Browsing by Author "Shih, CW"

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Amorphouslike chemical vapor deposited tungsten diffusion barrier for copper metallization and effects of nitrogen addition
(1997-08-01)
Chang, KM
;
Yeh, TH
;
Deng, IC
;
Shih, CW
;
電子工程學系及電子研究所
In this article, we propose an amorphouslike chemical vapor deposited tungsten (CVD-W) thin him as a diffusion barrier for copper metallization. Experimental results gave no evidence of interdiffusion and structural change for Cu/amorphouslike CVD-W/Si samples annealed up to 675 degrees C for 30 min in N-2. At higher temperatures (700 degrees C), Cu penetration results in the formation of eta ''-Cu3Si precipitates at the CVD-W/Si interface. This is due to the crystallization of the amorphouslike CVD-W film above 650 degrees C, rendering the grain-boundary structure and, hence, fast pathways for Cu diffusion. The Cu/amorphouslike CVD-W/p(+)n diodes, thus, sustain large increases in reverse leakage current. In addition, the effects of nitrogen addition by using an in situ nitridation on the amorphouslike CVD-W film are also discussed. The effectiveness of the nitrided barrier is attributed to the blocking of the grain boundaries in the tungsten film by nitrogen atoms. This slows down Cu diffusion significantly. Physical and chemical analyses indicate that interfaces in the Cu/WNx/W/Si multilayer maintain their integrity while the annealing is carried out at 750 degrees C. Moreover, the reverse leakage current densities of Cu/WNx/W/p(+)n diodes remain at 10(-7) A/cm(2) after 725 degrees C annealing. (C) 1997 American Institute of Physics.
Amorphouslike chemical vapor deposited tungsten diffusion barrier for copper metallization and effects of nitrogen addition
(1997-08-01)
Chang, KM
;
Yeh, TH
;
Deng, IC
;
Shih, CW
;
電子工程學系及電子研究所
In this article, we propose an amorphouslike chemical vapor deposited tungsten (CVD-W) thin him as a diffusion barrier for copper metallization. Experimental results gave no evidence of interdiffusion and structural change for Cu/amorphouslike CVD-W/Si samples annealed up to 675 degrees C for 30 min in N-2. At higher temperatures (700 degrees C), Cu penetration results in the formation of eta ''-Cu3Si precipitates at the CVD-W/Si interface. This is due to the crystallization of the amorphouslike CVD-W film above 650 degrees C, rendering the grain-boundary structure and, hence, fast pathways for Cu diffusion. The Cu/amorphouslike CVD-W/p(+)n diodes, thus, sustain large increases in reverse leakage current. In addition, the effects of nitrogen addition by using an in situ nitridation on the amorphouslike CVD-W film are also discussed. The effectiveness of the nitrided barrier is attributed to the blocking of the grain boundaries in the tungsten film by nitrogen atoms. This slows down Cu diffusion significantly. Physical and chemical analyses indicate that interfaces in the Cu/WNx/W/Si multilayer maintain their integrity while the annealing is carried out at 750 degrees C. Moreover, the reverse leakage current densities of Cu/WNx/W/p(+)n diodes remain at 10(-7) A/cm(2) after 725 degrees C annealing. (C) 1997 American Institute of Physics.
Asymptotic behaviors in a transiently chaotic neural network
(2004-04-01)
Chen, SS
;
Shih, CW
;
應用數學系
;
Department of Applied Mathematics
We are interested in the asymptotic behaviors of a discrete-time neural network. This network admits transiently chaotic behaviors which provide global searching ability in solving combinatorial optimization problems. As the system evolves, the variables corresponding to temperature in the annealing process decrease, and the chaotic behaviors vanish. We shall find sufficient conditions under which evolutions for the system converge to a fixed point of the system. Attracting sets and uniqueness of fixed point for the system are also addressed. Moreover, we extend the theory to the neural networks with cycle-symmetric coupling weights and other output functions. An application of this annealing process in solving travelling salesman problems is illustrated.
Asymptotic behaviors in a transiently chaotic neural network
(2003-04-01)
Chen, SS
;
Shih, CW
;
應用數學系
;
Department of Applied Mathematics
We are interested in the asymptotic behaviors of a discrete-time neural network. This network admits transiently chaotic behaviors which provide global searching ability in solving combinatorial optimization problems. As the system evolves, the variables corresponding to temperature in the annealing process decrease, and the chaotic behaviors vanish. We shall find sufficient conditions under which evolutions for the system converge to a fixed point of the system. Attracting sets and uniqueness of fixed point for the system are also addressed. Moreover, we extend the theory to the neural networks with cycle-symmetric coupling weights and other output functions. An application of this annealing process in solving travelling salesman problems is illustrated.
Barrier characteristics of chemical vapor deposited amorphous-like tungsten silicide with in situ nitrogen plasma treatment
(1999-07-01)
Chang, KM
;
Deng, IC
;
Yeh, TH
;
Shih, CW
;
電子工程學系及電子研究所
Our team investigated the characteristics of inserting an 80 nm amorphous-like WSi1.6N0.5N/WSi1.6 barrier layer between aluminum film and a shallow diode to retard aluminum and silicon interdiffusion. In one chamber without breaking vacuum, we used a nitrogen plasma treatment to stuff nitrogen atoms into the grain boundaries of amorphous-like tungsten silicide film. The nitrogen atoms eliminated the fast diffusion paths of film, thus giving the amorphous-like tungsten silicide film a smaller diffusion coefficient. We then examined the failure of diodes with amorphous-like WSi1.6N0.5/WSi1.6 barriers which were annealed at 575 degrees C for 30 min and which had leakage currents of 10(7) and 10(8) nA/cm(2). These diodes failed due to the diffusion of aluminum along the sidewalls of the barriers and the field oxide interface. In the search for a solution to this problem we investigated the use of tetraethylorthosilicate, which is known for its thermal stability as a stress buffer. In this experiment we used tetraelhylorthosilicate to form a "contact array structure" which in turn prevented diode failure at 575 degrees C annealing for 30 min, and furthermore, the diodes in the contact array structure only began to show evidence of degradation at 600 degrees C. (C) 1999 The Electrochemical Society. S0013-4651(98)09-086-7. All rights reserved.
Bifurcations of symmetric periodic orbits near equilibrium in reversible systems
(1997-03-01)
Shih, CW
;
交大名義發表
;
應用數學系
;
National Chiao Tung University
;
Department of Applied Mathematics
Consider a family of reversible systems (x) over dot = f(x, mu) with the origin being an equilibrium for each mu. Suppose D(x)f(0, 0) has only purely imaginary eigenvalues +/-iw(1),..., +/-iw(k). We investigate the typical bifurcations of symmetric periodic solutions near the origin. A suitable complex basis is chosen so that D(x)f(0, 0) and the involution are in respective simple form. Incorporated with putting f into normal form, a modified version of Lyapunov-Schmidt reduction can be applied to obtain the reduced bifurcation equations. We then focus on the cases in resonance, that is, w(j) = n(j)w(0), where w(0) is a nonzero real number and n(j) is an integer for each j. Some codimension-two bifurcations are illustrated for the system in non-semisimple resonance with n(j) = 1, 2. A few codimension-one cases are also given for comparison with earlier works by other researchers.
Complete stability for a class of cellular neural networks
(2001-01-01)
Shih, CW
;
應用數學系
;
Department of Applied Mathematics
This work investigates a class of lattice dynamical systems originated from cellular neural networks. In the vector field of this class, each component of the state vector and the output vector is related through a sigmoidal nonlinear output function. For two types of sigmoidal output functions, Liapunov functions have been constructed in the literatures. Complete stability has been studied for these systems using LaSalle's invariant principle on the Liapunov functions. The purpose of this presentation is two folds. The first one is to construct Liapunov functions for more general sigmoidal output functions. The second is to extend the interaction parameters into a more general class, using an approach by Fiedler and Gedeon. This presentation also emphasizes the complete stability when the equilibrium is not isolated for the standard cellular neural networks.
Complete stability for standard cellular neural networks
(1999-05-01)
Lin, SS
;
Shih, CW
;
應用數學系
;
Department of Applied Mathematics
We consider cellular neural networks with symmetric space-variant feedback template. The complete stability is proved via detailed analysis on the energy function. The proof is presented for the two-dimensional case with Dirichlet boundary condition. It can be extended to other dimensions with minor adjustments. Modifications to the cases of Neumann and periodic boundary conditions are also mentioned.
Cycle-symmetric matrices and convergent neural networks
(2000-11-15)
Shih, CW
;
Weng, CW
;
應用數學系
;
Department of Applied Mathematics
This work investigates a class of neural networks with cycle-symmetric connection strength. We shall show that, by changing the coordinates, the convergence of dynamics by Fiedler and Gedeon [Physica D 111 (1998) 288] is equivalent to the classical results. This presentation also addresses the extension of the convergence theorem to other classes of signal functions with saturations. In particular, the result of Cohen and Grossberg [IEEE Trans. Syst. Man Cybernet. SMC-13 (1983) 815] is recast and extended with a more concise verification. (C) 2000 Elsevier Science B.V. All rights reserved.
Dynamics for discrete-time cellular neural networks
(2004-08-01)
Chen, SS
;
Shih, CW
;
應用數學系
;
Department of Applied Mathematics
This presentation investigates the dynamics of discrete-time cellular neural networks (DT-CNN). In contrast to classical neural networks that are mostly gradient-like systems, DT-CNN possesses both complete stability and chaotic behaviours as different parameters are considered. An energy-like function which decreases along orbits of DT-CNN as well as the existence of a globally attracting set are derived. Complete stability can then be concluded, with further analysis on the sets on which the energy function is constant. The formations of saturated stationary patterns for DT-CNN are shown to be analogous to the ones in continuous-time CNN. Thus, DT-CNN shares similar properties with continuous-time CNN. By confirming the existence of snap-back repellers, hence transversal homoclinic orbits, we also conclude that DT-CNN with certain parameters exhibits chaotic dynamics, according to the theorem by Marotto.
Exact number of mosaic patterns in cellular neural networks
(2001-06-01)
Ban, JC
;
Lin, SS
;
Shih, CW
;
應用數學系
;
Department of Applied Mathematics
This work investigates mosaic patterns for the one-dimensional cellular neural networks with various boundary conditions. These patterns can be formed by combining the basic patterns. The parameter space is partitioned so that the existence of basic patterns can be determined for each parameter region. The mosaic patterns can then be completely characterized through formulating suitable transition matrices and boundary-pattern matrices. These matrices generate the patterns for the interior cells from the basic patterns and indicate the feasible patterns for the boundary cells. As an illustration, we elaborate on the cellular neural networks with a general 1 x 3 template. The exact number of mosaic patterns will be computed for the system with the Dirichlet, Neumann and periodic boundary conditions respectively. The idea in this study can be extended to other one-dimensional lattice systems with finite-range interaction.
Forced symmetry-breaking via boundary conditions
(2001-04-01)
Mei, Z
;
Shih, CW
;
應用數學系
;
Department of Applied Mathematics
Influence of boundary conditions on pattern formation and spatial chaos in lattice systems
(2000-07-19)
Shih, CW
;
應用數學系
;
Department of Applied Mathematics
This work elucidates the spatial structure of lattice dynamical systems, which is represented by equilibria of the systems. On a finite lattice, various boundary conditions are imposed. The effect from these boundary conditions on formation of pattern as well as spatial complexity, as the lattice size tends to infinity, is investigated. Two general propositions are proposed as a criteria to demonstrate that this effect is negligible. To illustrate the effectiveness of these criteria, the mosaic patterns in a cellular neural network model on one- and two-dimensional lattices are also studied. On a one-dimensional lattice, the influence of boundary conditions on pattern formation and spatial chaos for mosaic patterns is negligible. This result is justified by verifying the above-mentioned criteria and by using the transition matrices. These appropriately formulated matrices generate all the mosaic patterns on a one-dimensional infinite lattice and on any one-dimensional finite lattice with boundary conditions. On a two-dimensional lattice, two illustrative examples demonstrate that the boundary effect can be dominant. The results and analysis in this investigation have significant implications for circuit design in cellular neural networks.
Multistability in recurrent neural networks
(2006)
Cheng, CY
;
Lin, KH
;
Shih, CW
;
應用數學系
;
Department of Applied Mathematics
Stable stationary solutions correspond to memory capacity in the application of associative memory for neural networks. In this presentation, existence of multiple stable stationary solutions for Hopfield-type neural networks with delay and without delay is investigated. Basins of attraction for these stationary solutions are also estimated. Such a scenario of dynamics is established through formulating parameter conditions based on a geometrical setting. The present theory is demonstrated by two numerical simulations on the Hopfield neural networks with delays.
On the templates corresponding to cycle-symmetric connectivity in cellular neural networks
(2002-12-01)
Shih, CW
;
Weng, CW
;
應用數學系
;
Department of Applied Mathematics
In the architecture of cellular neural networks (CNN), connections among cells are built on linear coupling laws. These laws are characterized by the so-called templates which express the local interaction weights among cells. Recently, the complete stability for CNN has been extended from symmetric connections to cycle-symmetric connections. In this presentation, we investigate a class of two-dimensional space-invariant templates. We find necessary and sufficient conditions for the class of templates to have cycle-symmetric connections. Complete stability for CNN with several interesting templates is thus concluded.
Pattern formation and spatial chaos for cellular neural networks with asymmetric templates
(1998-10-01)
Shih, CW
;
應用數學系
;
Department of Applied Mathematics
The cellular neural networks with two kinds of two-parametered asymmetric templates are considered. The parameter space is partitioned into finitely many disjoint regions. In each region, the basic mosaic patterns are characterized. The feasible mosaic patterns corresponding to the parameters in each region can then be determined. To exhibit the spatial complexity of the system, we estimate the entropy of mosaic patterns for parameters in the regime of spatial chaos. In light of this characterization, the effect from the symmetry of the template on pattern formation properties can be seen in detail. We also discuss the existence of some fundamental class of feasible local defect patterns. It is shown that the feasible local k-defect patterns of vertical type cannot exist if the connection weights are anti-symmetric in the vertical direction. Same conclusion also holds for the ones of horizontal type and horizontal direction.
Pattern formation and spatial chaos for cellular neural networks with asymmetric templates
(1998-10-01)
Shih, CW
;
應用數學系
;
Department of Applied Mathematics
The cellular neural networks with two kinds of two-parametered asymmetric templates are considered. The parameter space is partitioned into finitely many disjoint regions. In each region, the basic mosaic patterns are characterized. The feasible mosaic patterns corresponding to the parameters in each region can then be determined. To exhibit the spatial complexity of the system, we estimate the entropy of mosaic patterns for parameters in the regime of spatial chaos. In light of this characterization, the effect from the symmetry of the template on pattern formation properties can be seen in detail. We also discuss the existence of some fundamental class of feasible local defect patterns. It is shown that the feasible local k-defect patterns of vertical type cannot exist if the connection weights are anti-symmetric in the vertical direction. Same conclusion also holds for the ones of horizontal type and horizontal direction.
Pattern formations and spatial entropy for spatially discrete diffusion equations
(2005-05-15)
Cheng, CY
;
Shih, CW
;
應用數學系
;
Department of Applied Mathematics
Formation of mosaic patterns for spatially discrete diffusion equations with cubic nonlinearity is investigated. We construct feasible basic patterns in each parameter region and combine these basic patterns into large patterns on one- and two-dimensional lattices. The basic patterns are characterized and constructed through formulating parameter conditions based on a geometrical setting. Spatial entropy associated with these patterns are computed or estimated. We also consider three typical boundary conditions and investigate their influences on pattern formations and spatial entropy. Several numerical computations are performed to illustrate such a formation of patterns. (c) 2005 Elsevier B.V. All rights reserved.
The characteristics of chemical vapor deposited amorphous-like tungsten film as a gate electrode
(1998-09-01)
Chang, KM
;
Deng, IC
;
Shih, CW
;
Lain, KD
;
Fu, CM
Tungsten films are often advantageously formed by the chemical vapor deposition system which using WF6 gas through SiH4 or H-2 reduction. The fluorine species will diffuse into poly-Si/SiO2/[Si] multilayers by a driving force which is the reaction of WF6 and poly-Si gate. When too many fluorine atoms diffused into the gate oxide, the fluorine atoms will cause more strain in the gate oxide and the electrical characteristics of device will shift. An amorphous-like tungsten layer was deposited at a flow rate ratio of 2.5 of SiH4/WF6. The driving force in the amorphous-like tungsten film deposition is far less than that in selective tungsten film deposition; therefore, the concentration of fluorine atoms in the amorphous-like tungsten film is much less than in the selective tungsten film. We proved that only few fluorine atoms were incorporated in amorphous-like tungsten film which has good characteristics in the application of gate electrode.
Transition to intermittent chaotic synchronization
(2005-09-01)
Zhao, L
;
Lai, YC
;
Shih, CW
;
應用數學系
;
Department of Applied Mathematics
Coupled chaotic oscillators can exhibit intermittent synchronization in the weakly coupling regime, as characterized by the entrainment of their dynamical variables in random time intervals of finite duration. We find that the transition to intermittent synchronization can be characteristically distinct for geometrically different chaotic attractors. In particular, for coupled phase-coherent chaotic attractors such as those from the Rossler system, the transition occurs immediately as the coupling is increased from zero. For phase-incoherent chaotic attractors such as those in the Lorenz system, the transition occurs only when the coupling is sufficiently strong. A theory based on the behavior of the Lyapunov exponents and unstable periodic orbits is developed to understand these distinct transitions.