Investigation of Inhibited Channel Potential of 3D NAND Flash Memory According to Word-Line Location

Natural local self-boosting (NLSB) was analyzed according to the location of a selected word-line (WL) where potential boosting occurs. When the same pattern occurred, it was found that the top cells (WL11 through WL15) and bottom cells (WL0 through WL4) have identically symmetrical potential boosting. In addition, in the region of the middle cells (WL6 through WL10), a slight change in the potential boosting was also almost the same. In the 3D NAND, where there was a dummy WL (DWL), the NLSB for the edge WL changed as the pattern of the DWL changed. The DWL did not affect the NLSB of the main cell, regardless of the pattern. Therefore, the high potential of the edge WL could reduce the potential difference between the main cell and the edge WL using the DWL.

Effects of symmetrical potential on particle transport in the presence of a periodic channel

In this paper, we aim to investigate influences of an asymmetrical potential on particle transport in the presence of a periodic channel by calculating particle current and effective diffusion coefficient. First, influences of external force on transport behaviors are researched. Results reveal that with the increase of the external force, particle current increases, and the effective diffusion coefficient decreases first and then increases. That is, large external forces can promote the movement of particles. Second, influences of potential asymmetry and amplitude on particle transport are studied. These two factors have a more complex mechanism of influence on particle transport. For example, an increase of positive amplitude value leads to a decrease of particle current, while a negative value makes particle current increase first and then decreases. In other words, the effect of amplitude depends on its sign and value. For positive amplitude, the larger its value is, the greater the suppression effect on particle transport. While for negative amplitude, as its value increases, it promotes particle transport. When its value increased to a certain extent, the effect of the amplitude on the particle motion changes from promotion to suppression. For asymmetry, it can promote particle transport for positive amplitude while suppress the transport for negative amplitude. These results can provide some bases for understanding biological systems and controlling particle transport.

EXACT SOLUTIONS TO THE THREE-DIMENSIONAL GROSS–PITAEVSKII EQUATION WITH MODULATED RADIAL NONLINEARITY

We study the Bose–Einstein condensate trapped in a three-dimensional spherically symmetrical potential. Exact solutions to the stationary Gross–Pitaevskii equation are obtained for properly modulated radial nonlinearity. The solutions contain vortices with different winding numbers and exhibit the shell-soliton feature in the radial distributions.

NOTES ON THE DISTRIBUTION OF PHASE SHIFTS

We consider three-dimensional inverse scattering with fixed energy for which the spherically symmetrical potential is nonvanishing only in a ball. We give exact upper and lower bounds for the phase shifts. We provide a variational formula for the Weyl–Titchmarsh m-function of the one-dimensional Schrödinger operator defined on the half-line.