Vibrational excitation and negative ion production in radio frequency parallel plate H2 plasmas

A theoretical study of the vibrational kinetics and attachment in low pressure hydrogen plasmas produced by Radio Frequency (RF) discharges is performed. In particular we study the influence of gas/surface kinetic processes such as the vibrational deactivation and the atomic recombination of molecules. The production of vibrationally excited molecules by the surface recombination of atoms is also considered. The study is realized by means of a self-consistent one dimensional kinetic model, and a parallel plate RF discharge test case is implemented. Results show that surface processes are able to affect the vibrational distribution function (vdf) and the negative ion (H-) density. The effect of vibrational exothermicity of H atom recombination is also discussed as a way to reduce the gap between theory and experimental results. Moreover, it is shown that the H- ion heating by the electric field strongly affects the detachment rate: this effect is specially important for negative ions produced through Rydberg states in this kind of discharges.     

Sheath characteristics in plasma carrying finite mass negative ions and ionization at low frequency

The sheath characteristics are investigated in a collisional environment by considering three electronegative plasmas, namely CF₄, Oxygen, and C₆₀ plasmas. Specifically, positive ion velocity, electrostatic potential, charged species densities and net space charged density are examined inside the sheath region with the variation of collisional parameter, mass ratio of negative to positive ions, temperature ratios of electrons to positive ions and electrons to negative ions, non-neutrality parameter and negative ion density. Collisional cross-section is assumed to have a power-law dependence, and both the cases of constant mobility and constant collisional cross-section are discussed and compared. In order to introduce the concept of finite mass of negative ions, both kinds of ions are considered to be governed by their fluid equations, where contribution of ionization, attachment, and detachment is also taken through the continuity equations.     

电子和负离子的反射运动对碰撞电负性磁鞘的影响

研究了鞘层中电子和负离子的反射运动对碰撞电负性磁鞘玻姆判据和鞘层结构的影响.通过理论推导得到了考虑鞘层中电子和负离子的反射运动时鞘层玻姆判据表达式,并通过数值模拟得到了电子和负离子采用玻尔兹曼模型和反射运动模型时离子马赫数的下限随参数的变化曲线以及鞘层中带电粒子密度的分布曲线.结果表明,电子和负离子的反射运动模型和玻尔兹曼模型离子马赫数的上限完全相同,下限表达式不同,反射运动模型中下限还与基板电势有关,且随着基板电势值的增加而增大,达到与玻尔兹曼分布中相同值后保持不变,随着鞘边负离子浓度和温度的不同达到最大值的速度不同;离子马赫数的下限在玻尔兹曼和反射运动模型中都随鞘边负离子浓度的增加和温度的降低而减小,只是在反射运动模型中的最大值要小;两种模型中离子马赫数的下限都随鞘边电场的增加而增加,但在玻尔兹曼模型中增加得更快最终值更大;两种模型离子马赫数的下限都随碰撞参数或磁场角度的增加而降低,但在玻尔兹曼模型中降低更快,随着碰撞参数或者磁场角度的增加两种模型中离子马赫数的下限趋于一致;当基板电势值较小时,电子和负离子的反射运动对鞘层结构影响较大,当基板电势值较大时电子和负离子反射运动对鞘层中带电粒子密度分布的影响很小.     

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     

不同成分等离子体鞘层的玻姆判据

在一维平板鞘层中采用流体模型分别研究了不同成分无碰撞等离子体鞘层的玻姆判据.通过拟牛顿法数值模拟了含有电子、离子、负离子以及二次电子的等离子体鞘层玻姆判据.结果表明二次电子发射增加了鞘层离子马赫数的临界值,且器壁发射二次电子温度越高,离子马赫数临界值越小.负离子使离子马赫数临界值减小.而在含有二次电子和负离子的等离子体鞘层中,当负离子较少时,二次电子发射对离子马赫数临界值影响较大;当负离子增加时,离子马赫数的临界值则主要受负离子的影响. 关键词： 鞘层 等离子体 玻姆判据     

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     

Probe Measurements in Electronegative Plasmas: Modeling the Perturbative Effects of the Probe‐Holder

A basic property of an electronegative plasma is its separation into two distinct regions: an ion‐ion region far from boundaries, where the densities of positive and negative ions are higher then electron density, and a near‐boundary electron‐ion region, where negative ions have practically negligible density. This is due to the influence of the ambipolar electric field, which depends on electron (not negative ion) plasma parameters. This electric field “holds off” negative ions from the boundary, as the ions have lower mobility and temperature compared to the electrons. Therefore, negative ions will be repelled by any object inserted into the plasma. This can lead to errors in measurements of negative ion and electron parameters by any invasive method. Numerical modeling of electric probes in an argon‐oxygen plasma clearly demonstrates possible errors of direct measurements of negative ion probe current. This can also affect results from the photo‐detachment method and direct measurements of negative ion energy distribution (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Kinetic modeling of positive ions in a low-pressure RF discharge

The evolution of the ion-velocity distribution function in a planar RF discharge is computed by numerically solving the Boltzmann equation in phase space. The electric field in this equation is computed with regard to the ion density, assuming Maxwellian electrons with a given uniform temperature. The collision term in the Boltzmann equation contains creation of ions by electron-impact ionization of the background gas and the effect of charge-exchange collisions. Examples are given of the behavior of discharges in argon at RF frequencies of 50 kHz, 300 kHz, and 15 MHz at a very low pressure and at a pressure of approximately 40 Pa. A good agreement is found with published experimental observations of the time-dependent behavior of the electric field profile in the RF sheath     

Electron detachment from negative hydrogen and lithium ions by an ultrashort laser pulse

A model of electron detachment from negative ions is based on the approximation of instantaneous perturbation. A simple analytical representation for the ground state of the weakly bound electron is chosen to reproduce the radial distribution of electron density at any distance from the center of the ion. The probabilities of electron detachment from negative hydrogen and lithium ions are derived as functions of the transferred momentum of the laser field. The contribution of the inner shells of ions to the electron detachment is estimated. The momentum distribution of electrons in the final state is obtained. The effect of a pulse train on the total probability of detachment is considered for different pulse polarities. The conditions for the partial electron return to the initial state are revealed.     

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     

Specific boundary conditions for the simulation of extraction for ECRIS,LIS, and H−-sources

The necessity of a three-dimensional simulation of the extraction has been accepted for electron cyclotron resonance ion sources (ECRIS) as well as for negative ion sources. For an ECRIS, the magnetic hexapole together with the solenoidal mirror field defines a minimum B structure which confines the plasma. Depending on the magnetic flux density distribution, the plasma density in front of the extraction electrode might be non-homogeneous. In H^?-sources, magnetic filter fields are used to separate electrons with different energies or to separate electrons from negative ions. These magnetic filters influence the ions as well. Besides these asymmetry effects other quantities have to be considered, namely the correct formulation of initial conditions of all present charged particles. For ECRIS the initial conditions for ions are assumed to be in the electronvolt range, whereas it can be in the kilo electronvolt range for laser ion sources. Another quantity of interest is the electron energy and the distribution of electrons in real space and their movability if magnetic fields are present.     

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     

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     

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     

Electron and Chemical Kinetics in the Low-Pressure RF Discharge Etching of Silicon in SF6

Monte Carlo simulation and Boltzmann equation solutions have been used to study the electron kinetics. All electronic excitation of SF6 is assumed to be dissociative in analogy with the known product channels in ionization and multiphoton dissociation. The electric-field-to-gas-density ratios are high (E/n ? 1000 Td, where 1 Td (Townsend) = 1 × 10-17 V . cm2) in low-pressure (p < 0.3 torr) radiofrequency (RF) discharges. At these high E/n values, the electron energy relaxation time is much shorter than the 74-ns period at 13.56 MHz. Furthermore, the time scale of the chemical kinetics is much longer than the period of the applied RF voltage. Therefore the electron energy distribution can "track" the time-varying electric field, and time- and space-averaged rate coefficients can be used in chemical kinetics models. A rate equation model has been used to study the chemical kinetic processes. Electron-impact dissociation and ionization are the dominant sources of chemically active species. An electron density of 1 × 108 cm-3 is estimated from the known average values of E/n and the discharge input power. Two limiting cases are studied for the positive and negative ion diffusion losses: a) trapped negative ions and positive ion loss at the ambipolar diffusion rate; and b) positive and negative ion losses at the free diffusion rates. Neutral particle diffusion losses are estimated by using an effective diffusion length which takes surface reflection into account and increases as the surface reflection probability increases.     

二次电子发射和负离子存在时的鞘层结构特性

 建立了包括电子、离子、器壁发射二次电子以及负离子多种成分的等离子体无碰撞鞘层的基本模型,讨论了二次电子发射和负离子对1维稳态等离子体鞘层结构的影响,并且分析了多种成分等离子体鞘层内的二次电子和负离子的相互作用。结果表明：二次电子发射系数的增加和负离子含量的增加,都将导致鞘层的厚度有所减小;二次电子发射系数超过临界发射系数之后,鞘层不再是离子鞘。随着器壁材料二次电子发射系数的增加,鞘层中的负离子密度分布也逐渐增加;负离子的增加,导致二次电子临界发射系数有所增加。另外,在等离子体鞘层中二次电子发射和负离子的存在,也影响着鞘层中电子的放电特性与器壁材料的腐蚀。     

Particle-in-cell/Monte Carlo simulation of radio frequencySiH4/H2 discharges

In this paper we report on a study of SiH₄/H₂ radio-frequency discharges using the particle-in-cell/Monte Carlo (PIC/MC) method. A special procedure based on the rate balance for negative ions has been developed to speed up the simulation for this kind of electronegative discharge. The electron energy distribution function and the angular and energy distribution function of ions arriving at the substrate have been studied at different discharge settings (frequency, pressure, voltage, and power). The simulations show that the electrons are heated ohmically, so the average electron energy can be increased only by increasing the voltage. A high radical density, a high and more directional ion flux, and a low average ion energy can be obtained by a combination of a high frequency and a low RF voltage. The behavior of the dissociation rate with the discharge parameters is consistent with the experimentally observed consumption of SiH₄. The simulated ion energy distribution functions are in good agreement with experimental results     

ANALYSIS OF DUAL FREQUENCY CONFINED CAPACITIVELY COUPLED PLASMA AT LOW POWER

Confined dual frequency hydrogen plasma discharge has been investigated with microwave interferometer method and radial profiles are taken by Abel inversion technique. Dual radio-frequency sources, operating at 27.12MHz and 1.94MHz, are coupled to each other through the plasma. 27.12MHz RF power is used to enhance plasma density and 1.94MHz power is used to enhance ion acceleration energy to the electrode. Radial density profiles has been taken for comparing the effects of low frequency source that the secondary RF source causes reduction in plasma density due to the sheath expansion. Instead radial density profile is assumed as flat by most of the models, there is about 2.5eV of potential drop occurs from centre to boundary at 40W of primary source power. It has been observed that increasing sheath width (increasing the secondary source power to primary source power) reduces the bulk plasma volume and makes potential profile flattening in y direction. While the high frequency power is dissipated by electrons in the bulk plasma; low frequency power is mostly dissipated by ions in the sheath region. Using both high and low frequency power, we may control plasma density and ion acceleration energy to the electrode simultaneously.     

Tonks-Langmuir problem for a bi-Maxwellian plasma

An analytical solution of the Tonks-Langmuir (TL) problem with a bi-Maxwellian electron energy distribution function (EEDF) is obtained for a plasma slab. The solution shows that the ambipolar potential, the plasma density distribution, and the ion flux to the wall are mainly governed by the cold electrons, while the ionization rate and voltage drop across the wall sheath are governed by the hot electrons. The ionization rate by direct electron impact is found to be spatially rather uniform, contrary to the T-L solution where it is proportional to the plasma density distribution. The temperature of hot electrons defined by the ionization balance is found to be close to that of the T-L solution for a mono-Maxwellian EEDF, and is in reasonable agreement with experiments carried out in a low pressure capacitance RF discharge. The energy balance for cold electrons in this discharge shows that their heating by hot electrons via Coulomb interaction is equalized by the cold electrons' escape to the RF electrodes during collapse of the RF sheath     

具有非广延分布电子的碰撞等离子体磁鞘的结构

很多关于等离子体鞘层的研究工作都是基于电子满足经典的麦克斯韦速度分布函数,而等离子体中的粒子具有长程电磁相互作用,使用Tsallis提出的非广延分布来描述电子更为恰当.本文建立一个具有非广延分布电子的碰撞等离子体磁鞘模型,理论推导出受非广延参数q影响的玻姆判据,离子马赫数的下限数值会随着参数q的增大而减小.经过数值模拟,发现与具有麦克斯韦分布(q=1)电子的碰撞等离子体磁鞘对比,具有超广延分布(q<1)和亚广延分布(q>1)电子的碰撞等离子体磁鞘的结构各有不同,包括空间电势分布、离子电子密度分布、空间电荷密度分布.模拟结果显示非广延分布的参数q对碰撞等离子体磁鞘的结构具有不可忽略的影响.希望这些结论对相关的天体物理、等离子体边界问题的研究有参考价值.