Band structures,density of states and optical properties of pure,N-doped,S-doped and N-S co-doped rutile TiO₂ are studied with plane-wave ultrasoft pseudopotential method based on first-principles density functional theory.It shows that the gap of N-doped TiO₂ reduces to 1.43 eV,and there is an impurity band on top of the valence band.S-doped TiO₂ results in Fermi level moves to the conduction band,and the gap decreases to 0.32 eV.N-S co-doped TiO₂ results in two impurity bands located in the band gap.One impurity band is apart from the bottom of conduction band by 0.35 eV,the other is apart from the top of valence band by 0.85 eV,which is mainly formed by N-atom 2p orbital and S-atom 3p orbital.It causes a red-shift in absorption wavelength,and gives rise to extremely great absorption coefficient in visible-light region,which shows a strong photocatalytic activity.

With influences of interconnect inductance,thermal-electric coupling effects and interconnect temperature distribution,a delay optimized method by repeater insertion is presented.A interconnect resistance model and a delay model are obtained respectively based on interconnect temperature distribution.The repeater insertion optimal delay is calculated considering electro-thermal coupling among power,delay and temperature.Optimized results are successfully obtained with Matlab software.Repeater insertion in 45 nm technology is simulated.It shows effectiveness of the method.In addition,it indicates that the optimal delay is overestimated without inductance effect.Optimal delay is underestimated without consideration of temperature distribution.As overestimated global interconnect width is 245nm,8.71% optimal delay can be underestimated without considering temperature distribution effect.

Mass and heat transfer between fluid molecules and a carbon tube is studied via molecular dynamic simulation with Lennard-Jones potential and Bernner-Tersoff potential. A valve hole of area 17.3~116.9Å2 is formed by removing different numbers of molecules from the flank of a (5,5) armchair carbon tube. The results indicate that diffusion behavior can not describe the phenomena completely, since the hydrogen atoms penetration rate Vb can also be affected by hole size at the same temperature. The Maxwell-Bohzmann energy distribution equation is modified. Atom release rate and valve hole size are interdependent. Variation of potential energy barrier, work function and energy gap at different valve sizes and influences on the dynamic behavior, such as flow rate and velocity by molecule penetration, are studied. The characteristic is used for design of nano-valve, particle separator or chemical reactor.