Volume 44 Issue 4
Apr.  2023
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CHEN Long, XIAO Xia, ZHANG Li, QI Haiyang. Surface Acoustic Wave Characterization of Equivalent Young's Moduli for Patterned Films[J]. Applied Mathematics and Mechanics, 2023, 44(4): 381-393. doi: 10.21656/1000-0887.430050
Citation: CHEN Long, XIAO Xia, ZHANG Li, QI Haiyang. Surface Acoustic Wave Characterization of Equivalent Young's Moduli for Patterned Films[J]. Applied Mathematics and Mechanics, 2023, 44(4): 381-393. doi: 10.21656/1000-0887.430050

Surface Acoustic Wave Characterization of Equivalent Young's Moduli for Patterned Films

doi: 10.21656/1000-0887.430050
  • Received Date: 2022-02-21
  • Rev Recd Date: 2022-09-04
  • Publish Date: 2023-04-01
  • 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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