Gold films on an elastomeric substrate can be stretched and relaxed reversibly by tens of percents.The films initially form in two different structures, one continuous and the other containing tri-branched microcracks.We have identified the mechanism of elastic stretchability in the films with microcracks.The metal, which is much stiffer than the elastomer, forms a percolating network.
Stresses inevitably arise in a microelectronic device due to mismatch in coefficients of thermal expansion, mismatch in lattice constants, and growth of materials. Moreover, in the technology of strained silicon devices, stresses have been deliberately introduced to increase carrier mobility. A device usually contains sharp features like edges and corners, which may intensify stresses, inject dislocations into silicon, and fail the device.
Attached is a set of slides presented at ASME Congress, 10 November 2006. Thermal strains and electromigration can cause voids to grow in conductor lines on semiconductor chips. This long-standing failure mode is exacerbated by the recent introduction of low-permittivity dielectrics. We describe a method to calculate the volume of a saturated void (VSV), attained in a steady state when each point in a conductor line is in a state of hydrostatic pressure, and the gradient of the pressure along the conductor line balances the electron wind. We show that the VSV will either increase or decrease when the coefficient of thermal expansion of the dielectric increases, and will increase when the elastic modulus of the dielectric decreases. The VSV will also increase when porous dielectrics and ultrathin liners are used. At operation conditions, both thermal strains and electromigration make significant contributions to the VSV. We discuss these results in the context of interconnect design.
The electromigration lifetime is measured for a large number of copper lines encapsulated in an organosilicate glass low-permittivity dielectric. Three testing variables are used: the line length, the electric current density, and the temperature. A copper line fails if a void near the upstream via grows to a critical volume that blocks the electric current. The critical volume varies from line to line, depending on line-end designs and chance variations in the microstructure. However, the statistical distribution of the critical volume (DCV) is expected to be independent of the testing variables. By contrast, the distribution of the lifetime (DLT) strongly depends on the testing variables. For a void to grow a substantial volume, the diffusion process averages over many grains along the line. Consequently, the void volume as a function of time, V(t), is insensitive to chance variations in the microstructure. As a simplification, we assume that the function V(t) is deterministic, and calculate this function using a transient model. We use the function V(t) to convert the experimentally measured DLT to the DCV. The same DCV predicts the DLT under untested conditions.
A (001) surface of silicon consists of terraces of two variants, which have an identical atomic structure, except for a 90° rotation. We formulate a model to evolve the terraces under the combined action of electric current and applied strain. The electric current motivates adatoms to diffuse by a wind force, while the applied strain motivates adatoms to diffuse by changing the concentration of adatoms in equilibrium with each step. To promote one variant of terraces over the other, the wind force acts on the anisotropy in diffusivity, and the applied strain acts on the anisotropy in surface stress. Our model reproduces experimental observations of stationary states, in which the relative width of the two variants becomes independent of time. Our model also predicts a new instability, in which a small change in experimental variables (e.g., the applied strain and the electric current) may cause a large change in the relative width of the two variants.
We propose a model of persistent step flow, emphasizing dominant kinetic processes and strain effects. Within this model, we construct a morphological phase diagram, delineating a regime of step flow from regimes of step bunching and island formation. In particular, we predict the existence of concurrent step bunching and island formation, a new growth mode that competes with step flow for phase space, and show that the deposition flux and temperature must be chosen within a window in order to achieve persistent step flow. The model rationalizes the diverse growth modes observed in pulsed laser deposition of SrRuO3 on SrTiO3
A recent discussion here about the effect of surface stress on vibrations of microcantilever has gained some interest from our members. A few years ago, Zhigang and I looked at surface effect on buckling of a thin elastic film on a viscous layer (Huang and Suo, Thin Solid Films 429, 273-281, 2003). Although the physical phenomena (buckling vs vibrations) are different, the conclusion is quite consistent with Wei Hong and Pradeep's comments toward the end of the discussion. That is, surface stress only contributes as a residual stress and thus does not affect the buckling wavelength (frequency in space in analogy to frequency in time for vibrations).
Thermal strains and electromigration can cause voids to grow in conductor lines on semiconductor chips.This long-standing failure mode is exacerbated by the recent introduction of low-permittivity dielectrics.We describe a method to calculate the volume of a saturated void (VSV), attained in a steady state when each point in a conductor line is in a state of hydrostatic pressure, and the gradient of the pressure along the conductor line balances the electron wind.We show that the VSV will either increase or decrease when the coefficient of thermal expansion of the dielectric increases, and will increase when the elastic modulus of the dielectric decreases.The VSV will also increase when porous dielectrics and ultrathin liners are used.At operation conditions, both thermal strains and electromigration make significant contributions to the VSV.We discuss these results in the context of interconnect design.
This has been published and the related references are listed here:
Z. Zhang, Z. Suo, and J. He, J. Appl. Physics, 98, 074501 (2005). link
J. He, Z. Suo, T.N. Marieb, and J.A. Maiz, Appl. Phys. Lett. 85, 4639 (2004). link
One possible design of stretchable integrated circuits consists of functional islands of stiff thin films on a polymer substrate.When such a structure is stretched, the substrate carries most of the deformation while the islands experience little strain.However, in practice, the island/substrate interface can never cohere perfectly.Existing experiments suggest that, interface debonding occurs if the island is larger than a certain size.I am now studying the critical size of stiff islands on stretchable polymer substrates due to thin film delamination, using finite element simulations.We show that the maximum energy release rate of interfacial cracking goes down as island size or substrate stiffness decreases. As a result, the critical island size can be enhanced if the substrate is chosen to be more compliant.An approximate formula is given to predict the energy release rate for the configuration of stiff islands on very compliant substrate.
A vicinal Si (001) surface may form stripes of terraces, separated by monatomic-layer-high steps of two kinds, SA and SB. As adatoms diffuse on the terraces and attach to or detach from the steps, the steps move.In equilibrium, the steps are equally spaced due to elastic interaction.During deposition, however, SAis less mobile than SB.We model the interplay between the elastic and kinetic effects that drives step motion, and show that during homoepitaxy all the steps may move in a steady state, such that alternating terraces have time-independent, but unequal, widths. The ratio between the widths of neighboring terraces is tunable by the deposition flux and substrate temperature.We study the stability of the steady state mode of growth using both linear perturbation analysis and numerical simulations.We elucidate the delicate roles played by the standard Ehrlich-Schwoebel (ES) barriers and inverse ES barriers in influencing growth stability in the complex system containing (SA+SB) step pairs.
For a crack impinging upon a bimaterial interface at an angle, the singular stress field is a linear superposition of two modes, usually of unequal exponents, either a pair of complex conjugates, or two unequal real numbers.In the latter case, a stronger and a weaker singularity coexist (known as split singularities).We define a dimensionless parameter, called the local mode mixity, to characterize the proportion of the two modes at the length scale where the processes of fracture occur.We show that the weaker singularity can readily affect whether the crack will penetrate, or debond, the interface.
The electromigration lifetime is measured for a large number of copper lines encapsulated in an organosilicate glass low-permittivity dielectric. Three testing variables are used: the line length, the electric current density, and the temperature. A copper line fails if a void near the upstream via grows to a critical volume that blocks the electric current. The critical volume varies from line to line, depending on line-end designs and chance variations in the microstructure. However, the statistical distribution of the critical volume (DCV) is expected to be independent of the testing variables. By contrast, the distribution of the lifetime (DLT) strongly depends on the testing variables. For a void to grow a substantial volume, the diffusion process averages over many grains along the line. Consequently, the void volume as a function of time, V(t), is insensitive to chance variations in the microstructure. As a simplification, we assume that the function V(t) is deterministic, and calculate this function using a transient model. We use the function V(t) to convert the experimentally measured DLT to the DCV. The same DCV predicts the DLT under untested conditions.
Recent comments