Shape evolution of electrodeposited bumps into deep cavities

Metal posts and finer pitch solder bumps are the indispensable microconnectors for chip size packaging and are formed by electrodeposition into deep cavities. It is difficult to stir inside these deep cavities. Natural convection due to density difference is effective in stirring inside cavity with 200 mum cathode width of aspect ratio of one. The bump shape increases toward lower side in a vertical cathode arrangement with placement angle of Theta = 90 degrees. This increase in bump height results from a collision of flow along the lower side of the resist sidewall which enlarges local current and thickens the lower edge of bumps. The effect of natural convection is also evident in the neighboring two cavities of 200 mum cathode width. The natural convection is not effective for cavities with less than 100 mum cathode width. The bump shapes become flat. Only diffusion occurs within these smaller than 100 mum cavities. (C) 2001 The Electrochemical Society. All rights reserved.</p

Interaction of massless Dirac field with a Poincar\'e gauge field

In this paper we consider a model of Poincar\'e gauge theory (PGT) in which a translational gauge field and a Lorentz gauge field are actually identified with the Einstein's gravitational field and a pair of ``Yang-Mills'' field and its partner, respectively.In this model we re-derive some special solutions and take up one of them. The solution represents a ``Yang-Mills'' field without its partner field and the Reissner-Nordstr\"om type spacetime, which are generated by a PGT-gauge charge and its mass.It is main purpose of this paper to investigate the interaction of massless Dirac fields with those fields. As a result, we find an interesting fact that the left-handed massless Dirac fields behave in the different manner from the right-handed ones. This can be explained as to be caused by the direct interaction of Dirac fields with the ``Yang-Mills'' field. Accordingly, the phenomenon can not happen in the behavior of the neutrino waves in ordinary Reissner-Nordstr\"om geometry. The difference between left- and right-handed effects is calculated quantitatively, considering the scattering problems of the massless Dirac fields by our Reissner-Nordstr\"om type black-hole.Comment: 10pages, RevTeX3.