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  • 1
    Electronic Resource
    Electronic Resource
    Grain-boundary diffusion modeling and efficiency evaluation of thin-film diffusion barriers considering microstructure effects (1995)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 78 (1995), S. 4438-4443 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We have developed a novel grain-boundary diffusion model using the transmission-line matrix method. In conjunction with a two-dimensional Monte Carlo thin-film growth simulator, this model can be employed for the analysis of impurity diffusion in thin-film diffusion barriers with realistic microstructures. In the model, the impurity at the upper surface of the barrier layer may diffuse through rapid and irregularly shaped grain-boundary diffusion paths to reach the bottom surface. Calculations of the impurity concentration and out-diffusion flux as a function of elapsed diffusion time and position enable the evaluation of the effectiveness of the barrier layer at a microstructure level. Consequently, the diffusion process is depicted with less assumptions and more precisely than previously available approaches. This paper details the grain-boundary diffusion modeling method outlined above, with the emphasis on the treatment of various boundary conditions. A representative application to titanium nitride (TiN) thin-film diffusion barriers is also demonstrated, as befits the high level of interest in this particular material for very large scale integrated devices. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.360744
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  • 2
    Electronic Resource
    Electronic Resource
    Numerical solution of the electromigration boundary value problem under pulsed dc conditions (1996)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 80 (1996), S. 4948-4951 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The one-dimensional electromigration boundary value problem under pulsed dc conditions is numerically investigated by utilizing the transmission-line matrix modeling method. A perfectly blocking boundary, where void formation and failure occur, is assumed at one end of an interconnection line. At the other end, two physically plausible boundary conditions are considered. From the design-rule point of view, an approach is proposed to convert conveniently the pulsed stress into an equivalent dc stress that would produce electromigration damage at a similar rate. Based on the fundamental diffusion-drift model, we show that the vacancy buildup behavior under a pulsed dc stress γp can be described accurately by the dc stress γdc scaled according to the duty factor r of the current pulse, namely, γdc=rγp. This study also represents a theoretical confirmation for the (jr)−2 dependence of the pulsed electromigration failure (where j is the current density), which has been observed in a number of experimental studies. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.363538
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  • 3
    Electronic Resource
    Electronic Resource
    Transmission-line-matrix modeling of grain-boundary diffusion in thin films (1993)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 74 (1993), S. 7173-7180 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The use of the transmission-line-matrix (TLM) method for analyzing the grain boundary and interfacial diffusion problems in thin films is demonstrated. The method employed has a variable mesh and automatic time-stepping capability, and is highly versatile in treating complex structures and incorporating various boundary conditions. The present model takes account of separate diffusion coefficients in grain boundaries, grains, interfaces, and the substrate. The combined diffusion problems are solved as a function of position and time, and the concentration distributions are presented as clearly visible isometric projections and contour plots. The results are compared with those of semi-infinite samples (Whipple's analysis [Philos. Mag. 45, 1225 (1954)]) and idealized thin-film systems (Gilmer and Farrell's analysis [J. Appl. Phys. 47, 3792 (1976)]), with the emphasis being placed on the differences due to the treatment of concentration flux along the interface between the film and the substrate and into the substrate. The TLM method is shown to have considerable potential in practical applications for diffusion processes in thin films.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.355034
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  • 4
    Electronic Resource
    Electronic Resource
    Symplectic Solution for a Plane Couple Stress Problem (2005)
    s.l. ; Stafa-Zurich, Switzerland
    Advanced materials research Vol. 9 (Sept. 2005), p. 143-152 
    Details
    ISSN: 1662-8985
    Source: Scientific.Net: Materials Science & Technology / Trans Tech Publications Archiv 1984-2008
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Based on the Pro-Hellinger-Reissner variational principle of plane couple stress problem, the dual PDEs are proposed corresponding to the force method extension. The duality solution methodology is thus extended to plane couple stress problem, and then the method of separation of variables and eigenfunction expansion in the symplectic space is used to find the analytical solutions. A long strip domain plate with both lateral edges free, fixed at one end and under simple tension at the far end, is solved analytically. The solution is composed of the inhomogeneous boundary condition solutions and the superposition of eigensolutions of homogeneous lateral boundary conditions. The method of separation of variables is used for the dual PDEs, from which the eigen-root transcendental equation is solved and the corresponding eigenvector functions are obtained. The boundary conditions at the fixed end are derived via the variational method. Numerical results show that due to the effect of couple stress, the stress distribution is no longer infinity as given by the classical theory of elasticity at the corner of fixed end
    Type of Medium: Electronic Resource
    URL: http://www.tib-hannover.de/fulltexts/2011/0528/01/41/transtech_doi~10.4028%252Fwww.scientific.net%252FAMR.9.143.pdf
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  • 5
    Electronic Resource
    Electronic Resource
    Preparing an Environment-Benignly Rare-Earth Based Chemical Conversion Coatings on 6063 Aluminium Alloy (2008)
    s.l. ; Stafa-Zurich, Switzerland
    Key engineering materials Vol. 373-374 (Mar. 2008), p. 224-227 
    Details
    ISSN: 1013-9826
    Source: Scientific.Net: Materials Science & Technology / Trans Tech Publications Archiv 1984-2008
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In order to develop an environment-benignly chemical conversion process to substitute thetoxic hexavalent chromium treatment on Al alloy surface, a new surface treatment technology basedon rare-earth element, which is to form chemical conversion coating on 6063 Al alloy was presented.In this process, Ce(NO3)3 was adopted in the chrome-free preparing solution, and KMnO4 was used asoxidant to accelerate the coating formation on 6063 Al alloy. Furthermore, an L16(43) orthogonalexperiment was carried out to examine the effect of Ce(NO3)3, KMnO4 and solution temperature onthe coating growth on 6063 Al alloy. Accelerants of SrCl2 and NH4VO3 were added to the preparingsolution to improve the coating performance. XRD, SEM and EDS were used to analyse the coatingsurface structure, morphology and composition. It was found that a good anti-corrosion coating whichis mainly composed of the elements of Al, Ce, O, Mn, Mg could be formed in the optimal preparingsolution of 5g/L Ce(NO3)3 , 4g/L KMnO4, 1.4g/L SrCl2 at the temperature of 20°C
    Type of Medium: Electronic Resource
    URL: http://www.tib-hannover.de/fulltexts/2011/0528/01/57/transtech_doi~10.4028%252Fwww.scientific.net%252FKEM.373-374.224.pdf
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  • 6
    Electronic Resource
    Electronic Resource
    Implementation of timestep changes in transmission-line matrix diffusion modelling (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 5 (1992), S. 251-257 
    Details
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: This paper details general expressions for implementing timestep transformations in transmission-line matrix (TLM) modelling of diffusion processes. The expressions can be conveniently incorporated into any TLM routine which models multidimensional problems using a variable meshing technique.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jnm.1660050406
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  • 7
    Electronic Resource
    Electronic Resource
    An error parameter in TLM diffusion modelling (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 5 (1992), S. 129-137 
    Details
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: This paper reports the results of a study of an error parameter, m, which has been proposed as a measure for determining the effects on accuracy of the basic assumptions upon which TLM modelling of diffusion and heat flow has been founded. The nature of the m parameter is studied in detail by using a two-dimensional thermal diffusion problem. The use of m in the implementation of automatic timestepping is discussed in a practical three-dimensional engineering problem.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jnm.1660050207
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  • 8
    Electronic Resource
    Electronic Resource
    A comparative study of two TLM networks for the modelling of diffusion processes (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 6 (1993), S. 161-164 
    Details
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: A comparative study of two alternative networks for TLM modelling of diffusion processes has been undertaken. Some of their inherent advantages and disadvantages are analysed according to the ratio between the impedance of the lossless transmission lines and the lumped resistance. Their relative accuracy and utility in controlling the timestep automatically are examined.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jnm.1660060208
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  • 9
    Electronic Resource
    Electronic Resource
    Transmission-line matrix method for solving the multidimensional continuity equation (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 6 (1993), S. 233-236 
    Details
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: We have extended the one-dimensional transmission-line modelling (TLM) of diffusion, drift and recombination of charge carriers in semiconductors to multiple dimensions. Detailed TLM formulation of the continuity transport equation in a more general form is presented.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jnm.1660060307
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  • 10
    Electronic Resource
    Electronic Resource
    TLM TREATMENT OF A GENERAL DIFFUSION FLUX BOUNDARY CONDITION (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 9 (1996), S. 327-333 
    Details
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: An approach of using a current-controlled voltage source analogy to account for a general boundary condition of particle or thermal flux in transmission-line matrix (TLM) diffusion modelling has been developed. For mass diffusion, this boundary condition is expressed as D ∂C/∂x + αC = 0, where C is the concentration, D is the diffusion coefficient, and α is a parameter characterizing the out-diffusion mobility across the boundary of interest. Confirmation of the TLM numerical treatment through comparison with analytical solutions is presented. Besides the open-circuit and short-circuit boundaries, the matched-load boundary is also found to be a special case of the present boundary condition. This extension of the boundary treatment allows the highly flexible TLM method to be applied to a greater variety of diffusion problems.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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