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     

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     

Frequency effects in capacitively coupled radio-frequency glowdischarges: a comparison between a 2-D fluid model and experiments

The results of a 2-D fluid model for argon radiofrequency (RF) discharges in a closed cylindrical vacuum chamber are compared with experimental data from an amorphous silicon deposition reactor operated in argon. Good agreement is obtained for the relation between the DC autobias voltage and the dissipated power in the frequency range 40-100 MHz at pressures between 10 and 60 Pa. Scaling laws are presented for the dissipated power and for the ion fluxes toward the electrodes. These quantities are expressed in the DC bias voltage, the RF excitation frequency and the background pressure. Also the uniformity of the ion fluxes is studied. The model yields a linear relation between the applied RF voltage and the DC bias voltage. This relation depends only on the geometry of the discharge chamber and shows an offset     

Electrical characteristics of argon radio frequency glow dischargesin an asymmetric cell

Measurements of the current and voltage at both electrodes of a parallel-plate, capacitively coupled RF discharge cell (the Gaseous Electronics Conference Reference Cell) were combined with measurements of the voltage on a wire inserted into the glow region between the electrodes, for argon discharges at pressures of 1.3-133 Pa and peak-to-peak applied voltages ⩽400 V. Together, these measurements determined the RF voltage, current, impedance, and power of each sheath of the plasma. Simple power laws were found to describe changes in sheath impedances observed as voltage and pressure were varied. An equivalent circuit model for the electrical behavior of the discharge was obtained. The equivalent circuit model can be used to relate the electrical data to plasma properties such as electron densities, ion currents, and sheath widths. The results differ from models previously proposed for asymmetric RF discharges, and the implications of this disagreement are discussed     

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     

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     

Gamma-electron dynamics and radio frequency capacitive sheathdiagnostics

Time-resolved measurements of gamma-electrons energy spectra in low-pressure capacitively coupled RF discharge are presented. Time dependence of the sheath voltage is calculated from experimental results and compared with theoretical predictions. Good quantitative agreement is observed for collisional sheath. In low pressure discharge sheath voltage time dependence is close to [1+cos(ωτ)], which qualitatively corresponds to the theoretical results. Asymmetry of electron energy spectra for increasing and decreasing sheath voltage is observed and explained by divergence and convergence of electron trajectories in plasma (klystron-effect)     

Particle simulation of radio-frequency plasma discharges of methanefor carbon film deposition

Particle-in-cell/Monte Carlo (PIC/MC) simulations of capacitively coupled radio-frequency (RF) glow discharges were carried out for low pressure CH₄ plasmas. The present computational scheme includes the motions and collisions of both neutral and charged particles. The CH₄ plasma is modeled by combining a one-dimensional PIC/MC method with a polyatomic particle collision scheme. The model considers the motions of CH₄, CH₄⁺, CH₃, C₂H₅, H₂, H, and electrons. Space and time dependent results show ionization rate is high at the sheath region. The dissociation rate of CH₄ is found to be high at the sheath as well as in the plasma bulk. Deposition rate of carbon film is calculated by sampling impinging particles at at the powered electrode. The calculations show that neutral radicals are the major depositing species for the cases studied. Ion energy impinging to the electrode was found to be strongly dependent on the “imposed” dc bias (as opposed to self-bias) voltage for a given RF voltage. Deposition rate was found to be almost independent of the “imposed” dc bias voltage as the RF voltage remained constant     

The space-time-averaging procedure and modeling of the RF discharge

An approach to modeling RF discharges and the ensuing analysis of fast electron and ion motions for the case of electrode sheaths in the high-pressure RF discharge is discussed. Time-averaging over fast electron motions with the applied voltage frequency gives analytic expressions for the average electric field and average ionization density. The resulting relatively simple equations for the ion density profile describe drift, diffusion, ionization, and recombination processes. The simple scaling rules, the approximate expressions for the density profile in various regions, the sheath length, the ion density at the plasma-sheath boundary, and the dimensionless criteria for various discharge regimes can be deduced. For the non-self-sustained discharge, it is demonstrated that the ion drag towards the electrode and the diffusion results in significant lowering of the ion density in the sheath compared with the positive column at not too high a pressure. The analytic transition criterion from α to γ forms of the self-sustained discharge is obtained. The numerical solution of the averaged ion equations yields the results which nearly coincide with the results of full-scale modeling     

Calculation of the auto-bias voltage for RF frequencies well abovethe ion-plasma frequency

A model is presented which describes the coupling of the two RF sheaths in the high-frequency regime for a reactor with different electrodes. The sheaths are coupled by the current-balance equation and the assumption of a harmonic potential difference between the two electrodes. In contrast with most existing models, no assumption is made for either the displacement current or the potential drops across the sheaths. The sheath dynamics are due to an oscillating, step-like electron density profile. The calculations show that the sheaths react nonlinearly to the applied potential. The auto-bias voltage and averaged ion-impact energy coincide reasonably well with experimental data for different reactor types only if one demands that the time-averaged conduction currents flowing towards the electrodes vanish     

Analytical solution for capacitive RF sheath

A self-consistent solution for the dynamics of a high voltage, capacitive radio frequency (RF) sheath driven by a sinusoidal current source is obtained under the assumptions of time-independent, collisionless ion motion and inertialess electrons. Expressions are obtained for the time-average ion and electron densities, electric field and potential within the sheath. The nonlinear oscillation motion of the electron sheath boundary and the nonlinear oscillating sheath voltage are also obtained. The effective sheath capacitance and conductance are also determined. It was found that: (1) the ion-sheath thickness S _m is √50/27 larger than a Child's law sheath for the DC voltage and ion current density; (2) the sheath capacitance per unit area for the fundamental voltage harmonic is 2.452 ϵ₀ /S_m, where ϵ₀ is the free space permittivity; (3) the ratio of the DC to peak value of the oscillating voltage is 54/125; (4) the second and third voltage harmonics are, respectively, 12.3 and 4.2% of the fundamental; and (5) the conductance per unit area for stochastic heating by the oscillating sheath is 2.98 (λ_D/S_m)^2/3 (e ²n₀/mu_e), where n ₀ is the ion density, λ_D is the Debye length at the plasma-sheath edge, and u_e is the mean electron speed     

ICP等离子体鞘层附近区域发光光谱特性分析

为了独立控制鞘层附近区域离子密度和离子能最分布,采用光发射谱(OES)测量技术,对不同射频功率、放电气压和基底偏压下感应耦合等离子体鞘层附近区域辉光特性进行了研究.原子谱线和离子谱线特性分析表明,在鞘层附近区域感应耦合等离子体具有较高的离子密度和较低的电子温度.改变放电气压和射频功率,对得到的光谱特性分析表明,鞘层附近区域离子密度随射频功率的增大而线性增大,在低压下随气压的升高而增大.低激发电位原子谱线强度增加迅速,高激发电位原子谱线强度增加缓慢,而离子谱线强度增加很不明显.改变基底直流偏压,对得到的发射光谱强度变化分析表明,谱线强度随基底正偏压的增加而增大.随着基底负偏压的加入,谱线强度先减小而后增大;直流偏压为-30 V时,光谱强度最弱.快速离子和电子是引起Ar激发和电离过程的主要能量来源.     

Experimental and theoretical investigation of high-pressure arcs.I. The cylindrical arc column (two-dimensional modeling)

The properties of the free-burning arc column are studied for ambient pressures of 0.1 MPa (i.e., atmospheric) to 10 MPa for applications in underwater welding and cutting as well as arc discharge lamps. The influence of transverse magnetic fields is studied in Part II. A DC current of 50-100 A is applied to an argon discharge with a conical tungsten cathode and a plane water-cooled anode which are separated by several millimeters. The electrical properties are measured, and the temperature distribution is determined by spectroscopic means utilizing a two-dimensional charge-coupled device (CCD) sensor. A self-consistent numerical solution of the conservation equations yields the temperature, velocity, pressure, and current distributions. The predicted arc temperatures agree well with the measured temperature distributions. An analysis of the conservation equations shows that the arc column becomes radiation dominated with increasing pressures resulting in small temperature gradients within the column and large gradients at the boundaries. It is found that a net emission coefficient might be used to account for the radiative heat transfer in the investigated parameter range. The arc constricts due to increased convective cooling especially at the cathode, while temperatures and velocities are decreasing. The power expended in the column scales approximately with the square root of the ambient pressure in line with the radiation dominance, whereas the voltage drop across the electrode sheaths exhibits no pressure dependence for a given current     

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。      

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     

Dynamics of a collisional ion sheath

Experiments on collisional ion sheaths are carried out by applying a pulsed negative bias on a disc electrode immersed in a collisional plasma. The pulse is characterized by a linear rise, followed by a constant voltage phase and then exponential decay. The measured currents to the electrode are compared to predictions from a dynamic collisional ion sheath model which is developed from the basic two fluid equations. The parameter determining the degree of collisionality is also defined. The agreement between the two in the rising and the flat top phases of the pulse is found to be good. Some residual discrepancies as well as the disagreement in the decay phase are discussed.     

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     

Effect of Cathode and Anode Voltage on an Ion Sheath Thickness in a Magnetically Confined Diffusion Plasma

This article reports about the ion sheath thickness variation occurring in front of a negatively biased plate immersed in the target plasma region of a double plasma device. The target plasma is produced due to the local ionization of neutral gas by the high energetic electrons coming from the source region (main discharge region). It is observed that for an increase in cathode voltage (filament bias voltage) in the source region, the ion flux into the plate increases. As a result, the sheath at the plate contracts. Again, for an increase in source anode voltage (magnetic cage bias), the ion flux to the plate decreases. As a result, the sheath expands at the plate. The ion sheath formed at the separation grid of the device is found to expand for an increase in cathode voltage and it contracts for an increase in the anode voltage of the main discharge region. One important observation is that the applied anode bias can control the Bohm speed of the ions towards the separation grid. Furthermore, it is observed that the ion current collected by the separation grid is independent of changes in plasma density in the diffusion region but is highly dependent on the source plasma parameters. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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     

Structural and optical properties of sputtered ZnO thin films

Zinc oxide (ZnO) and aluminium-doped zinc oxide (ZnO:Al) thin films were prepared by RF diode sputtering at varying deposition conditions. The effects of negative bias voltage and RF power on structural and optical properties were investigated. X-ray diffraction measurements (XRD) confirmed that both un-doped and Al-doped ZnO films are polycrystalline and have hexagonal wurtzite structure. The preferential 〈0 0 1〉 orientation and surface roughness evaluated by AFM measurements showed dependence on applied bias voltage and RF power. The sputtered ZnO and ZnO:Al films had high optical transmittance (>90%) in the wavelength range of 400-800 nm, which was not influenced by bias voltage and RF power. ZnO:Al were conductive and highly transparent. Optical band gap of un-doped and Al-doped ZnO thin films depended on negative bias and RF power and in both cases showed tendency to narrowing.