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  • 1
    Electronic Resource
    Electronic Resource
    Elastic energy release due to domain formation in the strained epitaxy of ferroelectric and ferroelastic films (1993)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 74 (1993), S. 6012-6019 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Twin related domain formation is examined as a strain relaxation mechanism for a heteroepitaxial tetragonal film on a cubic substrate. Elastic relaxations are calculated for a single twin band in which the c axis of the tetragonal domains is either related by a 90° rotation about an axis in the plane of the film or by a 90° rotation about the surface normal. In all cases, the strain energy change is evaluated for both the film and the substrate. A domain pattern map is developed that predicts single domain and multiple domain fields depending on the relative misfit strains and domain wall energy. The concept of a critical thickness, hc, for domain formation is developed. For cases in which the c axis is rotated 90° about an axis in the plane of the film, the critical thickness depends only on the relative coherency strain between the substrate and film and the ratio of the domain wall energy to the stored elastic energy. For the case of a pattern consisting of energetically equivalent domains with the c axis in plane, the equilibrium distance of multiple domains is derived. For such multiple domains, a minimum wall separation distance exists that depends nonlinearly on the film thickness.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.355215
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  • 2
    Electronic Resource
    Electronic Resource
    Stress-dependent surface reactions and implications for a stress measurement technique (2000)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 87 (2000), S. 1211-1218 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In contact with an environment, a solid may gain or lose mass due to, for example, deposition or etching. As the reaction proceeds, the surface of the solid moves, either extending or receding. If the solid is under stress, the elastic energy adds to the driving force of the reaction, and may cause the surface to roughen. This phenomenon has recently led to a novel experimental technique to determine the stress state in a solid by using an atomic force microscope to scan the surface profiles before and after etching. Stress is also known to change the mobility of a reaction. By this mechanism, the stress may either roughen or stabilize a flat surface. This article describes a linear perturbation analysis of a three-dimensional solid surface evolving under stress, using a general kinetic law. It is found that when the reaction is near equilibrium, the stress effect on driving force dominates; when the reaction is far from equilibrium, the stress effect on mobility dominates. Under these two conditions, the surface profile spectra have different patterns and length scales. The implications for the stress measurement technique are discussed. It is suggested that the same experimental procedure be used to measure surface energy and activation strains. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.371999
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  • 3
    Electronic Resource
    Electronic Resource
    High-resolution determination of the stress in individual interconnect lines and the variation due to electromigration (1995)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 78 (1995), S. 1614-1622 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Large tensile stresses usually exist in metallic interconnect lines on silicon substrates as a result of thermal mismatch. When a current is subsequently passed any divergence of atomic flux can create superimposed stress variations along the line. Together, these stresses can significantly influence the growth of voids and therefore affect interconnect reliability. In this work, a high-resolution (∼2 μm) optical spectroscopy method has been used to measure the localized stresses around passivated aluminum lines on a silicon wafer, both as-fabricated and after electromigration testing. The method is based on the piezospectroscopic properties of silicon, specifically the frequency shift of the Raman line at 520 R cm−1. By focusing a laser beam at points adjacent to the aluminum lines, the Raman signal was excited and collected. The stresses in the aluminum lines can then be derived from the stresses in the silicon using finite element methods. Large variations of stress along an electromigration-tested line were observed and compared to a theoretical model based on differences in effective diffusivities from grain to grain in a polycrystalline interconnect line. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.360255
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  • 4
    Electronic Resource
    Electronic Resource
    Diffusive void bifurcation in stressed solid (1994)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 76 (1994), S. 3410-3421 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Interconnects are susceptible to solid diffusion under residual stress, electric current, and elevated temperature. As atoms diffuse, voids nucleate, drift, and enlarge. At some point, the voids of rounded shape can collapse to narrow slits and sever the interconnects. The fatal slits are often found to be transgranular, i.e., each slit cuts across a single grain. They have raised many concerns, but the underlying mechanism has remained unclear. It is proposed that a void changes shape due to surface diffusion under the combined action of surface energy, elastic energy, and electric current. The void will be rounded if surface energy prevails, but will collapse to a slit if the elastic energy or the electric current prevails. A cylindrical void in an infinite crystal under biaxial stresses, but under no electric current, is analyzed. Four things are done, as follows: (1) A suitable thermodynamic potential is minimized and maximized to select, among a family of ellipses, equilibrium void shapes. The bifurcation diagram consists of a subcritical pitchfork and two Griffith cracks. (2) A void under biased stresses is analyzed to illustrate the effect of imperfections. (3) Exact initial bifurcation modes are determined. The critical loads for the successive modes are closely separated, indicating that the shape evolution will be sensitive to initial imperfections. (4) A variational principle for shape evolution under stress, current and surface energy is identified. Stress-induced evolution time is estimated by using this variational principle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.357471
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  • 5
    Electronic Resource
    Electronic Resource
    A simulation of electromigration-induced transgranular slits (1996)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 79 (1996), S. 2394-2403 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: An on-chip aluminum interconnect carries an intense electric current at an elevated temperature, motivating atoms to diffuse in the solid state, and inducing voids that may cause an open failure. Recent observations have shown that a void sometimes collapses to a slit running nearly perpendicular to the electric current direction. Such a slit often lies inside a grain rather than along a grain boundary. An earlier calculation showed that diffusion on the void surface, driven by the electric current, can cause a circular void to translate in an infinite, isotropic interconnect. It was suggested recently that this solution may be unstable, and that two forces compete in determining the void stability: surface tension favors a rounded void, and the electric current favors a slit. A linear perturbation analysis, surprisingly, revealed that the translating circular void is stable against infinitesimal shape perturbation. Consequently, the slit instability must have resulted from finite imperfections. This article reviews the experimental and theoretical findings, and describes a numerical simulation of finite void shape change. We determine the electric field by a conformal mapping of complex variables, and update the void shape for a time step by a variational method. The simulation shows that a finite void shape imperfection or surface tension anisotropy can cause a void to collapse to a slit. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.361166
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  • 6
    Electronic Resource
    Electronic Resource
    Electromigration instability: Transgranular slits in interconnects (1994)
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 64 (1994), S. 1944-1946 
    Details
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Evidence has recently accumulated that an interconnect under intense electric current can fail by a transgranular slit. A rounded void first forms, enlarges, and drifts. When the void becomes sufficiently large, a narrow slit emerges at the expense of the void, running across the linewidth. In this letter we describe a physical mechanism that explains this instability. Both electric current and surface energy drive atoms to diffuse on the void surface, but in the opposite directions. The slit emerges if the electric current prevails. An approximate analysis shows how the slit selects its width and velocity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.111750
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  • 7
    Electronic Resource
    Electronic Resource
    Mechanics of rollable and foldable film-on-foil electronics (1999)
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 74 (1999), S. 1177-1179 
    Details
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The mechanics of film-on-foil devices is presented in the context of thin-film transistors on steel and plastic foils. Provided the substrates are thin, such transistors function well after the foils are rolled to small radii of curvature. When a substrate with a lower elastic modulus is used, smaller radii of curvature can be achieved. Furthermore, when the transistors are placed in the neutral surface by sandwiching between a substrate and an encapsulation layer, even smaller radii of curvature can be attained. Transistor failure clearly shows when externally forced and thermally induced strains add to, or subtract from, each other. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.123478
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  • 8
    Electronic Resource
    Electronic Resource
    Theory of lithographically-induced self-assembly (2001)
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 78 (2001), S. 3971-3973 
    Details
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Recent experiments show that, when a two-phase fluid confined between parallel substrates is subject to an electric field, one phase can self-assemble into a triangular lattice of islands in another phase. We describe a theory of the stability of the island lattice. It is well known that the total interface energy reduces when the island diameter increases. We show that, under certain conditions, the electrostatic free energy reduces when the island diameter decreases. The islands select the equilibrium diameter to minimize the combined interface energy and electrostatic energy. We describe the conditions for electrostatic field to stabilize the island lattice, and analyze an idealized model. The theory suggests considerable experimental control over stable island size. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1380728
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  • 9
    Electronic Resource
    Electronic Resource
    Stable island arrays by height-constrained Stranski–Krastanov growth (2001)
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 79 (2001), S. 3251-3253 
    Details
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In the Stranski–Krastanov system, the lattice mismatch between the film and the substrate causes the film to break into islands. During annealing, both surface energy, and elastic energy drive the islands to coarsen: some islands enlarge and others shrink, keeping the total island volume constant. The islands produced this way are usually uneven in size and spacing. Motivated by several related studies, we suggest that stable, uniform islands should form when a stiff ceiling is placed at a small gap above the film. After contacting the ceiling, the islands are constrained to grow laterally and remain coherent with the substrate, preventing further stress relaxation. In fact, we show that the role of elasticity is reversed: with the ceiling, the total elastic energy stored in the system increases as the islands coarsen laterally. On the other hand, the total surface energy decreases as the islands coarsen. Consequently, the islands select an equilibrium size to minimize the combined elastic energy and surface energy. We estimate the equilibrium island size by analyzing an idealized model.© 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1415403
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  • 10
    Electronic Resource
    Electronic Resource
    Precipitate drifting and coarsening caused by electromigration (1993)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 74 (1993), S. 5457-5462 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A mechanism is proposed to explain electromigration-enhanced precipitate coarsening in Al-Cu alloy interconnects. The interface between the α-phase matrix and a θ-phase Al2Cu precipitate is incoherent, along which both Al and Cu atoms diffuse under an applied electric field. Depending on the relative mobility of Al and Cu, the diffusion causes the precipitate to migrate toward either the positive or the negative electrode. The velocity of a spherical precipitate is proportional to the electric field and the mobilities and inversely proportional to its radius. A critical electric field or precipitate radius exists, above which the precipitate can penetrate a grain boundary. Consequently, the precipitates agglomerate by the synergism between the Ostwald ripening and the current-induced migration. The resulting particles are distantly separated, depleting Cu atoms from the rest of the interconnect. The mechanism appears to limit the lifetime of interconnects having bamboo-like grains, tested below 300 °C, less than half of the melting temperature of Al. Experiments taking advantage of migration of various inhomogeneities are suggested which may illuminate several basic issues in the field of electromigration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.354225
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