An O(N) Algorithm for Three-Dimensional N-Body Simulations

We develop an algorithm that computes the gravitational potentials and forces on N point-masses interacting in three-dimensional space. The algorithm, based on analytical techniques developed by Rokhlin and Greengard, runs in order N time. In contrast to other fast N-body methods such as tree codes, which only approximate the interaction potentials and forces, this method is exact ?? computes the potentials and forces to within any prespecified tolerance up to machine precision. We present an implementation of the algorithm for a sequential machine. We numerically verify the algorithm, and compare its speed with that of an O(N2) direct force computation. We also describe a parallel version of the algorithm that runs on the Connection Machine in order 0(logN) time. We compare experimental results with those of the sequential implementation and discuss how to minimize communication overhead on the parallel machine.

Preliminary Characterisation of Low-Temperature Bonded Copper Interconnects for 3-D Integrated Circuits

Three dimensional (3-D) integrated circuits can be fabricated by bonding previously processed device layers using metal-metal bonds that also serve as layer-to-layer interconnects. Bonded copper interconnects test structures were created by thermocompression bonding and the bond toughness was measured using the four-point test. The effects of bonding temperature, physical bonding and failure mechanisms were investigated. The surface effects on copper surface due to pre-bond clean (with glacial acetic acid) were also looked into. A maximum average bond toughness of approximately 35 J/m² was obtained bonding temperature 300 C.