform and always tends to adapt to the contour of the substrate, which is believed to be the moulding effect. Affected by the structure of the substrate surface, the potential and electric field near the inner and outer sidewalls of the trench exhibit obvious non-uniformity, which will inevitably lead to non-uniformity in etching, such as notching. Furthermore, with a fixed amplitude of the rf current source, the potential drops and the sheath thickness decrease with an increase in aspect ratio.     

Effects of Ion Temperature on Collisionless and Collisional RF Sheath

A numerical two-fluid simulation of the non-ionized radio frequency （rf） sheath model, has been carried out. This model is ＂global＂ and thus applicable to the sheath, pre-sheath and plasma regions, In the model all variables in the ion force balance equation, including the electrical force, ion pressure and neutral particle friction, are considered. The model is solved through a finite difference scheme and sheath characteristics are obtained. The effects of the ion temperature on both the collisionless and collisional sheath characteristics are discussed. Then it is concluded that 1） the model is in a good agreement with Bohm Theorem; 2） the ion temperature has significant effects on the rf sheath characteristics. The effects are far more significant on a collisional rf sheath than on a collisionless sheath.     

Determination of Plasma Parameters in a Dual-Frequency Capacitively Coupled CF4 Plasma Using Optical Emission Spectroscopy

Optical emission spectroscopy measurements of dual-frequency capacitively coupled CF4 plasmas were carried out.The gas temperature(Tg) was acquired by fitting the optical emission spectra of a CF B X system in 201~206 nm.The atomic fluorine concentration and the electron temperature(Te) were obtained by trace rare gas optical emission spectroscopy and a modified Boltzmann plot technique,respectively.It was found that the gas temperature was about 620±30 K at 50 mTorr and the atomic fluorine concentration increased while the electron temperature decreased with increasing gas pressure and power of high frequency(60 MHz).With increasing low frequency(2 MHz) power,the electron temperature also increased,but the atomic fluorine concentration was insensitive to this change.The generation and disappearance mechanisms of F atoms are discussed.     

Simulation of Dual-Electrode Capacitively Coupled Plasma Discharges

Dual-electrode capacitively coupled plasma discharges are investigated here to lower the non-uniformity of plasma density. The dual-electrode structure proposed by Jung splits the electrode region and increases the flexibility of fine tuning non-uniformity. Different RF voltages,frequencies, phase-shifts and electrode areas are simulated and the influences are discussed. RF voltage and electrode area have a non-monotonic effect on non-uniformity, while frequency has a monotonic effect. Phase-shift has a cyclical influence on non-uniformity. A special combination of 224 V voltage and 11% area ratio with 10 MHz lowers the non-uniformity of the original set(200 V voltage and 0% area ratio with 10 MHz) by 46.5%. The position of the plasma density peak at the probe line has been tracked and properly tuning the phase-shift can obtain the same trace as tuning frequency or voltage.     

Dynamics of Dust in a Plasma Sheath with Magnetic Field

Dynamics of dust in a plasma sheath with a magnetic field was investigated using a single particle model. The result shows that the radius, initial position, initial velocity of the dust particles and the magnetic field do effect their movement and equilibrium position in the plasma sheath. Generally, the dust particles with the same size, whatever original velocity and position they have, will locate at the same position in the end under the net actions of electrostatic, gravitational, neutral collisional, and Lorentz forces. But the dust particles will not locate in the plasma sheath if their radius is beyond a certain value.     

Characteristics of a Collisional Sheath Biased by a Dual Frequency Source

A hybrid model is used to simulate the characteristics of a collisional sheath in a capacitively coupled plasma （CCP） driven by a dual frequency source includin...     

离子初始速度对等离子体鞘层厚度的影响

本文从理论上研究了离子初始速度对等离子体鞘层厚度的影响,建立了理论计算公式和数值模拟方法,考察了离子初始速度对鞘层厚度的影响因子。在离子初始能量为3.2 eV情况下,用粒子模拟程序进行了数值模拟,模拟与理论计算得到的空间电场分布十分接近。     

Experimental investigation of the electromagnetic effect and improvement of the plasma radial uniformity in a large-area,very-high frequency capacitive argon discharge

We performed an experimental investigation on the electromagnetic effect and the plasma radial uniformity in a larger-area, cylindrical capacitively coupled plasma reactor. By utilizing a floating hairpin probe, dependences of the plasma radial density on the driving frequency and the radio-frequency power over a wide pressure range of 5–40 Pa were presented. At a relatively low frequency(LF, e.g. 27 MHz), an evident peak generally appears near the electrode edge for all pressures investigated here due to the edge field effect, while at a very high frequency(VHF, e.g.60 or 100 MHz), the plasma density shows a sharp peak at the discharge center at lower pressures, indicating a strong standing wave effect. As the RF power increases, the center-peak structure of plasma density becomes more evident. With increasing the pressure, the standing wave effect is gradually overwhelmed by the ‘stop band' effect, resulting in a transition in the plasma density profile from a central peak to an edge peak. To improve the plasma radial uniformity, a LF source is introduced into the VHF plasma by balancing the standing wave effect with the edge effect. A much better plasma uniformity can be obtained if one chooses appropriate LF powers, pressures and other corresponding discharge parameters.     

Effect of Addition of Nitrogen to a Capacitively Radio-Frequency Hydrogen Discharge

A hybrid PIC/MC model is developed in this work for H2-xN2 capacitively coupled radio-frequency （CCRF） discharges in which we take into account 43 kinds of collisions reaction processes between charged particles （e-, H3＋, H＋, H＋, N＋, N＋） and ground-state molecules （H2, H＋ N2）. In addition, the mean energies and densities of electrons and ions （ 3, H＋, H＋）, and electric field distributions in the H2-N2 CCRF discharge are simulated by this model. Furthermore, the effects of addition of a variable percentage of nitrogen （0-30%） into the H2 discharge on the plasma processes and discharge characteristics are studied. It is shown that by increasing the percentage of nitrogen added to the system, the RF sheath thickness will narrow, the sheath electric field will be enhanced, and the mean energy of hydrogen ions impacting the electrodes will be increased. Because the electron impact ionization and dissociative ionization rates increase when N2 is added to the system, the electron mean density will increase while the electron mean energy and hydrogen ion density near the electrodes will decrease. This work aims to provide a theoretical basis for experimental studies and technological developments with regard to H2-N2 CCRF plasmas.     

Simulation study on electron heating characteristics in magnetic enhancement capacitively coupled plasmas with a longitudinal magnetic field

The electron heating characteristics of magnetic enhancement capacitively coupled argon plasmas in presence of both longitudinal and transverse uniform magnetic field have been explored through both theoretical and numerical calculations. It is found that the longitudinal magnetic field can affect the heating by changing the level of the pressure heating along the longitudinal direction and that of the Ohmic heating along the direction which is perpendicular to both driving electric field and the applied transverse magnetic field, and a continuously increased longitudinal magnetic field can induce pressure heating to become dominant. Moreover, the electron temperature as well as proportion of some low energy electrons will increase if a small longitudinal magnetic field is introduced, which is attributed to the increased average electron energy. We believe that the research will provide guidance for optimizing the magnetic field configuration of some discharge systems having both transverse and longitudinal magnetic field.     

Effects of electron temperature on the ion extraction characteristics in a decaying plasma confined between two parallel plates

In this paper, a one-dimension particle-in-cell (PIC) code (EDIPIC) is employed to simulate the parallel-plate ion extraction process under an externally applied electrostatic field, focusing on the analysis of the influence of the initial electron temperature on the extracted ion fluxes to the metal plates during the ion extraction process. Compared with previously published results, the plasma oscillations on a timescale of the electron plasma period, and the excitation of the ion acoustic rarefaction waves resulting from the plasma oscillations originating from both the negative and positive electrodes, are studied for the first time. The modeling results show that both the negative and positive extractors can collect ions due to the plasma oscillations and the propagation of the ion acoustic rarefaction waves. With the increase of the initial electron temperature achieved by keeping other parameters unchanged, on the one hand, both the ion speed and flux to the negative and positive plates increase, which leads to a significant decrease of the ion extraction time, while on the other hand, the ion flux to the positive plate after the formation of a Child–Langmuir sheath is much more sensitive to an increase of the initial electron temperature than that to the negative plate. The PIC simulation results provide a deeper physical understanding of the influence of the initial electron temperature on the characteristics of the entire ion extraction process in a decaying plasma.