Pulsed-current duty cycle dependence of electromigration-inducedstress generation in aluminum conductors

The effect of duty cycle of pulsed dc currents on the critical length-current density product, (jl_c), was measured using the Blech-Kinsbron edge-displacement technique [Thin Solid Films 25, 327 (1975)]. Unencapsulated Al edge-displacement segments mere stressed at various duty cycles and the critical lengths, the so-called “Blech lengths”, were measured. It was found that jl_c increased with decreasing duty cycle. We measured a factor of 2.6 increase in jl_c for the 25% duty cycle as compared to dc. This duty cycle dependence of Blech length implies that electromigration resistance for an integrated circuit would be increased for small duty cycle operation by increasing the fraction of interconnects which are sub-Blech-length and are not susceptible to EM damage     

Electromigration drift and threshold in Cu thin-film interconnects

The electromigration-induced ionic drift velocity and critical length-current density product, (jl_c) of Cu thin film conductors, were measured using the Blech-Kinsbron edge-displacement technique. Unencapsulated Cu edge-displacement segments on TiN conductors were stressed in vacuum at a modest current density of 6×10⁵ A/cm² in the temperature range of 175-275°C. Drift velocity was observed to be between 1-1/2 to 3 orders-of-magnitude lower than that previously measured for unencapsulated Al in this temperature range. We measured an activation energy for EM-induced drift of 1.25±0.08 eV which corresponds to grain boundary diffusion in Cu. Critical lengths were measured and the jl_c threshold was estimated to range between 900-1600 A/cm. We calculated a Cu grain boundary Z* value of -0.7, to our knowledge, this study is the first to measure Z* for electromigration in Cu thin film conductors     

Prediction of an effective cooling output of the fin-and-tube heat exchanger under frosting conditions

In the paper, an analysis of heat and mass transfer during frost formation on a fin-and-tube heat exchanger has been presented. For calculation of an exchanged heat flux, a transient two-dimensional mathematical model of frost formation has been developed and numerically solved. The mathematical model and numerical procedure have been experimentally validated. For determination of an effectively exchanged heat flux inside the heat exchanger, the influence of the augmented heat transfer resistance and impact of the defrosting process have been taken into account. A detailed calculation of the frost growth rate has been a base for determination of heat transfer resistance of the frost layer. The influence of frost formation on the overall heat transfer coefficient has also been analysed. The effective exchanged heat flux has been calculated for different operating conditions, durations of cooling cycle as well as defrosting heat fluxes. Results have shown that the effectively exchanged heat flux significantly depends on operating conditions, such as air humidity and temperature, as well as the cooling cycle duration.     

Transient two-dimensional model of frost formation on a fin-and-tube heat exchanger

In the paper, numerical and experimental analyses of heat and mass transfer during frost formation on a fin-and-tube heat exchanger have been presented. Modelling of the frost formation on cold surfaces placed in a humid air stream, requires a complex mathematical approach. A transient two-dimensional mathematical model of frost formation has been developed. The applied mathematical model has been defined using governing equations for the boundary layer that include air and frost sub-domains as well as a boundary condition on the air–frost interface. The mathematical model with initial and boundary conditions has been discretised according to the finite volume method and solved numerically using the SIMPLER algorithm for the velocity–pressure coupling. Results have shown that the frost layer formation significantly influences the heat transfer between air and fins. As a result of numerical calculations, time-wise frost thickness variations for different air humidities, temperatures and velocities have been presented. Using the developed mathematical model, the algorithm and the computer code, which have been experimentally validated, it is possible to predict a decrease of exchanged heat flux in the heat exchanger under frost growth conditions.     

A novel micromachining technique for the formation of extrusions

A novel micro-extrusion process (MEP) has been developed for micromachining applications. Extrusions on the micrometer scale were realized using the compressive stresses resulting from electromigration-induced mass transport in planarized conductors. Electromigration produced compressive stresses at the anodes of passivated metallic interconnects that exceeded the plastic deformation stress, and allowed extrusions to form through simple die patterns etched through the passivation at the anode ends of edge-displacement conductor segments     

Agent-based scheduling in production systems

The object in a flexible manufacturing system is optimal system resources scheduling. The production scheduling of such a system may be resolved by a set of individual agents, who can work in parallel and their coordination may bring a more effective way of finding an optimal solution. The criteria for the optimal solution may be created on a time or economical (cost) basis but each may have a different priority depending on each situation. In this paper, we will analyse an approach to find a feasible schedule of all products, which could minimize costs and satisfy all constraints related to each product.