甚高频容性耦合等离子体中电磁效应的数值研究
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摘要
容性耦合等离子体被广泛地应用于半导体工业中,如薄膜沉积、材料刻蚀以及表面处理等。众所周知,在容性耦合等离子体放电中,较高的频率能够产生较高密度的等离子体和较低能量的离子。因此近年来,甚高频容性耦合等离子体源受到人们越来越广泛的关注。然而当放电频率较高时,尤其是在大面积反应腔室中,电磁效应(如驻波效应和趋肤效应)会显著地影响放电过程,并引起等离子体的不均匀性。由于电磁波的波长随着频率的增加而减小,当波长与腔室尺寸相当时,驻波效应会对等离子体产生显著的影响,使得等离子体密度的最大值出现在放电中心处。另一方面,等离子体密度随着放电的频率而增加。当等离子体密度较高时,射频波在等离子体中的趋肤深度将小于等离子体的厚度。此时,电磁波只能在等离子体表面传播,因此趋肤效应会使得等离子体密度的最大值出现在径向边缘处。由此可见,电磁效应会显著影响刻蚀和沉积过程的均匀性,因而需要对电磁效应进行系统的研究,以便于进一步优化等离子体工艺过程。
在本论文的第一章,详细回顾了甚高频容性耦合等离子体源的研究背景、优势,以及研究过程中所面临的挑战。
在第二章中,首先介绍了在数值模拟过程中所使用的二维等离子体流体力学模型。各种带电粒子和中性粒子的密度由连续性方程来描述,其中电子通量由漂移扩散近似方法来确定,而离子通量则通过求解完整的动量平衡方程来获得。在流体模型中,假设离子的温度与室温相等,因此仅需要求解电子的能量方程。为了考虑电磁效应,该模型与完整的麦克斯韦方程组进行耦合,以便确定出等离子体中电磁场的瞬时空间分布。此外,本章还介绍了所涉及到的边界条件以及模拟方法。
在第三章中,针对氩气放电,通过比较由静电模型(仅求解泊松方程)和电磁模型(求解麦克斯韦方程组)得到的结果,研究了不同放电条件下电磁效应对等离子体的影响。结果表明：电磁效应对等离子体特性有着重要影响,尤其是在甚高频放电情况下,电磁效应导致等离子体密度显著地上升,电离率也呈现出不同的空间分布形式。当放电频率一定时,电磁效应随着电压的增加而减小。随着气压上升,由电磁模型得到的等离子体密度的最大值首先出现在径向边缘处,随后逐渐变得均匀,最后密度的最大值出现在放电中心处。此外,随着放电频率和气压的增加,边缘效应减弱。随着电压增加,趋肤效应取代驻波效应,成为影响等离子体分布的最主要的因素。
在第四章中,针对H2放电等离子体,重点考察了两个同频率甚高频电源之间的相位差对等离子体瞬时行为以及径向均匀性的影响。结果表明：在不同的相位差下,等离子体中各状态参量的时空分布不仅形貌不同,幅值差异更是明显。当频率为13.56MHz,两个射频源为同相位时,径向电子流首先向侧壁移动,随后方向反转；而当两个射频源反相位时,径向电子通量在一个周期内呈现出两个峰值。当频率为100MHz,相位差为π时,径向电子通量在一个周期内出现四个峰值,而电离过程则主要发生在鞘层区域。此外,在不同的放电频率下,两个同频率电源之间的相位差对等离子体的径向均匀性有着不同的调制作用。
在第五章中,针对Ar/CF4混合气体放电,研究了两个同频率电源之间的相位差对等离子体径向均匀性以及等离子体组分的影响。结果表明：当CF4含量仅为10%时,Ar+是最主要的正离子。在不同的放电频率下,相位差对等离子体的径向均匀性有着不同的影响。固定放电频率为100MHz,当CF4含量从10%增加为90%时,CF3+成为最主要的正离子,而且当相位差为π时,其密度的最大值从边缘处过度到放电中心处,这说明趋肤效应受到等离子体电负性的抑制。此外,负离子密度之和与电子密度的比率随着CF4含量的增加而增加,但是却随着频率的增加而降低。
在第六章中,采用HPEM模型(Hybrid Plasma Equipment Model)并与全波麦克斯韦方程组耦合,研究了CF4/02等离子体中的电磁效应对等离子体特性的影响。此外,还从实验方面研究了射频源功率对刻蚀率均匀性的影响。结果表明：当放电频率为27MHz以及60MHz时,电磁效应使得等离子体密度有所增加,并对其空间分布产生显著影响。与单频放电相比,在双频2/60MHz放电中,刻蚀速率的均匀性得到显著改善。随着低频源功率增加,刻蚀过程增强,且放电中心处的刻蚀率明显高于边缘处。固定低频源功率为300W,刻蚀速率随着高频源功率的增加显著上升,且均匀性变差。
Capacitively coupled plasmas (CCP) are widely applied in the semiconductor industry, for instance, for deposition of thin films, etching of materials and surface treatment. It is well known that a higher frequency produces higher-density plasmas with lower-energy ions. Thus, special attention has been paid to very high frequency (VHF) plasma sources due to their higher ion flux and lower ion bombarding energy. However, at high frequency (i.e., tens of MHz to hundreds of MHz) in large-area reactors, the so-called electromagnetic effects (i.e. standing-wave effect and skin effect) have an important influence on the capacitive discharge, which may limit the plasma spatial uniformity. Indeed, when the excitation wavelength becomes comparable to the electrode dimension, the standing-wave effect becomes dominant, and it results in a substantial power deposition at the reactor center. On the other hand, when the skin depth is not large compared with the plasma thickness due to the high plasma density, the skin effect has a significant influence, and it yields a pronounced power deposition at the reactor edge. These effects are important for plasma processing applications, as they affect the uniformity of the etch and deposition processes. Therefore, it is important to understand the electromagnetic effects, and to suppress the nonuniformity, in order to control the discharge process and to improve the application.
In this dissertation, we first briefly review the background, recent advances, and challenges of VHF-CCP, and also the problems we face in Chapter1. The contents of Chapter2to Chapter6are presented as follows.
The two dimensional fluid model used in the dissertation is described in Chapter2. In this model, the continuity equations are used to give information on the density evolution for all species. The drift diffusion approximation is assumed for electrons; the momentum balance equation based on the cold fluid approximation is adopted for ions. Because the ions and the neutral species are assumed at room temperature, only the electron energy balance equation is needed. In order to take the electromagnetic effects into account, the full set of Maxwell equations is included instead of solving the electric field by Poisson equation directly. Besides, boundary conditions are also specified in order to complete the problem.
The electromagnetic effects at various discharge conditions have been investigated in Ar plasmas by comparing the plasma characteristics obtained from the so-called electrostatic model (i.e., without taking into account the electromagnetic effects) and the electromagnetic model (which includes the electromagnetic effects) in Chapter3. The results indicate that the electromagnetic effects have an important influence on the plasma properties, especially at very high frequencies. Indeed, when the excitation source is in the high frequency regime and the electromagnetic effects are taken into account, the plasma density increases significantly and meanwhile the ionization rate profile evolves to a very different distribution. Furthermore, we also investigated the dependence of the plasma characteristics on the voltage and pressure, at constant frequency. It is observed that when the voltage is low, the difference between these two models becomes more obvious than at higher voltages. As the pressure increases, the plasma density profiles obtained from the electromagnetic model shift smoothly from edge-peaked over uniform to a broad maximum in the center. In addition, the edge effect becomes less pronounced with increasing frequency and pressure, and the skin effect instead of the standing-wave effect becomes dominant when the voltage is high.
In Chapter4, the phase-shift effect on the transient behaviour of electrodynamics and power deposition, as well as the influence on the radial uniformity of several plasma characteristics in a hydrogen capacitively coupled plasma has been investigated. It is shown that the spatiotemporal distributions of the plasma characteristics obtained for various phase shift cases are obviously different both in shape and especially in absolute values. At the frequency of13.56MHz, the radial electron flux moves towards the chamber wall first and then is forced in the opposite direction, whereas it exhibits two peaks within one period at the reverse-phase case. In the very high frequency discharge, i.e.,100MHz, the radial electron flux is alternately positive and negative with four peaks during one period, and the ionization mainly occurs in the sheath region at a phase difference equal to π. Furthermore, the phase shift has different influences on the plasma radial uniformity at various frequencies.
Chapter5shows the phase-shift effect on the plasma radial uniformity and the plasma composition at various frequencies and gas mixture ratios in Ar/CF4capacitively coupled plasmas. At low concentration of CF4(10%), Ar+are the major positive ions in the entire range of frequencies, and the phase-shift control shows different effects on the plasma uniformity at various frequencies. When the frequency is fixed at100MHz, the phase-shift control shows a different behavior at high concentration of CF4. For instance, the CF3+density profiles shift from edge-high over uniform to center-high at the reverse phase case, as the CF4content increases from10%to90%, which indicates that the skin effect is suppressed by the high electronegativity of the Ar/CF4=0.1/0.9mixture. Besides, the ratio of the total negative ion density to electron density decreases with increasing frequency, and it increases with CF4content.
In chapter6, a2D hybrid model, called HPEM (Hybrid Plasma Equipment Model), incorporating a full-wave solution of Maxwell's equations, is employed to investigate the electromagnetic effects on the plasma characteristics, as well as the power effect on the etch rate in CF4/O2discharges. It is shown that the electromagnetic effects have an important influence on the plasma density distribution. When the electromagnetic effects are taken into account, the plasma density becomes higher, and exhibits different shapes. At the frequency of60MHz, the etch rate has a center-high profile. When adding a low frequency power into the discharge, the etch rate becomes higher and more uniform. As the low frequency power increases from300W to1000W, the etch rate at the reactor center increases faster than at the edge, and therefore the uniformity of the etch rate becomes worse. When the low frequency power is fixed at300W, the etch rate becomes nonuniform with increasing high frequency power, and it becomes higher due to the higher plasma density.
在本论文的第一章,详细回顾了甚高频容性耦合等离子体源的研究背景、优势,以及研究过程中所面临的挑战。
在第二章中,首先介绍了在数值模拟过程中所使用的二维等离子体流体力学模型。各种带电粒子和中性粒子的密度由连续性方程来描述,其中电子通量由漂移扩散近似方法来确定,而离子通量则通过求解完整的动量平衡方程来获得。在流体模型中,假设离子的温度与室温相等,因此仅需要求解电子的能量方程。为了考虑电磁效应,该模型与完整的麦克斯韦方程组进行耦合,以便确定出等离子体中电磁场的瞬时空间分布。此外,本章还介绍了所涉及到的边界条件以及模拟方法。
在第三章中,针对氩气放电,通过比较由静电模型(仅求解泊松方程)和电磁模型(求解麦克斯韦方程组)得到的结果,研究了不同放电条件下电磁效应对等离子体的影响。结果表明：电磁效应对等离子体特性有着重要影响,尤其是在甚高频放电情况下,电磁效应导致等离子体密度显著地上升,电离率也呈现出不同的空间分布形式。当放电频率一定时,电磁效应随着电压的增加而减小。随着气压上升,由电磁模型得到的等离子体密度的最大值首先出现在径向边缘处,随后逐渐变得均匀,最后密度的最大值出现在放电中心处。此外,随着放电频率和气压的增加,边缘效应减弱。随着电压增加,趋肤效应取代驻波效应,成为影响等离子体分布的最主要的因素。
在第四章中,针对H2放电等离子体,重点考察了两个同频率甚高频电源之间的相位差对等离子体瞬时行为以及径向均匀性的影响。结果表明：在不同的相位差下,等离子体中各状态参量的时空分布不仅形貌不同,幅值差异更是明显。当频率为13.56MHz,两个射频源为同相位时,径向电子流首先向侧壁移动,随后方向反转；而当两个射频源反相位时,径向电子通量在一个周期内呈现出两个峰值。当频率为100MHz,相位差为π时,径向电子通量在一个周期内出现四个峰值,而电离过程则主要发生在鞘层区域。此外,在不同的放电频率下,两个同频率电源之间的相位差对等离子体的径向均匀性有着不同的调制作用。
在第五章中,针对Ar/CF4混合气体放电,研究了两个同频率电源之间的相位差对等离子体径向均匀性以及等离子体组分的影响。结果表明：当CF4含量仅为10%时,Ar+是最主要的正离子。在不同的放电频率下,相位差对等离子体的径向均匀性有着不同的影响。固定放电频率为100MHz,当CF4含量从10%增加为90%时,CF3+成为最主要的正离子,而且当相位差为π时,其密度的最大值从边缘处过度到放电中心处,这说明趋肤效应受到等离子体电负性的抑制。此外,负离子密度之和与电子密度的比率随着CF4含量的增加而增加,但是却随着频率的增加而降低。
在第六章中,采用HPEM模型(Hybrid Plasma Equipment Model)并与全波麦克斯韦方程组耦合,研究了CF4/02等离子体中的电磁效应对等离子体特性的影响。此外,还从实验方面研究了射频源功率对刻蚀率均匀性的影响。结果表明：当放电频率为27MHz以及60MHz时,电磁效应使得等离子体密度有所增加,并对其空间分布产生显著影响。与单频放电相比,在双频2/60MHz放电中,刻蚀速率的均匀性得到显著改善。随着低频源功率增加,刻蚀过程增强,且放电中心处的刻蚀率明显高于边缘处。固定低频源功率为300W,刻蚀速率随着高频源功率的增加显著上升,且均匀性变差。
Capacitively coupled plasmas (CCP) are widely applied in the semiconductor industry, for instance, for deposition of thin films, etching of materials and surface treatment. It is well known that a higher frequency produces higher-density plasmas with lower-energy ions. Thus, special attention has been paid to very high frequency (VHF) plasma sources due to their higher ion flux and lower ion bombarding energy. However, at high frequency (i.e., tens of MHz to hundreds of MHz) in large-area reactors, the so-called electromagnetic effects (i.e. standing-wave effect and skin effect) have an important influence on the capacitive discharge, which may limit the plasma spatial uniformity. Indeed, when the excitation wavelength becomes comparable to the electrode dimension, the standing-wave effect becomes dominant, and it results in a substantial power deposition at the reactor center. On the other hand, when the skin depth is not large compared with the plasma thickness due to the high plasma density, the skin effect has a significant influence, and it yields a pronounced power deposition at the reactor edge. These effects are important for plasma processing applications, as they affect the uniformity of the etch and deposition processes. Therefore, it is important to understand the electromagnetic effects, and to suppress the nonuniformity, in order to control the discharge process and to improve the application.
In this dissertation, we first briefly review the background, recent advances, and challenges of VHF-CCP, and also the problems we face in Chapter1. The contents of Chapter2to Chapter6are presented as follows.
The two dimensional fluid model used in the dissertation is described in Chapter2. In this model, the continuity equations are used to give information on the density evolution for all species. The drift diffusion approximation is assumed for electrons; the momentum balance equation based on the cold fluid approximation is adopted for ions. Because the ions and the neutral species are assumed at room temperature, only the electron energy balance equation is needed. In order to take the electromagnetic effects into account, the full set of Maxwell equations is included instead of solving the electric field by Poisson equation directly. Besides, boundary conditions are also specified in order to complete the problem.
The electromagnetic effects at various discharge conditions have been investigated in Ar plasmas by comparing the plasma characteristics obtained from the so-called electrostatic model (i.e., without taking into account the electromagnetic effects) and the electromagnetic model (which includes the electromagnetic effects) in Chapter3. The results indicate that the electromagnetic effects have an important influence on the plasma properties, especially at very high frequencies. Indeed, when the excitation source is in the high frequency regime and the electromagnetic effects are taken into account, the plasma density increases significantly and meanwhile the ionization rate profile evolves to a very different distribution. Furthermore, we also investigated the dependence of the plasma characteristics on the voltage and pressure, at constant frequency. It is observed that when the voltage is low, the difference between these two models becomes more obvious than at higher voltages. As the pressure increases, the plasma density profiles obtained from the electromagnetic model shift smoothly from edge-peaked over uniform to a broad maximum in the center. In addition, the edge effect becomes less pronounced with increasing frequency and pressure, and the skin effect instead of the standing-wave effect becomes dominant when the voltage is high.
In Chapter4, the phase-shift effect on the transient behaviour of electrodynamics and power deposition, as well as the influence on the radial uniformity of several plasma characteristics in a hydrogen capacitively coupled plasma has been investigated. It is shown that the spatiotemporal distributions of the plasma characteristics obtained for various phase shift cases are obviously different both in shape and especially in absolute values. At the frequency of13.56MHz, the radial electron flux moves towards the chamber wall first and then is forced in the opposite direction, whereas it exhibits two peaks within one period at the reverse-phase case. In the very high frequency discharge, i.e.,100MHz, the radial electron flux is alternately positive and negative with four peaks during one period, and the ionization mainly occurs in the sheath region at a phase difference equal to π. Furthermore, the phase shift has different influences on the plasma radial uniformity at various frequencies.
Chapter5shows the phase-shift effect on the plasma radial uniformity and the plasma composition at various frequencies and gas mixture ratios in Ar/CF4capacitively coupled plasmas. At low concentration of CF4(10%), Ar+are the major positive ions in the entire range of frequencies, and the phase-shift control shows different effects on the plasma uniformity at various frequencies. When the frequency is fixed at100MHz, the phase-shift control shows a different behavior at high concentration of CF4. For instance, the CF3+density profiles shift from edge-high over uniform to center-high at the reverse phase case, as the CF4content increases from10%to90%, which indicates that the skin effect is suppressed by the high electronegativity of the Ar/CF4=0.1/0.9mixture. Besides, the ratio of the total negative ion density to electron density decreases with increasing frequency, and it increases with CF4content.
In chapter6, a2D hybrid model, called HPEM (Hybrid Plasma Equipment Model), incorporating a full-wave solution of Maxwell's equations, is employed to investigate the electromagnetic effects on the plasma characteristics, as well as the power effect on the etch rate in CF4/O2discharges. It is shown that the electromagnetic effects have an important influence on the plasma density distribution. When the electromagnetic effects are taken into account, the plasma density becomes higher, and exhibits different shapes. At the frequency of60MHz, the etch rate has a center-high profile. When adding a low frequency power into the discharge, the etch rate becomes higher and more uniform. As the low frequency power increases from300W to1000W, the etch rate at the reactor center increases faster than at the edge, and therefore the uniformity of the etch rate becomes worse. When the low frequency power is fixed at300W, the etch rate becomes nonuniform with increasing high frequency power, and it becomes higher due to the higher plasma density.
引文
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