One-dimensional nano-grating standard(ODNGS)is widely recognized as a crucial nanometric standard for metrological technology.However,achieving the ultratiny size of ODNGS with high consistent uniformity and low rough...One-dimensional nano-grating standard(ODNGS)is widely recognized as a crucial nanometric standard for metrological technology.However,achieving the ultratiny size of ODNGS with high consistent uniformity and low roughness by conventional processes such as the inductively coupled plasma(ICP)etching methodpresents a significant challenge in obtaining accurate calibration values.In this work,a 50-nm ODNGS with a conformal buffer layer(Al_(2)O_(3))is successfully obtained,indicating outstanding stability and abrasion resistance.Remarkably,the introduction of hydrogen silsesquioxane(HSQ)and amorphous Al_(2)O_(3)simultaneously guarantees an incredibly small expanded uncertainty(0.5 nm)and repeatability of the standard uniformity(less than 0.3 nm)in the grating dimensions.TheⅠ-Ⅴcurves of ODNGS with an Al_(2)O_(3)buffer layer at room temperature(RT)and200℃are depicted respectively to showcase the sustained favorable insulation properties.Notably,the nanostructure fluctuation,line edge roughness(LER)and line width roughness(LWR)of the standard can be decreased obviously by 64.1%,63%and 70%,respectively.Our results suggest that the ODNGS with Al_(2)O_(3)exhibits exceptional precision and robust calibration reliability for calibrating nanoscale measuring instruments.It holds tremendous potential for manufacturing high-precision nanostructures and grating arrays with precisely controllable dimensions,which will play a pivotal role in the fabrication of microfluidics chips,metasurface and photodetectors in the future.展开更多
In this paper,we consider the initial boundary value problem for the 2-D hyperbolic viscous Cahn-Hilliard equation.Firstly,we prove the existence and uniqueness of the local solution by the Galerkin method and contrac...In this paper,we consider the initial boundary value problem for the 2-D hyperbolic viscous Cahn-Hilliard equation.Firstly,we prove the existence and uniqueness of the local solution by the Galerkin method and contraction mapping principle.Then,using the potential well theory,we study the global well-posedness of the solution with initial data at different levels of initial energy,i.e.,subcritical initial energy,critical initial energy and arbitrary positive initial energy.For subcritical initial energy,we prove the global existence,asymptotic behavior and finite time blowup of the solution.Moreover,we extend these results to the critical initial energy using the scaling technique.For arbitrary positive initial energy,including the sup-critical initial energy,we obtain the sufficient conditions for finite time blow-up of the solution.As a further study for estimating the blowup time,we give a unified expression of the lower bound of blowup time for all three initial energy levels and estimate the upper bound of blowup time for subcritical and critical initial energy.展开更多
基金financially supported by the National Natural Science Foundation of China(No.52175434)the National Key Research and Development Program of China(No.2022YFB3204801)
文摘One-dimensional nano-grating standard(ODNGS)is widely recognized as a crucial nanometric standard for metrological technology.However,achieving the ultratiny size of ODNGS with high consistent uniformity and low roughness by conventional processes such as the inductively coupled plasma(ICP)etching methodpresents a significant challenge in obtaining accurate calibration values.In this work,a 50-nm ODNGS with a conformal buffer layer(Al_(2)O_(3))is successfully obtained,indicating outstanding stability and abrasion resistance.Remarkably,the introduction of hydrogen silsesquioxane(HSQ)and amorphous Al_(2)O_(3)simultaneously guarantees an incredibly small expanded uncertainty(0.5 nm)and repeatability of the standard uniformity(less than 0.3 nm)in the grating dimensions.TheⅠ-Ⅴcurves of ODNGS with an Al_(2)O_(3)buffer layer at room temperature(RT)and200℃are depicted respectively to showcase the sustained favorable insulation properties.Notably,the nanostructure fluctuation,line edge roughness(LER)and line width roughness(LWR)of the standard can be decreased obviously by 64.1%,63%and 70%,respectively.Our results suggest that the ODNGS with Al_(2)O_(3)exhibits exceptional precision and robust calibration reliability for calibrating nanoscale measuring instruments.It holds tremendous potential for manufacturing high-precision nanostructures and grating arrays with precisely controllable dimensions,which will play a pivotal role in the fabrication of microfluidics chips,metasurface and photodetectors in the future.
基金supported by the NSFC(12271122)the Fundamental Research Funds for the Central Universities.Han’s research was supported by the Fundamental Research Funds for the Central Universities(3072023GIP2401).
文摘In this paper,we consider the initial boundary value problem for the 2-D hyperbolic viscous Cahn-Hilliard equation.Firstly,we prove the existence and uniqueness of the local solution by the Galerkin method and contraction mapping principle.Then,using the potential well theory,we study the global well-posedness of the solution with initial data at different levels of initial energy,i.e.,subcritical initial energy,critical initial energy and arbitrary positive initial energy.For subcritical initial energy,we prove the global existence,asymptotic behavior and finite time blowup of the solution.Moreover,we extend these results to the critical initial energy using the scaling technique.For arbitrary positive initial energy,including the sup-critical initial energy,we obtain the sufficient conditions for finite time blow-up of the solution.As a further study for estimating the blowup time,we give a unified expression of the lower bound of blowup time for all three initial energy levels and estimate the upper bound of blowup time for subcritical and critical initial energy.
