In this paper,we prove the optimal error estimates in L2 norm of the semidiscrete local discontinuous Galerkin(LDG)method for the thin film epitaxy problem without slope selection.To relax the severe time step restric...In this paper,we prove the optimal error estimates in L2 norm of the semidiscrete local discontinuous Galerkin(LDG)method for the thin film epitaxy problem without slope selection.To relax the severe time step restriction of explicit time marching methods,we employ a class of exponential time differencing(ETD)schemes for time integration,which is based on a linear convex splitting principle.Numerical experiments of the accuracy and long time simulations are given to show the efficiency and capability of the proposed numerical schemes.展开更多
In this paper the elastic properties of SiOx film are investigated quantitatively for local fixed point and qualitatively for overall area by atomic force acoustic microscopy （AFAM） in which the sample is vibrated a...In this paper the elastic properties of SiOx film are investigated quantitatively for local fixed point and qualitatively for overall area by atomic force acoustic microscopy （AFAM） in which the sample is vibrated at the ultrasonic frequency while the sample surface is touched and scanned with the tip contacting the sample respectively for fixed point and continuous measurements. The SiOx films on the silicon wafers are prepared by the plasma enhanced chemical vapour deposition （PECVD）, The local contact stiffness of the tip-SiOx film is calculated from the contact resonance spectrum measured with the atomic force acoustic microscopy. Using the reference approach, indentation modulus of SiOx film for fixed point is obtained. The images of cantilever amplitude are also visualized and analysed when the SiOx surface is excited at a fixed frequency. The results show that the acoustic amplitude images can reflect the elastic properties of the sample.展开更多
YBCO textured thick film was prepared by direct peritectic growth method. Microstructure of the film was characterized. Electron backscattered diffraction （EBSD） technique was applied to the film for quantitative te...YBCO textured thick film was prepared by direct peritectic growth method. Microstructure of the film was characterized. Electron backscattered diffraction （EBSD） technique was applied to the film for quantitative texture analysis. The main difficulty in resolving the orientation of YBCO pseudo-cubic structure was investigated. Automated orientation mapping was performed on YBCO thick film. Local texture was presented in the form of orientation maps. Misorientation distribution and crystal growth characterization in the YBCO thick film were revealed. Large domains with well-aligned YBCO grains were formed. Each domain presented clear in-plane and out-plane textures.展开更多
Effects of deposition layer position film are systematically investigated. Because the and number/density on local bending of a thin deposition layer interacts with the thin film at the interface and there is an offse...Effects of deposition layer position film are systematically investigated. Because the and number/density on local bending of a thin deposition layer interacts with the thin film at the interface and there is an offset between the thin film neutral surface and the interface, the deposition layer generates not only axial stress but also bending moment. The bending moment induces an instant out-of-plane deflection of the thin film, which may or may not cause the socalled local bending. The deposition layer is modeled as a local stressor, whose location and density are demonstrated to be vital to the occurrence of local bending. The thin film rests on a viscous layer, which is governed by the Navier-Stokes equation and behaves like an elastic foundation to exert transverse forces on the thin film. The unknown feature of the axial constraint force makes the governing equation highly nonlinear even for the small deflection chse. The constraint force and film transverse deflection are solved iteratively through the governing equation and the displacement constraint equation of immovable edges. This research shows that in some special cases, the deposition density increase does not necessarily reduce the local bending. By comparing the thin film deflections of different deposition numbers and positions, we also present the guideline of strengthening or suppressing the local bending.展开更多
基金This work is supported by NSFC grants No.11601490.
文摘In this paper,we prove the optimal error estimates in L2 norm of the semidiscrete local discontinuous Galerkin(LDG)method for the thin film epitaxy problem without slope selection.To relax the severe time step restriction of explicit time marching methods,we employ a class of exponential time differencing(ETD)schemes for time integration,which is based on a linear convex splitting principle.Numerical experiments of the accuracy and long time simulations are given to show the efficiency and capability of the proposed numerical schemes.
基金Project supported by the National Natural Science Foundation of China(Grant No.50775005)
文摘In this paper the elastic properties of SiOx film are investigated quantitatively for local fixed point and qualitatively for overall area by atomic force acoustic microscopy （AFAM） in which the sample is vibrated at the ultrasonic frequency while the sample surface is touched and scanned with the tip contacting the sample respectively for fixed point and continuous measurements. The SiOx films on the silicon wafers are prepared by the plasma enhanced chemical vapour deposition （PECVD）, The local contact stiffness of the tip-SiOx film is calculated from the contact resonance spectrum measured with the atomic force acoustic microscopy. Using the reference approach, indentation modulus of SiOx film for fixed point is obtained. The images of cantilever amplitude are also visualized and analysed when the SiOx surface is excited at a fixed frequency. The results show that the acoustic amplitude images can reflect the elastic properties of the sample.
文摘YBCO textured thick film was prepared by direct peritectic growth method. Microstructure of the film was characterized. Electron backscattered diffraction （EBSD） technique was applied to the film for quantitative texture analysis. The main difficulty in resolving the orientation of YBCO pseudo-cubic structure was investigated. Automated orientation mapping was performed on YBCO thick film. Local texture was presented in the form of orientation maps. Misorientation distribution and crystal growth characterization in the YBCO thick film were revealed. Large domains with well-aligned YBCO grains were formed. Each domain presented clear in-plane and out-plane textures.
基金supported by the National Natural Science Foundation of China (No.10721202)the LNM Initial Funding for Young Investigators
文摘Effects of deposition layer position film are systematically investigated. Because the and number/density on local bending of a thin deposition layer interacts with the thin film at the interface and there is an offset between the thin film neutral surface and the interface, the deposition layer generates not only axial stress but also bending moment. The bending moment induces an instant out-of-plane deflection of the thin film, which may or may not cause the socalled local bending. The deposition layer is modeled as a local stressor, whose location and density are demonstrated to be vital to the occurrence of local bending. The thin film rests on a viscous layer, which is governed by the Navier-Stokes equation and behaves like an elastic foundation to exert transverse forces on the thin film. The unknown feature of the axial constraint force makes the governing equation highly nonlinear even for the small deflection chse. The constraint force and film transverse deflection are solved iteratively through the governing equation and the displacement constraint equation of immovable edges. This research shows that in some special cases, the deposition density increase does not necessarily reduce the local bending. By comparing the thin film deflections of different deposition numbers and positions, we also present the guideline of strengthening or suppressing the local bending.
