双频容性耦合等离子体物理特性的混合模拟
|
摘要
双频容性耦合等离子体(dual-frequency capacitively coupled plasma DF-CCP)源是半导体工业中重要的刻蚀设备,由于其可以产生大面积均匀的等离子体,通过调节高、低频源的放电参数可以有效地控制等离子体密度与离子能量、角度分布,并且结构简单成本较低,符合工业生产上的要求,双频CCP源被广泛应用在新一代的半导体刻蚀机的生产上。双频CCP源中的各物理参量(如:密度、电势、电场、离子能量与角度分布等)以及其中的物理过程对等离子体刻蚀工艺有着直接的影响,有必要对其进行深入细致的研究。而传统的理论模型分别存在着计算精度不高,计算效率较低等缺陷,无法实现对双频CCP中的物理过程进行快速准确的求解。为此,本文采用流体力学-蒙特卡洛混合模型对双频CCP中的物理过程进行全面的研究。该模型在整个放电区采用流体方法进行快速求解,在鞘层区采用蒙特卡洛方法得出入射到极板上各种粒子的能量与角度分布,既提高了计算速度又保证了计算的精度。
在第二章中首先采用一维的流体力学模型对刻蚀工艺中所关心的等离子体密度分布,鞘层区的鞘层电位降进行了研究。发现等离子体密度主要受高频电源的控制,提高高频电源的频率、电压幅值与增加放电气压均能有效的提高等离子体密度。低频电源对等离子体密度的影响很小,只有当低频频率较高,高、低频电源产生相互耦合时,提高低频频率可以增加等离子密度。在鞘层区由于电子与离子密度出现差异,使得该处的电场明显增强,电子受到鞘层电场的作用获得很高的能量,使得电子温度在鞘层区有所升高。
在第三章中采用一维的混合模型对双频CCP的Ar放电进行了模拟,对入射到极板上的离子和高能中性粒子的能量与角度分布进行了研究。双频CCP的离子能量分布呈现出多峰结构,随着放电气压的减小,轰击到基片上的离子能量显著增加。两个射频电源的参数也对离子能量分布有着显著的影响。在一定的电压幅值下,减小低频源的频率,可以使更多的离子有效的被低频电源加速,使得轰击到基板上的离子能量显著增大。通过增大施加在低频源上的电压幅值可以使得离子在穿越鞘层的过程中获得更多的能量,轰击到极板上的离子能量显著增加。随着高频源频率的增加,离子的碰撞效应减小。离子角度分布在小角度区域存在明显的峰值,多数离子以小于3°的角度垂直入射到极板上,增加低频电压与高频频率均能使更多的离子以小角度入射。高能中性粒子与Ar原子间的碰撞效应占主导地位,入射到极板上的高能中性粒子能量小于离子能量,且入射角度远大于离子入射角度。最后,我们对混合模型得出的离子能量分布进行了实验验证,发现能量分布中的能峰位置、宽度以及能量平均值与实验测量的结果基本符合,随着放电参数的改变,理论计算与实验测量结果的变化趋势也基本相同。
在第四章中对实际刻蚀工艺上应用的CF_4反应性气体进行了一维的流体力学—蒙特卡洛混合模拟。结果表明:在其放电产物中,F占较大的比重,其密度远大于电子密度,只比CF_3~+的密度稍小。由于受到鞘层电场的约束作用,负离子主要分布在等离子体区内,在鞘层附近负离子密度迅速下降,电子密度在鞘层边缘处接近正离子密度,由双极扩散形成鞘层电场。CF_4放电中正离子低能峰所对应的能量更高,并且在低气压下,低能区(0-100eV)的离子分布几乎为零。对于不同种类的离子,其能量分布曲线也各不相同,质量较低的离子由于穿越鞘层时间较短,容易受到瞬时的高频电场影响,使得其能量分布在双峰的基础上出现多个次级小峰,而质量较大的离子受高频电场调制不明显,没有次级峰的存在。模拟结果同时显示了离子能量分布也会受到化学活性的影响,活性较高的CF_3~+离子,最容易与其他活性粒子发生化学反应生成其他种类的离子并造成能量损失,因此入射到极板上CF_3~+的能量相对较低;F~+由于发生化学反应的几率相对较小,不容易与其他种类粒子发生化学反应损失能量,因而保持了较高的能量。
在第五章应用二维混合模型对CF_4放电进行了模拟,主要考察了等离子体放电在径向和轴向的二维特性以及装置的几何尺寸对等离子体参量的影响。结果表明,等离子体鞘层区在极板与侧壁处的特性并不相同,在侧壁处由于受射频源影响较小,鞘层主要由双极扩散机制形成,鞘层较薄,径向电场的强度较小。在上下两个极板附近,受到射频电场的影响,鞘层区的厚度明显增加,轴向电场的强度要远大于侧壁处的径向电场。离子能量分布在整个电极区域内基本保持不变,只是在电极的边界处受到不同方向电场的影响而稍有不同;离子通量在电极区域内呈均匀分布,在电极边缘与侧壁的区间内,由于电场强度减小离子通量迅速衰减。离子角度分布随径向的变化更为明显,在电极的中心区域,入射离子角度分布并没有明显的变化,但是在电极的边缘处,由于受到较强径向电场的影响离子的入射角度明显增大,绝大部分离子以更大的角度入射到电极上。
Dual-frequency capacitively coupled plasma (DF-CCP) is one of the crucial components for etching in microelectronic manufacturing, and has been widely used in the next generation etching applications due to its simple structure and ability to control the plasma density, the ion energy distributions(IEDs), and the ion angle distributions(IADs) separately. Because the etching process is determined directly by the physical process and the plasma parameters such as plasma density, electric field, potential, IEDs, and IADs, it is important to investigate the phenomena in a dual frequency CCP. However, the traditional theory models have their own shortcomings in accuracy and in efficiency respectively. Therefore, we use a hybrid model based on a fluid model used in the entire region for the fast calculation and a Monte-Carlo model in the sheath for the simulation of the IEDs and IADs to achieve a accurate and efficient simulation of the DF-CCP discharge.
In Chapter 2, the plasma parameters, concerned in etching process, such as plasma density, sheath potential, and electric field have been studied based on a fluid model. It finds that, the plasma density is mainly controlled by the high-frequency (HF) source and can be increased effectively by increasing either the frequency on the HF source or the pressure. The low-frequency (LF) source has little affect on it, however, when the low frequency is getting higher and the two sources begin to couple with each other, the LF source starts to affect the plasma density. The electron and ion densities remain the same value at the bulk region and begin to separate in the sheath region, which leads to an increase of the electric field at the sheath region. The electron temperature also increases in the sheath due to the acceleration to the electron by the strong electric field in this region.
In Chapter 3, a one-dimensional hybrid model has been developed to investigate the characteristics of energy and angular distributions of the ions and fast neutrals impinging on the rf-biased electrode in a dual frequency capacitively coupled Ar discharge. It shows that, the IEDs appear to have multiple peaks in the dual frequency capacitively coupled rf discharge rather than bimodal shape in a conventional single frequency rf discharge. With the decrease of the pressure, the maximum energy of IEDs and the peaks of IADs increase. The parameters of the two sources have a significant effect on the structures of IEDs. By decreasing the frequency of the LF source, more ions can be accelerated by the LF field effectively which increases the maximum energy in the IEDs. With the increase of the LF voltage, the ions gain more energy from the sheath region, therefore, they strike the process surface with a much higher energy. The IADs have a significant peak at the small angle region, and most ions strike the process surface with the angle less than 3 degrees. More ions strike the electrode with a small angle by increasing either the voltage of LF source or the frequency of HF source. The energy and angular distributions of the fast neutrals are correlative with that of the ions. Compared with the ions, the fast neutrals have a much lower energy and the scattering effect becomes more prominent. In the end we provide a group of experiment results for comparison. The position and the width of the energy peaks, and the average energy are in agreement in general, and by changing the discharge parameters, the evolution of the simulation and experiment result is almost the same.
In Chapter 4, a one-dimension hybrid model has been used to study the CF4 discharge, which is frequently used in the etching process. It shows that, the CF4 discharge has a large proportion of negative ions, and the density of F is much larger than the density of electron. Because the negative ions are constrained in the plasma region by the strong electric field in the sheath, their densities decrease apparently near the sheath region, where the density of positive ions and electrons get closer. The minimum energy in the IEDs of the positive ions correspond to a higher energy region, and in the condition of low pressure, the values of IEDs are near zero in the low energy region (typically 0-100eV). The shapes of IEDs change among the species of positive ions. The ions with a small mass traverse the sheath in a short period, which allows these ions sense the influence of the HF source, therefore, the IEDs remain some small peaks in the characteristic bimodal distribution. For the much massive ions, the transit time is much longer, resulting these ions sense a more average sheath potential, therefore, the influence of the HF source becomes less prominent on these ions, and the small peaks in the IEDs disappear while the mass of ions increases. Because an ion after a chemical reaction may consume the total energy or convert to other species, the ions with higher chemical activity which has a higher probability of reacting with other particles have a lower energy in the IEDs.
In Chapter 5, a two-dimensional hybrid model is used to study the 2D characters of the plasma parameter in axial and redial direction and the influence of the geometry structure. It finds that, the sheath structure and the electric field near the side wall are different with that near the electrode, due to the influence of the electrode, the electric field in the axial direction is much stronger than radial electric field, and the sheath in the top and the bottom region are much thicker than in the side wall of the reacting chamber. The IEDs and the ion flux incident on the electrode have little change over the electrode region, however, the electric field decreases from the edge of electrode to side wall, which leads a decrease in the ion flux in this region. IADs are almost the same at the center of the electrode, however, in the edge of the electrode, the radial electric field increases which leads more ions strike the electrode with a much larger angle.
在第二章中首先采用一维的流体力学模型对刻蚀工艺中所关心的等离子体密度分布,鞘层区的鞘层电位降进行了研究。发现等离子体密度主要受高频电源的控制,提高高频电源的频率、电压幅值与增加放电气压均能有效的提高等离子体密度。低频电源对等离子体密度的影响很小,只有当低频频率较高,高、低频电源产生相互耦合时,提高低频频率可以增加等离子密度。在鞘层区由于电子与离子密度出现差异,使得该处的电场明显增强,电子受到鞘层电场的作用获得很高的能量,使得电子温度在鞘层区有所升高。
在第三章中采用一维的混合模型对双频CCP的Ar放电进行了模拟,对入射到极板上的离子和高能中性粒子的能量与角度分布进行了研究。双频CCP的离子能量分布呈现出多峰结构,随着放电气压的减小,轰击到基片上的离子能量显著增加。两个射频电源的参数也对离子能量分布有着显著的影响。在一定的电压幅值下,减小低频源的频率,可以使更多的离子有效的被低频电源加速,使得轰击到基板上的离子能量显著增大。通过增大施加在低频源上的电压幅值可以使得离子在穿越鞘层的过程中获得更多的能量,轰击到极板上的离子能量显著增加。随着高频源频率的增加,离子的碰撞效应减小。离子角度分布在小角度区域存在明显的峰值,多数离子以小于3°的角度垂直入射到极板上,增加低频电压与高频频率均能使更多的离子以小角度入射。高能中性粒子与Ar原子间的碰撞效应占主导地位,入射到极板上的高能中性粒子能量小于离子能量,且入射角度远大于离子入射角度。最后,我们对混合模型得出的离子能量分布进行了实验验证,发现能量分布中的能峰位置、宽度以及能量平均值与实验测量的结果基本符合,随着放电参数的改变,理论计算与实验测量结果的变化趋势也基本相同。
在第四章中对实际刻蚀工艺上应用的CF_4反应性气体进行了一维的流体力学—蒙特卡洛混合模拟。结果表明:在其放电产物中,F占较大的比重,其密度远大于电子密度,只比CF_3~+的密度稍小。由于受到鞘层电场的约束作用,负离子主要分布在等离子体区内,在鞘层附近负离子密度迅速下降,电子密度在鞘层边缘处接近正离子密度,由双极扩散形成鞘层电场。CF_4放电中正离子低能峰所对应的能量更高,并且在低气压下,低能区(0-100eV)的离子分布几乎为零。对于不同种类的离子,其能量分布曲线也各不相同,质量较低的离子由于穿越鞘层时间较短,容易受到瞬时的高频电场影响,使得其能量分布在双峰的基础上出现多个次级小峰,而质量较大的离子受高频电场调制不明显,没有次级峰的存在。模拟结果同时显示了离子能量分布也会受到化学活性的影响,活性较高的CF_3~+离子,最容易与其他活性粒子发生化学反应生成其他种类的离子并造成能量损失,因此入射到极板上CF_3~+的能量相对较低;F~+由于发生化学反应的几率相对较小,不容易与其他种类粒子发生化学反应损失能量,因而保持了较高的能量。
在第五章应用二维混合模型对CF_4放电进行了模拟,主要考察了等离子体放电在径向和轴向的二维特性以及装置的几何尺寸对等离子体参量的影响。结果表明,等离子体鞘层区在极板与侧壁处的特性并不相同,在侧壁处由于受射频源影响较小,鞘层主要由双极扩散机制形成,鞘层较薄,径向电场的强度较小。在上下两个极板附近,受到射频电场的影响,鞘层区的厚度明显增加,轴向电场的强度要远大于侧壁处的径向电场。离子能量分布在整个电极区域内基本保持不变,只是在电极的边界处受到不同方向电场的影响而稍有不同;离子通量在电极区域内呈均匀分布,在电极边缘与侧壁的区间内,由于电场强度减小离子通量迅速衰减。离子角度分布随径向的变化更为明显,在电极的中心区域,入射离子角度分布并没有明显的变化,但是在电极的边缘处,由于受到较强径向电场的影响离子的入射角度明显增大,绝大部分离子以更大的角度入射到电极上。
Dual-frequency capacitively coupled plasma (DF-CCP) is one of the crucial components for etching in microelectronic manufacturing, and has been widely used in the next generation etching applications due to its simple structure and ability to control the plasma density, the ion energy distributions(IEDs), and the ion angle distributions(IADs) separately. Because the etching process is determined directly by the physical process and the plasma parameters such as plasma density, electric field, potential, IEDs, and IADs, it is important to investigate the phenomena in a dual frequency CCP. However, the traditional theory models have their own shortcomings in accuracy and in efficiency respectively. Therefore, we use a hybrid model based on a fluid model used in the entire region for the fast calculation and a Monte-Carlo model in the sheath for the simulation of the IEDs and IADs to achieve a accurate and efficient simulation of the DF-CCP discharge.
In Chapter 2, the plasma parameters, concerned in etching process, such as plasma density, sheath potential, and electric field have been studied based on a fluid model. It finds that, the plasma density is mainly controlled by the high-frequency (HF) source and can be increased effectively by increasing either the frequency on the HF source or the pressure. The low-frequency (LF) source has little affect on it, however, when the low frequency is getting higher and the two sources begin to couple with each other, the LF source starts to affect the plasma density. The electron and ion densities remain the same value at the bulk region and begin to separate in the sheath region, which leads to an increase of the electric field at the sheath region. The electron temperature also increases in the sheath due to the acceleration to the electron by the strong electric field in this region.
In Chapter 3, a one-dimensional hybrid model has been developed to investigate the characteristics of energy and angular distributions of the ions and fast neutrals impinging on the rf-biased electrode in a dual frequency capacitively coupled Ar discharge. It shows that, the IEDs appear to have multiple peaks in the dual frequency capacitively coupled rf discharge rather than bimodal shape in a conventional single frequency rf discharge. With the decrease of the pressure, the maximum energy of IEDs and the peaks of IADs increase. The parameters of the two sources have a significant effect on the structures of IEDs. By decreasing the frequency of the LF source, more ions can be accelerated by the LF field effectively which increases the maximum energy in the IEDs. With the increase of the LF voltage, the ions gain more energy from the sheath region, therefore, they strike the process surface with a much higher energy. The IADs have a significant peak at the small angle region, and most ions strike the process surface with the angle less than 3 degrees. More ions strike the electrode with a small angle by increasing either the voltage of LF source or the frequency of HF source. The energy and angular distributions of the fast neutrals are correlative with that of the ions. Compared with the ions, the fast neutrals have a much lower energy and the scattering effect becomes more prominent. In the end we provide a group of experiment results for comparison. The position and the width of the energy peaks, and the average energy are in agreement in general, and by changing the discharge parameters, the evolution of the simulation and experiment result is almost the same.
In Chapter 4, a one-dimension hybrid model has been used to study the CF4 discharge, which is frequently used in the etching process. It shows that, the CF4 discharge has a large proportion of negative ions, and the density of F is much larger than the density of electron. Because the negative ions are constrained in the plasma region by the strong electric field in the sheath, their densities decrease apparently near the sheath region, where the density of positive ions and electrons get closer. The minimum energy in the IEDs of the positive ions correspond to a higher energy region, and in the condition of low pressure, the values of IEDs are near zero in the low energy region (typically 0-100eV). The shapes of IEDs change among the species of positive ions. The ions with a small mass traverse the sheath in a short period, which allows these ions sense the influence of the HF source, therefore, the IEDs remain some small peaks in the characteristic bimodal distribution. For the much massive ions, the transit time is much longer, resulting these ions sense a more average sheath potential, therefore, the influence of the HF source becomes less prominent on these ions, and the small peaks in the IEDs disappear while the mass of ions increases. Because an ion after a chemical reaction may consume the total energy or convert to other species, the ions with higher chemical activity which has a higher probability of reacting with other particles have a lower energy in the IEDs.
In Chapter 5, a two-dimensional hybrid model is used to study the 2D characters of the plasma parameter in axial and redial direction and the influence of the geometry structure. It finds that, the sheath structure and the electric field near the side wall are different with that near the electrode, due to the influence of the electrode, the electric field in the axial direction is much stronger than radial electric field, and the sheath in the top and the bottom region are much thicker than in the side wall of the reacting chamber. The IEDs and the ion flux incident on the electrode have little change over the electrode region, however, the electric field decreases from the edge of electrode to side wall, which leads a decrease in the ion flux in this region. IADs are almost the same at the center of the electrode, however, in the edge of the electrode, the radial electric field increases which leads more ions strike the electrode with a much larger angle.
引文
[1]Lieberman M A,and Lichtenberg A J,Principles of Plasma Discharges and Material Processing.New York:Wiley,2005.中文版为:蒲以康译.等离子体放电原理与材料处理 北京:科学出版社 2007.
[2]Oehrlein G S,and Rembetski J F,Plasma-based dry etching techniques in the silicon integrated circuit technology.IBM J.Res.Develop,1992,36:140-157.
[3]Manos D M,and D L,Flamm Plasma Etching:An Introduciton.Academic Press,1989.
[4]Inayoshi M,Ito M,Hori Met al.Surface reaction of CF2 radicals for fluorocarbon film formation in SiO2/Si selective etching process.J.Vac.Sci.Technol.A,1998,16(1):233-238.
[5]Armacost M,Hoh PD,Wise R et al.Plasma-etching processes for ULSI semiconductor circuits.IBM J.Res.Develop,1999,43:39.
[6]Chang J P,Mahorowala A P,and Sawin H H,Plasma-surface kinetics and feature profile evolution in chlorine etching of polysilicon.J.Vac.Sci.Technol.A,1997,16(1):217-224(1997).
[7]Yeom G Y,and Kushner M J,Si/SiO2 etch properties using CF4 and CHF3 in radio frequency cylindrical magnetron discharges,Appl.Phys.Lett,1990,56(9):857.
[8]Kuah S H,and Wood P C,Inductively coupled plasma etching of poly-SiC in SF6chemistries,J.Vac.Sci.Technol.A,2005 23(4):947-952.
[9]Lieberman M A,Analytical solution for capacitive RF sheath.IEEE Trans.Plasma Sci.1988,16(6):638-644.
[10]Lieberman M A,Dynamics of a collisional,capacitive RF sheath.IEEE Trans.Plasma Sci.1989,17(2):338-341.
[11]Godyak V A,Piejak R B,and Sternberg N,A comparison of RF electrode sheath models.IEEE Trans.Plasma Sci.1993,21(4):378-382.
[12]Gierling J,and Riemann K U,Comparison of a consistent theory of radio frequency sheaths with step models.J.Appl.Phys.1998,83(7):3521-3528.
[13]Edelberg E A,and Aydil E S,Modeling of the sheath and the energy distribution of ions bombarding rf-biased substrates in high density plasma reactors and comparison to experimental measurements.J.Appl.Phys.1999,86(9):4799-4812.
[14]Qiu H T,Wang Y N,and Ma T C,Collisional effects on the radio-frequency sheath dynamics.J.Appl.Phys.2001,90(12):5884-5888.
[15]Dai Z L,Wang Y N,and Ma T C,Spatiotemporal characteristics of the collisionless rf sheath and the ion energy distributions arriving at rf-biased electrodes.Phys.Rev.E.2002,65:036403(1-7).
[16]Dai Z L,and Wang Y N,Multiple ion dynamics model for the collisionless rf sheaths and the ion energy distributions at rf-biased electrodes in fluorocarbon plasmas.Phys.Rev.E.2002,66:026413(1-7).
[17]Dai Z L,and Wang Y N,Simulations of ion transport in a collisional radio-frequency plasma sheath.Phys.Rev.E.2004,69:036403(1-6).
[18]戴忠玲,毛明,王友年.等离子体刻蚀工艺的物理基础.物理.2006,35(8):693-698.
[19]Chapman B N,Glow Discharge Processes,John Wiley & Sons Inc.,New York,1980.
[20]Choi S J,Ventzek P L G,Hoekstra R J et al.Spatial distributions of dust particles in plasmas generated by capacitively coupled radiofrequency discharges.Plasma Sources Sci. Technol., 1994, 3: 418-425 (1994).
[21] Wilson J L, Caughraan II J B 0, Nguyen P L et al. Measurements of time varying plasma potential, temperature, and density in a 13. 56 MHz radio-frequency discharge. J. Vac. Sci.Technol. A, 1989, 7(3): 972-976.
[22] Asmussen J, Grotjohn T A et al. The design and application of electron cyclotron resonance discharges. IEEE Trans. Plasma Sci., 1997, 25, 1196-1221.
[23] Popov 0, In Physics of Films, Edited by M. H. Francombe and J. L. Vossen, New York:Academic, 1994.
[24] Foo P D, Manocha A S, Miner J F et al. US Patent 1992, No. 5,124,014..
[25] Fujiwara N, Ogino S, Maruyama T et al. Charge accumulation effects on profile distortion in ECR plasma etching. Plasma Sources Sci. Technol., 1996, 5: 126-131.
[26] Doh H H, Kim J H, Lee S H et al. Effect of hydrogen addition to fluorocarbon gases (CF4,C4F8) in selective SiO2/Si etching by electron cyclotron resonance plasma. J. Vac. Sci.Technol. A, 1996, 14: 1088-1091.
[27] Coultas D K, and Keller J H, European Patent. 1990, No. 0379828 A2. M. Puttock, Problems and solutions for low pressure, high density, inductively coupled plasma dry etch applications. Surface and Coatings Technol., 1997, 97(1): 10-14.
[28] Carter J B, Holland J P, Peltzer E et al. Transformer coupled plasma etch technology for the fabrication of subhalf micron structures. J. Vac. Sci. Technol. A, 1993, 11(4):1301-1306.
[29] Ogle J S U.S. Patent 1990, No. 4,948,458.
[30] Keller J H, Forster J C, and Barnes S M, Novel radio-frequency induction plasma processing techniques. J. Vac. Sci. Technol. A, 1993, 11: 2487-2491.
[31] Jung K B, Lambers E S, Childress J R et al. C12-Based Inductively Coupled Plasma Etching of NiFe and Related Materials. J. Electrochemical Society, 1998, 145 (14): 4025-4028.
[32] Hopwood J, Guarnieri C R, Whitehair S J et al. Electromagnetic fields in a radio-frequency induction plasma. J. Vac. Sci. Technol. A, 1993, 11: 147-151.
[33] Hopwood J, Guarnieri C R, Whitehair S J et al. Langmuir probe measurements of a radio frequency induction plasma. J. Vac. Sci. Technol. A, 1993, 11: 152-156.
[34] Mahoney L J, Wendt A E, Barriros E et al. Electron-density and energy distributions in a planar inductively coupled discharge. J. Appl. Phys. 1994, 76: 2041-2047.
[35] Ventzek P L G, Hoekstra R J, and Kushner M J, Two-dimensional modeling of high plasma density inductively coupled sources for materials processing. J. Vac. Sci. Technol. B, 1994,12(1): 461-477.
[36] DiPeso G, Vahedi V, Hewett D W et al. Two-dimensional Self-consistent Fluid Simulation of Radio Frequency Inductive Sources. J. Vac. Sci. Technol. A, 1994, 12(4): 1387-1396.
[37] Stewart R, Vitello P, and Graves D B, Two-dimensional fluid model of high density inductively coupled plasma sources. J. Vac. Sci. Technol. B, 1994, 12(1): 478-485.
[38] Lee J K, Babaeva N Y, Kim H C et al. Simulation of capacitively coupled single- and dual-frequency RF discharges. IEEE Trans. Plasma Sci. 2004, 32(1): 47-53.
[39] Lee J K. Modeling of Processing Plasmas and Their Fundamentals, (academic report)
[40] Goto H H, Lowe H D, and Ohmi T, Dual excitation reactive ion etcher for low energy plasma processing. J. Vac. Sci. Technol. A, 1992, 10: 3048-3054.
[41] Kitajima T, Takeo Y, and Makabe T. Two-dimensional CT images of two-frequency capacitively coupled plasma. J. Vac. Sci. Technol. A 1999, 17: 2510-2516.
[42] Sekine M. Study for plasma etching of dielectric film in semiconductor device manufacturing. Review of ASET research project Pure Appl. Chem., 2002, 74(3): 381-395.
[43] Ohmori T. Takeshi Goto and Toshiaki Makabe Negative charge injection to a wafer in a pulsed two-frequency capacitively coupled plasma for oxide etching; diagnostics by emission-selected computerized tomography, J. Phys. D: Appl. Phys. 2004, 37: 2223-2231.
[44] Braginsky O V, Kovalev A S, Lopaev D V. Experimental Study of Dual Frequency RF Discharges in Argon for different gas pressures, 28th ICPIG, 2007 Prague, Czech Republi July 15-20: 2114-2117
[45] Lee C H, Kim D H and Lee N E. Effect of different frequency combination on ArF photoresist deformation and silicon dioxide etching in the dual frequency superimposed capacitively coupled plasmas, J. Vac. Sci. Technol. A, 2006, 24(4): 1386-1394
[46] Gans T, Schulze J, Turner M M et al. Frequency coupling in dual frequency capacitively coupled radio-frequency plasmas, Applied Physics Letters, 2006, 89: 261502(1-3).
[47] Turner M M, and Chabert P. Collisionless Heating in Capacitive Discharges Enhanced by Dual-Frequency Excitation. Phys. Rev. Lett. 2006, 96: 205001 (1-4).
[48] Myers F R, Ramaswami M, and Cale T S. Prediction of Ion Energy and Angular Distributions in Single and Dual Frequency Plasmas. J. Electrochem. Soc. 1994, 141: 1313-1320.
[49] Robiche J, Boyle P C, Turner M M et al. Analytical model of a dual frequency capacitive sheath J. Phys. D, 2003, 36:1810-1816.
[50] Kim H C, and Lee J K. Dual radio-frequency discharges: Effective frequency concept and effective frequency transition. J. Vac. Sci. Technol. A. 2005,23: 651-657.
[51] Guan Z Q, Daia Z L, and Wang Y N. Simulations of dual rf-biased sheaths and ion energy distributions arriving at a dual rf-biased electrode Phys. Plasmas 2005 12: 123502 1-8.
[52] Salabas A and Brinkmann R P. Numerical investigation of dual frequency capacitively coupled hydrogen plasmas, Plasma Sources Sci. Technol. 2005,14: S53 - S59.
[53] Kim H C, Manousiouthakis V I. J. Vac. Sci. Technol. A, 1998,16: 2162
[54] V. Georgieva, A. Bogaerts, and R. J. Gijbels, Numerical simulation of dual frequency etching reactors: Influence of the external process parameters on the plasma characteristics. Appl. Phys. 2005, 98: 023308 1-13..
[55] Lee J K, Manuilenkol 0 V, Babaeval N Y et al. Ion energy distribution control in single and dual frequency capacitive plasma sources. Plasma Sources Sci. Technol. 2005, 14: 89-97.
[56] Lee J K, Babaeva, Yu N et al, Simulation of capacitively coupled single and dual-frequency RF discharges, Plasma Science IEEE Transactions on, 2004, 32(1): 47-53.
[57] Wakayama G and Nanbu K. Study on the Dual Frequency Capacitively Coupled Plasmas by the Particle-in-Cell/Monte Carlo Method IEEE TRANSACTIONS ON PLASMA SCIENCE, 2003, 31(4):638-644.
[58] Rauf S, Kushner M J, Nonlinear dynamics of radio frequency plasma processing reactorspowered by multifrequency sources. IEEE Trans. Plasma Sci., 1999, 27(5): 1329-1338.
[59] Rauf S, Dual radio frequency sources in a magnetized capacitively coupled plasma discharge. IEEE Trans. Plasma Sci., 2003, 31(4): 471-478.
[60] Tsai J H and Wu C, Two-dimensional simulations of rf glow discharges in N2 and SF6.Phys. Rev. A, 1990, 41: 5626-5644.
[61] Boeuf J P, Numerical model of rf glow discharges. Phys. Rev., 1987, A36: 2782-2792.
[62] Boeuf J P, Pitchford L C, Fiala A et al. Modelling of discharges and non-thermal plasmas :applications to plasma processing. Surf. And Coat. Technol., 1993, 59: 32-40.
[63] Young F F, and Wu C, Radial flow effects in a multidimensional, three-moment fluid model of radio frequency glow discharges. Appl. Phys. Lett., 1993, 62: 473.
[64] Young F F and Wu C, Two-dimensional, self-consistent, three-moment simulation of RFglow discharge. IEEE Trans. Plasma Sci., 1993, 21(3): 312-321.
[65] Georgieva V, Bogaerts A, and Gijbels R, Numerical investigation of ion-energy-distribution functions in single and dual frequency capacitively coupled plasma reactors. Phys. Rev. E., 2004, 69: 0264061-0264071.
[66] Georgieva V, Bogaerts A., Negative ion behavior in single- and dual-frequency plasma etching reactors: Particle-in-cell/Monte Carlo collision study. Phys. Rev. E, 2006, 73:036402-036410.
[67] Kim H C, Lee J K, Dual radio-frequency discharges: Effective frequency concept and effective frequency transition. J. Vac. Sci. Technol. A, 2005, 23: 651-657.
[68] Lee J K, Manuilenko 0 V, Babaeva N et al., Ion energy distribution control in single and dual frequency capacitive plasma sources. Plasma Sources Sci. Technol., 2005, 14:89-97.
[69] Birdsall C K, Traveling-wave-tube simulation: The IBC code. IEEE Trans. Plasma Sci.,1990, 18: 482-489.
[70] Surendra M, and Graves D B, Particle simulations of radio-frequency glow discharges.IEEE Trans. Plasma Sci., 1991, 19(2): 144-157.
[71] Alves M V, Lieberman M A, Vahedi V et al. A one-dimensional collisional model for plasma-immersion ion implantation. J. Appl. Phys., 1991, 69(4): 3823,
[72] Turner M M, and Hopkins H B, Anomalous sheath heating in a low pressure rf discharge in nitrogen. Phys. Rev. Lett., 1992, 69: 3511-3514.
[73] Vahedi V, Birdsall C K, M. A. Lieberman, G. DiPeso, and T. D. Rognlien, Capacitive RF discharges modelled by particle-in-cell Monte Carlo simulation. II. Comparisons with laboratory measurements of electron energy distribution functions. Plasma Sources Sci.Technol., 1993, 2: 273-278.
[74] Godyak V A and Piejak R B, Abnormally low electron energy and heating-mode transition in a low-pressure argon rf discharge at 13.56 MHz. Phys. Rev. Lett., 1990, 65: 996-999.
[75] Georgieva V, Bogaerts A, and Gijbels R, Particle-in-cell/Monte Carlo simulation of a capacitively coupled radio frequency Ar/CF4 discharge: Effect of gas composition. J. Appl.Phys., 2003, 93: 2369-2379.
[76] Georgieva V, Bogaerts A, and Gijbels R, Numerical study of Ar/CF4/N2 discharges in single - and dual - frequency capacityively coupled plasma reactors. J. Appl. Phys.,2003, 94: 3748-3756.
[77] Birdsall C K, and Langdon A B, Plasma Physics via Computer Simulation (Hilger, New York,1991
[78] Sommerer T J, and Kushner M J, Numerical investigation of the kinetics and chemistry of rf glow discharge plasmas sustained in He, N_2, O_2, He/N_2/O_2, He/CF_4/O_2, and SiH_4/NH_3 using a Monte Carlo-fluid hybrid model. J. Appl. Phys., 1992, 71: 1654-1673.
[79] Ventzek P L, Hoekstra R J, Sommerer T J et al. Two-dimensional hybrid model of inductively coupled plasma sources for etching. Appl. Phys. Lett., 1993, 63: 605-607
[80] Kratzer M, Brinkmann R P, Sabischa W et al. Hybrid model for the calculation of ion distribution functions behind a direct current or radio frequency driven plasma boundary sheath. J. Appl. Phys. 2001, 90: 2169-2179.
[81] Sato N, and Tagashira H, A hybrid Monte Carlo/fluid model of RF plasmas in aSiH_4/H_2 mixture IEEE Trans. Plasma Sci. 1991, 19: 102-112.
[82] Georgieva V and Bogaerts A, Numerical investigation of ion-energy-distribution functions in single and dual frequency capacitively coupled plasma reactors. Phys. Rev.E 2004, 69: 026406.
[83] Mizutani N.and Hayashi T, Charge Exchange Ion Energy Distribution at the RF Electrode in a Plasma Etching Chamber. Jpn. J. Appl. Phys. 1999,38: 4206-4212.
[84] Manenschijn A and Goedheer W J, Angular ion and neutral energy distribution in a collisional rf sheath. J. Appl. Phys. 1991,69: 2923-2930.
[85] Mizutani N and Hayashi T, Ion energy distribution at an r. f. -biased electrode in an inductively coupled plasma affected by collisions in a sheath. Thin Solid Films, 2000, 374:167-174.
[86] Bukowski J D, Graves D B, and Vitello P, Two-dimensional fluid model of an inductively coupled plasma with comparison to experimental spatial profiles J. Appl. Phys.. 1996, 80(5):2614-2623.
[87] Boeuf J P and Pitchford L C, Two-dimensional model of a capacitively coupled rf discharge and comparisons with experiments in the Gaseous Electronics Conference reference reactor.Phys. Rev. E. 1995, 51: 1376-1390.
[88] Passchier J D, Goedheer W J, A two-dimensional fluid model for an argon rf discharge.J. Appl. Phys.. 1993, 74(6): 3744-3751.
[89] Boris J P, Book D L, Flux-corrected transport. I.SHASTA, a fluid transport algorithm that works, J. Comput. Phys., 1973, 11(1):38-69.
[90] Book D L, Boris J P, Hain K, Flux-corrected transport II: Generalizations of the method.J. Comput. Phys., 1975, 18(3):248-283.
[91] Zalesak S T, Fully multidimensional flux-corrected transport algorithms for fluids.J. Comput. Phys., 1979, 31(3):335-362.
[92] Kim H C, Lee J K, and Shon J W, Analytic model for a dual frequency capacitive discharge.Phys. Plasmas, 2003, 10:4545-4551.
[93] Surendra M, Graves D B, and Jellum G M, Self-consistent model of a direct-current glow discharge: Treatment of fast electrons. Phys. Rev. A. 1990, 41: 1112-1125.
[94] Vahedi V, and Surendra M, A Monte Carlo collision model for the particle-in-cell method:applications to argon and oxygen discharges. Computer Physics Communications. 1995, 87,179-198.
[95] Vahedi V, Birdsall C K, Lieberman M A et al. Verification of frequency scaling laws for capacitive radio-frequencydischarges using two-dimensional simulations, Phys. Fluids B 1993, 5:2719-2729.
[96] Birdsall C K, Particle-in-cell charged-particle simulations, plus Monte Carlo collisions with neutral atoms, PIC-MCC. IEEE Trans. Plasma Sci. 1991, 19(2): 65-85.
[97] Phelps A V, Verification of frequency scaling laws for capacitive radio-frequency discharges using two-dimensional simulations J. Appl. Phys. 1994,76: 747.
[98] Xiao-Song Li, Zhen-Hua Bi, Da-Lei Chang, Zhi-Cheng Li, Shuai Wang, Xiang Xu, Yong Xu,Wen-Qi Lu, Ai-Min Zhu and You-Nian Wang. Modulating effects of low-frequency source on ion energy distributions for dual frequency capacitively coupled argon plasma. Applied Physics Letters, 2008, 92 (24):
[99] Butterbaugh J W, Gray DC, and H. H. Sawin, Plasma - surface interactions in fluorocarbon etching of silicon dioxide. J. Vac. Sci. Technol. B,1991, 9: 1461-1470.
[100] Cheeks T L, and Ruoff A L, The effect of fluorine atoms on silicon and fluorocarbon etching in reactive ion beam etching. J. Vac. Sci. Technol. A, 1987, 5: 1917-1920.
[101] Chinzei Y, Feurprier Y, Ozawa M, Kikuchi T et al. High aspect ratio Si02 etching with high resist selectivity improved by addition of organosilane to tetrafluoroethyl trifluoromethyl ether. J. Vac. Sci. Technol. A, 2000, 18: 158-165.
[102] Booth J P, Optical and electrical diagnostics of fluorocarbon plasma etching processes. Plasma Sources Sci. Technol., 1999, 8: 249-257.
[103] Oehrlein G S, Zhang Y, Vender D et al. Fluorocarbon high-density plasmas. II. Silicon dioxide and silicon etching using CF4 and CHF3. J. Vac. Sci. Technol. A, 1994, 12:333-344.
[104] Bariya A J, Frank C W, and McVittie J P, A Surface Kinetic Model for Plasma Polymerization with Application to Plasma Etching. J. Electrochem. Soc., 1990, 137:2575-2581.
[105] Kastenmeiter B E E, Matsuo P J, Oehrlein G S et al. Remote plasma etching of silicon nitride and silicon dioxide using NF3/02 gas mixtures. J. Vac. Sci. Technol. A, 1998, 16:2047-2056.
[106] Samukawa S, and Furuoya S, Polymerization for Highly Selective Si02 Plasma Etching.Jpn. J. Appl. Phys., Part 2, 1993, 32: L1289-L1292.
[107] Standaert F M, Schaepkens M, Rueger N R et al. High density fluoFocarbon etching of silicon in an inductively coupled plasma: Mechanism of etching through a thick steady state fluorocarbon layer. J. Vac. Sci. Technol. A, 1998, 16: 239-249.
[108] Schaepkens M, Oehrlein G S, Hedlund C et al. Selective Si02-to-Si3N4 etching in inductively coupled fluorocarbon plasmas: Angular dependence of Si02 and Si3N4 etching rates. J. Vac. Sci. Technol. A, 1998, 16: 3281-3286.
[109] Mantzaris N V, Boudouvis A,and Gogolides E, Radio-frequency plasmas in CF4:Self-consistent modeling of the plasma physics and chemistry. Journal of Applied Physics.1995, 77: 6169-6180.
[110] So S Y, Oda A, Sugawara H et al. Transient behaviour of CF4 rf plasmas after step changes of power source voltage. J. Phys. D, 2001, 34: 1919-1927.
[111] Denpoh K, and Nanbu K, Self-consistent particle simulation of radio-frequency CF4 discharge with implementation of all ion-neutral reactive collisions. Journal of Vacuum Science & Technology A. 1998, 16(3):1201-1206.
[112] Hoekstra R J, Grapperhaus M J, and Kushner M J, Integrated plasma equipment model for polysilicon etch profiles in an inductively coupled plasma reactor with subwafer and superwafer topography. J. Vac. Sci. Technol. A, 1997, 15(4):1913-1921.
[2]Oehrlein G S,and Rembetski J F,Plasma-based dry etching techniques in the silicon integrated circuit technology.IBM J.Res.Develop,1992,36:140-157.
[3]Manos D M,and D L,Flamm Plasma Etching:An Introduciton.Academic Press,1989.
[4]Inayoshi M,Ito M,Hori Met al.Surface reaction of CF2 radicals for fluorocarbon film formation in SiO2/Si selective etching process.J.Vac.Sci.Technol.A,1998,16(1):233-238.
[5]Armacost M,Hoh PD,Wise R et al.Plasma-etching processes for ULSI semiconductor circuits.IBM J.Res.Develop,1999,43:39.
[6]Chang J P,Mahorowala A P,and Sawin H H,Plasma-surface kinetics and feature profile evolution in chlorine etching of polysilicon.J.Vac.Sci.Technol.A,1997,16(1):217-224(1997).
[7]Yeom G Y,and Kushner M J,Si/SiO2 etch properties using CF4 and CHF3 in radio frequency cylindrical magnetron discharges,Appl.Phys.Lett,1990,56(9):857.
[8]Kuah S H,and Wood P C,Inductively coupled plasma etching of poly-SiC in SF6chemistries,J.Vac.Sci.Technol.A,2005 23(4):947-952.
[9]Lieberman M A,Analytical solution for capacitive RF sheath.IEEE Trans.Plasma Sci.1988,16(6):638-644.
[10]Lieberman M A,Dynamics of a collisional,capacitive RF sheath.IEEE Trans.Plasma Sci.1989,17(2):338-341.
[11]Godyak V A,Piejak R B,and Sternberg N,A comparison of RF electrode sheath models.IEEE Trans.Plasma Sci.1993,21(4):378-382.
[12]Gierling J,and Riemann K U,Comparison of a consistent theory of radio frequency sheaths with step models.J.Appl.Phys.1998,83(7):3521-3528.
[13]Edelberg E A,and Aydil E S,Modeling of the sheath and the energy distribution of ions bombarding rf-biased substrates in high density plasma reactors and comparison to experimental measurements.J.Appl.Phys.1999,86(9):4799-4812.
[14]Qiu H T,Wang Y N,and Ma T C,Collisional effects on the radio-frequency sheath dynamics.J.Appl.Phys.2001,90(12):5884-5888.
[15]Dai Z L,Wang Y N,and Ma T C,Spatiotemporal characteristics of the collisionless rf sheath and the ion energy distributions arriving at rf-biased electrodes.Phys.Rev.E.2002,65:036403(1-7).
[16]Dai Z L,and Wang Y N,Multiple ion dynamics model for the collisionless rf sheaths and the ion energy distributions at rf-biased electrodes in fluorocarbon plasmas.Phys.Rev.E.2002,66:026413(1-7).
[17]Dai Z L,and Wang Y N,Simulations of ion transport in a collisional radio-frequency plasma sheath.Phys.Rev.E.2004,69:036403(1-6).
[18]戴忠玲,毛明,王友年.等离子体刻蚀工艺的物理基础.物理.2006,35(8):693-698.
[19]Chapman B N,Glow Discharge Processes,John Wiley & Sons Inc.,New York,1980.
[20]Choi S J,Ventzek P L G,Hoekstra R J et al.Spatial distributions of dust particles in plasmas generated by capacitively coupled radiofrequency discharges.Plasma Sources Sci. Technol., 1994, 3: 418-425 (1994).
[21] Wilson J L, Caughraan II J B 0, Nguyen P L et al. Measurements of time varying plasma potential, temperature, and density in a 13. 56 MHz radio-frequency discharge. J. Vac. Sci.Technol. A, 1989, 7(3): 972-976.
[22] Asmussen J, Grotjohn T A et al. The design and application of electron cyclotron resonance discharges. IEEE Trans. Plasma Sci., 1997, 25, 1196-1221.
[23] Popov 0, In Physics of Films, Edited by M. H. Francombe and J. L. Vossen, New York:Academic, 1994.
[24] Foo P D, Manocha A S, Miner J F et al. US Patent 1992, No. 5,124,014..
[25] Fujiwara N, Ogino S, Maruyama T et al. Charge accumulation effects on profile distortion in ECR plasma etching. Plasma Sources Sci. Technol., 1996, 5: 126-131.
[26] Doh H H, Kim J H, Lee S H et al. Effect of hydrogen addition to fluorocarbon gases (CF4,C4F8) in selective SiO2/Si etching by electron cyclotron resonance plasma. J. Vac. Sci.Technol. A, 1996, 14: 1088-1091.
[27] Coultas D K, and Keller J H, European Patent. 1990, No. 0379828 A2. M. Puttock, Problems and solutions for low pressure, high density, inductively coupled plasma dry etch applications. Surface and Coatings Technol., 1997, 97(1): 10-14.
[28] Carter J B, Holland J P, Peltzer E et al. Transformer coupled plasma etch technology for the fabrication of subhalf micron structures. J. Vac. Sci. Technol. A, 1993, 11(4):1301-1306.
[29] Ogle J S U.S. Patent 1990, No. 4,948,458.
[30] Keller J H, Forster J C, and Barnes S M, Novel radio-frequency induction plasma processing techniques. J. Vac. Sci. Technol. A, 1993, 11: 2487-2491.
[31] Jung K B, Lambers E S, Childress J R et al. C12-Based Inductively Coupled Plasma Etching of NiFe and Related Materials. J. Electrochemical Society, 1998, 145 (14): 4025-4028.
[32] Hopwood J, Guarnieri C R, Whitehair S J et al. Electromagnetic fields in a radio-frequency induction plasma. J. Vac. Sci. Technol. A, 1993, 11: 147-151.
[33] Hopwood J, Guarnieri C R, Whitehair S J et al. Langmuir probe measurements of a radio frequency induction plasma. J. Vac. Sci. Technol. A, 1993, 11: 152-156.
[34] Mahoney L J, Wendt A E, Barriros E et al. Electron-density and energy distributions in a planar inductively coupled discharge. J. Appl. Phys. 1994, 76: 2041-2047.
[35] Ventzek P L G, Hoekstra R J, and Kushner M J, Two-dimensional modeling of high plasma density inductively coupled sources for materials processing. J. Vac. Sci. Technol. B, 1994,12(1): 461-477.
[36] DiPeso G, Vahedi V, Hewett D W et al. Two-dimensional Self-consistent Fluid Simulation of Radio Frequency Inductive Sources. J. Vac. Sci. Technol. A, 1994, 12(4): 1387-1396.
[37] Stewart R, Vitello P, and Graves D B, Two-dimensional fluid model of high density inductively coupled plasma sources. J. Vac. Sci. Technol. B, 1994, 12(1): 478-485.
[38] Lee J K, Babaeva N Y, Kim H C et al. Simulation of capacitively coupled single- and dual-frequency RF discharges. IEEE Trans. Plasma Sci. 2004, 32(1): 47-53.
[39] Lee J K. Modeling of Processing Plasmas and Their Fundamentals, (academic report)
[40] Goto H H, Lowe H D, and Ohmi T, Dual excitation reactive ion etcher for low energy plasma processing. J. Vac. Sci. Technol. A, 1992, 10: 3048-3054.
[41] Kitajima T, Takeo Y, and Makabe T. Two-dimensional CT images of two-frequency capacitively coupled plasma. J. Vac. Sci. Technol. A 1999, 17: 2510-2516.
[42] Sekine M. Study for plasma etching of dielectric film in semiconductor device manufacturing. Review of ASET research project Pure Appl. Chem., 2002, 74(3): 381-395.
[43] Ohmori T. Takeshi Goto and Toshiaki Makabe Negative charge injection to a wafer in a pulsed two-frequency capacitively coupled plasma for oxide etching; diagnostics by emission-selected computerized tomography, J. Phys. D: Appl. Phys. 2004, 37: 2223-2231.
[44] Braginsky O V, Kovalev A S, Lopaev D V. Experimental Study of Dual Frequency RF Discharges in Argon for different gas pressures, 28th ICPIG, 2007 Prague, Czech Republi July 15-20: 2114-2117
[45] Lee C H, Kim D H and Lee N E. Effect of different frequency combination on ArF photoresist deformation and silicon dioxide etching in the dual frequency superimposed capacitively coupled plasmas, J. Vac. Sci. Technol. A, 2006, 24(4): 1386-1394
[46] Gans T, Schulze J, Turner M M et al. Frequency coupling in dual frequency capacitively coupled radio-frequency plasmas, Applied Physics Letters, 2006, 89: 261502(1-3).
[47] Turner M M, and Chabert P. Collisionless Heating in Capacitive Discharges Enhanced by Dual-Frequency Excitation. Phys. Rev. Lett. 2006, 96: 205001 (1-4).
[48] Myers F R, Ramaswami M, and Cale T S. Prediction of Ion Energy and Angular Distributions in Single and Dual Frequency Plasmas. J. Electrochem. Soc. 1994, 141: 1313-1320.
[49] Robiche J, Boyle P C, Turner M M et al. Analytical model of a dual frequency capacitive sheath J. Phys. D, 2003, 36:1810-1816.
[50] Kim H C, and Lee J K. Dual radio-frequency discharges: Effective frequency concept and effective frequency transition. J. Vac. Sci. Technol. A. 2005,23: 651-657.
[51] Guan Z Q, Daia Z L, and Wang Y N. Simulations of dual rf-biased sheaths and ion energy distributions arriving at a dual rf-biased electrode Phys. Plasmas 2005 12: 123502 1-8.
[52] Salabas A and Brinkmann R P. Numerical investigation of dual frequency capacitively coupled hydrogen plasmas, Plasma Sources Sci. Technol. 2005,14: S53 - S59.
[53] Kim H C, Manousiouthakis V I. J. Vac. Sci. Technol. A, 1998,16: 2162
[54] V. Georgieva, A. Bogaerts, and R. J. Gijbels, Numerical simulation of dual frequency etching reactors: Influence of the external process parameters on the plasma characteristics. Appl. Phys. 2005, 98: 023308 1-13..
[55] Lee J K, Manuilenkol 0 V, Babaeval N Y et al. Ion energy distribution control in single and dual frequency capacitive plasma sources. Plasma Sources Sci. Technol. 2005, 14: 89-97.
[56] Lee J K, Babaeva, Yu N et al, Simulation of capacitively coupled single and dual-frequency RF discharges, Plasma Science IEEE Transactions on, 2004, 32(1): 47-53.
[57] Wakayama G and Nanbu K. Study on the Dual Frequency Capacitively Coupled Plasmas by the Particle-in-Cell/Monte Carlo Method IEEE TRANSACTIONS ON PLASMA SCIENCE, 2003, 31(4):638-644.
[58] Rauf S, Kushner M J, Nonlinear dynamics of radio frequency plasma processing reactorspowered by multifrequency sources. IEEE Trans. Plasma Sci., 1999, 27(5): 1329-1338.
[59] Rauf S, Dual radio frequency sources in a magnetized capacitively coupled plasma discharge. IEEE Trans. Plasma Sci., 2003, 31(4): 471-478.
[60] Tsai J H and Wu C, Two-dimensional simulations of rf glow discharges in N2 and SF6.Phys. Rev. A, 1990, 41: 5626-5644.
[61] Boeuf J P, Numerical model of rf glow discharges. Phys. Rev., 1987, A36: 2782-2792.
[62] Boeuf J P, Pitchford L C, Fiala A et al. Modelling of discharges and non-thermal plasmas :applications to plasma processing. Surf. And Coat. Technol., 1993, 59: 32-40.
[63] Young F F, and Wu C, Radial flow effects in a multidimensional, three-moment fluid model of radio frequency glow discharges. Appl. Phys. Lett., 1993, 62: 473.
[64] Young F F and Wu C, Two-dimensional, self-consistent, three-moment simulation of RFglow discharge. IEEE Trans. Plasma Sci., 1993, 21(3): 312-321.
[65] Georgieva V, Bogaerts A, and Gijbels R, Numerical investigation of ion-energy-distribution functions in single and dual frequency capacitively coupled plasma reactors. Phys. Rev. E., 2004, 69: 0264061-0264071.
[66] Georgieva V, Bogaerts A., Negative ion behavior in single- and dual-frequency plasma etching reactors: Particle-in-cell/Monte Carlo collision study. Phys. Rev. E, 2006, 73:036402-036410.
[67] Kim H C, Lee J K, Dual radio-frequency discharges: Effective frequency concept and effective frequency transition. J. Vac. Sci. Technol. A, 2005, 23: 651-657.
[68] Lee J K, Manuilenko 0 V, Babaeva N et al., Ion energy distribution control in single and dual frequency capacitive plasma sources. Plasma Sources Sci. Technol., 2005, 14:89-97.
[69] Birdsall C K, Traveling-wave-tube simulation: The IBC code. IEEE Trans. Plasma Sci.,1990, 18: 482-489.
[70] Surendra M, and Graves D B, Particle simulations of radio-frequency glow discharges.IEEE Trans. Plasma Sci., 1991, 19(2): 144-157.
[71] Alves M V, Lieberman M A, Vahedi V et al. A one-dimensional collisional model for plasma-immersion ion implantation. J. Appl. Phys., 1991, 69(4): 3823,
[72] Turner M M, and Hopkins H B, Anomalous sheath heating in a low pressure rf discharge in nitrogen. Phys. Rev. Lett., 1992, 69: 3511-3514.
[73] Vahedi V, Birdsall C K, M. A. Lieberman, G. DiPeso, and T. D. Rognlien, Capacitive RF discharges modelled by particle-in-cell Monte Carlo simulation. II. Comparisons with laboratory measurements of electron energy distribution functions. Plasma Sources Sci.Technol., 1993, 2: 273-278.
[74] Godyak V A and Piejak R B, Abnormally low electron energy and heating-mode transition in a low-pressure argon rf discharge at 13.56 MHz. Phys. Rev. Lett., 1990, 65: 996-999.
[75] Georgieva V, Bogaerts A, and Gijbels R, Particle-in-cell/Monte Carlo simulation of a capacitively coupled radio frequency Ar/CF4 discharge: Effect of gas composition. J. Appl.Phys., 2003, 93: 2369-2379.
[76] Georgieva V, Bogaerts A, and Gijbels R, Numerical study of Ar/CF4/N2 discharges in single - and dual - frequency capacityively coupled plasma reactors. J. Appl. Phys.,2003, 94: 3748-3756.
[77] Birdsall C K, and Langdon A B, Plasma Physics via Computer Simulation (Hilger, New York,1991
[78] Sommerer T J, and Kushner M J, Numerical investigation of the kinetics and chemistry of rf glow discharge plasmas sustained in He, N_2, O_2, He/N_2/O_2, He/CF_4/O_2, and SiH_4/NH_3 using a Monte Carlo-fluid hybrid model. J. Appl. Phys., 1992, 71: 1654-1673.
[79] Ventzek P L, Hoekstra R J, Sommerer T J et al. Two-dimensional hybrid model of inductively coupled plasma sources for etching. Appl. Phys. Lett., 1993, 63: 605-607
[80] Kratzer M, Brinkmann R P, Sabischa W et al. Hybrid model for the calculation of ion distribution functions behind a direct current or radio frequency driven plasma boundary sheath. J. Appl. Phys. 2001, 90: 2169-2179.
[81] Sato N, and Tagashira H, A hybrid Monte Carlo/fluid model of RF plasmas in aSiH_4/H_2 mixture IEEE Trans. Plasma Sci. 1991, 19: 102-112.
[82] Georgieva V and Bogaerts A, Numerical investigation of ion-energy-distribution functions in single and dual frequency capacitively coupled plasma reactors. Phys. Rev.E 2004, 69: 026406.
[83] Mizutani N.and Hayashi T, Charge Exchange Ion Energy Distribution at the RF Electrode in a Plasma Etching Chamber. Jpn. J. Appl. Phys. 1999,38: 4206-4212.
[84] Manenschijn A and Goedheer W J, Angular ion and neutral energy distribution in a collisional rf sheath. J. Appl. Phys. 1991,69: 2923-2930.
[85] Mizutani N and Hayashi T, Ion energy distribution at an r. f. -biased electrode in an inductively coupled plasma affected by collisions in a sheath. Thin Solid Films, 2000, 374:167-174.
[86] Bukowski J D, Graves D B, and Vitello P, Two-dimensional fluid model of an inductively coupled plasma with comparison to experimental spatial profiles J. Appl. Phys.. 1996, 80(5):2614-2623.
[87] Boeuf J P and Pitchford L C, Two-dimensional model of a capacitively coupled rf discharge and comparisons with experiments in the Gaseous Electronics Conference reference reactor.Phys. Rev. E. 1995, 51: 1376-1390.
[88] Passchier J D, Goedheer W J, A two-dimensional fluid model for an argon rf discharge.J. Appl. Phys.. 1993, 74(6): 3744-3751.
[89] Boris J P, Book D L, Flux-corrected transport. I.SHASTA, a fluid transport algorithm that works, J. Comput. Phys., 1973, 11(1):38-69.
[90] Book D L, Boris J P, Hain K, Flux-corrected transport II: Generalizations of the method.J. Comput. Phys., 1975, 18(3):248-283.
[91] Zalesak S T, Fully multidimensional flux-corrected transport algorithms for fluids.J. Comput. Phys., 1979, 31(3):335-362.
[92] Kim H C, Lee J K, and Shon J W, Analytic model for a dual frequency capacitive discharge.Phys. Plasmas, 2003, 10:4545-4551.
[93] Surendra M, Graves D B, and Jellum G M, Self-consistent model of a direct-current glow discharge: Treatment of fast electrons. Phys. Rev. A. 1990, 41: 1112-1125.
[94] Vahedi V, and Surendra M, A Monte Carlo collision model for the particle-in-cell method:applications to argon and oxygen discharges. Computer Physics Communications. 1995, 87,179-198.
[95] Vahedi V, Birdsall C K, Lieberman M A et al. Verification of frequency scaling laws for capacitive radio-frequencydischarges using two-dimensional simulations, Phys. Fluids B 1993, 5:2719-2729.
[96] Birdsall C K, Particle-in-cell charged-particle simulations, plus Monte Carlo collisions with neutral atoms, PIC-MCC. IEEE Trans. Plasma Sci. 1991, 19(2): 65-85.
[97] Phelps A V, Verification of frequency scaling laws for capacitive radio-frequency discharges using two-dimensional simulations J. Appl. Phys. 1994,76: 747.
[98] Xiao-Song Li, Zhen-Hua Bi, Da-Lei Chang, Zhi-Cheng Li, Shuai Wang, Xiang Xu, Yong Xu,Wen-Qi Lu, Ai-Min Zhu and You-Nian Wang. Modulating effects of low-frequency source on ion energy distributions for dual frequency capacitively coupled argon plasma. Applied Physics Letters, 2008, 92 (24):
[99] Butterbaugh J W, Gray DC, and H. H. Sawin, Plasma - surface interactions in fluorocarbon etching of silicon dioxide. J. Vac. Sci. Technol. B,1991, 9: 1461-1470.
[100] Cheeks T L, and Ruoff A L, The effect of fluorine atoms on silicon and fluorocarbon etching in reactive ion beam etching. J. Vac. Sci. Technol. A, 1987, 5: 1917-1920.
[101] Chinzei Y, Feurprier Y, Ozawa M, Kikuchi T et al. High aspect ratio Si02 etching with high resist selectivity improved by addition of organosilane to tetrafluoroethyl trifluoromethyl ether. J. Vac. Sci. Technol. A, 2000, 18: 158-165.
[102] Booth J P, Optical and electrical diagnostics of fluorocarbon plasma etching processes. Plasma Sources Sci. Technol., 1999, 8: 249-257.
[103] Oehrlein G S, Zhang Y, Vender D et al. Fluorocarbon high-density plasmas. II. Silicon dioxide and silicon etching using CF4 and CHF3. J. Vac. Sci. Technol. A, 1994, 12:333-344.
[104] Bariya A J, Frank C W, and McVittie J P, A Surface Kinetic Model for Plasma Polymerization with Application to Plasma Etching. J. Electrochem. Soc., 1990, 137:2575-2581.
[105] Kastenmeiter B E E, Matsuo P J, Oehrlein G S et al. Remote plasma etching of silicon nitride and silicon dioxide using NF3/02 gas mixtures. J. Vac. Sci. Technol. A, 1998, 16:2047-2056.
[106] Samukawa S, and Furuoya S, Polymerization for Highly Selective Si02 Plasma Etching.Jpn. J. Appl. Phys., Part 2, 1993, 32: L1289-L1292.
[107] Standaert F M, Schaepkens M, Rueger N R et al. High density fluoFocarbon etching of silicon in an inductively coupled plasma: Mechanism of etching through a thick steady state fluorocarbon layer. J. Vac. Sci. Technol. A, 1998, 16: 239-249.
[108] Schaepkens M, Oehrlein G S, Hedlund C et al. Selective Si02-to-Si3N4 etching in inductively coupled fluorocarbon plasmas: Angular dependence of Si02 and Si3N4 etching rates. J. Vac. Sci. Technol. A, 1998, 16: 3281-3286.
[109] Mantzaris N V, Boudouvis A,and Gogolides E, Radio-frequency plasmas in CF4:Self-consistent modeling of the plasma physics and chemistry. Journal of Applied Physics.1995, 77: 6169-6180.
[110] So S Y, Oda A, Sugawara H et al. Transient behaviour of CF4 rf plasmas after step changes of power source voltage. J. Phys. D, 2001, 34: 1919-1927.
[111] Denpoh K, and Nanbu K, Self-consistent particle simulation of radio-frequency CF4 discharge with implementation of all ion-neutral reactive collisions. Journal of Vacuum Science & Technology A. 1998, 16(3):1201-1206.
[112] Hoekstra R J, Grapperhaus M J, and Kushner M J, Integrated plasma equipment model for polysilicon etch profiles in an inductively coupled plasma reactor with subwafer and superwafer topography. J. Vac. Sci. Technol. A, 1997, 15(4):1913-1921.