2-D analytic model for inductively coupled plasma sources. I.Electromagnetic model and kinetic analysis

Inductively coupled plasma sources (ICPS) have recently received increasing interest for semiconductor etching and deposition. A 2-D (r, z) electromagnetic (EM) model of ICPS is developed in terms of the mode analysis (MA) technique. Based upon the eigenmode expansion, a closed-form of the vector and scalar potentials of the EM fields is obtained, which provides exact and fast computing for the EM fields in the structure. By means of the Boltzmann-Vlasov equation, a 2-D model is established to describe the kinetic behaviors of plasmas. The closed-form solution for calculating induced space-currents is given, in which a collisionless coupled damping dominates the interaction mechanism between the induced RF wave and plasmas. In this connection, the 2-D coupled damping effect will be analyzed in detail in the following paper     

Self-consistent multidimensional electron kinetic analysis forinductively coupled plasma sources

Based upon the kinetic equations coupled with electromagnetic analysis for the recently developed inductively coupled plasma sources (ICPS), a self-consistent electron kinetic model is presented for 2-D (r, z) in a cylindrically symmetric configuration space and 2-D (ν _∂, ν_z) in the velocity space, The EM model is based on the mode analysis, while the kinetic analysis gives the perturbed Maxwellian distribution of electrons by solving the Boltzmann-Vlasov equation. The kinetic analysis shows that the RF energy in an ICPS is extracted by a collisionless dissipation mechanism, once the electron thermovelocity is close to the RF phase velocities determined by the reactor height and mode indexes. In this context, the effect of varying the reactor geometry is reported in terms of the electron energy distribution function. The analytical results are compared to the experimental data of Barnes et al. (see Appl. Phys. Lett., vol.62, no.21, p.2622-4 (1993)), which shows qualitative agreements in many aspects     

Plasma characteristics and broadband electromagnetic wave absorption in argon and helium capacitively coupled plasma

A one-dimensional self-consistent calculation model of capacitively coupled plasma(CCP) discharge and electromagnetic wave propagation is developed to solve the plasma characteristics and electromagnetic wave transmission attenuation.Numerical simulation results show that the peak electron number density of argon is about 12 times higher than that of helium, and that the electron number density increases with the augment of pressure, radio frequency(RF) power, and RF frequency. However, the electron number density first increases and then decreases as the discharge gap increases. The transmission attenuation of electromagnetic wave in argon discharge plasma is 8.5-d B higher than that of helium. At the same time, the transmission attenuation increases with the augment of the RF power and RF frequency, but it does not increase or decrease monotonically with the increase of gas pressure and discharge gap. The electromagnetic wave absorption frequency band of the argon discharge plasma under the optimal parameters in this paper can reach the Ku band. It is concluded that the argon CCP discharge under the optimal discharge parameters has great potential applications in plasma stealth.     

二维光子晶体耦合腔阵列的慢波效应研究

设计了一种六角晶格二维光子晶体耦合腔阵列,平面波展开法计算能带表明,处于禁带中的耦合缺陷腔模的色散曲线在光子晶体平面内所有k矢量方向更加平坦.模拟了横电波沿ΓK方向的透射谱.与光子晶体单缺陷腔相比,耦合腔阵列结构的缺陷腔模透射率提高三个量级以上,而群速度降低一个量级,得到0.007c的结果.该慢波效应在构造微型可调谐光延迟器和低阈值光子晶体激光器等方面具有潜在的应用前景. 关键词： 光子晶体 耦合腔阵列 慢波 透射率     

Fast electrons generation by RF and random fields near the antenna I. One dimensional model and regular fields

Test particle motion and acceleration has been explored in strong radio frequency (RF) fields, for which quasilinear ponderomotive force approximation is not valid. By nonlinear acceleration in spatially varying wave amplitude of RF travelling wave, electrons may be accelerated to time averaged velocities significantly larger than the RF wave phase velocity, and than the boundary plasma thermal velocity, in RF fields of several Volts per centimeter at wave frequency of 7 MHz. It is also demonstrated that even weak spatial gradients, much weaker than those expected in experiments, of the RF wave field amplitude, have significant consequences for the particle motion. Estimates are presented of the total energy transferred from the near antenna RF field to the plasma due to the nonlinear electron acceleration effects.     

Damped dust lattice shock wave in a strongly coupled complex (dusty) plasma

Taking into account “hydrodynamic damping” due to irreversible processes that occur within the system and the neutral drag due to the dust-neutral collision, a Burgers’ equation with a linear damping term is derived for a 1D nonlinear longitudinal dust lattice wave (LDLW) in homogeneous strongly coupled complex (dusty) plasma. The hydrodynamic damping generated-dissipative effect causes the generation of a shock wave in a dusty plasma crystal, whereas the neutral drag-induced dissipative effect causes the decay of the shock intensity with time. The width of the observed compressive shock increases (decreases) with an increase in shielding parameter κ (characteristic length L). Its implication in a glow-discharge plasma is briefly discussed. The text was submitted by the author in English.     

Kinetic theory of surface waves in a semibounded plasma flow

A study is made of the spectrum of surface waves in a semibounded plasma flow. The frequency spectra and damping rates of the waves propagating along the flow are analyzed both in the high-frequency range (in which the spatial dispersion is weak and the wave damping is governed primarily by electron collisions) and the low-frequency range (in which the spatial-dispersion effects dominate), with focus on the effect of the flow velocity on the propagation of ion-acoustic waves. Special attention is paid to the penetration of a static field into a plasma flowing at a supersonic velocity.     

Landau damping in a bounded magnetized plasma column

The damping decrement of Landau damping and the effect of thermal velocity on the frequency spectrum of a propagating wave in a bounded plasma column are investigated.The magnetized plasma column partially filling a cylindrical metallic tube is considered to be collisionless and non-degenerate.The Landau damping is due to the thermal motion of charge carriers and appears whenever the phase velocity of the plasma waves exceeds the thermal velocity of carriers.The analysis is based on a self-consistent kinetic theory and the solutions of the wave equation in a cylindrical plasma waveguide are presented using Vlasov and Maxwell equations.The hybrid mode dispersion equation for the cylindrical plasma waveguide is obtained through the application of appropriate boundary conditions to the plasma-vacuum interface.The dependence of Landau damping on plasma parameters and the effects of the metallic tube boundary on the dispersion characteristics of plasma and waveguide modes are investigated in detail through numerical calculations.     

Measurements of plasma parameters in capacitively coupled radio frequency plasma from discharge characteristics: Correlation with optical emission spectroscopy

Plasma parameters from the discharge characteristics of a 13.56 MHz capacitively coupled radio frequency Ar plasma are evaluated on the basis of homogeneous discharge model for wide range of operating pressure. The homogeneous discharge model of capacitively coupled radio frequency discharge is modified to take into account the nonlinear plasma series resonance effect. The effect of drift velocity of the electron due to change in radio frequency electric field and operating pressure is also considered. Considerable dependent of plasma parameters on the drift velocity of the electron as well as on the plasma series resonance effect are observed in low pressure. An irregular variation of calculated plasma density with operating pressure is observed, which is reconfirmed with optical emission spectroscopy.     

Relativistic Spherical Plasma Waves in a Collisional and Warm Plasma

Under Lagrange coordinates, the relativistic spherical plasma wave in a collisional and warm plasma is discussed theoretically. Within the Lagrange coordinates and using the Maxwell and hydrodynamics equations, a wave equation describing the relativistic spherical wave is derived. The damped oscillating spherical wave solution is obtained analytically using the perturbation theory. Because of the coupled effects of spherical geometry,thermal pressure, and collision effect, the electron damps the periodic oscillation. The oscillation frequency and the damping rate of the wave are related to not only the collision and thermal pressure effect but also the space coordinate. Near the center of the sphere, the thermal pressure significantly reduces the oscillation period and the damping rate of the wave, while the collision effect can strongly influence the damping rate. Far away from the spherical center, only the collision effect can reduce the oscillation period of the wave, while the collision effect and thermal pressure have weak influence on the damping rate.     

甚高频激发的容性耦合Ar+O_2等离子体电负特性研究

利用探针辅助的脉冲激光诱导负离子剥离诊断技术对掺入5%O_2的容性耦合Ar等离子体电负特性进行了诊断研究.首先详细解析了脉冲激光剥离后探针的电信号,分析了探针偏压在低于或高于空间电位下的探针收集信号特征;根据探针偏压与探针收集信号之间的依赖关系,用来描述Ar+O_2等离子体电负特性的等离子体电负度被定义为脉冲激光剥离出的电子电流与偏压高于空间电位的探针收集到的背景电子电流的饱和比值,并对等离子体电负度随放电气压、射频功率以及轴向位置的变化进行了诊断测量.实验结果表明等离子体的电负度随着射频功率的增加而减小、随着放电气压的上升而变大;由于非对称电极的分布特性,在轴向方向上靠近功率电极时等离子体电负度有升高的趋势,这种趋势可能与鞘层边界附近二次电子的动力学行为以及负离子的产生与消失过程有关.     

Simulation and analysis of magnetic resonance elastography wave images using coupled harmonic oscillators and Gaussian local frequency estimation.

New methods for simulating and analyzing Magnetic Resonance Elastography (MRE) images are introduced. To simulate a two-dimensional shear wave pattern, the wave equation is solved for a field of coupled harmonic oscillators with spatially varying coupling and damping coefficients in the presence of an external force. The spatial distribution of the coupling and the damping constants are derived from an MR image of the investigated object. To validate the simulation as well as to derive the elasticity modules from experimental MRE images, the wave patterns are analyzed using a Local Frequency Estimation (LFE) algorithm based on Gauss filter functions with variable bandwidths. The algorithms are tested using an Agar gel phantom with spatially varying elasticity constants. Simulated wave patterns and LFE results show a high agreement with experimental data. Furthermore, brain images with estimated elasticities for gray and white matter as well as for exemplary tumor tissue are used to simulate experimental MRE data. The calculations show that already small distributions of pathologically changed brain tissue should be detectable by MRE even within the limit of relatively low shear wave excitation frequency around 0.2 kHz.     

Cherenkov radiation waves in inhomogeneous dusty plasma

A kinetic theory is employed to study Cherenkov wave in an inhomogeneous dusty plasma. Two different frequency regimes are considered incorporating the plasma species temperatures. The dispersion relation for one-dimensional Cherenkov wave is derived and analyzed. The plasma species temperatures, their cyclotron frequencies, and the plasma density inhomogeneity effect the growth/damping of Cherenkov waves. It is shown that the plasma inhomogeneity contributes to damping of Cherenkov waves.     

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.     

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采用波长532nm的高能脉冲激光束照射40.68MHz激发的容性耦合氧等离子体,并给处于激光束中央的探针施加一定的正偏压,由此诊断氧等离子体的空间电位和电负度.实验结果表明,探针偏压从0V逐渐增加时,探针搜集的电流波形从V型向倒U型转变,转变电压点正是电负性等离子体的空间电位.尝试着给出了运用激光诱导光致剥离技术诊断电负性等离子体空间电位的经验方法.另外,探针上施加的正偏压高于等离子体空间电位时,等离子体的电负度基本保持不变.实验还表明,氧等离子体的电负度随着射频输入功率的增加而呈现下降的趋势.     

容性耦合电负性氧等离子体的激光诱导光致剥离技术诊断研究

采用波长532nm的高能脉冲激光束照射40.68MHz激发的容性耦合氧等离子体,并给处于激光束中央的探针施加一定的正偏压,由此诊断氧等离子体的空间电位和电负度。实验结果表明,探针偏压从0V逐渐增加时,探针搜集的电流波形从V型向倒U型转变,转变电压点正是电负性等离子体的空间电位。尝试着给出了运用激光诱导光致剥离技术诊断电负性等离子体空间电位的经验方法。另外,探针上施加的正偏压高于等离子体空间电位时,等离子体的电负度基本保持不变。实验还表明,氧等离子体的电负度随着射频输入功率的增加而呈现下降的趋势。     

非Maxwell电子速度分布对受激散射的影响

从考虑动理学效应的受激散射不稳定性的线性理论出发,对于n=2的Maxwell分布函数直到n=5的饱和情况的超高斯分布函数,计算了电子等离子体波和离子声波的频率和阻尼率。对受激喇曼散射和受激布里渊散射进行分析,结果表明,在激光高Z等离子体中,或者在具有激光热斑的中等Z等离子体中,电子等离子体波的阻尼率降低很多,离子声波的频率比Maxwell分布情况升高约15%。这些结果可和实验进行比较。     

Effects of suprathermal particles on the dust ion-acoustic waves in a complex plasma

Dust ion-acoustic waves propagating in a complex plasma containing dusty particles and suprathermal electrons and ions are kinetically analyzed. The suprathermal particles are effectively modeled by the Lorentzian (kappa) velocity distribution function. For a collisionless and unmagnetized plasma, the full spectrum of the dispersion relation is obtained and the suprathermal particle effects on the wave frequency and the Landau damping are investigated. For a given wave number, the wave frequency decreases as the spectral index κ decreases, especially very rapidly in the low κ region. The Landau damping of the wave and its maximum are derived. They are found to be enhanced by the increase of suprathermal particles. The ion-to-electron density ratio also enhances the damping rate greatly.     

等离子体填充耦合腔链特性研究

 用严格的场匹配方法分析了填充等离子体的耦合腔链，研究了等离子体 腔混合模的形成以及“冷带宽”和“热带宽”的展宽效应。等离子体填充周期性耦合腔链后，形成周期性的截止频率为0的等离子体TG模式。当填充的等离子体密度较大，且腔模和TG模式发生部分重叠时，两者相互耦合，形成等离子体 腔混合模式。工作在混合模式下，其“冷带宽”和“热带宽”大大增宽，且耦合阻抗比真空时提高了近5倍，因此在填充等离子体后，耦合腔链的慢波特性得到了显著的改善。     

射频功率对氢气与反式二丁烯的低压电感耦合等离子体的影响（英）

利用等离子体聚合技术制备的GDP壳层是目前ICF靶丸的主要烧蚀层材料。为了了解GDP薄膜沉积过程中的CH等离子体的状态,采用朗缪尔探针和质谱仪对C4H8/H2等离子体的组分和状态参数进行了诊断,并对等离子体的电子能量分布函数、电子密度、电子温度等进行了深入分析。同时讨论了等离子体状态与放电参数之间的关系。研究发现,射频功率对等离子体参数有明显的影响。从10 W到35 W,电子密度正比于射频功率。随着射频功率的增加,在两步电离机制作用下,电子温度和等离子体电势呈现先减小后增大的变化趋势。另外,在高气压下,质谱诊断中发现了大量的稳定的小质量碎片离子,这表明在高气压下等离子体气相中的离子碎片聚合反应被抑制。