| Surface Acoustic Wave Characterization of Equivalent Young's Moduli for Patterned Films北大核心CSCD |
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| 引用本文： | 陈龙,肖夏,张立,戚海洋.Surface Acoustic Wave Characterization of Equivalent Young's Moduli for Patterned Films北大核心CSCD[J].应用数学和力学,2023,44(4):381-393. |
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| 作者姓名： | 陈龙 肖夏 张立 戚海洋 |
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| 作者单位： | 1.天津大学 微电子学院，天津 300072 |
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| 基金项目： | 国家自然科学基金项目61571319 |
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| 摘 要： | Based on the equivalent elasticity theory for layered materials, the micro-mechanics equivalent models for single and dual damascene structures were established. The equivalent elastic constant of the patterned structure was introduced, to establish the propagation model for the surface acoustic waves propagating in the layered structure of the patterned film/ substrate, and the theoretical dispersion curves of the surface acoustic waves were calculated with Green’s function and the matrix method. The finite element method was used to calculate 24 numerical examples of damascene structures with different volume ratios, and the results were compared with those of the strain energy method. The results show that, the average relative errors of the equivalent Young’s moduli of the 300 nm-thick dual damascene film and the 100 nm-thick single damascene film are 2.06% and 2.27%, respectively. The research verifies the correctness of the equivalent patterned structure model and the feasibility of the surface acoustic wave method to characterize the mechanical properties of patterned films, and provides a reference for the development of suitable chemico-mechanical polishing technologies for patterned films under low pressure. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.
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| 关 键 词： | 声表面波 大马士革结构 图形化薄膜 等效弹性模量 数值模拟 |
| 收稿时间： | 2022-02-21 |
Surface Acoustic Wave Characterization of Equivalent Young's Moduli for Patterned Films |
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| Chen L.,Xiao X.,Zhang L.,Qi H..Surface Acoustic Wave Characterization of Equivalent Young's Moduli for Patterned Films[J].Applied Mathematics and Mechanics,2023,44(4):381-393. |
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| Authors: | Chen L Xiao X Zhang L Qi H |
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| Affiliation: | 1.School of Microelectronics, Tianjin University, Tianjin 300072, P.R.China2.Zhejiang Institute of Metrology, Hangzhou 310063, P.R.China |
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| Abstract: | Based on the equivalent elasticity theory for layered materials, the micro-mechanics equivalent models for single and dual damascene structures were established. The equivalent elastic constant of the patterned structure was introduced, to establish the propagation model for the surface acoustic waves propagating in the layered structure of the patterned film/substrate, and the theoretical dispersion curves of the surface acoustic waves were calculated with Green's function and the matrix method. The finite element method was used to calculate 24 numerical examples of damascene structures with different volume ratios, and the results were compared with those of the strain energy method. The results show that, the average relative errors of the equivalent Young's moduli of the 300 nm-thick dual damascene film and the 100 nm-thick single damascene film are 2.06% and 2.27%, respectively. The research verifies the correctness of the equivalent patterned structure model and the feasibility of the surface acoustic wave method to characterize the mechanical properties of patterned films, and provides a reference for the development of suitable chemico-mechanical polishing technologies for patterned films under low pressure. |
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| Keywords: | damascene structure equivalent Young’s modulus numerical simulation patterned film surface acoustic wave |
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