Tuning the quality factor of bulk micromachined structures using squeezed-film damping

This report demonstrates the tuning the quality factor of a micromachined structure using the air damping of a small squeezed-film area (300 m² to 800 m²). Two micromachining processes have successfully been established to fabricate novel stationary structures using thin films and bulk silicon, in which the stationary structure and a vibrating micromachined cantilever form a squeezed-film region. Measurements showed that, under the assistant of bulk silicon stationary structure, the quality factor of the vibrating beam decreased by 48% when the squeezed-film area was increased from 300 m² to 800 m² under a 760-torr ambient pressure. Moreover, even when the ambient pressure was only 20 mtorr, the quality factor of the beam still decreased by 20% for the same increase in area. Under the assistant of thin film stationary structure, the quality factor of the vibrating beam decreased by 35% when the squeezed-film area was increased from 300 m² to 500 m² under a 760-torr ambient pressure. Consequently, the proposed two stationary structures can be exploited to significantly alter the quality factor of dynamic systems.This material is based (in part) upon work supported by the Ministry of Economic Affairs, R.O.C. under contract No. 91-EC-17-A-07-S1-0011, and the Asia Pacific Microsystems Inc. The author would like to express his appreciation to the NSC Central Regional MEMS Research Center (Taiwan), Electrical Engineering Department of National Tsing Hua University (Taiwan), Semiconductor Center of National Chiao Tung University (Taiwan), and National Nano Device Laboratories (Taiwan) in providing fabrication facilities.     

High aspect ratio fabrication method using O2 RIE and electroplating

A polyimide-based process for the fabrication of vertical structures with high aspect ratio has been developed. O₂ reactive ion etching (O₂ RIE) has been employed in the polyimide processing. Achieved etching characteristics of the O₂ RIE system are: 4.0 m/min etching rate, 15 aspect ratio, 75 m etching depth. Polyimide has excellent chemical and thermal properties which makes it a good building material for micromachines. Polyimide could be also used as molds for electroplating. Electroplated copper structures were formed in the polyimide molds and metal gears were fabricated by these fabrication technologies. New possibilities for micromachining were opened by the use of O₂ RIE and electroplating.This work was supported by Japanese ministry of Education Science and Culture under a grant-in-Aid No. 03102001.     

Local determinacy of abstract local dynamical systems

O. Hájek proved in his book Dynamical Systems in the Plane (Chapter III) that there isat most one abstract local dynamical system which is locally equivalent to, or equivalently an extension of, a given elementary dynamical system, and suggested a question of finding reasonable conditions on the latter for the existence ofat least one such abstract local dynamical system. An elementary dynamical system is said to satisfy the No-Intersection Axiom and is called an abstract germ if(x ₁, t) = (x ₂,t) impliesx ₁ =x ₂. We show that is (uniquely) extendable to an abstract local dynamical system if and only if is an abstract germ, and hence the question is completely answered. After introducing various kinds of isomorphisms of abstract germs and abstract local dynamical systems corresponding to those of continuous germs and continuous local dynamical systems, we obtain some sufficient conditions for extendability of isomorphisms and possibility of restriction of them, and thus establish the local determinacy of abstract local dynamical systems up to isomorphisms in some wider categories.Dedicated to Professor Yusuke HAGIHARA in Commemoration of His Seventy-Seventh Anniversary     

Deep X-ray lithography using mask with integrated electrothermal actuator

We present a deep X-ray mask with integrated bent-beam electrothermal actuator for the fabrication of 3D microstructures with curved surface. The mask absorber is electroplated on the shuttle mass, which is supported by a pair of 20-m-thick single crystal silicon bent-beam electrothermal actuators and oscillated in a rectilinear direction due to the thermal expansion of the bent-beams. The width of each bent-beam is 10 m or 20 m and the length and bending angle are 1 mm and 0.1 rad, respectively, and the shuttle mass size is 1 mm × 1 mm. For 10-m-wide bent-beams, the shuttle mass displacement is around 15 m at 180 mW (3.6 V) dc input power. For 20-m-wide bent-beams, the shuttle mass displacement is around 19 m at 336 mW (4.2 V) dc input power. Sinusoidal cross-sectional PMMA microstructures with a pitch of 40 m and a height of 20 m are fabricated by 0.5 Hz, 20-m-amplitude sinusoidal shuttle mass oscillation.This research, under the contract project code MS-02-338-01, has been supported by the Intelligent Microsystem Center, which carries out one of the 21st centurys Frontier R & D Projects sponsored by the Korea Ministry of Science & Technology. Experiments at PLS were supported in part by MOST and POSCO.     

Three-valued representative systems

A representative system defined onn voters or propositionsi = 1,,n is a functionF: {1,0, -1} ⁿ {1,0, -1} which is monotonic (D E F(D) F(E)), unanimous (F(1,, 1) = 1), dual (F(-D) = -F(D)), and satisfies a positivity property which says that the set of all non-zero vectors in {1, 0, -1} ⁿ for whichF(D) = 0 can be partitioned into two dual subsets each of which has the property that ifD andE are in the subset thenD _i+E _i > 0 for somei. Representative systems can be defined recursively from the coordinate projectionsS _i (D) = D _i using sign functions, and in this format they are interpreted as hierarchical voting systems in which outcomes of votes in lower levels act as votes in higher levels of the system. For each positive integern, (n) is defined as the smallest positive integer such that all representative systems defined on {1, 0, -1} ⁿ can be characterized by(n) or fewer hierarchical levels. The function is nondecreasing inn, unbounded above, and satisfies(n) n–1 for alln. In addition,(n) = n–1 forn {1, 2, 3, 4}, and it is conjectured that does not continue to grow linearly asn increases.     

A variotherm mold for micro metal injection molding

In this paper, a variotherm mold was designed and fabricated for the production of 316L stainless steel microstructures by micro metal injection molding (MIM). The variotherm mold incorporated a rapid heating/cooling system, vacuum unit, hot sprue and cavity pressure transducer. The design of the variotherm mold and the process cycle of MIM using the variotherm mold were described. Experiments were conducted to evaluate the molded microstructures produced using variotherm mold and conventional mold. The experiments showed that microstructures of higher aspect ratio such as 60 m × height 191 m and 40 m × height 174 m microstructures could be injection molded with complete filling and demolded successfully using the variotherm mold. Molded microstructures with dimensions of 60 m × height 191 m were successfully debound and sintered without visual defects.     

Deep sub micron high aspect ratio polymer structures produced by hard X-ray lithography

Microfabrication using X-ray lithography is a well established process in many laboratories worldwide. Radiation spectra, mask technology and process conditions are optimized for patterning resist thicknesses of several hundred micrometers with lateral dimensions of a few microns. This article provides first results as to how far these technologies can be extended to form structures with sub-micrometer lateral dimensions in resist layers of a few micrometers thickness. Available equipment and processes of the 2.5 GeV electron storage ring ANKA and the process technology of the Institut für Mikrostrukturtechnik (IMT) in Karlsruhe, Germany, have been applied. An X-ray mask with a 2.7 m Ti-membrane and 20 m thick Au-absorbers is used to expose 1.6 m PMMA resist on silicon wafers. As the smallest features on the mask are 2 m, a double exposure with an intermediate deliberate relative movement between mask and resist generated sub-micron resist test structures. Smallest feature sizes are between 300 and 400 nm. They are not yet limited by diffraction, but by different process conditions that lead to adhesion loss, resist cracking and surface rounding. It has been shown that an intermediate layer of 1.2 m thick polyimide between resist and substrate significantly enhances adhesion and reduces resist cracking. Reducing the beam power impinging onto the sample from typically 21 to 0.4 W leads to a 50% reduction of the surface rounding at the top of the microstructures. To demonstrate the capability to pattern thicker resist layers, first samples with an increased resist thickness of 4.1 m and an aspect ratio of up to 8 were processed. Finally, a metal mesh with 2 m thick Au-absorbers and 900 nm hexagonal holes was applied to pattern showpieces of sub micron features using a reduced electron energy of 1.3 GeV.The high resolution metal mesh was provided by R. Fettig of IMT.     

A surface micromachining process for suspended RF-MEMS applications using porous silicon

A porous silicon (PS) surface micromachining technology for suspended RF-MEMS device fabrication is proposed. Using PS as sacrificial layer and SiO₂ film as support membrane, suspended metallic structure has been realized. The lateral size of the obtained suspended inductor is 450 × 425 m². Sputtered aluminum with 1 m thickness is used as structural materials. To avoid any damage of the Al structure during the process, TMAH solution with Si powder and (NH₄)₂S₂O₈ is used to remove the PS layer through etching holes.This work is supported by the National 985 Project and 973 Project (G1999033105) of China. And the SEM measurements were sponsored by the THSJZ in Tsinghua University.     

On the Impact of Systematic Noise on the Evolutionary Optimization Performance—A Sphere Model Analysis

Quality evaluations in optimization processes are frequently noisy. In particular evolutionary algorithms have been shown to cope with such stochastic variations better than other optimization algorithms. So far mostly additive noise models have been assumed for the analysis. However, we will argue in this paper that this restriction must be relaxed for a large class of applied optimization problems. We suggest systematic noise as an alternative scenario, where the noise term is added to the objective parameters or to environmental parameters inside the fitness function. We thoroughly analyze the sphere function with systematic noise for the evolution strategy with global intermediate recombination. The progress rate formula and a measure for the efficiency of the evolutionary progress lead to a recommended ratio between and . Furthermore, analysis of the dynamics identifies limited regions of convergence dependent on the normalized noise strength and the normalized mutation strength. A residual localization error R can be quantified and a second to ratio is derived by minimizing R .     

Fabrication of a ZnO piezoelectric micro cantilever with a high-aspect-ratio nano tip

This paper reports on a ZnO piezoelectric micro cantilever with a high-aspect-ratio (HAR) nano tip, which is proposed for a ferroelectric material based nano storage system. The system uses the interaction between the nano tip and a storage medium, and the HAR nano tip is needed to suppress undesirable effects caused by the small gap between the cantilever and the storage medium. The fabrication process for the cantilever with the HAR nano tip consists of three parts: the HAR nano tip formation, the cantilever fabrication, and the bonding/releasing process. The HAR nano tip is formed by the Si deep reactive ion etching for a long shaft and the anisotropic wet etching for a nano tip end. The cantilever is made up of 1 m-thick LPCVD poly-Si layer and 0.2 m-thick Si nitride layer, and has 0.5 m-thick ZnO actuation layer. A final releasing process is followed by an anodic bonding process. The fabricated HAR nano tip has 6 m side length, over 18 m height, and less than 15 nm tip radius, which is built on the 85 m-wide, 300 m-long, and 1.2 m-thick cantilever. The experimental results show a linear behavior with respect to input voltage of 1 to 5 V and the first resonance frequency at 17.9 kHz.     

A Representation of the Interval Hull of a Tolerance Polyhedron Describing Inclusions of Function Values and Slopes

Given a nonempty set of functions

Generating Boolean \mu-expressions

In this paper, we consider the class of Boolean -functions, which are the Boolean functions definable by -expressions (Boolean expressions in which no variable occurs more than once). We present an algorithm which transforms a Boolean formulaE into an equivalent -expression-if possible-in time linear in E times , where E is the size ofE andn _m is the number of variables that occur more than once inE. As an application, we obtain a polynomial time algorithm for Mundici's problem of recognizing -functions fromk-formulas [17]. Furthermore, we show that recognizing Boolean -functions is co-NP-complete for functions essentially dependent on all variables and we give a bound close to co-NP for the general case.     

Material characterization of composite laminates using dynamic response and real parameter-coded microgenetic algorithm

An efficient nondestructive evaluation procedure is proposed for inversely determining material constants of composite laminates using dynamic response at one point on the plate surface. Material constants of composite laminates are determined by minimizing the difference between the measured dynamic response of the actual plate and the computed response of the plate with assumed material properties. For robust and efficient function minimization, a real parameter-coded microgenetic algorithm (real-GA) is proposed on the basis of the existing binary coded uniform microgenetic algorithm (uniform GA). Four different crossover operators are constructed for the real-GA. Performances of the present real-GA and the existing uniform GA are studied using several typical benchmark test functions and an order-3 deceptive function. The present real-GA is then implemented as the inverse solver in the minimization process of material characterization. From hundreds of tests conducted on the benchmark functions, the order-3 deceptive function, and the material characterization problems, it is found that the real-GA is two to five times faster in converging to the global optimum compared with the uniform GA. Numerical examples for material characterization of composite laminates have demonstrated the robustness, efficiency, and accuracy of the proposed procedure.     

Minimization of norms and logarithmic norms by diagonal similarities

It is a commonly occurring problem to find good norms · or logarithmic norms (·) for a given matrix in the sense that they should be close to respectively the spectral radius (A) and the spectral abscissa (A). Examples may be the certification thatA is convergent, i.e. (A)A<1 or stable, i.e. (A)(A)<0. Often the ordinary norms do not suffice and one would like to try simple modifications of them such as using an ordinary norm for a diagonally transformed matrix. This paper treats this problem for some of the ordinary norms.

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Minimisierung von Normen und Logarithmischen Normen durch Diagonale Transformationen

Zusammenfassung Ein oft vorkommendes praktisches Problem ist die Konstruktion von guten Normen · und logarithmischen Normen (·) für eine gegebene MatrixA. Mit gut wird dann verstanden, daß A den Spektralradius (A)=max |₁| und (A) die Spektralabszisse (A)=max Re _i gut approximieren. Beispiele findet man für konvergente Matrizen wo (A)A<1 gewünscht ist, und für stabile Matrizen wo (A)(A)<0 zu zeigen ist. Wir untersuchen hier, wie weit man mit Diagonaltransformationen und dengewöhnlichsten Normen kommen kann.

     

Formalizing process algebraic verifications in the calculus of constructions

This paper reports on the first steps towards the formal verification of correctness proofs of real-life protocols in process algebra. We show that such proofs can be verified, and partly constructed, by a general purpose proof checker. The process algebra we use isCRL, ACP augmented with data, which is expressive enough for the specification of real-life protocols. The proof checker we use is Coq, which is based on the Calculus of Constructions, an extension of simply typed lambda calculus. The focus is on the translation of the proof theory ofCRL andCRL-specifications to Coq. As a case study, we verified the Alternating Bit Protocol.     

On the minimal number of trajectories determining a multidimensional system

The minimal number(S) of generators of a multidimensional systemS is constructively determined. Such anS is the solution space of a linear system of partial differential or difference equations with constant coefficients. The main theorem generalizes recent results of Heij and Zampieri who calculated the number(S) in the one- (resp. two-) dimensional discrete case. There is also a direct connection with Macaulay's inverse systems in the multidimensional discrete situation, in particular with his principal systems characterized by the relation(S)1. It is surprising that, for dimensions greater than one, very many large systems are principal in this sense.     

Constructing strongly convex hulls using exact or rounded arithmetic

One useful generalization of the convex hull of a setS ofn points is the -strongly convex -hull. It is defined to be a convex polygon with vertices taken fromS such that no point inS lies farther than outside and such that even if the vertices of are perturbed by as much as , remains convex. It was an open question as to whether an -strongly convexO()-hull existed for all positive . We give here anO(n logn) algorithm for constructing it (which thus proves its existence). This algorithm uses exact rational arithmetic. We also show how to construct an -strongly convexO( + )-hull inO(n logn) time using rounded arithmetic with rounding unit . This is the first rounded-arithmetic convex-hull algorithm which guarantees a convex output and which has error independent ofn.     

Thermal bubble powered microactuators

Thermal bubble powered micro mechanical actuators have been successfully demonstrated in working liquids. Micro mechanical plates which function as the mechanical actuators are 70×60×2 m³ in size. They have been fabricated by surface-micromachining technology and suspended 2 m above the substrate by the supports of cantilever beams. Micro thermal bubbles which are generated by heavily phosphorus doped polysilicon line resistive heaters have been used to lift the mechanical plates in a controllable manner. The typical current required to generate a single, spherical thermal bubble as the actuation source on top of the micro line resistors (60×2×0.3 m³ in size) is 8.4 mA (80 m Watt) in FC 43 liquid (an inert, dielectrical fluid available from the 3M company). The thermal bubbles have been demonstrated to actuate the mechanical plate perpendicularly to the substrate with a maximum elevation distance of 140 m and a maximum actuation force of 2 N. This new actuation mechanism is expected to find applications for micro fluidic devices.The authors would like to thank Prof. V.P. Carey, Mechanical Engineering department, U.C. Berkeley and Dr. A.P. Lee for valuable discussions. The devices were fabricated in the UC Berkeley Microfabrication Laboratory and the FC liquid was provided by 3M company. This work has been supported by Berkeley Sensor and Actuator Center, an NSF/Industry/University Co-operative Research Center.     

On the Quadratic Convergence of the Levenberg-Marquardt Method without Nonsingularity Assumption

Recently, Yamashita and Fukushima [11] established an interesting quadratic convergence result for the Levenberg-Marquardt method without the nonsingularity assumption. This paper extends the result of Yamashita and Fukushima by using _k=||F(x_k)||, where [1,2], instead of _k=||F(x_k)||² as the Levenberg-Marquardt parameter. If ||F(x)|| provides a local error bound for the system of nonlinear equations F(x)=0, it is shown that the sequence {x_k} generated by the new method converges to a solution quadratically, which is stronger than dist(x_k,X^*)0 given by Yamashita and Fukushima. Numerical results show that the method performs well for singular problems.     

From Pre-Historic to Post-Modern Symbolic Model Checking

Symbolic model checking, which enables the automatic verification of large systems, proceeds by calculating expressions that represent state sets. Traditionally, symbolic model-checking tools are based on backward state traversal; their basic operation is the function pre, which, given a set of states, returns the set of all predecessor states. This is because specifiers usually employ formalisms with future-time modalities, which are naturally evaluated by iterating applications of pre. It has been shown experimentally that symbolic model checking can perform significantly better if it is based, instead, on forward state traversal; in this case, the basic operation is the function post, which, given a set of states, returns the set of all successor states. This is because forward state traversal can ensure that only parts of the state space that are reachable from an initial state and relevant for the satisfaction or violation of the specification are explored; that is, errors can be detected as soon as possible.In this paper, we investigate which specifications can be checked by symbolic forward state traversal. We formulate the problems of symbolic backward and forward model checking by means of two -calculi. The pre- calculus is based on the pre operation, and the post- calculus is based on the post operation. These two -calculi induce query logics, which augment fixpoint expressions with a boolean emptiness query. Using query logics, we are able to relate and compare the symbolic backward and forward approaches. In particular, we prove that all -regular (linear-time) specifications can be expressed as post- queries, and therefore checked using symbolic forward state traversal. On the other hand, we show that there are simple branching-time specifications that cannot be checked in this way.