Let M be a compact m-dimensional Riemannian manifold, let d denote, its diameter, -R(R>O) the lower bound of the Ricci curvature, and λ_1 the first eigerivalue for the Laplacian on M. Then there exists a constant ...Let M be a compact m-dimensional Riemannian manifold, let d denote, its diameter, -R(R>O) the lower bound of the Ricci curvature, and λ_1 the first eigerivalue for the Laplacian on M. Then there exists a constant C_m=max{2^(1/m-1),2^(1/2)}, Such that λ_1≥π~2/d^2·1/(2-(11)/(2π~2))+11/2π~2e^cm、展开更多
Extreme ultraviolet lithography is most promising for the next generation lithography. However, debris from laser-produced plasma, particularly energetic ions, severely decreases the lifetime of extreme ultraviolet op...Extreme ultraviolet lithography is most promising for the next generation lithography. However, debris from laser-produced plasma, particularly energetic ions, severely decreases the lifetime of extreme ultraviolet optics. We measured the characteris- tics of ions from tin plasma by the time of flight method with a frequency-doubled Nd： YAG laser at the intensity of 3.5x1010 W/cm2 （532 nm, 8 ns）. Our measurement shows that the maximum and peak of tin ions energies from plasma under the above experimental parameters are about 4.2 and 1.8 keV, respectively. Moreover, it is found that kinetic energy angular distribution of tin ions can be fitted by cos0.8（θ）, where θ is the angle with respect to the target normal. We also investigated the mitigation effect of argon, helium gases to the tin ions, and found that tin ions from the plasma can be mitigated effectively at the pressure -38 mTorr for argon or -375 mTorr for helium, respectively.展开更多
文摘Let M be a compact m-dimensional Riemannian manifold, let d denote, its diameter, -R(R>O) the lower bound of the Ricci curvature, and λ_1 the first eigerivalue for the Laplacian on M. Then there exists a constant C_m=max{2^(1/m-1),2^(1/2)}, Such that λ_1≥π~2/d^2·1/(2-(11)/(2π~2))+11/2π~2e^cm、
基金supported by the National Natural Science Foundation ofChina (Grant Nos. 60978014,61178022 and 11074027)the Basic Research Fund from Sci. & Tech. Department of Jilin Province (Grant Nos.20100521,20100168 and 20111812)
文摘Extreme ultraviolet lithography is most promising for the next generation lithography. However, debris from laser-produced plasma, particularly energetic ions, severely decreases the lifetime of extreme ultraviolet optics. We measured the characteris- tics of ions from tin plasma by the time of flight method with a frequency-doubled Nd： YAG laser at the intensity of 3.5x1010 W/cm2 （532 nm, 8 ns）. Our measurement shows that the maximum and peak of tin ions energies from plasma under the above experimental parameters are about 4.2 and 1.8 keV, respectively. Moreover, it is found that kinetic energy angular distribution of tin ions can be fitted by cos0.8（θ）, where θ is the angle with respect to the target normal. We also investigated the mitigation effect of argon, helium gases to the tin ions, and found that tin ions from the plasma can be mitigated effectively at the pressure -38 mTorr for argon or -375 mTorr for helium, respectively.
