Lucia Nicola

Discrete dislocation analysis of size effects in thin films

A discrete dislocation plasticity analysis of plastic deformation in metal thin films caused by thermal stress is carried out. The calculations use a two-dimensional plane-strain formulation with only edge dislocations. Single crystal films with a specified set of slip systems are considered. The film-substrate system is subjected to a prescribed temperature history and a boundary value problem is formulated and solved for the evolution of the stress field and for the evolution of the dislocations structure in the film. A hard boundary layer forms at the interface between the film and the substrate, which does not scale with the film thickness and thus gives rise to a size effect. It is found that a reduction in the rate of dislocation nucleation can occur abruptly, which gives rise to a two-stage hardening behavior.

Glass-to-glass anodic bonding with standard IC technology thin films as intermediate layers

Glass-to-glass wafer bonding has recently attracted considerable interest. Especially for liquid manipulation applications and on-chip chemical analysis systems, all-glass sealed channels with integrated metal electrodes are very attractive. In this paper, we present a novel anodic bonding process in which the temperature does not exceed 400°C. This is a crucial requirement if metal patterns are present on the wafers. A number of thin film materials available in most conventional IC processes deposited on the glass wafers have been tested as intermediate bonding layers. Successful bonding is obtained for various layer combinations and an explanation of the bonding mechanism is given.

Dislocation climb in two-dimensional discrete dislocation dynamics

In this paper, dislocation climb is incorporated in a two-dimensional discrete dislocation dynamics model. Calculations are carried out for polycrystalline thin films, passivated on one or both surfaces. Climb allows dislocations to escape from dislocation pile-ups and reduces the strain-hardening rate, especially for fully passivated films. Within the framework of this model, climb modifies the dislocation structures that develop during plastic deformation and results in the formation of pile-ups on slip planes that do not contain any dislocation sources.

Two hardening mechanisms in single crystal thin films studied by discrete dislocation plasticity

Two-dimensional discrete dislocation plasticity simulations of the evolution of thermal stress in single crystal thin films on a rigid substrate are used to study size effects. The relation between the residual stress and the dislocation structure in the films after cooling is analyzed using dislocation dynamics. A boundary layer characterized by a high stress gradient and a high dislocation density is found close to the impenetrable film-substrate interface. There is a material-dependent threshold film thickness above which the dislocation density together with the boundary layer thickness and stress state are independent of film thickness. In such films the stress outside the boundary layer is on average very low, so that the film-thickness-independent boundary layer is responsible for the size effect. A larger size effect is found for films thinner than the threshold thickness. The origin of this size effect stems from nucleation activity being hindered by the geometrical constraint of the small film thickness, so that by decreasing film thickness, the dislocation density decreases while the stress in the film increases. The size dependence is only described by a Hall–Petch type relation for films thicker than the threshold value.

2D dislocation dynamics in thin metal layers

The paper deals with a discrete dislocation dynamics study of plastic deformation in a thin film caused by thermal mismatch with its substrate. A unit cell analysis is carried out, with dislocations in the film being represented by line singularities in an isotropic linear elastic medium. Their mutual interactions as well as the interactions with the interface and the free surface are accounted for by means of a coupled dislocation dynamics-finite element technique. The formulation includes a set of constitutive rules to model generation, glide, annihilation and pinning of dislocations at point obstacles. The simulation tracks the evolution of the dislocation structure as thermal stress builds up as well as during relaxation under constant temperature, leading to dense dislocation distributions near the interface and a dislocation-free zone along the stress-free surface of the film.

Multi-asperity contact: A comparison between discrete dislocation and crystal plasticity predictions

Plane strain indentation of single crystals by a periodic array of flat rigid contacts is analyzed. The calculations are carried out, with the mechanical response of the crystal characterized by conventional continuum crystal plasticity or by discrete dislocation plasticity. The properties used in the conventional crystal plasticity description are chosen so that both theories give essentially the same response in uniform plane strain compression. The indentation predictions are then compared, focusing in particular on the effect of contact size and spacing. The limiting cases of frictionless contacts and of perfectly sticking contacts are analyzed. Conventional continuum plasticity predicts a size-independent response. Unless the contact spacing to size ratio is very small, the predicted deformation mode under the contacts is a wedging mechanism of the type described by slip line theory, which is only weakly sensitive to friction conditions. For the micron scale contacts analyzed, discrete dislocation plasticity predicts a response that depends on the contact size as well as on the contact spacing to size ratio. When contacts are spaced sufficiently far apart, discrete dislocation plasticity predicts that the deformation is localized beneath the contacts, whereas for more closely spaced contacts, deformation occurs by shear bands extending relatively far into the crystal. Unless the contacts are sufficiently close together so that the response is essentially one of plane strain compression, the mean contact pressure predicted by discrete dislocation plasticity is substantially greater than that predicted by conventional continuum crystal plasticity and is more sensitive to the friction conditions.

Bauschinger effect in unpassivated freestanding thin films

Two-dimensional (2D) discrete dislocation plasticity simulations are carried out to investigate the Bauschinger effect (BE) in freestanding thin films. The BE in plastic flow of polycrystalline materials is generally understood to be caused by inhomogeneous deformation during loading, leading to residual stress upon unloading. This inhomogeneity can be caused by dislocation pile-ups, variations in texture, grain orientations, and grain size. To study the BE, columnar-grained films as well as films with multiple grains across the thickness are considered. The film is modeled in a 2D framework by a unit cell consisting of an array of grains with different orientation. In order to capture the interaction among grains, we motivate and explore the use of an affine deformation assumption on the grain level to mimic the three-dimensional geometry in this framework. It is shown that the dispersion of grain size in a film together with the size-dependence of yield strength leads to significant BEs in bare films. Quantitative comparison of simulations with experimental data is provided.

Bauschinger effect in thin metal films: Discrete dislocation dynamics study

The effects of dislocation climb on plastic deformation during loading and unloading are studied using a two-dimensional discrete dislocation dynamics model. Simulations are performed for polycrystalline thin films passivated on both surfaces. Dislocation climb lowers the overall level of the stress inside thin films and reduces the work hardening rate. Climb decreases the density of dislocations in pile-ups and reduces back stresses. These factors result in a smaller Bauschinger effect on unloading compared to simulations without climb. As dislocations continue to climb at the onset of unloading and the dislocation density continues to increase, the initial unloading slope increases with decreasing unloading rate. Because climb disperses dislocations, fewer dislocations are annihilated during unloading, leading to a higher dislocation density at the end of the unloading step.

Plastic Ploughing of a Sinusoidal Asperity on a Rough Surface

Part of the friction between two rough surfaces is due to the interlocking between asperities on opposite surfaces. In order for the surfaces to slide relative to each other, these interlocking asperities have to deform plastically. Here, we study the unit process of plastic ploughing of a single micrometer-scale asperity by means of two-dimensional dislocation dynamics simulations. Plastic deformation is described through the generation, motion, and annihilation of edge dislocations inside the asperity as well as in the subsurface. We find that the force required to plough an asperity at different ploughing depths follows a Gaussian distribution. For self-similar asperities, the friction stress is found to increase with the inverse of size. Comparison of the friction stress is made with other two contact models to show that interlocking asperities that are larger than similar to 2 mu m are easier to shear off plastically than asperities with a flat contact.

Discrete dislocation plasticity analysis of contact between deformable bodies of simple geometry

A contact mechanical model is presented where both metal bodies can deform by discrete dislocation plasticity. The model intends to improve on previous dislocation dynamics models of contact, where only a plastically deformable body was considered, flattened by a rigid platen. The effect of the rigid platen was mimicked through boundary conditions acting on the deformable body. While the formulation is general, the simulations presented here are only performed for contact between a plastically deforming body with sinusoidal surface and a flat body that is either elastic or rigid. Results show that the contact conditions, i.e. frictionless and full stick, affect the morphology of the contact as well as the contact pressure distribution. This is because dislocations can glide through the frictionless contact and fragment it, but do not penetrate a sticking contact. Average quantities like mean apparent contact pressure and total plastic slip are, instead, independent of contact conditions and of the details of the contact area. A size dependence is observed in relation to the onset of plastic deformation, where surfaces with smaller wavelength and amplitude require a larger contact pressure to yield than self similar surfaces with larger wavelength. The size dependence is very pronounced when the flat body is rigid, but fades when the compliance of the flat body is large.