47,705 research outputs found

    On finite complete rewriting systems and large subsemigroups

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    Let SS be a semigroup and TT be a subsemigroup of finite index in SS (that is, the set S∖TS\setminus T is finite). The subsemigroup TT is also called a large subsemigroup of SS. It is well known that if TT has a finite complete rewriting system then so does SS. In this paper, we will prove the converse, that is, if SS has a finite complete rewriting system then so does TT. Our proof is purely combinatorial and also constructive.Comment: We have made major changes to the paper and simplified most of the proof

    Double-Layer No-Flow Underfill Process for Flip-Chip Applications

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    ©2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.No-flow underfill technology shows potential advances over the conventional underfill technology toward a low-cost flop-chip underfill process. However, due to the filler entrapment in between solder bumps and contact pads on board, no-flow underfills are mostly unfilled or filled with very low filler loading. The high coefficient of thermal expansion (CTE) of the polymer material has significantly lowered the reliability of flip chip assembly and has limited its application to large chip assemblies. This paper presents a double-layer no-flow underfill process approach to incorporate silica filler into a no-flow underfill. Two layers of underfills are applied on to the substrate before chip placement. The bottom underfill layer facing the substrate is fluxed and unfilled; the upper layer facing the chip is filled with silica fillers. The total filler loading of the mixture is estimated to be around 55 wt%. The material properties of each layer of underfills, the underfill mixture, and a control unfilled underfill are characterized using differential scanning calorimeter (DCS), thermo-mechanical analyzer (TMA), dynamic mechanical analyzer (DMA), and a stress rheometer. FB250 daisy-chained test chips are assembled on FR-4 boards using the novel approach. A 100% assembly yield of solder Interconnect is achieved with the double-layer no-flow underfill while in the single-layer no-flow underfill process, no solder joint yield is observed. Scanning electronic microscope (SEM) and optical microscope are used to investigate the cross-section of both assemblies. A US provisional patent has been filed for this invention

    A Novel Nanocomposite with Photo-Polymerization for Wafer Level Application

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    ©2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.A novel nanocomposite photo-curable material which can act both as a photoresist and a stress redistribution layer applied on the wafer level was synthesized and studied. In the experiments, 20-nm silica fillers were modified by a silane coupling agent through a hydrolysis and condensation reaction and then incorporated into the epoxy matrix. A photo-sensitive initiator was added into the formulation which can release cations after ultraviolet exposure and initiate the epoxy crosslinking reaction. The photo-crosslinking reaction of the epoxy made it a negative tone photoresist. The curing reaction of the nanocomposites was monitored by a differential scanning calorimeter with the photo-calorimetric accessory. The thermal mechanical properties of photo-cured nanocomposites thin film were also measured. It was found that the moduli change of the nanocomposites as the filler loading increasing did not follow the Mori–Tanaka model, which indicated that the nanocomposite was not a simple two-phase structure as the composite with micron size filler. The addition of nano-sized silica fillers reduced the thermal expansion and improved the stiffness of the epoxy, with only a minimal effect on the optical transparency of the epoxy, which facilitated the complete photo reaction in the epoxy
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