电磁波在非均匀大气等离子体中的传播低气压电容耦合等离子体的实验研究
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摘要
本文包括两个部分的内容。
第一部分主要讨论电磁波在大气等离子体中的传播。结合隐式差分格式和辛普森积分算法数值求解电磁波在一维非均匀大气等离子体中传播的微分-积分方程,讨论了电磁波的传播行为与等离子体参数的关系。相位移与等离子体的厚度以及平均电子密度成正比;当电子-中性粒子的碰撞频率等于电磁波的角频率时,透射波的衰减达到最大;反射率的大小由电子密度分布的空间梯度以及平均电子密度决定;除经典电子-中性粒子碰撞吸收外,还有迹象表明在等离子体内入射电磁波对应的临界密度附近发生了电磁波-静电波的波模转换,然后静电波可能通过碰撞阻尼或朗道阻尼被电子吸收;当电子-中性粒子的碰撞频率低于电磁波的角频率时,碰撞会加强电子的碰撞吸收和静电波的吸收;当电子-中性粒子的碰撞频率高于电磁波的角频率时,电子的碰撞吸收占主导,且碰撞频率的增加不利于波的被吸收。最后通过与WKB近似的解析解比较发现,若电子密度的空间分布平缓,两种方法得到的结果几乎重合。但电子-中性粒子的碰撞频率小、电子密度分布具有很大的变化率时,WKB近似的误差最大,因此WKB近似不适合描述空间分布很不均匀的等离子体或其他介质内波的传播。
第二部分是基于低气压电容耦合等离子体的实验。
首先介绍利用Smith图实现不同频率下的功率匹配,发现匹配器内的串联调节电容主要由放电的等效电抗决定而并联调节电容由放电的等效电阻决定。利用系统的等效电路估算不同频率下等离子体与腔室的等效阻抗,得出功率耦合效率随着频率的增加而下降以及腔室在低频时等效为电容和高频下等效为电感的结论。其次解释腔室的非对称性结构会使地电极面积小于驱动电极的系统出现负偏压,并介绍如何利用直流偏压的突变观察等离子体状态的突变,如小孔泄漏。
实验的重点是离子能量分布的测量。结论如下:
1)离子通量由电子吸收的能量与产生单个电子-离子对的等效电子碰撞能量损失决定。增加频率、极板电压以及气压会增加电子吸收的能量,但是同时会改变等离子体内部的电子能量分布、化学反应过程,这些都会强烈的影响等效电子碰撞能量损失,因此离子通量与放电条件的关系复杂。
2)固定射频电压,测量了不同频率下Ar等离子体的离子能量分布,获得了离子通量与频率的关系,同时给出离子的平均能量、展宽、平均鞘层厚度与频率、气压的关系。
3)固定输入射频功率,测量了不同频率下O2等离子体的离子能量分布,获得了离子通量与频率的关系,同时给出离子的平均能量、展宽、平均鞘层厚度与频率、功率的关系。
4)估算电子碰撞能量损失并推测不同气体放电时的电子行为。根据电子碰撞能量损失,判断实验中出现的模式跳变源于电子加热过程的改变(从随机加热为主导向γ模式的转变)。
The thesis includes two parts.
The first part focuses on the propagation of an Electromagnetic (EM) wave in Atmospheric Pressure Plasma (APP) slab. The wave propagation is described with an integral-differential wave equation, and solved numerically by the arithmetic of average conceal difference method combined Simpson integral method. The behaviors of the wave depended on the plasma parameter are discussed. The phase shift is increasing with the width and electrons density of the plasma slab, the attenuation of transmission wave become largest when the electron-neutral collision frequency equal to the EM wave angular frequency; the reflection is determined by the spatial gradient of the electrons density and average electron density. Besides collision absorption, there is evidence of resonant mode conversion of the incident EM wave into the electrostatic wave near the critical density region in the plasma slab,and the energy of the electrostatic wave transfer to the electrons through collisional damping or Landau damping. When the electrons-neutral collision frequency is less than the EM angular frequency, the collision absorption rates increase with the electron-neutral collision. When electrons-neutral collision frequency is larger than the EM angular frequency, the collision absorption rate will decrease with the electron-neutral collision frequency. In the last, our numerical results are compared with Appleton’s Equation derived from WKB approximation. The two kinds of results match very well when the electrons density profiles are gentle in space. But, the departure of Appleton equation from the numerical solutions becomes obvious when the electron-neutral collision frequency is small and electron density has great spatial gradient,so the WKB approximation is not suitable to describe the wave propagation in a plasma or other media with steep density profiles.
The second part is on the experimental study of the ion energy distribution function (IEDF) in low-pressure capacitively coupled plasma (CCP) system.
First, the power matching network is designed by using the Smith Chart and the conclusion is that the adjustable serial capacitor depends mainly on the equivalent reactance of the discharge and the adjustable shunt capacitor depends mainly on the equivalent resistance of the discharge. The equivalent impedance is deduced from the equivalent circuits of the discharge system with different frequencies and then we find that the power efficiency (or power absorbed by the plasma) decreases with frequency. And the chamber is capacitive at low frequency and become inductive at very high frequency. Second, it is possible to have a negative self-bias voltage between the two electrodes due to the unsymmetrical configuration of the chamber, though the area of ground electrode is less than the driven electrode. And the mode transition such as plasma leak through hole can be observed easily by the abrupt change of self-bias voltage.
The experiments focus on the measurement of IEDF. The conclusions are:
1) The ion flux is determined by the power delivered into electrons and the effective collisional energy loss of electrons for creating a pair of electron-ion. The energy absorbed by electrons increases with driving frequency, voltage between the two electrodes and pressure, however, the effective collisional energy loss of electrons is quite different due to the change of electron energy distribution function and chemical reactions in plasma under various discharge conditions. As a result, the ion flux changes with these conditions in a complicated way.
2) At constant RF voltage, the IEDF in Ar plasmas are measured with different driving frequencies and the ion flux dependence on frequency is obtained. The variations of average ion energy, energy spread and the average sheath thickness with frequency and pressure are presented.
3) At constant RF power, the IEDF in O2 plasmas are measured with different driving frequencies and the ion flux dependence on frequency is obtained. The variations of average ion energy, energy spread and the average sheath thickness with frequency and power are presented.
4) The electron collisional energy loss is estimated and the different electrons behaviors are speculated under various discharge conditions. According to the electron energy loss, the mode transition is suggested to be caused by the change of heating processes (from stochastic dominant toγmode).
第一部分主要讨论电磁波在大气等离子体中的传播。结合隐式差分格式和辛普森积分算法数值求解电磁波在一维非均匀大气等离子体中传播的微分-积分方程,讨论了电磁波的传播行为与等离子体参数的关系。相位移与等离子体的厚度以及平均电子密度成正比;当电子-中性粒子的碰撞频率等于电磁波的角频率时,透射波的衰减达到最大;反射率的大小由电子密度分布的空间梯度以及平均电子密度决定;除经典电子-中性粒子碰撞吸收外,还有迹象表明在等离子体内入射电磁波对应的临界密度附近发生了电磁波-静电波的波模转换,然后静电波可能通过碰撞阻尼或朗道阻尼被电子吸收;当电子-中性粒子的碰撞频率低于电磁波的角频率时,碰撞会加强电子的碰撞吸收和静电波的吸收;当电子-中性粒子的碰撞频率高于电磁波的角频率时,电子的碰撞吸收占主导,且碰撞频率的增加不利于波的被吸收。最后通过与WKB近似的解析解比较发现,若电子密度的空间分布平缓,两种方法得到的结果几乎重合。但电子-中性粒子的碰撞频率小、电子密度分布具有很大的变化率时,WKB近似的误差最大,因此WKB近似不适合描述空间分布很不均匀的等离子体或其他介质内波的传播。
第二部分是基于低气压电容耦合等离子体的实验。
首先介绍利用Smith图实现不同频率下的功率匹配,发现匹配器内的串联调节电容主要由放电的等效电抗决定而并联调节电容由放电的等效电阻决定。利用系统的等效电路估算不同频率下等离子体与腔室的等效阻抗,得出功率耦合效率随着频率的增加而下降以及腔室在低频时等效为电容和高频下等效为电感的结论。其次解释腔室的非对称性结构会使地电极面积小于驱动电极的系统出现负偏压,并介绍如何利用直流偏压的突变观察等离子体状态的突变,如小孔泄漏。
实验的重点是离子能量分布的测量。结论如下:
1)离子通量由电子吸收的能量与产生单个电子-离子对的等效电子碰撞能量损失决定。增加频率、极板电压以及气压会增加电子吸收的能量,但是同时会改变等离子体内部的电子能量分布、化学反应过程,这些都会强烈的影响等效电子碰撞能量损失,因此离子通量与放电条件的关系复杂。
2)固定射频电压,测量了不同频率下Ar等离子体的离子能量分布,获得了离子通量与频率的关系,同时给出离子的平均能量、展宽、平均鞘层厚度与频率、气压的关系。
3)固定输入射频功率,测量了不同频率下O2等离子体的离子能量分布,获得了离子通量与频率的关系,同时给出离子的平均能量、展宽、平均鞘层厚度与频率、功率的关系。
4)估算电子碰撞能量损失并推测不同气体放电时的电子行为。根据电子碰撞能量损失,判断实验中出现的模式跳变源于电子加热过程的改变(从随机加热为主导向γ模式的转变)。
The thesis includes two parts.
The first part focuses on the propagation of an Electromagnetic (EM) wave in Atmospheric Pressure Plasma (APP) slab. The wave propagation is described with an integral-differential wave equation, and solved numerically by the arithmetic of average conceal difference method combined Simpson integral method. The behaviors of the wave depended on the plasma parameter are discussed. The phase shift is increasing with the width and electrons density of the plasma slab, the attenuation of transmission wave become largest when the electron-neutral collision frequency equal to the EM wave angular frequency; the reflection is determined by the spatial gradient of the electrons density and average electron density. Besides collision absorption, there is evidence of resonant mode conversion of the incident EM wave into the electrostatic wave near the critical density region in the plasma slab,and the energy of the electrostatic wave transfer to the electrons through collisional damping or Landau damping. When the electrons-neutral collision frequency is less than the EM angular frequency, the collision absorption rates increase with the electron-neutral collision. When electrons-neutral collision frequency is larger than the EM angular frequency, the collision absorption rate will decrease with the electron-neutral collision frequency. In the last, our numerical results are compared with Appleton’s Equation derived from WKB approximation. The two kinds of results match very well when the electrons density profiles are gentle in space. But, the departure of Appleton equation from the numerical solutions becomes obvious when the electron-neutral collision frequency is small and electron density has great spatial gradient,so the WKB approximation is not suitable to describe the wave propagation in a plasma or other media with steep density profiles.
The second part is on the experimental study of the ion energy distribution function (IEDF) in low-pressure capacitively coupled plasma (CCP) system.
First, the power matching network is designed by using the Smith Chart and the conclusion is that the adjustable serial capacitor depends mainly on the equivalent reactance of the discharge and the adjustable shunt capacitor depends mainly on the equivalent resistance of the discharge. The equivalent impedance is deduced from the equivalent circuits of the discharge system with different frequencies and then we find that the power efficiency (or power absorbed by the plasma) decreases with frequency. And the chamber is capacitive at low frequency and become inductive at very high frequency. Second, it is possible to have a negative self-bias voltage between the two electrodes due to the unsymmetrical configuration of the chamber, though the area of ground electrode is less than the driven electrode. And the mode transition such as plasma leak through hole can be observed easily by the abrupt change of self-bias voltage.
The experiments focus on the measurement of IEDF. The conclusions are:
1) The ion flux is determined by the power delivered into electrons and the effective collisional energy loss of electrons for creating a pair of electron-ion. The energy absorbed by electrons increases with driving frequency, voltage between the two electrodes and pressure, however, the effective collisional energy loss of electrons is quite different due to the change of electron energy distribution function and chemical reactions in plasma under various discharge conditions. As a result, the ion flux changes with these conditions in a complicated way.
2) At constant RF voltage, the IEDF in Ar plasmas are measured with different driving frequencies and the ion flux dependence on frequency is obtained. The variations of average ion energy, energy spread and the average sheath thickness with frequency and pressure are presented.
3) At constant RF power, the IEDF in O2 plasmas are measured with different driving frequencies and the ion flux dependence on frequency is obtained. The variations of average ion energy, energy spread and the average sheath thickness with frequency and power are presented.
4) The electron collisional energy loss is estimated and the different electrons behaviors are speculated under various discharge conditions. According to the electron energy loss, the mode transition is suggested to be caused by the change of heating processes (from stochastic dominant toγmode).
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