甚高频激发容性耦合氩等离子体的电子能量分布函数的演变

甚高频激发的容性耦合等离子体由于离子通量和能量的相对独立可控而受到人们的关注. 本文采用朗缪尔探针诊断技术测量了40.68 MHz激发的容性耦合Ar等离子体的特性(如电子能量概率分布、电子温度和密度等)随宏观参量的演变情况. 实验结果表明, 电子能量概率分布随着气压的增加从双麦克斯韦分布逐步转变为单麦克斯韦分布并最终演变为Druyvesteyn分布, 而射频激发功率的增加促进了低能电子布居数的增强; 在从等离子体放电中心移向边界的过程中, 低能电子的布居数显著下降, 而高能电子的布居则有所上升; 放电极板间距的变化直接导致了等离子体中电子加热模式的转变. 另外, 我们也对等离子体中的高低能电子密度和温度的分配情况进行了讨论.     

Model Calculations on the Positive Column of a Medium Pressure Neon Gas-discharge

Model calculations on the positive column of a neon gas-discharge for gas pressures between 50 and 350 torr and currents between 5 and 100 mA are presented. In these calculations a Druyvesteyn distribution for the electron energy has been used. Volume recombination and radially dependent electron and gas temperatures have been taken into account. Numerical results are compared with available experimental data. In particular, the axial field strength, electron density, electron temperature and ambipolar field strength are considered. In general, the agreement between experimental and numerical data is good.     

Free electron gas spectrum parameters of noble gases in dc electric field

Free electron gas is present in every gas, whether it is of atomic or molecular structure. Since the Maxwell spectrum type is the consequence of only thermal motion of constitutive gas particles; therefore, the presence of electric field leads to change the spectrum of charged particles due to their directed motion. However, it has been shown that in the case of occurrence only of elastic interactions between electrons and neutral gas particles (a condition that has been met in the case of weakly ionized noble gases of a relatively huge volume) the deviation of the gas spectrum of free electrons in the electric field from the Maxwell type is negligible. In such a case, the gas spectrum of free electrons is either of Maxwell type (if the frequency collision value is energy-independent) or of Druyvesteyn type (if the mean free electron path value is energy-independent). The Maxwell and Druyvesteyn distribution types are very similar. The only noticeable difference is that the tail of the Maxwell distribution decreases with the energy exponent to the first degree of energy, and the tail of Druyvesteyn distribution with the energy exponent to the second degree of energy. The aim of this paper is to determine whether the gas spectrum of free electrons in weakly ionized noble gases at small values of the product pd (pressure and inter-electrode distance) follows either the Maxwell's or Druyvesteyn's type, as well as to determine the dependence of spectrum parameters on the product pd. It has been established that better results are obtained on the assumption that the mean value of collision frequency is energy-independent.     

射频辉光放电CH4等离子体中电子的能量分布

通过求解Lorentz简化的玻尔兹曼方程,得到射频放电CH₄等离子体中电子的能量分布函数.求解过程中使用一个简化的射频电场模型代替泊松方程求解放电电场.共计包含6类环境气体及27种电子碰撞反应.通过EEDF对等离子体中的电子反应率系数、电子平均能量、电子的传输率系数等进行求解分析.结果表明,在等离子体鞘层区域电子能量具有Maxwell分布形式,在正柱区域具有Druyvesteyn分布形式.最高电子能量和最大反应率系数出现在鞘层区域.电子的迁移率系数和扩散率系数随射频周期的演化时空分布不均匀.     

60MHz电容耦合等离子体中电子能量分布函数特性研究

甚高频(频率大于30 MHz)耦合放电源由于能产生大面积高密度的等离子体而受到了人们的广泛关注. 采用电流、电压探针以及朗缪尔探针诊断技术对60MHz射频激发产生的容性耦合等离子体的放电特性及电子行为进行了研究. 实验结果表明,等离子体的等效电阻/电容随着射频输入功率的增加而减小/增加;等离子体中电子行为不仅依赖于射频输入功率,还与放电气压密切相关;放电气压的增加导致电子能量概率分布函数(EEPF)从双温Maxwellian分布向Druyvesteyn分布转变,而且转变气压远低于文献所报道的数值,这主要是由于在60MHz容性耦合等离子体中电子反弹共振加热效率大为降低. 关键词： 甚高频容性耦合等离子体 朗缪尔探针诊断 电子加热模式     

Langmuir探针诊断低压氢等离子体电子密度与温度

为研究实验参数对螺旋波诱导的低压氢等离子体状态的影响,用Langmuir探针对等离子体伏安特性曲线进行了原位诊断,采用双曲正切函数的指数变换模型拟合曲线,根据Druyvesteyn方法得到状态参数电子密度、有效电子温度和电子能量几率函数,分析了它们随实验参数的变化规律。结果表明:射频输入功率、气压和约束磁场对等离子体状态有较大影响。随着射频射入功率增大,放电模式发生转变,电子密度跳跃增长;随着气压增大,电子密度先增大后减小,1.5 Pa为最佳电离气压,随约束磁场的增强呈线性增长;有效电子温度随功率和气压的增大而下降,随约束磁场的增强线性降低,电子能量几率函数曲线峰位和高能部分都向低能移动,与有效电子温度变化规律吻合。     

Floating double probe in non‐Maxwellian plasmas: Determination of the electron density and mean electron energy

A theoretical study of the floating double probe based on the Druyvesteyn theory is developed in the case of non‐Maxwellian electron energy distribution functions (EEDFs). It is used to calculate the EEDF in the electron energy range larger than –e(V_f ? V_p) from the I–V double probe characteristics. V_f and V_p are the floating and plasma potential, respectively. The analytical distribution function corresponding to the best fit of EEDF in the energy range larger than e(V_f ? V_p) allows the determination of the total electron density (n_e) and the mean electron energy (<?_e>). The method is detailed and tested in the case of a theoretical Maxwell–Boltzmann distribution function. It is applied for experiments that are performed in expanding microwave plasmas sustained in argon. Analytical EEDFs determined by this method are compared with those measured by means of single probes under the same experimental conditions. A good agreement is observed between single and double probe measurements. Results obtained under different experimental conditions are used to define the best conditions to obtain reliable results by means of the double probe technique.     

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采用Langmuir探针法结合发射光谱法对螺旋波诱导的低压氢等离子体进行诊断,根据Druyvesteyn 方法和日冕模型分析电子能量几率函数(EEPF)、有效电子温度(Teff)、电子密度(ne)及激发态氢原子密度(nH*)随实验参数的变化规律.结果表明:随射频功率(Prf)、气压(p)和约束磁场(B)的增大,EEPF峰位由高能向低能移动,Teff 下降;当Prf从25W增大至35W左右时,ne发生跳跃增长,而nH*始终随Prf增大线性增长;随p增大,ne和nH*都呈现先增加后减小的变化规律;随B增强,ne线性增长,而nH*先增大后减小.     

EEDF Determination by Numerical Processing of the Probe Data in Neon DC Discharge

Numerical processing of the data from single probe measurements allows determination of the electron energy distribution function (EEDF) from the second derivative of the probe current. The current‐voltage probe characteristics are measured by acquisition system for further smoothing and differentiation. The developed procedure is a combination of the Savitzky‐Golay (S‐G) smoothing filter and three‐point differentiator with varying step. The above methods are modified for irregularly sampled data which enables more accurate determination of EEDF. Advantages of this approach are data smoothing with minimum information loss and improved noise reduction at the differentiation procedure. The procedure is applied for EEDF calculation in low current low pressure neon discharge. The shape of EEDF shows deviation from both Maxwellian and Druyvesteyn distributions. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mode transition induced by low-frequency current in dual-frequency capacitive discharges

The mode transition induced by varying the low-frequency current in low-pressure dual-frequency discharges in argon is found through particle-in-cell or Monte Carlo simulations. As the low-frequency (2 MHz) current increases for the fixed high-frequency (27 MHz) current, the electron distribution function (EDF) changes from Druyvesteyn to bi-Maxwellian (in alpha mode) or Maxwellian-type (in gamma mode), along with the significant drop in the effective electron temperature. It is shown that this EDF evolution is attributed to the transition from collisional to collisionless property (but not stochastic heating) of the low-energy electrons as well as the alpha-gamma transition.     

Time-resolved analysis of a transversely excited nitrogen laser

Time-resolved measurements have been made of stimulated and spontaneous emission, voltage and current in a transversely excited nitrogen laser giving 50 kW peak power at 337 nm. The excitation rates to the laser levels were calculated from literature data using the results of electrical measurements, a check being obtained from measurements of spontaneous emission. The Druyvesteyn electron energy distribution gives better agreement with measurements than the Maxwellian. Laser pulses were calculated by solving numerically the space-dependent rate equations for population and photon number densities. Recent literature data on the transition probabilities and the pressure-dependence of the lifetime of the upper laser level were introduced into the calculations. The formation of a thin discharge channel was found to be essential for the high gain achieved. The onset of stimulated emission as observed on oscilloscope pictures was found to have a delay of the order of 1 ns in relation to the onset of current and spontaneous emission. This delay was confirmed by the calculations and explained as the time required to build up the population inversion and radiation density.     

Zur allgemeinen kinetischen Theorie von partiell ionisierten Plasmen in zeitabhängigen Magnetfeldern und elektromagnetischen Zusatzfeldern

A general method is given for the calculation of the electron distribution function of a weakly ionized plasma in external time-dependent magnetic fields and additional electromagnetic fields. The Boltzmann equation of kinetic theory is solved taking into account elastic collisions between electrons and neutrals. The isotropic part f⁰ of the distribution function follows from a general linear integro-differential equation and contains all known standard distributions (Druyvesteyn, Davydov, Margenau and others) as special cases. The direction-dependent part f¹ gives the transport tensors.     

Zur mikrophysikalischen Beschreibung des schwachionisierten Säulenplasmas von Glimmentladungen in Stickstoff-Neon-Gemischen. I. Vergleich zwischen gemessenen und berechneten Geschwindigkeitsverteilungsfunktionen der Elektronen

The isotropic part of the velocity distribution function of electrons is determined experimentally and theoretically for the plasma of the positive column of glow discharges in N₂-Ne mixtures. The distribution functions are measured with electrical probes using the Druyvesteyn method. The calculation of the isotropic part of the distribution functions for homogeneous and stationary conditions from the Boltzmann equation takes into consideration the essential elastical and unelastical collision processes. The character of the obtained distribution functions is fixed by the reduced field strength E/p₀ and the mixture ratio x = N₂/N₂ + Ne), which is varied in this paper in the range between pure nitrogen and pure neon. The distribution functions are found to be influenced by elastic and unelastic collisions of electrons with nitrogen molecules even at smal admixtures of N₂. Comparing the experimental results for the distribution functions with those received by the calculations a good agreement is observed.     

低能电子穿越绝缘体微孔膜动力学过程研究

采用二维位置灵敏的微通道板探测器对能量为1500 eV的低能电子束穿过孔径为400 nm、未经照射过的的聚对苯二甲酸乙二醇酯(PET)微孔膜后的全角分布以及时间演化进行了测量,同时采用自制的积分式能谱测量装置测量了穿透电子的能量分布。实验结果表明:在充电阶段,当入射电子束束流较弱时,透射电子强度随充电时间逐渐上升;充电过程中,透射电子的角分布宽度由小变大,但是角分布中心基本不随膜的倾角移动。对出射电子达到平衡态时的电子能谱的测量表明,穿透电子的能量保持着入射时的能量。对于理解电子在绝缘体微孔中的传输给出了新的实验证据,给出了可能形成“导向效应”的微孔内部电场的条件。     

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     

Mean energy of electrons in the oxygen discharge plasma

The mean energy of electrons in the homogeneous form of the positive column in an oxygen discharge is determined. The mean energy of electrons is calculated from double-probe characteristics under the assumption of a Druyvesteyn distribution using volt-equivalents of the electron temperature. The relation between the mean energy of electrons andE/p is compared with the theoretical results of another author. As a result of this comparison it can be concluded that for some discharge conditions the energy distribution of electrons is very close to a Druyvesteynian. We also analyze the influence of the negative ions on the double-probe characteristics.The author is obliged to Dr. O.tirand, Dr. L.Pekárek and Dr. J.Skála for their support of this work and helpful comments.     

High field transport properties in a GaN/AlGaN heterostructure

The drift velocity, electron temperature, electron energy and momentum loss rates of a two-dimensional electron gas are calculated in a GaN/AlGaN heterojunction (HJ) at high electric fields employing the energy and momentum balance technique, assuming the drifted Fermi–Dirac (F–D) distribution function for electrons. Besides the conventional scattering mechanisms, roughness induced new scattering mechanisms such as misfit piezoelectric and misfit deformation potential scatterings are considered in momentum relaxation. Energy loss rates due to acoustic phonons and polar optical phonon scattering with hot phonon effect are considered. The calculated drift velocity, electron temperature and energy loss rate are compared with the experimental data and a good agreement is obtained. The hot phonon effect is found to reduce the drift velocity, energy and momentum loss rates, whereas it enhances the electron temperature. Also the effect of using drifted F–D distribution, due to high carrier density in GaN/AlGaN HJs, contrary to the drifted Maxwellian distribution function used in the earlier calculations, is brought out.     

Monte Carlo方法模拟低能电子在Al中的散射

基于文献[1]的工作,电子在固体中的弹性散射用Mott微分截面计算;非弹性散射分为单电子激发和等离子激发并由Streitwolf、Gryzinski及Quinn的截面描述.模拟了低能电子在Al块样及薄膜中的散射过程,对不同能量低能电子作用下Al的背散射系统、能谱又透射系数作了计算,结果与实验符合较好.也对背散射电子、低能损背散射电子表面分布作了计算,结果表明低能损背散射电子具有较好的空间分辨率.     

直流空心阴极放电中鞘层区电子的输运过程

采用蒙特－卡洛方法对空心阴极放电中鞘层区电子的输运过程进行了研究，电子在鞘层区被非均匀电场加速，两次碰撞之间的步长是由电子与中性粒子的碰撞频率确定。模型中三种碰撞截面积是由实验和理论数据拟合而来。研究了电子平均能量、电子密度和电离系数在径向的分布。电子能量的空间分布结果与实验很好地符合。 关键词：     

n型硅微尖场发射电子能谱的模拟计算

结合金属的场发射电子能谱,模拟计算了场渗透对n型半导体硅微尖的场发射能谱的影响,并与n型硅微尖的场发射能谱实验结果进行了比较,讨论了模拟计算误差的来源。计算结果表明电场渗透现象导致硅的场发射能谱向低能方向偏移,表面电场越高,能谱的偏移量越大,其偏移程度可超过1eV。导致硅微尖的场发射能谱偏移的主要因素是半导体的场渗透现象。