By incorporating the contribution of solute atoms to the Helmholtz free energy of solid solution,a linear relation is derived between Young's modulus and the concentration of solute atoms.The solute atoms can eith...By incorporating the contribution of solute atoms to the Helmholtz free energy of solid solution,a linear relation is derived between Young's modulus and the concentration of solute atoms.The solute atoms can either increase or decrease Young's modulus of solid solution,depending on the first-order derivative of the Helmholtz free energy with respect to the concentration of solute atoms.Using this relation,a closed-form solution of the chemical stress in an elastic plate is obtained when the diffusion behavior in the plate can be described by the classical Fick's second law with convection boundary condition on one surface and zero flux on the other surface.The plate experiences tensile stress after short diffusion time due to asymmetrical diffusion,which will likely cause surface microcracking.The results show that the effect of the concentration dependence of Young's modulus on the evolution of chemical stress in elastic plates is negligible if the change of Young's modulus due to the diffusive motion of solute atomsis is not compatible in magnitude with Young's modulus of the pure material.Also,a new diffusion equation is developed for strictly regular binary solid solution.The effective diffusivity is a nonlinear function of the concentration of solute atoms.展开更多
A finite element analysis(FEA)model is developed for the chemical-mechanical polishing(CMP)process on the basis of a 12-in five-zone polishing head.The proposed FEA model shows that the contact stress non-uniformity i...A finite element analysis(FEA)model is developed for the chemical-mechanical polishing(CMP)process on the basis of a 12-in five-zone polishing head.The proposed FEA model shows that the contact stress non-uniformity is less dependent on the material property of the membrane and the geometry of the retaining ring.The larger the elastic modulus of the pad,the larger contact stress non-uniformity of the wafer.The applied loads on retaining ring and zone of the polishing head significantly affect the contact stress distribution.The stress adjustment ability of a zone depends on its position.In particular,the inner-side zone has a high stress adjustment ability,whereas the outer-side zone has a low stress adjustment ability.The predicted results by the model are shown to be consistent with the experimental data.Analysis results have revealed some insights regarding the performance of the multi-zone CMP.展开更多
文摘By incorporating the contribution of solute atoms to the Helmholtz free energy of solid solution,a linear relation is derived between Young's modulus and the concentration of solute atoms.The solute atoms can either increase or decrease Young's modulus of solid solution,depending on the first-order derivative of the Helmholtz free energy with respect to the concentration of solute atoms.Using this relation,a closed-form solution of the chemical stress in an elastic plate is obtained when the diffusion behavior in the plate can be described by the classical Fick's second law with convection boundary condition on one surface and zero flux on the other surface.The plate experiences tensile stress after short diffusion time due to asymmetrical diffusion,which will likely cause surface microcracking.The results show that the effect of the concentration dependence of Young's modulus on the evolution of chemical stress in elastic plates is negligible if the change of Young's modulus due to the diffusive motion of solute atomsis is not compatible in magnitude with Young's modulus of the pure material.Also,a new diffusion equation is developed for strictly regular binary solid solution.The effective diffusivity is a nonlinear function of the concentration of solute atoms.
基金supported by the Science Fund for Creative Research Groups (Grant No. 51021064)the National Natural Science Foundation of China (Grant No. 51205226)the China Postdoctoral Science Foundation (Grant No. 2012M510420)
文摘A finite element analysis(FEA)model is developed for the chemical-mechanical polishing(CMP)process on the basis of a 12-in five-zone polishing head.The proposed FEA model shows that the contact stress non-uniformity is less dependent on the material property of the membrane and the geometry of the retaining ring.The larger the elastic modulus of the pad,the larger contact stress non-uniformity of the wafer.The applied loads on retaining ring and zone of the polishing head significantly affect the contact stress distribution.The stress adjustment ability of a zone depends on its position.In particular,the inner-side zone has a high stress adjustment ability,whereas the outer-side zone has a low stress adjustment ability.The predicted results by the model are shown to be consistent with the experimental data.Analysis results have revealed some insights regarding the performance of the multi-zone CMP.
