Vortex precession and exchange in a Bose-Einstein condensate

Vortices in a Bose-Einstein condensate are modelled as spontaneously symmetry breaking minimum energy solutions of the time dependent Gross-Pitaevskii equation, using the method of constrained optimization. In a non-rotating axially symmetric trap, the core of a single vortex precesses around the trap center and, at the same time, the phase of its wave function shifts at a constant rate. The precession velocity, the speed of phase shift, and the distance between the vortex core and the trap center, depend continuously on the value of the conserved angular momentum that is carried by the entire condensate. In the case of a symmetric pair of identical vortices, the precession engages an emergent gauge field in their relative coordinate, with a flux that is equal to the ratio between the precession and shift velocities.

Resolve of OTP Failures through Electrical Simulation Using AFP Nanoprobing in Wafer Fabrication

This paper illustrated the beauty of AFP nanoprobing as the critical failure analysis tool in resolving the one-time programmable (OTP) non-volatile memory data retention failures through electrical simulation in wafer fabrication. Layout analysis, electrical simulation using Meilke’s method, UV erase methodology (to differentiate between mobile ion Meilke’s method contamination and charge trap centers) and a few other FA approaches were employed to determine the different root causes in the three OTP failure case detailed in this paper.. These include SiN trap center issue, poly stringers and abnormal layer at the initial CESL (Contact etch stop layer) nitride. This paper placed a strong emphasis on systematic problem solving approach, deep dive and use of right FA approach/tool that are essentially critical to FA analysts in wafer foundry since there is always minimal available data provided. It would serve as a good reference to wafer Fab that encountered such issue

Stability of the half-vortex in spin-orbit coupled Bose–Einstein condensate

The half-vortex stability of the stripe phase in spin-orbit (SO) coupled Bose–Einstein condensate (BEC) is discussed through the multi-mode theory. We find that when the energy of the Rabi coupling is close to zero, the half-vortex in the trap center is always dynamically stable; when the energy becomes larger, the vortex may be structurally unstable. Both of the results are confirmed by the numerical simulation of the full Gross–Pitaevskii equation.

Non-Visible Defect Analysis of OTP Device

Several product lots were found to suffer from data retention failures in OTP (one time program) devices. PFA (physical failure analysis) was performed on these devices, but nothing abnormal was observed. Cross-sectional TEM (transmission electron microscopy) revealed no physical defects or abnormal CDs (critical dimensions). In order to isolate the failed layer or location, electrical analysis was conducted. Several electrical simulation experiments, designed to test the data retention properties of OTP devices, were preformed. Meilke's method [1] was also used to differentiate between mobile ion contamination and charge trap centers. Besides Meilke's method, a new electrical analysis method was used to verify the analysis results. The results of our analysis suggests that SiN charge trap centers are the root cause for the data retention failures, and the ratio of Si/N is the key to charge trap center formation. Auger analysis was used to physically check the Si/N ratio of OTP devices. The results support our hypothesis. Subsequent DOE (Design Of Experiment) experiments also confirm our analysis results. Key Words: OTP, data retention, Non-visible defect, AFP, charge trap center, mobile ion.