Reactor modeling of magnetically enhanced capacitive RF discharge

Magnetic and collisional effects on capacitive radio frequency (RF) discharges for magnetically enhanced reactive ion etching (MERIE) are investigated. Using simplified plasma and sheath models, a collisional magnetic-sheath equation that governs the sheath dynamics under a de magnetic field crossed with a sinusoidal RF electric field is obtained. The sheath equation includes global effects of the bulk plasma. Together with the power-balance equation and the particle-conservation equation, the sheath equation is used to extract a circuit model and predict the electrical behavior of MERIE reactors. Numerical results on the plasma density and the power in MERIE reactors agree well with reported experimental results and the circuit model describes the repeated discharge properties well     

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     

射频放电阻抗测量用于等离子体诊断研究

利用自行研制的传感器和测量装置,通过对射频放电电压、电流以及其相位角的精确测定,算出放电管的总阻抗,结合放电管的等效电路模型与Godyak等建立的射频放电模型,对射频激励铜离子激光管在氦气中的放电特性进行了研究,得出射频激励铜离子激光器不同气压及电流密度下的等离子体电阻、容抗、鞘层厚度及电子密度 关键词： 射频放电 阻抗测量 等离子体诊断     

Investigations on ionic processes and dynamics in the sheath region of helium and hydrogen discharges by laser spectroscopic electric field measurements

Temporally and spatially resolved measurements of the electric field distribution in the sheath region of RF and dc discharges provide a detailed insight into the sheath and ion dynamics. The electric field is directly related to the sheath ion and electron densities, the sheath voltage, and the displacement current density. Under certain assumptions also the electron and ion conduction current densities at the electrode, the ion current density into the sheath from the plasma bulk, the ion energy distribution function, and the power dissipated in the discharge can be inferred. Furthermore, the electric field distribution can give an indication of the collision-induced conversion between different ion species in the sheath. Laser spectroscopic techniques allow the noninvasive in situ measurement of the electric field with high spatial and temporal resolution. These techniques are based on the spectroscopic measurement of the Stark splitting of Rydberg states of helium and hydrogen atoms. Two alternative techniques are applied to RF discharges at 13.56 MHz in helium and hydrogen and a pulsed dc discharge in hydrogen. The measured electric field profiles are analyzed, and the results discussed with respect to the ion densities, currents, energies, temporal dynamics and species composition. Received: 26 July 2000 / Accepted: 12 December 2000 / Published online: 3 April 2001     

A comparison of RF electrode sheath models

Analytic expressions have been found from different time-averaged and dynamic models for the electrode sheath width in a capacitively driven RF discharge. The sheath widths predicted from all the models under consideration are shown to practically coincide if they are expressed in terms of DC sheath voltage and ion current to the RF electrode. However, these models have fundamental differences in their RF discharge scaling laws that result in different theoretical predictions for RF discharge electrical characteristics. Analytic expressions for the sheath width with arbitrary collisionality at moderate RF voltages are found to be in good agreement with experimental measurements made over a wide range of discharge voltage and gas pressure     

Power absorption corresponding to ion losses in parallel-plate RFdischarges

A simple model of a symmetric parallel-plate RF discharge is studied to illustrate how such discharges may absorb power from an RF power supply in order to sustain DC power losses corresponding to the steady acceleration of ions through the sheaths. The motions of the sheath boundaries over one period are derived assuming that the current density varies sinusoidally. One finds that the sheath thickness increases discontinuously at one sheath whenever the plasma contacts the opposing electrode. This implies that the external power supply delivers an electron pulse from the electrode at higher potential to the electrode at lower potential, so that some power is being absorbed in a pulsed fashion. The power absorbed by the discharge is also calculated for the portions of the RF cycle where the current varies sinusoidally. It is found that power is supplied by the discharge in this phase of the RF cycle, with the energy coming from the deflating sheaths. It is further shown that the sum of the pulsed power absorption and smooth power generation, averaged over one RF period, is equal to the DC ion power losses arising from ions falling through the time-averaged sheath potentials     

Discharge characteristics of an atmospheric-pressure capacitively coupled radio-frequency argon plasmas

In this Letter, the electrical discharge characteristics of plasmas generated in coaxial cylindrical electrodes capacitively powered by radio-frequency power supply at atmospheric pressure are investigated with respect to argon gas. The electrical discharge parameters, the current and voltage characteristics (I–V) and the current and power characteristics (I–P), are measured for argon plasmas, and the electron temperatures and electron densities are estimated based on the equivalent circuit model and by making use of the power balance equation. Furthermore, the influence of the additive gas, oxygen gas, on the electrical discharge characteristics is also investigated in the argon plasmas, which is closely related to the electron temperature of plasmas.     

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     

Model of magnetically enhanced, capacitive RF discharges

Magnetically enhanced, capacitive RF discharges (called RF magnetrons or MERIE discharges) are playing an increasing role in thin film etching for integrated circuit processing. In these discharges, a weak DC magnetic field is imposed, lying parallel to the powered electrode surface. The authors determine the RF power transferred to the discharge electrons by the oscillating electron sheath in the presence of the magnetic field. Using this, along with particle and energy conservation, they obtain discharge parameters such as the ion flux and ion bombarding energy at the powered electrode as functions of pressure, RF power, and the magnetic field. Some results of the model show good agreement with experiments done on a commercial MERIE system     

Modeling of plasma behavior in a plasma electrode Pockels cell

We present three interrelated models of plasma behavior in a plasma electrode Pockels cell (PEPC). In a PEPC, plasma discharges are formed on both sides of a thin, large-aperture electro-optic crystal (typically KDP). The plasmas act as optically transparent, highly conductive electrodes, allowing uniform application of a longitudinal field to induce birefringence in the crystal. First, we model the plasma in the thin direction, perpendicular to the crystal, via a one-dimensional fluid model. This yields the electron temperature and the density and velocity profiles in this direction as functions of the neutral pressure, the plasma channel width, and the discharge current density. Next, me model the temporal response of the crystal to the charging process, combining a circuit model with a model of the sheath which forms near the crystal boundary. This model gives the time-dependent voltage drop across the sheath as a function of electron density at the sheath entrance. Finally, we develop a two dimensional MHD model of the planar plasma, in order to calculate the response of the plasma to magnetic fields. We show how the plasma uniformity is affected by the design of the current return, by the longitudinal field from the cathode magnetron, and by fields from other sources. This model also gives the plasma sensitivity to the boundary potential at which the top and bottom of the discharge are held. We validate these models by showing how they explain observations in three large Pockels cells built at Lawrence Livermore National Laboratory     

容性耦合射频氩等离子体放电诊断研究及仿真模拟

针对中等气压、中等功率下射频容性耦合(CCRF)等离子体的放电特性,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为工作气体,研究同一气压时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。同时依据仿真模型设计制作相同尺寸的密闭玻璃腔体和平板电极,实验测量了不同射频输入功率时放电等离子体的有效电流电压及发射光谱,进而计算等离子体的电子温度及电子密度;利用玻耳兹曼双线测温法,得到光谱法下等离子体的电子温度及电子密度。结果表明:当气体压强为250 Pa、输入功率为100~450 W时,等离子体电压电流呈线性关系,电子密度随功率的增大而增大,而电子温度并未随功率的变化而有明显变化,其与功率无关。运用仿真模拟验证了实验的准确性,通过比较,三种方法所得的结果相近。通过结合等效回路法、光谱法和数值模拟仿真法初步诊断出中等气压下等离子体的放电参数,提出了结合三种方法作为实验研究的方法,使实验结果更具说服力,证明其方法的可靠性,也为进一步的等离子体特性研究提供依据。     

Simulation study of a capacitively coupled plasma torch array

Using capacitively coupled electrical discharges, an array of three plasma torches powered by a single 60-Hz source are lit up simultaneously to produce a dense plasma in the open air. The discharge voltage and current of each torch is measured for three cases of one to three torches being lit up in the array. The results determine the ν-i characteristic of the discharge which indicates that the torch is operating in a diffuse are mode. The torch array is modeled by an equivalent circuit for simulating its operation. The simulation results of the discharge voltage and current of a torch are shown to agree well with those from the experimental measurements for the three cases. The lump circuit model is then used to carry out numerical simulations of the discharge for a broad parameter space of plasma species. By fitting the simulation results, a function giving the parametric dependence of the consumed average power density 〈P〉 on the normalized average electron density 〈n_e〉 maintained in the plasma is determined to be 〈P〉 48 〈n_e〉 ^1.9α_^0.4(W/cm³), where 〈n_e〉 is normalized to 10¹³cm^-3 and α_, the electron-ion recombination coefficient normalized to 10^-7 cm³·s^-1, is used as a variable parameter in the simulation     

Particle simulations of radio-frequency glow discharges

Particle-in-cell (PIC) simulations are used to study the structure of radio-frequency (RF) glow discharges in helium between parallel-plate electrodes. The authors have examined a range of conditions and report on a variety of observed phenomena. Comparisons to experiment and analytical models are made, when possible. The differences between discharges in which secondary electrons play a key role in sustaining the discharge and those in which secondary electrons are unimportant are examined in three cases which illustrate the importance of the discharge-sustaining mechanisms. Electron-energy distributions are found to be, in general, non-Maxwellian, with shapes that depend in complex ways on discharge conditions. In the absence of secondary electron emission, electron heating in the sheath regions of the discharge is enhanced at higher voltages compared to ohmic heating in the bulk of the plasma. Fast electrons accelerated by the advancing sheath can carry a substantial fraction of the conduction current in the bulk of the discharge, reducing the effective bulk ohmic heating of electrons. Ion-energy distributions at electrode surfaces have been predicted and are compared to experimental measurements     

Nonlinear dynamics of radio frequency plasma processing reactorspowered by multifrequency sources

The source frequency has a strong influence on plasma characteristics in RF discharges. Multiple sources at widely different frequencies are often simultaneously used to separately optimize the magnitude and energy of ion fluxes to the substrate. In doing so, the sources are relatively independent of each other. These sources can, however, nonlinearly interact if the frequencies are sufficiently close. The resulting plasma and electrical characteristics can then be significantly different from those due to the sum of the individual sources. In this paper, a plasma equipment model is used to investigate the interaction of multiple frequency sources in capacitively and inductively coupled RF excited plasmas. In capacitively coupled systems, we confirmed that the plasma density increases with increasing frequency but also found that the magnitude of the DC bias and DC sheath voltage decreases. To produce a capacitively coupled discharge having a high plasma density with a large DC bias, we combined low and high frequency sources. The plasma density did increase using the dual frequency system as compared to the single low frequency source. The sources, however, nonlinearly interacted at the grounded wall sheath, thereby shifting both the plasma potential and DC bias. In inductively coupled plasmas (ICP), the frequency of the capacitive substrate bias does not have a significant effect on electron temperature and density. The DC bias and DC sheath voltage at the substrate were, however, found to strongly depend on source frequency. By using additional RF sources at alternate locations in ICP reactors, it was found that the DC bias at the substrate was varied without significantly changing other plasma parameters, such as the substrate sheath potential     

Discontinuity of mode transition and hysteresis in hydrogen inductively coupled plasma via a fluid model

A new type of two-dimensional self-consistent fluid model that couples an equivalent circuit module is used to investigate the mode transition characteristics and hysteresis in hydrogen inductively coupled plasmas at different pressures,by varying the series capacitance of the matching box. The variations of the electron density, temperature, and the circuit electrical properties are presented. As cycling the matching capacitance, at high pressure both the discontinuity and hysteresis appear for the plasma parameters and the transferred impedances of both the inductive and capacitive discharge components, while at low pressure only the discontinuity is seen. The simulations predict that the sheath plays a determinative role on the presence of discontinuity and hysteresis at high pressure, by influencing the inductive coupling efficiency of applied power. Moreover, the values of the plasma transferred impedances at different pressures are compared, and the larger plasma inductance at low pressure due to less collision frequency, as analyzed, is the reason why the hysteresis is not seen at low pressure, even with a wider sheath. Besides, the behaviors of the coil voltage and current parameters during the mode transitions are investigated. They both increase(decrease) at the E to H(H to E) mode transition, indicating an improved(worsened) inductive power coupling efficiency.     

Sheath motion in a capacitively coupled radio frequency discharge

The sheath motion in a capacitively coupled RF discharge is highly nonlinear. The voltage waveform on a cylindrical probe placed in the sheath region is measured as a function of position and time. A circuit model of the probe-discharge system relates the observed probe voltage to the sheath motion. The equations derived from this circuit model are solved numerically with varying nonlinear sheath motions; the resulting waveforms are compared with the experimental observations to determine the actual sheath motion. The time-varying plasma potential is also determined, indirectly, from the comparison. The authors also report observation of oscillations related to the plasma frequency, whose peak harmonic component can be calculated from a single plasma model. These oscillations can be a useful plasma diagnostic for determining plasma density. The presence of these high-frequency oscillations may significantly enhance the rate of stochastic heating of electrons     

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     

Circuit model for two-electrode AC discharge

This paper presents a circuit model for a two-electrode AC discharge, which has two electrodes separated from the discharge gap by an insulator. The model consists of a series connection of an equivalent circuit for plasma and two capacitors for insulator. The equivalent circuit for plasma was constructed using the measured electrical properties of a two-electrode DC discharge. The validity of model was checked with experiments on a three-electrode test device; two electrodes exposed to the discharge gap and the other electrode separated from the discharge gap by an insulator. The measured voltages of the test device are compared with those obtained by circuit simulation. For various waveforms, which are being used widely to drive an AC plasma display panel, the results of circuit simulation agree well with experiment.     

脉冲放电射流辅助射频辉光放电研究

通过实验研究了脉冲放电射流辅助下大气压氦气射频辉光放电的电学和光学特性。采用组合电极结构,在射频放电前段增加脉冲电极,脉冲放电产生的射流以等离子体子弹形式注入射频放电区域,主要研究脉冲射流辅助射频放电的电流电压曲线、最低放电维持电压、放电强度和空间结构时空分布。研究结果表明:等离子体子弹经过射频放电区域后,由于等离子体子弹引入的活性粒子,会使射频放电区域等离子体强度增强;而射频放电最低维持电压也从0.93 kV降低至0.43 kV。