大面积矩形表面波等离子体源的数值模拟
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摘要
表面波等离子体(SWP)是由沿着介质-等离子体交界面传播的表面波电场产生和维持的等离子体。从上个世纪90年代以来，随着大规模集成电路、太阳能电池、平板显示器、微电子机械系统等领域的迅速发展，可用于大面积材料处理的SWP源受到了前所未有的关注。和其他的传统的等离子体源相比，SWP源有诸多优点，如不需要外磁场，无须电极，等离子体密度高，容易实现大面积等。由于SWP源复杂的天线阵列-表面波-等离子体耦合机制，迫切需要通过计算机数值模拟对相关物理问题进行研究以及对实体装置进行优化设计。
本文数值模拟的研究对象是大面积矩形SWP源，主要工作包括：
1、采用时域有限差分(FDTD)方法结合麦克斯韦方程组和冷等离子体模型模拟了任意天线激发的表面波传播。分别研究了等离子体密度、电子碰撞频率、石英玻璃厚度及介电常数、石英和天线之间有无空气间隙等对表面波传播的影响。结果显示，不同天线激发的表面波具有线性叠加性质，受到天线的影响表面波模式和本征模不一致；石英玻璃太厚、上方有空气间隙都不利于表面波的激发；当介质的相对介电常数在3.7左右时天线可以激发较强的表面波。
2、基于等离子体空间均匀分布和沉积功率水平面均匀分布两个假设模拟了SWP源均匀稳态工作时候的装置电磁场分布、等离子体密度和温度分布。分析了不同天线阵列对波导内电磁场、激发的表面波传播和微波功率沉积的影响。数值模拟发现，在1.0×10~(18) m~(-3)的等离子体密度附近，装置的微波功率反射率小于20％。当天线激发的表面波模式紧凑、强度大时微波功率反射率也较小。当装置均匀稳态工作时，在距离石英大约2-4 cm会出现电子密度峰值，且密度峰值位置随着气压增大而靠近石英。气压比较大时，会出现等离子体密度饱和现象。
3、用准稳态时间步进模型模拟了等离子体在表面波“推动”下的自发扩展过程，获得了自洽的等离子体电子密度、温度空间分布，分析了不同天线阵列、微波输入功率、气压、空气间隙等对等离子体自发扩展以及均匀性的影响。提出可以通过表面波行波而非驻波产生大面积表面波等离子体的观点。
4、用粒子模拟(PIC+MCC)方法研究了微波功率共振吸收问题。模拟得出的局部共振宽度和共振电场时空分布与解析理论计算完全吻合。根据模拟结果推算出SWP源共振宽度小于0.1 mm，且气压越大共振点越靠近石英玻璃。用二维PIC模拟了不同电子温度下的表面波传播，得出的表面波模式与基于流体的冷等离子体模型模拟结果完全相同。
Surface wave plasma(SWP) is produced and sustained by the electric field of surfacewave propagating along the dielectric-plasma interface. With the rapid development ofultra-large-scale integrated(ULSI) devices, solar cells, flat panel displayer,microelectromechanical systems ere, SWP source, as a potential large-scale plasmaprocessing tool, has received unprecedented attention since the 90's of last century.Compared with conventional plasma source, SWP source has many advantages such asfree from the use of electrodes and external magnet field, permits the generation oflarge-scale high-density and uniform plasmas. Due to the complex coupling mechanismsbetween antenna array, surface wave and plasma in the SWP source, it urgently needscomputer numerical simulation to study relevant physical problems and as well as tooptimize the design of the device.
The large-scale rectangular SWP source is the research object of numerical simulationin this dissertation. The main works are described as follows:
1. The propagation of surface wave excited by arbitrary slot antenna is simulated bythe finite difference time domain(FDTD) method combined with the Maxwell's equationsand the cold plasma model. The dependences of surface wave propagation on variousfactors such as plasma density, electron collision frequency, quartz thickness, quartzpermittivity, and the air gap below antenna are investigated separately. The results showthat surface waves excited by different antennas have the nature of linear superposition,and the mode is inconsistent with eigen mode because of the influence of antennas. Thickquartz and the existence of air gap are not conducive to the excitation of surface wave.When the permittivity of dielectric is around 3.7, the antenna can excite more intensivesurface wave.
2. The distributions of electromagnetic fields, electron density and temperature whendevice working at uniform and stable states are simulated based on two assumptions:plasma is uniform distributed in the chamber and deposited power is uniform distributedin horizontal plane. The influences of different antenna arrays on the electromagneticfields in the waveguide, the propagation of surface wave and the microwave depositedpower are analyzed. It is found that when plasma density is at around 1.0×10~(18)m~(-3), thereflection rate of microwave power can be lower than 20%. The more compact andintensive the surface wave is, the less reflection rate would be. At around 2-4 cm from the quartz there appears a peak of electron density and the peak position moves towards thequartz as the increase of gas pressure. When the gas pressure increases to a certain value,plasma density will saturate.
3. The spontaneous outspread of plasma under the "push" of surface wave issimulated using a quasi-steady-state time-stepping model. Self-consistent generatedelectron density and temperature spatial distributions are presented. The impacts ofdifferent antenna arrays, microwave input power, gas pressure, air gap on the spontaneousoutspread of plasma are analyzed. The viewpoint that producing large-scale SWP bytraveling surface wave rather than standing surface wave is proposed.
4. Microwave resonant absorption is studied using the particle-in-cell plus MonteCarlo collision(PIC+MCC) method. Simulated local resonant width and Spatial andtemporal distribution of resonant electric field are in coincidence with theoreticalcalculations. The resonance occurred in SWP source must be not more than 0.1 mm wideaccording to the simulation results, and resonant point moves towards quartz as gaspressure increases. Surface wave propagations under different electron temperature aresimulated using two-dimensional PIC method, the modes are identical to the resultobtained by the fluid based cold plasma model.
本文数值模拟的研究对象是大面积矩形SWP源，主要工作包括：
1、采用时域有限差分(FDTD)方法结合麦克斯韦方程组和冷等离子体模型模拟了任意天线激发的表面波传播。分别研究了等离子体密度、电子碰撞频率、石英玻璃厚度及介电常数、石英和天线之间有无空气间隙等对表面波传播的影响。结果显示，不同天线激发的表面波具有线性叠加性质，受到天线的影响表面波模式和本征模不一致；石英玻璃太厚、上方有空气间隙都不利于表面波的激发；当介质的相对介电常数在3.7左右时天线可以激发较强的表面波。
2、基于等离子体空间均匀分布和沉积功率水平面均匀分布两个假设模拟了SWP源均匀稳态工作时候的装置电磁场分布、等离子体密度和温度分布。分析了不同天线阵列对波导内电磁场、激发的表面波传播和微波功率沉积的影响。数值模拟发现，在1.0×10~(18) m~(-3)的等离子体密度附近，装置的微波功率反射率小于20％。当天线激发的表面波模式紧凑、强度大时微波功率反射率也较小。当装置均匀稳态工作时，在距离石英大约2-4 cm会出现电子密度峰值，且密度峰值位置随着气压增大而靠近石英。气压比较大时，会出现等离子体密度饱和现象。
3、用准稳态时间步进模型模拟了等离子体在表面波“推动”下的自发扩展过程，获得了自洽的等离子体电子密度、温度空间分布，分析了不同天线阵列、微波输入功率、气压、空气间隙等对等离子体自发扩展以及均匀性的影响。提出可以通过表面波行波而非驻波产生大面积表面波等离子体的观点。
4、用粒子模拟(PIC+MCC)方法研究了微波功率共振吸收问题。模拟得出的局部共振宽度和共振电场时空分布与解析理论计算完全吻合。根据模拟结果推算出SWP源共振宽度小于0.1 mm，且气压越大共振点越靠近石英玻璃。用二维PIC模拟了不同电子温度下的表面波传播，得出的表面波模式与基于流体的冷等离子体模型模拟结果完全相同。
Surface wave plasma(SWP) is produced and sustained by the electric field of surfacewave propagating along the dielectric-plasma interface. With the rapid development ofultra-large-scale integrated(ULSI) devices, solar cells, flat panel displayer,microelectromechanical systems ere, SWP source, as a potential large-scale plasmaprocessing tool, has received unprecedented attention since the 90's of last century.Compared with conventional plasma source, SWP source has many advantages such asfree from the use of electrodes and external magnet field, permits the generation oflarge-scale high-density and uniform plasmas. Due to the complex coupling mechanismsbetween antenna array, surface wave and plasma in the SWP source, it urgently needscomputer numerical simulation to study relevant physical problems and as well as tooptimize the design of the device.
The large-scale rectangular SWP source is the research object of numerical simulationin this dissertation. The main works are described as follows:
1. The propagation of surface wave excited by arbitrary slot antenna is simulated bythe finite difference time domain(FDTD) method combined with the Maxwell's equationsand the cold plasma model. The dependences of surface wave propagation on variousfactors such as plasma density, electron collision frequency, quartz thickness, quartzpermittivity, and the air gap below antenna are investigated separately. The results showthat surface waves excited by different antennas have the nature of linear superposition,and the mode is inconsistent with eigen mode because of the influence of antennas. Thickquartz and the existence of air gap are not conducive to the excitation of surface wave.When the permittivity of dielectric is around 3.7, the antenna can excite more intensivesurface wave.
2. The distributions of electromagnetic fields, electron density and temperature whendevice working at uniform and stable states are simulated based on two assumptions:plasma is uniform distributed in the chamber and deposited power is uniform distributedin horizontal plane. The influences of different antenna arrays on the electromagneticfields in the waveguide, the propagation of surface wave and the microwave depositedpower are analyzed. It is found that when plasma density is at around 1.0×10~(18)m~(-3), thereflection rate of microwave power can be lower than 20%. The more compact andintensive the surface wave is, the less reflection rate would be. At around 2-4 cm from the quartz there appears a peak of electron density and the peak position moves towards thequartz as the increase of gas pressure. When the gas pressure increases to a certain value,plasma density will saturate.
3. The spontaneous outspread of plasma under the "push" of surface wave issimulated using a quasi-steady-state time-stepping model. Self-consistent generatedelectron density and temperature spatial distributions are presented. The impacts ofdifferent antenna arrays, microwave input power, gas pressure, air gap on the spontaneousoutspread of plasma are analyzed. The viewpoint that producing large-scale SWP bytraveling surface wave rather than standing surface wave is proposed.
4. Microwave resonant absorption is studied using the particle-in-cell plus MonteCarlo collision(PIC+MCC) method. Simulated local resonant width and Spatial andtemporal distribution of resonant electric field are in coincidence with theoreticalcalculations. The resonance occurred in SWP source must be not more than 0.1 mm wideaccording to the simulation results, and resonant point moves towards quartz as gaspressure increases. Surface wave propagations under different electron temperature aresimulated using two-dimensional PIC method, the modes are identical to the resultobtained by the fluid based cold plasma model.
引文
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