The influence of the distribution of nano-pores on the mechanical properties evaluation of porous low-k films by surface acoustic waves （SAW） is studied. A theoretical SAW propagation model is set up to characterize...The influence of the distribution of nano-pores on the mechanical properties evaluation of porous low-k films by surface acoustic waves （SAW） is studied. A theoretical SAW propagation model is set up to characterize the periodic porous dielectrics by transversely isotropic symmetry. The theoretical deductions of SAW propagating in the low-k film/Si substrate layered structure are given in detail. The dispersive characteristics of SAW in differ- ent propagation directions and the effects of the Young＇s moduli E, E′ and shear modulus G′ of the films on these dispersive curves are found. Computational results show that E′ and G′ cannot be measured along the propagation direction that is perpendicular to the nano-pores＇ direction.展开更多
The classical Hashin-Shtrikman variational principle was re-generalized to the heterogeneous piezoelectric materials.The auxiliary problem is very much simplified by selecting the reference medium as a linearly isotro...The classical Hashin-Shtrikman variational principle was re-generalized to the heterogeneous piezoelectric materials.The auxiliary problem is very much simplified by selecting the reference medium as a linearly isotropic elastic medium.The electromechanical fields in the inhomogeneous piezoelectrics are simulated by introducing into the homogeneous reference medium certain eigenstresses and eigen electric fields.A closed-form solution can be obtained for the disturbance fields,which is convenient for the manipulation of the energy functional.As an application,a two-phase piezoelectric composite with nonpiezoelectric matrix is considered.Expressions of upper and lower bounds for the overall electromechanical moduli of the composite can be developed.These bounds are shown better than the Voigt-Reuss type ones.展开更多
文摘The influence of the distribution of nano-pores on the mechanical properties evaluation of porous low-k films by surface acoustic waves （SAW） is studied. A theoretical SAW propagation model is set up to characterize the periodic porous dielectrics by transversely isotropic symmetry. The theoretical deductions of SAW propagating in the low-k film/Si substrate layered structure are given in detail. The dispersive characteristics of SAW in differ- ent propagation directions and the effects of the Young＇s moduli E, E′ and shear modulus G′ of the films on these dispersive curves are found. Computational results show that E′ and G′ cannot be measured along the propagation direction that is perpendicular to the nano-pores＇ direction.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11072179 and 11090334)Shanghai Leading Academic Discipline Project (Grant No. B302)
文摘The classical Hashin-Shtrikman variational principle was re-generalized to the heterogeneous piezoelectric materials.The auxiliary problem is very much simplified by selecting the reference medium as a linearly isotropic elastic medium.The electromechanical fields in the inhomogeneous piezoelectrics are simulated by introducing into the homogeneous reference medium certain eigenstresses and eigen electric fields.A closed-form solution can be obtained for the disturbance fields,which is convenient for the manipulation of the energy functional.As an application,a two-phase piezoelectric composite with nonpiezoelectric matrix is considered.Expressions of upper and lower bounds for the overall electromechanical moduli of the composite can be developed.These bounds are shown better than the Voigt-Reuss type ones.
