Study on micro hot embossing of low temperature co-firable ceramic green substrates

Multi-layered ceramic substrates with embedded micro patterns are becoming increasingly important, for example, in harsh environment electronics, enabling microsystems and microfluidic devices. Fabrication of these embedded micro patterns, such as micro channels, cavities and vias, is a challenge. This study focuses on the process aspects of patterning micro features on low temperature co-firable ceramic (LTCC) green substrates using micro hot embossing. Green ceramic tapes that possessed near-zero shrinkage in the x–y plane were used, six layers of which were stacked and laminated as a substrate. The process parameters that impact on the embossing fidelity were investigated and optimized in this study. Micro features with channel-width as small as several micrometers were formed on green ceramic substrates. The dynamic thermo-mechanical analysis indicated that extending the holding time at a certain temperature range would harden the substrates with little effect on improving the embossing fidelity. Ceramic substrates with embossed micro patterns were obtained after co-firing; the shrinkage ratios of the embossed depth and channel-width were 8–15 and 12–17%, respectively. The changes of pitches between two embossed channels were within ±1.0% due to the interlocking effect of the ceramic tapes.     

Hot embossing of microstructures: characterization of friction during demolding

Today, hot embossing and injection molding belong to the established plastic molding processes in microengineering. Based on experimental findings, a variety of microstructures have been replicated so far using the above processes. However, with increasing requirements regarding the embossing surface and the simultaneous decrease of the structure size down into the nanorange, increasing know––how is needed to adapt hot embossing to industrial standards. To reach this objective, a German–Canadian cooperation project has been launched to study hot embossing theoretically by a process simulation and experimentally. The present publication shall report about an important aspect––the determination of friction during the demolding of microstructures.     

Roll-to-roll hot embossing of microstructures

In this paper we present a new roll-to-roll embossing process allowing the replication of micro patterns with feature sizes down to 0.5 μm. The embossing process can be run in ‘continuous mode’ as well as in ‘discontinuous mode’. Continuous hot embossing is suitable for the continuous output of micro patterned structures. Discontinuous hot embossing has the advantage that it is not accompanied by waste produced during the initial hot embossing phase. This is because in ‘discontinuous mode’, embossing does not start before the foil has reached the target temperature. The foil rests between two parallel heating plates and foil movement and embossing starts only after the part of the foil resting between the heating plates has reached a thermal steady state. A new type of embossing master is used which is based on flexible silicon substrates. The embossing pattern with sub-μm topographic resolution is prepared on silicon wafers by state of the art lithography and dry etching techniques. The wafers are thinned down to a thickness of 40 μm, which guarantees the mechanical flexibility of the embossing masters. Up to 20 individual chips with a size of 20 × 20 mm2 were assembled on a roller. Embossing experiments with COC foils showed a good replication of the silicon master structures in the foil. The maximum depth of the embossed holes was about 70% of the master height.     

All-Pairs Shortest Paths with Real Weights in <Emphasis Type="Italic">O</Emphasis>(<Emphasis Type="Italic">n</Emphasis><Superscript>3</Superscript>/log <Emphasis Type="Italic">n</Emphasis>) Time

We describe an O(n ³/log n)-time algorithm for the all-pairs-shortest-paths problem for a real-weighted directed graph with n vertices. This slightly improves a series of previous, slightly subcubic algorithms by Fredman (SIAM J. Comput. 5:49–60, 1976), Takaoka (Inform. Process. Lett. 43:195–199, 1992), Dobosiewicz (Int. J. Comput. Math. 32:49–60, 1990), Han (Inform. Process. Lett. 91:245–250, 2004), Takaoka (Proc. 10th Int. Conf. Comput. Comb., Lect. Notes Comput. Sci., vol. 3106, pp. 278–289, Springer, 2004), and Zwick (Proc. 15th Int. Sympos. Algorithms and Computation, Lect. Notes Comput. Sci., vol. 3341, pp. 921–932, Springer, 2004). The new algorithm is surprisingly simple and different from previous ones. A preliminary version of this paper appeared in Proc. 9th Workshop Algorithms Data Struct. (WADS), Lect. Notes Comput. Sci., vol. 3608, pp. 318–324, Springer, 2005.     

Micro-metalforming with silicon dies

 The introduction of forming technology into MEMS manufacturing demands forming dies being characterized by a high strength and hardness, a good microstructurability, a low surface roughness, and a high precision of the microgeometry to be molded. Silicon structured by lithography and etching processes meeting these requirements especially concerning precision and surface roughness. For micro-metalforming silicon dies with different structural dimensions (>1 μm) have been used. The microstructures could be molded in different materials using cold and superplastic embossing. The precision and surface quality of the formed parts correspond to the high quality of the microstructured die. Both the low surface roughness and the accurate edges of the silicon structures are nearly represented in the molded structures. However, in particular during cold embossing die wear or even die failure could be observed limiting the implementation of silicon for micro-metalforming.     

Static and dynamic behaviour of gas bubbles in T-shaped non-clogging micro-channels

Preventing micro-channels from clogging is a major issue in most micro and nanofluidic systems (Gravesen et al., J Micromech Microeng 3(4):168–182, 1993; Jensen et al., In: Proc. of MicroTAS 2002, Nara, Japan, pp 733–735, 2002; Wong et al., J Fluid Mech 292:71–94, 1995). The T-shaped channel first reported by Kohnle et al. (In: IEEE MEMS, the 15th international IEEE micro electro mechanical conference (ed), Las Vegas, pp 77–80, 2002) prevents micro-channels from clogging by the aid of the equilibrium bubble position in such a geometry. This work is concerned with the static and dynamic behaviour of bubbles in such T-shaped micro-channels. The aspect ratio of a rectangle enclosing the T-shaped channel and the contact angle of the walls are the main parameters influencing the static and dynamic bubble behaviour. It is investigated in this article how these parameters relate to the equilibrium bubble shape and how optimum bubble velocities can be achieved inside the channel. An analytical model depending on the contact angle and the channel geometry is presented that allows to determine the bubble configuration inside the channel by minimizing the bubble’s surface energy. A second model is derived to predict the velocity of gas bubbles driven by buoyancy in vertical T-shaped channels. The model is applied to design T-shaped channels with a maximum mobility of gas bubbles. Experiments with MEMS fabricated devices and CFD simulations are used to verify the models. Furthermore design rules for an optimum non-clogging channel geometry which provides the highest gas bubble mobility are given.     

Effect of Stochastic Noise on Superior Julia Sets

Julia sets are considered one of the most attractive fractals and have wide range of applications in science and engineering. The strong physical meaning of Mandelbrot and Julia sets is broadly accepted and nicely connected by Christian Beck (Physica D 125(3–4):171–182, 1999) to the complex logistic maps, in the former case, and to the inverse complex logistic map, in the latter. Argyris et al. (Chaos Solitons Fractals 11(13):2067–2073, 2000) have studied the effect of noise on Julia sets and concluded that Julia sets are stable for noises of low strength, and a small increment in the strength of noise may cause considerable deterioration in the configuration of the Julia sets. It is well-known that the method of function iterates plays a crucial role in discrete dynamics utilizing the techniques of fractal theory. However, recently Rani and Kumar (J. Korea Soc. Math. Edu. Ser. D: Res. Math. Edu. 8(4):261–277, 2004) introduced superior iterations as a generalization of function iterations in the study of Julia sets and studied superior Julia sets. This technique is further utilized to study effectively new Mandelbrot sets and related properties (see, for instance, Negi and Rani, Chaos Solitons Fractals 36(2):237–245, 2008; 36(4):1089–1096, 2008, Rani and Kumar, J. Korea Soc. Math. Edu. Ser. D: Res. Math. Edu. 8(4):279–291, 2004). The intent of this paper is to study certain effects of noise on superior Julia sets. We find that the superior Julia sets are drastically more stable for higher strength of noises than the classical Julia sets. Finally, we make a humble attempt to discuss some applications of superior orbit in discrete dynamics and of superior Julia sets in particle dynamics.     

Orientation contrast sensitive cells in primate V1 <Emphasis Type="Italic">a computational model</Emphasis>

Many cells in the primary visual cortex respond differently when a stimulus is placed outside their classical receptive field (CRF) compared to the stimulus within the CRF alone, permitting integration of information at early levels in the visual processing stream that may play a key role in intermediate-level visual tasks, such a perceptual pop-out [Knierim JJ, van Essen DC (1992) J Neurophysiol 67(5):961–980; Nothdurft HC, Gallant JL, Essen DCV (1999) Visual Neurosci 16:15–34], contextual modulation [Levitt JB, Lund JS (1997) Nature 387:73–76; Das A, Gilbert CD (1999) Nature 399:655–661; Dragoi V, Sur M (2000) J Neurophysiol 83:1019–1030], and junction detection [Sillito AM, Grieve KL, Jones HE, Cudiero J, Davis J (1995) Nature 378:492–496; Das A, Gilbert CD (1999) Nature 399:655–661; Jones HE, Wang W, Sillito AM (2002) J Neurophysiol 88:2797–2808]. In this article, we construct a computational model in programming environment TiViPE [Lourens T (2004) TiViPE—Tino’s visual programming environment. In: The 28th Annual International Computer Software & Applications Conference, IEEE COMPSAC 2004, pp 10–15] of orientation contrast type of cells and demonstrate that the model closely resembles the functional behavior of the neuronal responses of non-orientation (within the CRF) sensitive 4Cβ cells [Jones HE, Wang W, Sillito AM (2002) J Neurophysiol 88:2797–2808], and give an explanation of the indirect information flow in V1 that explains the behavior of orientation contrast sensitivity. The computational model of orientation contrast cells demonstrates excitatory responses at edges near junctions that might facilitate junction detection, but the model does not reveal perceptual pop-out.     

New Results on Web Caching with Request Reordering

We study web caching with request reordering. The goal is to maintain a cache of web documents so that a sequence of requests can be served at low cost. To improve cache hit rates, a limited reordering of requests is allowed. Feder et al. (Proceedings of the 13th ACM–SIAM Symposium on Discrete Algorithms, pp. 104–105, 2002), who recently introduced this problem, considered caches of size 1, i.e. a cache can store one document. They presented an offline algorithm based on dynamic programming as well as online algorithms that achieve constant factor competitive ratios. For arbitrary cache sizes, Feder et al. (Theor. Comput. Sci. 324:201–218, 2004) gave online strategies that have nearly optimal competitive ratios in several cost models.     

Focussed ion beam based fabrication of micro-electro-mechanical resonators

A simple and fast process to fabricate micro-electro-mechanical (MEM) resonators with deep sub-micron transduction gaps in thin SOI is presented. The proposed process is realized on both 350 nm and 1.5 μm thin silicon-on-insulator (SOI) substrates, evaluating the possibilities for MEMS devices on thin SOI for future co-integration with CMOS circuitry on a single chip. Through the combination of conventional UV-lithography and focused ion beam (FIB) milling the process needs only two lithography steps, achieving ∼100 nm gaps, thus ensuring an effective transduction. Different FIB parameters and etching parameters and their effect on the process are reported.     

Influence of tool fabrication process on characteristics of hot embossed polymer microfluidic chips for electrospray

Fabrication techniques for mass manufacture of disposable polymer microfluidic chips are important for electrospray application used in mass spectrometry. Hot embossing offers advantages over traditional MEMS fabrication techniques and is the focus of this research. The aim of the paper is to evaluate hot embossed open channel polymer chips using two different hot embossing tools. One tool was fabricated in nickel using the electroforming process, and the other in high carbon bright steel by laser machining technique using a pulsed Nd:YAG laser that is normally used for conventional applications. Process parameters are determined and measurement of dimensions and surface roughness of tools and chips are presented. Depending on the fabrication method, each tool exhibits its own characteristic profile feature and surface roughness. Polystyrene and polycarbonate substrates embossed with the electroformed tool exhibited lowest surface roughness of 48 nm compared to 450 nm for the laser machined tool. The embossed microfluidic chips were tested for fluid flow and electrospray and showed good performance.     

A posteriori error analysis of time-dependent Stokes problem by Chorin-Temam scheme

We present a posteriori-residual analysis for the approximate time-dependent Stokes model Chorin-Temam projection scheme (Chorin in Math. Comput. 23:341–353, 1969; Temam in Arch. Ration. Mech. Appl. 33:377–385, 1969). Based on the multi-step approach introduced in Bergam et al. (Math. Comput. 74(251):1117–1138, 2004), we derive error estimators, with respect to both time and space approximations, related to diffusive and incompressible parts of Stokes equations. Using a conforming finite element discretization, we prove the equivalence between error and estimators under specific conditions.     

Generalizing Inverse Compositional and ESM Image Alignment

Inverse compositional (IC) image alignment (Baker and Matthews in Int. J. Comput. Vis. 56(3):221–255, 2004) uses the symmetry between the roles of the fixed and moving images for faster processing. However, it requires implementation of compositional optimizer update steps. The IC approach can be viewed as an efficient way of computing the similarity measure derivative relative to the fixed image warp parameters. Since the mapping between the fixed and moving warp parameters is continuous and differentiable, this derivative can be converted into the moving warp space using the chain rule. This avoids the need for compositional update steps. Our generalization also allows the efficient second order method (ESM) (Malis in Proceedings of the 2004 IEEE International Conference on Robotics and Automation (ICRA04), pp. 1843–1848, 2004; Benhimane and Malis in IEEE/RSJ International Conference on Intelligent Robots and Systems, 2004; Malis and Benhimane in Robot. Auton. Syst. 52(1):39–52, 2005) to be applied to general parameterizations of the transformation. Experiments using multiple similarity measures and optimizers show that our generalized IC method equals or exceeds the performance of the original IC approach. The generalized ESM approach is more reliable than the classic approach as it increases the capture radius of the optimization.     

Edge Pricing of Multicommodity Networks for Selfish Users with Elastic Demands

We examine how to induce selfish heterogeneous users in a multicommodity network to reach an equilibrium that minimizes the social cost. In the absence of centralized coordination, we use the classical method of imposing appropriate taxes (tolls) on the edges of the network. We significantly generalize previous work (Yang and Huang in Transp. Res. Part B 38:1–15, [2004]; Karakostas and Kolliopoulos in Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 268–276, [2004]; Fleischer et al. in Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 277–285, [2004]) by allowing user demands to be elastic. In this setting the demand of a user is not fixed a priori but it is a function of the routing cost experienced, a most natural assumption in traffic and data networks. Research supported by MITACS and a NSERC Discovery grant.     

A MEMS guide plate for a high temperature testing of a wafer level packaged die wafer

This paper describes the design and fabrication of a MEMS guide plate, which was used for a vertical probe card to test a wafer level packaged die wafer. The size of the fabricated MEMS guide plate was 10.6 × 10.6 cm. The MEMS guide plate consisted of 8,192 holes to insert pogo pins, and four holes for bolting between the guide plate and the housing. To insert pogo pins easily, an inclined plane was defined at the back of each hole. Pitch and diameter of the hole were 650 and 260 μm, respectively. In order to define inserting holes and inclined planes at an exact position, silicon MEMS technology was used such as anisotropic etching, deep reactive etching and more. Silicon was used as the material of the guide plate to reduce alignment mismatch between the pogo pins and solder bumps during a high temperature testing. A combined probe card with the fabricated MEMS guide plate showed good x–y alignment and planarity errors within ±9 and ±10 μm at room temperature, respectively. In addition, x–y alignment and planarity are ±20 and ±16 μm at 125°C, respectively. The proposed MEMS guide plate can be applied to a vertical probe card for burn-in testing of a wafer level packaged die wafer because the thermal expansion coefficient of the MEMS guide plate and die wafer is same.     

Speed-Up Theorems in Type-2 Computations Using Oracle Turing Machines

A classic result known as the speed-up theorem in machine-independent complexity theory shows that there exist some computable functions that do not have best programs for them (Blum in J. ACM 14(2):322–336, 1967 and J. ACM 18(2):290–305, 1971). In this paper we lift this result into type-2 computations. Although the speed-up phenomenon is essentially inherited from type-1 computations, we observe that a direct application of the original proof to our type-2 speed-up theorem is problematic because the oracle queries can interfere with the speed of the programs and hence the cancellation strategy used in the original proof is no longer correct at type-2. We also argue that a type-2 analog of the operator speed-up theorem (Meyer and Fischer in J. Symb. Log. 37:55–68, 1972) does not hold, which suggests that this curious speed-up phenomenon disappears in higher-typed computations beyond type-2. The result of this paper adds one more piece of evidence to support the general type-2 complexity theory under the framework proposed in Li (Proceedings of the Third International Conference on Theoretical Computer Science, pp. 471–484, 2004 and Proceedings of Computability in Europe: Logical Approach to Computational Barriers, pp. 182–192, 2006) and Li and Royer (On type-2 complexity classes: Preliminary report, pp. 123–138, 2001) as a reasonable setup.     

Robust scalability analysis and SPM case studies

Scalability has become an attribute of paramount importance for computer systems used in business, scientific and engineering applications. Although scalability has been widely discussed, especially for pure parallel computer systems, it conveniently focuses on improving performance when increasing the number of computing processors. In fact, the term “scalable” is so much abused that it has become a marketing tool for computer vendors independent of the system’s technical qualifications. Since the primary objective of scalability analysis is to determine how well a system can work on larger problems with an increase in its size, we introduce here a generic definition of scalability. For illustrative purposes only, we apply this definition to PC clusters, a rather difficult subject due to their long communication latencies. Since scalability does not solely depend on the system architecture but also on the application programs and their actual management by the run-time environment, for the sake of illustration, we evaluate scalability for programs developed under the super-programming model (SPM) (Jin and Ziavras in IEEE Trans. Parallel Distrib. Syst. 15(9):783–794, 2004; J. Parallel Distrib. Comput. 65(10):1281–1289, 2005; IEICE Trans. Inf. Syst. E87-D(7):1774–1781, 2004).     

A combinative technique to fabricate hot embossing master for PMMA tunneling sensors

A combinative approach of anisotropic bulk etching and modified plasma etching has been successfully employed in a single wafer to fabricate silicon masters for the hot embossing process. The masters hold both pyramid pits and positive profile sidewalls with smooth surfaces and steep angles. The SiO₂ layer is utilized as a etching mask with the aid of photoresist in three steps of photolithography patterning. The first polymethyl-methacrylate (PMMA)-based tunneling transducer with polymer membrane structures is fabricated by hot embossing replication with the silicon master. Consequently, the exponential relations between tunneling currents and applied deflection voltages are also reported.This work is partially supported by grants NSF/LEQSF (2001–04)-RII-02, DARPA DAAD19–02–1-0338, and NASA (2002)-Stennis-22.     

Various replication techniques for manufacturing three-dimensional metal microstructures

 In microsystem technology a large range of different 6materials will be available only after the necessary micromanufacturing techniques have been developed or adapted. Existing manufacturing techniques are structuring or shaping techniques producing three-dimensional microstructures out of silicon (silicon etching, silicon surface micromechanics), mostly unfilled plastics (lithographic techniques, injection molding, hot embossing, reaction molding) or a few pure metals or binary alloys (electroforming). The choice of materials for microcomponents is determined by the function and conditions of use of microsystems. Especially the range of metals is still restricted considerably because the only processes available are electroforming and thin-layer techniques. It is for these reasons that we are developing various processes for manufacturing three-dimensional metal microstructures. In addition to direct electroforming of injection molding lost plastic micromolds, these are a new microcasting process and Micro Metal Injection Molding (Micro MIM). Microstructures have already been molded from mold inserts made by micromechanical cutting or by the LIGA technique. The results achieved, and future prospects, are outlined below. Received: 25 August 1997/Accepted: 3 September 1997     

Studies of polymer deformation and recovery in micro hot embossing

In large areas of micro hot embossing, process temperature plays a critical role to both the local-area fidelity and global uniformity of microstructure formation. Higher embossing temperature could improve structure fidelity, however, at the expense of demoulding easiness. Micro embossing at the lowest possible temperature with acceptable fidelity can improve global flatness after demoulding. This study focuses on polymer deformation and recovery in micro embossing when the process temperature is below the polymer glass transition temperature (Tg). PMMA (Polymethyl Methacrylate) substrates (Tg = 105°C) were employed with the process temperature ranging from 25°C to its Tg. At temperature below Tg −55°C, significant recovery occurred after processing, but permanent structures could still be formed with sufficiently high applied stress. With an increase in temperature, plastic deformation increased and was the dominant polymer deformation mode for permanent cavities formation. However, the formation of protrusive structures was not complete since there was little polymer flow. The polymer will lose its storage modulus at an even higher temperature and microstructures could be formed with high fidelity. A compromise between local fidelity of embossed patterns and global flatness of substrate has to be reached in micro hot embossing.