Electron collision cross section data in plasma etching modeling

Chen Jin-Feng; Zhu Lin-Fan

doi:10.7498/aps.73.20231598

Abstract

Semiconductor chips are the cornerstone of the information age, which play a vital role in the rapid development of emerging technologies such as big data, machine learning, and artificial intelligence. Driven by the growing demand for computing power, the chip manufacturing industry has been committed to pursuing higher level of integration and smaller device volumes. As a critical step in the chip manufacturing processes, the etching process therefore faces great challenges. Dry etching (or plasma etching) process based on the low-temperature plasma science and technology is the preferred solution for etching the high-precision circuit pattern. In the low-temperature plasma, electrons obtain energy from the external electromagnetic field and transfer the energy to other particles through collision process. After a series of complex physical and chemical reactions, a large number of active particles such as electrons, ions, atoms and molecules in excited states, and radicals are finally generated, providing the material conditions for etching the substrate. Dry etching chamber is a nonlinear system with multiple space-time dimensions, multiple reaction levels and high complexity. Facing such a complex system, only by fully understanding the basic physical and chemical reaction of the etching process can we optimize the process parameters and improve the etching conditions, so as to achieve precision machining of the semiconductor and meet the growing demand of the chip industry for etching rate and yield. In the early days, the process conditions of dry etching were determined through the trial-and-error method, which is characterized by high cost and low yield. However, with the help of plasma simulation, nowadays people have been able to narrow the scope of experiment to a large extent, and find out efficiently the optimal process conditions in a large number of parameters. In this review, we first introduce the basic theory of the mostly used models for plasma simulation including kinetic, fluid dynamic, hybrid and global models, in which the electron collision cross sections are the key input parameters. Since the formation of the low-temperature plasma is driven by the electron-heavy particle collision processes, and the active species for plasma etching are generated in the reactions induced by electron impact, the accuracy and completeness of the cross-section data greatly affect the reliability of the simulation results. Then, the theoretical and experimental methods of obtaining the cross-section data of etching gases are summarized. Finally, the research status of the electron collision cross sections of etching atoms and molecules is summarized, and the future research prospect is discussed.

Keywords:

Authors and contacts

Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China

Corresponding author: Zhu Lin-Fan, lfzhu@ustc.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12334010).

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图 1 湿法刻蚀(各向同性)与干法刻蚀(各向异性)示意图

Figure 1. Schematic diagram of wet etching (isotropic) and dry etching (anisotropic).

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图 2 (a)以CHF₃为原料气体的ICP刻蚀腔室(作图参考了文献[12]), 匹配器用于匹配电源输出阻抗与等离子体阻抗, 红色与蓝色线条分别代表磁场与电场, 鞘层区域的偏压可以将离子加速到几百eV, 高能离子垂直轰击表面导致各向异性刻蚀. 使用两个射频源, 可实现离子密度与能量的去耦合: 上方电源通过电感耦合供能, 可以控制离子密度; 下方电源通过电容耦合调节鞘层偏压, 可以控制离子的轰击能量; (b) 表面刻蚀部分, C_mF_n聚合物的钝化效应有助于各向异性刻蚀; (c) 等离子体内部及晶圆表面发生的主要物理化学过程

Figure 2. (a) ICP etching chamber with CHF₃ as feed gas (this picture was made with reference to Ref. [12]), the matching device is used to match the output impedance of the power supply and the plasma impedance, the red and blue lines represent the magnetic and electric fields respectively, the bias voltage in the sheath region can accelerate the ions to several hundred eV, and the high energy ions can vertically bombard the surface, leading to anisotropic etching. Using two RF sources, the decoupling of the ion density and energy can be achieved: the upper power supply can control the ion density through inductive coupling; the lower power supply can control the ion bombardment energy by adjusting the sheath bias through capacitive coupling. (b) The surface etching part, the passivation effect of C_mF_n polymer contributes to anisotropic etching. (c) The main physical and chemical processes that occur inside the plasma and on the wafer surface.

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图 3 干法刻蚀系统与各部分对应的处理模块, 各个模块的理论模型见文献[42,43]

Figure 3. Dry etching system and the processing modules corresponding to each part, theoretical models of each module can be found in Refs. [42,43].

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图 4 电子与粒子s的两体碰撞示意图, 粒子s可视为静止. 右图为左图的逆过程

Figure 4. Diagram of binary encounter between an electron and a particle s which can be regarded as stationary. The right picture is the inverse process of the left picture.

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图 5 电子与双原子分子AB相互作用的初级过程①与次级过程②, 原子或多原子分子的情况是类似的. 注意到②中产生的处于激发态的原子分子或离子还会进一步演化

Figure 5. Primary process ① and secondary process ② of electron interaction with diatomic molecule AB, and the interaction processes for atoms or polyatomic molecules are similar. Note that the excited atoms, molecules, and ions produced in ② will evolve further.

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图 6 双原子分子AB的电子碰撞中性解离的两步过程示意图. 处于基态的分子AB首先被激发到解离态AB*, 随后沿着激发态势能曲线解离生成A*+B. 图示表明了次级过程的演化与初级过程无关, 只与原子分子所处激发态的性质(势能曲线)有关

Figure 6. Schematic diagram of the two-step processes of electron-impact neutral dissociation of diatomic molecule AB. AB in the ground state is first excited to the dissociative state AB*, and then dissociates along the potential curve to form A*+B. The diagram indicates that the evolution of the secondary process is independent of the primary process, which is only related to the properties of the corresponding excited states (e. g. the potential curve).

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图 7 电子群实验(脉冲汤森装置)示意图^[46,77]. 被激光照射后, 阴极放出的电子在电场作用下向阳极漂移, 与背景气体碰撞发生贴附、激发、电离等过程. 产生的电流(包括电子电流和离子电流)由探测电路监控, 背景气体的气压则由气压计检测

Figure 7. Schematic diagram of swarm experiment (pulsed Townsend apparatus)^[46,77]. The electrons released by photoemission drift towards the anode under the electric field, and the collision with the background gas leads to attachment, excitation, ionization, etc. The generated currents (including electronic current and ion current) are monitored by the detection circuit, and the pressure of the background gas is detected by the manometer.

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图 8 典型的电子束散射实验装置: 高分辨快电子能量损失谱仪^[78]. 由电子枪发出的电子被静电半球单色器单色后在反应腔室中与样品气体碰撞(交叉束布局), 散射电子经过静电半球能量分析器后被位置灵敏探测器探测. 转动分析器可改变测量的散射角. 透镜(F, L)、偏转板(Q)、膜孔(P)等电子光学器件用于电子束的聚焦、准直、加(减)速与监测. 图中还展示了用于测量正、负离子的飞行时间质谱

Figure 8. A typical apparatus for electron beam scattering experiment: high-resolution fast electron energy loss spectrometer^[78]. The electrons emitted by the electron gun are monochromized by the electrostatic hemispherical monochromator and then collide with the sample gas in the reaction chamber (cross-beam layout), and the scattered electrons are detected by a position sensitive detector after passing through the electrostatic hemispherical energy analyzer. The measured scattering angle can be varied by rotating the analyzer. Electron optics such as lens (F, L), deflection plate (Q), and aperture (P) are used for focusing, collimating, acceleration (deceleration) and monitoring of the electron beam. Time-of-flight mass spectrometers used to measure positive and negative ions are also shown.

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图 9 CO分子A¹Π电子激发态不同振动能级的积分截面. *由文献[94]中测量的GOS计算得到. 可以看到, 虽然Born积分截面(虚线)在低能区比积分0°—180°微分散射截面得到的实验值(点)^[95–98]大很多, 但是BE-scaled积分截面(实线)与实验值符合得很好

Figure 9. Integral cross sections of the vibrational states of A¹Π in carbon monoxide. * calculated from the GOSs reported in Ref. [94]. It can be seen that although the Born cross sections (dashed line) at the low energy region are much larger than the experimental values obtained by integrating the differential cross sections in the region of 0°–180° (dots)^[95–98], the BE-scaled integral cross sections (solid line) agree very well with the experimental values.

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图 10 CHF₃总中性解离截面的测量结果^[13]. Sugai 等^[101] 重新标定了他们之前的测量结果^[100], 由于测量仅考虑了中性碎片CF_x (x = 1—3), 加入了解离到CHF₂和CHF的贡献进行修正

Figure 10. Measured total dissociation cross sections into neutral species for CHF₃^[13]. Sugai et al.^[101] recalibrated their previous experimental results^[100]. Since their measurement only considered neutral fragments CF_x (x = 1–3), the contributions of dissociation to CHF₂ and CHF were added for correction.

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图 11 Ar原子4s[3/2]₁, 4s′[1/2]₁激发态的积分截面^[93]. 数据点是低(中)能电子碰撞的实验结果^[106–110]. 阴影区代表了BE-scaled积分截面(黑色实线)15%的实验误差^[93], 其他曲线来自LXCat数据库^[27,58]

Figure 11. Integral cross sections for the 4s[3/2]₁ and 4s′[1/2]₁ states of Ar^[93]. Dots are the experimental results measured by low (medium) energy electron impact^[106–110]. The shaded areas indicate an experimental uncertainty of 15% of the BE-scaled integral cross sections (black solid lines)^[93]. The other lines are the data from the LXCat database^[27,58].

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表 1 常用刻蚀气体. 等离子体刻蚀建模涉及的对象包含表格中的刻蚀气体本身、相应的解离碎片以及处于亚稳态的原子分子.

Table 1. Commonly used etching gases. The objects involved in plasma etching modeling include the etching gases in the table, the corresponding dissociation fragments, and the atoms and molecules in metastable states.

刻蚀气体	举例
氟碳化合物	CF₄, CHF₃, CH₂F₂, CH₃F, C₂F₆, C₃F₈, C₄F₈, C₄F₆······
含氟分子	NF₃, SF₆, SiF₄, CCl₂F₂······
含氯与含溴分子	HBr, Cl₂, BCl₃······
含氢分子	H₂, CH₄······
附加气体	O₂, N₂, Ar, He······

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表 2 等离子体刻蚀建模所需的电子碰撞截面类型. 表格中的截面描述了低温等离子体中主要的电子碰撞过程

Table 2. Types of electron collision cross sections required for plasma etching modeling. The cross sections in the table describe the main electron collision processes in low temperature plasma.

建模所需截面类型	备注
总截面	与电子输运系数相关
弹性/动量转移截面	与电子输运系数相关
转动/振动激发截面	转动激发能量低, 可包含在弹性截面中; 振动亚稳态可以是多步解离(电离)的中间态
电子态激发截面	刻蚀分子的电子激发态常常是解离态
解离截面	解离产物具有刻蚀活性
电离截面	电子、正离子产生过程
电子贴附截面	电子损失过程、负离子产生过程
中性解离/电离解离/ 贴附解离截面	解离为中性/正离子/负离子碎片

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