Matching an RF sheath model to a bulk plasma model

In this paper, we present a combined plasma-sheath model designed for the study of high density discharges, or other systems with thin sheaths. Sheaths in high density plasmas are typically less than 1 mm in thickness. When modeling multidimensional discharges, fully resolving the sheaths can be prohibitively expensive computationally, especially when RF power is coupled capacitively into the discharge. However, the sheath impedance often strongly affects instantaneous and period-averaged plasma potential, which in turn can strongly influence crucial processing characteristics such as the ion energy and angular distributions impacting surfaces. In the combined plasma-sheath model we present, the sheaths are treated independently from the plasma region, and different length scales are employed for each. The Godyak-Sternberg sheath model [Phys. Rev. A, 42, 2299 (1990)] is used to represent the sheaths. The bulk plasma portion of the discharge is represented using a fluid model. Boundary conditions at the plasma-sheath interfaces transfer information dynamically between the sheath and bulk plasma portions of the model. Results from the combined plasma-sheath model are compared to results from a discharge model that fully resolves the sheaths, with generally good to excellent agreement     

Two‐dimensional magnetosonic shock wave propagation in dense electron–positron–ion plasmas

Two‐dimensional (2D) magnetosonic wave propagation in magnetized quantum dissipative plasmas is studied. The plasma system is comprised of inertial ions, inertia‐less electrons, and positrons. The multi‐fluid quantum hydrodynamic model is used, in which quantum statistical and quantum tunnelling effects of electrons and positrons are included. Reductive perturbation analysis is performed to derive the Zabolotskaya–Khokhlov equation for the 2D propagation of a magnetosonic shock wave in a magnetized qauntum plasma. The effects of varying the different plasma parameters such as positron density and magnetic field intensity on the propagation characteristics of magnetosonic shock waves are discussed with non‐relativistic degenerate plasma parameters in astrophysical plasma situations.     

Electrical characteristics of parallel-plate RF discharges in argon

Electrical characteristics were measured in a parallel-plate, capacitively coupled (E-type), low-pressure, symmetrical RF discharge driven at 13.56 MHz. The discharge voltage, current, and phase shift between them were measured over a very wide range of discharge parameters (gas pressures between 3 mtorr and 3 torr with discharge power between 20 mW and 100 W). From these measurements the discharge impedance components, the power dissipated in the plasma and in the sheaths, the sheath width, and the ion current to the RF electrodes were found over a wide range of discharge conditions. Some of the general relationships between the various measured and determined parameters are discussed. The experimental results can be used as a database for straightforward comparison with existing RF discharge models and numerical simulations     

射频容性耦合等离子体放电特性的光谱诊断

利用流体模型模拟和发射光谱实验诊断相结合的方法,研究了中等气压、中等功率下射频容性耦合等离子体的放电特性。理论上,采用基于流体模型的COMSOL软件仿真,建立一维等离子体放电模型,以Ar气为工作气体,研究了不同气压以及不同射频输入功率下等离子体电子温度和电子密度的分布规律。实验上,依据仿真模型设计制作了相同尺寸的密闭玻璃腔体和平板电极,采用13.56 MHz射频放电技术电离腔体内的工作气体Ar气,测量了不同气压、不同射频输入功率时放电等离子体的发射光谱。通过分析和选择适当的Ar Ⅰ和Ar Ⅱ的特征谱线,分别利用玻尔兹曼斜率法以及沙哈-玻尔兹曼方程计算了等离子体的电子温度与电子密度,并结合模拟仿真结果对光谱诊断结果进行了修正。结果表明：当气体压强为300~400 Pa、输入功率为600~800 W时,等离子体近似服从玻尔兹曼分布,此时利用光谱法得到的等离子体参数与仿真结果相符合。仿真模拟与光谱实验诊断相结合的方法可初步诊断出中等气压下等离子体的放电参数,增加了玻尔兹曼斜率法和沙哈-玻尔兹曼方程在等离子体放电中的使用范围,扩大了光谱法在低电子密度容性耦合等离子体参数诊断的应用场合,为中等气压容性耦合等离子体在工业与军事上的应用研究提供了重要物理状态的分析手段。     

Fluid simulation of inductively coupled Ar/O_2 plasmas:Comparisons with experiment

In this work, a two-dimensional fluid model has been employed to study the characteristics of Ar/O2 radio frequency(RF) inductively coupled plasma discharges. The emphasis of this work has been put on the influence of the external parameters(i.e., the RF power, the pressure, and the Ar/O2 gas ratio) on the plasma properties. The numerical results show that the RF power has a significant influence on the amplitude of the plasma density rather than on the spatial distribution.However, the pressure and the Ar/O2 gas ratio affect not only the amplitude of the plasma density, but also the spatial uniformity. Finally, the comparison between the simulation results and the experimental data has been made at different gas pressures and oxygen contents, and a good agreement has been achieved.     

A hybrid Monte Carlo/fluid model of RF plasmas in aSiH4/H2 mixture

A fluid model for simulating the capacitively coupled steady RF plasmas in a monosilane-hydrogen mixture under plasma-processing conditions is developed. This model includes Monte Carlo treatment for electron transport properties in the mixture. The Monte Carlo simulation shows that the electron transport phenomena in the nonuniform RF field of 10 MHz are not in equilibrium with the local electric field. The nonequilibrium transport properties are incorporated in the fluid model (hybrid model) by modifying the equilibrium values of the swarm parameters using data from the Monte Carlo simulation. Using this model, the spatiotemporal variations of the charged species and the electric field in the sheath region of the RF plasma are calculated. For obtaining the steady RF plasma structure, ion-induced slow processes such as recombination and diffusion of ions are calculated by combining the hybrid model with rate equations for ions. Using the calculated steady RF plasma structure, a preliminary calculation of the silyl (SiH ₃) and hydrogen (H) radical distributions caused by the generation, diffusion, and reaction of the radicals are carried out. The effect of sticking on the profile of the radical distribution is presented     

Modelling of DC Electric Fields Induced by RF Sheath in Front of ICRF Antenna

Reducing the ICRH (ion cyclotron range frequency) antenna-plasma interaction is one of the key points for reaching very long tokamak discharges. One problem which limits such discharges, is the appearance of hot spots on the surface of the antenna: Radio Frequency (RF) sheaths modify the properties of the edge plasma by rectifying the RF potential along open magnetic field lines and can induce hot spots. This paper investigates the corrections to sheath potentials introduced by the interactions between adjacent flux tubes. Our theoretical study started from an oscillating double Langmuir probe model, in which a transverse influx of current was included. This model was confronted with 1D PIC simulations along a magnetic field line, and demonstrated that current exchanges can decrease mean potentials. A 2D electrostatic fluid code was then developed, which couples adjacent flux tubes in a poloidal cross section with collisional conductivity or polarization currents. It showed that transverse currents are able to smooth structures smaller than a characteristic size in the sheath potential maps (results for Tore Supra). These computed rectified potentials can be used to obtain the DC electric fields in front of the antenna. And then, it gives an estimate of the particle drift and the energy flux on the antenna structure, which can explain hot spots.     

射频等离子体鞘层动力学模型

在流体力学方程的基础上建立了一种自洽的无碰撞射频等离子体鞘层动力学模型.这种自洽性包含两个方面:一方面,由于考虑了瞬时鞘层电场对离子运动的影响,因此该模型适用于描述任意频率段的射频鞘层演化过程;另一方面,在模型中采用等效电路方法来自洽地确定极板上的瞬时电位与瞬时鞘层厚度之间的关系.采用数值方法模拟出鞘层的瞬时厚度及极板的瞬时电位变化、鞘层内离子密度和电场强度等物理量的时空变化.结果表明,当射频场的频率小于或等于离子等离子体频率时,离子流密度明显地随时间变化 关键词： 射频 离子 鞘层 流体力学     

Modeling the pressure dependence of DC bias voltage in asymmetric,capacitive RF sheaths

A semianalytical model for capacitively coupled radio frequency (RF) sheaths of asymmetric (unequal electrode area) systems has been developed. It can be applied in the high-frequency (ω > ω _pi) regime at different pressures. An analytical approximation to the pressure-dependent ion density profile is used. The time-varying electric field and potential within the sheath are obtained by solving Poisson's equation. The current balance and zero net DC current conditions are applied to solve for the RF sheath parameters and DC bias voltage. The DC voltage ratio between the powered and grounded electrode sheaths increases as the pressure decreases, which results in a larger DC bias voltage at lower pressures     

The Radio Frequency Hollow Cathode Discharge Induced by the RF Discharge in the Plasma‐Jet Chemical Reactor

In the recent decade an RF driven, low‐pressure plasma reactor with supersonic plasma jet was developed (RPJ). This reactor was successfully used for deposition of thin films of various materials. The deposition of thin films indicates that the properties of the deposited films are dependent on the sputtering or reactive sputtering processes appearing inside the nozzle (hollow athode). The nozzle (hollow athode) fabricated of different kinds of materials and alloys works both as a cathode of the radio frequency (RF) hollow cathode discharge and as a nozzle for plasma jet channel generation as well. The RF hollow cathode discharge is a secondary discharge, which is induced by the primary RF plasma generated in the reactor chamber. The present paper deals with the experimental study of this RF hollow cathode discharge. The stress is laid on the investigation of the axial distribution of discharge parameters and sputtering processes inside the nozzle. On the base of experiments, the simple model of the axial distribution of the investigated RF hollow cathode discharge has been developed.     

Mechanisms for Power Deposition in Ar/SiH4 Capacitively Coupled RF Discharges

In low-pressure capacitively coupled parallel-plate radiofrequency (RF) discharges, such as those used in plasma processing of semiconductor materials, power deposition and the rate of electron-impact excitation collisions depend upon time during the RF cycle and position in the discharge. Power is coupled into the discharge in at least two ways: by way of a high-energy "e-beam" component of the electron distribution resulting from electrons falling through or being accelerated by the oscillating sheaths, and by "joule heating" in the body of plasma. This paper will discuss the method of power deposition by electrons and the spatial dependence of electron-impact excitation rates in low-pressure capacitively coupled RF discharges with results from a Monte Carlo plasma simulation code. Mixtures of argon and silane will be examined as typical examples of discharges used for the plasma deposition of amorphous silicon.     

高频感应等离子体流动模型与微型电推进器流场特性分析

微型射频离子推力器具有结构简单、 工作寿命长、 推力动态范围大、 性能调节响应灵敏等特点,是国际微电推进领域的研究热点之一.射频离子推力器电离室内的感性耦合放电等离子体特性和推力器的性能密切相关.为此,文章建立了低气压、小尺寸微型射频离子推力器电离室内感性耦合等离子体流体模型,开展了电磁场、流场、化学反应浓度场的多物理...     

A self-consistent particle model for the simulation of RF glowdischarges

A self-consistent particle model of an argon RF glow discharge has been developed. Electric field and charged-particle density profiles determined from simulations with the RF glow discharge model are consistent with results obtained from continuum models. The average ion energy is found to vary greatly between the bulk of the discharge and sheaths, contrary to the assumption that the ion energy is uniform, as is assumed in some continuum models. The accuracy of the particle cross sections and collision representation used in the model is verified with a simplified DC model which calculates swarm parameters. Electron swarm parameters determined with this model are in excellent agreement with experimental data taken from the literature     

Fabrication of zinc oxide nano-structures in RF inductively-coupled thermal plasma and their photoluminescence effects

Zinc oxide (ZnO) nanoparticles and nano-structures were synthesized using RF inductively-coupled thermal plasma system. The ZnO nanoparticles synthesized in high enthalpy plasmas showed high purity and extremely small crystalline characteristics with the (30–50) nm size distribution applicable in various areas. The resultant morphology of the ZnO nanoparticles was influenced by process parameters such as chamber pressure, a cooling method and a reactor configuration. Thus, the effects of process conditions were discussed with perspective of the re-crystallization. In addition, by controlling the operational parameters, flower-like shaped ZnO nano-structures consisting of many hexagonal nano-rods with six facets were also obtained. The ZnO nano-structures showed a good optical property in photoluminescence analysis.     

One-dimensional fluid model of ECR discharge with inhomogeneityeffects of external magnetic field

A one-dimensional fluid model of the microwave electron cyclotron resonance (ECR) discharge, which includes the inhomogeneity effects of the external magnetic field, is developed. We use fluid equations which are obtained from the one-dimensional Bolzmann equation expressed in terms of magnetic moment and parallel velocity. We model the plasma and sheath separately, and appropriate plasma-sheath boundary conditions are utilized. Microwave is represented by an energy flow, and treated by a ray tracing technique. For the argon discharge, we obtain various quantities such as the axial profiles of plasma density, electron temperature, electrostatic potential, fluid velocity, and microwave power deposition. The results of simulation compare well with the experimental observation of the mirror field effects on the plasma parameters     

Electrical characteristics of helicon wave plasmas

The external electrical characteristics of helicon wave plasmas have been studied over a wide range of magnetic fields, radio frequency (RF) power, frequencies, and Ar gas pressures. External parameters, such as antenna voltage, current, and phase shifts, and internal parameters, such as electron density, are measured. The equivalent discharge resistance, reactance, and power transfer efficiency are calculated through these measurements. The characteristics of helicon mode is compared with inductively coupled plasma (ICP) and low mode. The power efficiency of the helicon mode is better than that of other modes. Consequently, electron density of helicon mode is much higher than that of other modes. This means the existence of a mechanism where electrons are very efficiently accelerated by the electric field of the antenna in the helicon mode. The power efficiency of helicon mode is higher at lower RF frequency and at optimum gas pressure than that of other modes     

碰撞对非对称射频鞘层特性的影响

对于大多数活性射频等离子体刻蚀工艺，由于放电室中两个电极的面积不等，使得两个电极附近的等离子体鞘层是非对称性的.考虑离子与中性粒子的碰撞效应，建立了一种描述这种非对称射频鞘层动力学特性的自洽动力学模型.数值结果显示碰撞效应对极板上的瞬时电压降、瞬时电子鞘层厚度、鞘层内的离子密度和动能的空间分布以及两个极板上电压之差等物理量的影响. 关键词： 射频鞘层 非对称电极 碰撞效应 离子     

大气压脉冲调制射频氩气放电等离子体特性的数值研究

基于等离子体流体理论,建立了大气压脉冲调制射频氩气放电的一维流体模型。通过数值模拟的方 法研究了放电参数(放电电极间距、射频频率)对氩等离子体特性的影响。研究结果表明：当电压固定时,随着电 极间距的增加,等离子体区逐渐增大,最大电子密度也增加,在 0.20cm 达到最大值后略有降低;放电电流密度 与输入功率密度随着电极间距的增加而增加;鞘层区电子温度随着电极间距的增加而降低;在脉冲开启前期,等 离子体区电子温度随着电极间距的增加而增加,但当脉冲开启后期,电极间距对等离子体区电子温度影响较小。 不同射频频率下最大电子密度随电极间隙的增加而减小,也具有一个最优值。      

Numerical modeling of low-pressure RF plasmas

A particle-in-cell simulation is used to model the plasma generated in a parallel plate RF reactor at low pressure. Nonperiodic boundary conditions are used, and the electric field and particle motion are obtained by finite-difference methods leading to the self-consistent creation of sheaths on the boundaries. Model cross sections are used to describe collisions between particles. Ionization is included, and the plasma is maintained by fast electrons generated in the RF sheaths. Most of the power dissipation is due to the acceleration of ions in the time-average sheath fields. At high applied voltage, the power dissipation is described well by the power law P∝V^5/2. Simple scaling laws for the density and plasma potential are obtained. The effect of ion mass and charge-exchange colisions on the ion energy spectrum collected by the electrodes is examined. The ion loss rate drops in the presence of charge-exchange collisions, and this leads to an increase in the density. The collisions also markedly alter the ion energy distribution function     

Synthesis of well-aligned carbon nanotubes by inductively coupled plasma chemical vapor deposition

Uniform and well-aligned carbon nanotubes (CNTs) have been grown using a high density inductively coupled plasma chemical vapor deposition (ICP-CVD) system. A gas mixture of methane-hydrogen was used as the source and Ni as the catalyst for the CNT growth. The effect of process parameters, such as inductive RF power, DC bias voltage and CH₄/H₂ ratio, on the growth characteristics of CNTs was investigated. It was found that both plasma intensity and ion flux to the substrate, as controlled by the inductive RF power and DC bias voltage, respectively, can greatly affect the growth of CNTs. The relative importance of the generation of ions and the subsequent transport of ions to the substrate as serial process steps are considered as the two underlying factors in determining the growth characteristics of CNTs. PACS 81.05.Uw; 81.07.De; 81.15.Gh