A Mathemataical model for a modified micro- cylinder electrode in which polyphenol oxidase ( PPO) occurs for all values of the concentration of catechol and o-quinone is analysed. This model is based on system of reac...A Mathemataical model for a modified micro- cylinder electrode in which polyphenol oxidase ( PPO) occurs for all values of the concentration of catechol and o-quinone is analysed. This model is based on system of reaction-diffusion Equations containing a non-linear term related to Michaelis Menten kinetics of the enzymatic reaction. Here a new analytical technique Homotopy Perturbation Method is used to solve the system of non-linear differential Equations that describe the diffusion coupled with a Michaelis-Menten kinetics law. Here we report an analytical expressions pretaining to the concentration of catechol and o-quinone and corresponding current in terms of dimensionless reaction-diffusion parameters in closed form. An excellent agreement with available limiting case is noticed.展开更多
Microstructure and texture of electrodeposited Cu micro-cylinders in the blind hole play a vitally im- portant role in the electrical and mechanical properties of the three-dimensional （3-D） IC （integrated circuit...Microstructure and texture of electrodeposited Cu micro-cylinders in the blind hole play a vitally im- portant role in the electrical and mechanical properties of the three-dimensional （3-D） IC （integrated circuit）/Si integrations. In this paper, a new commercial additive system, which is specifically devel- oped for the high-aspect-ratio through-silicon-via （TSV） filling, was used to electrodeposit Cu in the blind holes. The microstructure of electrodeposited Cu micro-cylinder in the blind hole with a diameter of 40 μm and a depth of 140 μm was investigated by electron back-scattered diffraction （EBSD） technique. Grain size distribution of the Cu micro-cylinder in the blind hole differed from the bottom to the top. The grain boundaries contained a high fraction of Z3 CSL （coincident site lattice） boundaries. It has been reported that the Cu overburden film on the surface of the blind hole influenced the crystallographic orientation of Cu grains inside the damascene trench. So the effects of the current density and additive concentra- tion on the crystal structure of the overburden Cu film were also studied in this study. The experimental results indicated that the preferred orientation of the Cu overburden film changed from {111} to {220} when the current density increased from 2 to 80 mA cm-2. However, the effect of additives on the crystal structure of the Cu overburden film was dependent on the crystal structure of the seed layer.展开更多
文摘A Mathemataical model for a modified micro- cylinder electrode in which polyphenol oxidase ( PPO) occurs for all values of the concentration of catechol and o-quinone is analysed. This model is based on system of reaction-diffusion Equations containing a non-linear term related to Michaelis Menten kinetics of the enzymatic reaction. Here a new analytical technique Homotopy Perturbation Method is used to solve the system of non-linear differential Equations that describe the diffusion coupled with a Michaelis-Menten kinetics law. Here we report an analytical expressions pretaining to the concentration of catechol and o-quinone and corresponding current in terms of dimensionless reaction-diffusion parameters in closed form. An excellent agreement with available limiting case is noticed.
基金sponsored by Chinese National Science and Technology Major Project (No. 2011ZX02702-003)
文摘Microstructure and texture of electrodeposited Cu micro-cylinders in the blind hole play a vitally im- portant role in the electrical and mechanical properties of the three-dimensional （3-D） IC （integrated circuit）/Si integrations. In this paper, a new commercial additive system, which is specifically devel- oped for the high-aspect-ratio through-silicon-via （TSV） filling, was used to electrodeposit Cu in the blind holes. The microstructure of electrodeposited Cu micro-cylinder in the blind hole with a diameter of 40 μm and a depth of 140 μm was investigated by electron back-scattered diffraction （EBSD） technique. Grain size distribution of the Cu micro-cylinder in the blind hole differed from the bottom to the top. The grain boundaries contained a high fraction of Z3 CSL （coincident site lattice） boundaries. It has been reported that the Cu overburden film on the surface of the blind hole influenced the crystallographic orientation of Cu grains inside the damascene trench. So the effects of the current density and additive concentra- tion on the crystal structure of the overburden Cu film were also studied in this study. The experimental results indicated that the preferred orientation of the Cu overburden film changed from {111} to {220} when the current density increased from 2 to 80 mA cm-2. However, the effect of additives on the crystal structure of the Cu overburden film was dependent on the crystal structure of the seed layer.
