The objective of this work is to develop a microstructure-based simulation approach to assess the fatigue life of solder joints that are used by the microelectronics industry. The developed approach can generate solder joints with random grain morphologies by means of 3D Voronoi tessellation. The anisotropic material behavior of each grain is described by the Garofalo creep equation combined with Hill's definition of the equivalent stress for anisotropic materials. Grain boundaries are implemented as interface elements, with an isotropic creep constitutive model. The stochastic variability in the creep response of solder joints was qualitatively estimated by generating 100 unique solder joints containing 5 to 9 grains, each having a random material orientation. These joints were independently loaded with a realistic stress level for microelectronic products during thermal cycling. The volume-averaged creep strain energy density in the solder joints was used to predict the fatigue life of the solder joints. The results showed a factor of ~4 difference in expected lifetime of the individual solder joints. Next, nine randomly picked solder joints from the above-mentioned pool of 100 were sandwiched between a silicon die and a printed circuit board to form a simulation model of a Wafer-Level Chip-Scale package (WLCSP). The creep strain energy density in the joints was computed for 34 unique cases of the WLCSP. A factor of ~2.5 between the highest and lowest estimate for the solder joint life was found. The slope of the corresponding Weibull distribution equals ~6, which falls within the slopes typical reported for solder joint reliability of WLCSPs.

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Tarnishing of the reflective silver layer in LED packages is an important failure mechanism, leading to both a decrease in luminous flux by up to 75% and a change in color spectrum.

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We present theoretical models for the time-dependent voltage of an electrochemical cell in response to a current step, including effects of diffuse charge (or "space charge") near the electrodes on Faradaic reaction kinetics. The full model is based on the classical Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions to describe electron-transfer reactions across the Stern layer at the electrode surface. In practical situations, diffuse charge is confined to thin diffuse layers (DLs), which poses numerical difficulties for the full model but allows simplication by asymptotic analysis. For a thin quasi-equilibrium DL, we derive effective boundary conditions on the quasi-neutral bulk electrolyte at the diffusion time scale, valid up to the transition time, where the bulk concentration vanishes due to diffusion limitation. We integrate the thin-DL problem analytically to obtain a set of algebraic equations, whose (numerical) solution compares favorably to the full model. In the Gouy-Chapman and Helmholtz limits, where the Stern layer is thin or thick compared to the DL, respectively, we derive simple analytical formulas for the cell voltage versus time. The full model also describes the fast initial capacitive charging of the DLs and superlimiting currents beyond the transition time, where the DL, expands to a transient non-equilibrium structure. We extend the well-known Sand equation for the transition time to include all values of the superlimiting current beyond the diffusion-limiting current.@en

We present a time-dependent numerical model for corrosion in microelectronics, focusing on aluminum bondpads, which can be very beneficial for the design as well as the interpretation of reliability data of microelectronics. The model includes charge transport through the polymer microelectronics encapsulant as well as the formation of layers of space charge at all polymer interfaces, which strongly influences the electrochemical charge transfer rate at the polymer¿metal interfaces via the generalized Frumkin¿Butler¿Volmer equation. The system we consider consists of two parallel gold bondwires that are each electrically connected to two aluminum bondpads, which are assumed to contain weak spots in the protective native oxide layer, i.e. pits. This system is encapsulated in an epoxy molding compound, which is the usual low-conductive, and slightly hydrophilic, microelectronic encapsulant. We assume that a cathodic reaction takes place at the gold wires, and an anodic reaction at the weak spots of the aluminum bondpads. Furthermore,weassume the presence of a large excess of inert supporting salt compared to the reactive hydroxyl ions. Numerical calculations were made in a two-dimensional geometry as function of the applied voltage difference between the two wires, the concentration of absorbed moisture in the encapsulation, and the ambient temperature. We show that the model results predict trends similar to the empirical industrial standards for failure of microelectronic products due to corrosion.@en

We study the effect of an inert supporting electrolyte on the steady-state ionic current through galvanic cells by solving the full Poisson-Nernst-Planck transport equation coupled to the generalized Frumkin-Butler-Volmer boundary equation for the electrochemical charge transfer at the electrodes. Consequently, the model presented here allows for non-zero space charge densities locally at the electrodes, thus extending the frequently used models based on the local electroneutrality condition by including diffuse layer (DL) effects. This extension is necessary since the DLs determine the ion concentration and electrical field at the reaction planes, which uniquely determine the charge transfer at the electrodes. In this work we present numerical results for systems which contain added inert supporting electrolyte using finite element discretization and compare those with semi-analytical results obtained using singular perturbation theory (limit of negligibly thin DLs). In case of negligibly thin DLs the presence of supporting electrolyte will introduce a limiting current below the classical diffusion-limiting current. Just as for systems without supporting electrolyte, the supporting electrolyte, induced limiting current formally does not occur for systems having non-negligibly thin double DLs. For thin, however still finite, double layers this limit can still be seen as a steepening of the polarization curve for current vs. voltage.@en

Despite extensive research over the past decades, corrosion of aluminum bond pads is still a major reliability risk for plastic encapsulated microelectronics. Nowadays even an increase in susceptibility for corrosion is observed for new waferfab technologies and encapsulation materials during reliability tests. The recent trend for the new generation encapsulation materials is to decrease the glass transition temperature. As a result reliability tests could be performed at temperatures well above this temperature, such that traditionally used translations between test and operational lifetime, i.e. the acceleration factor, are no longer valid. Consequently, a new acceleration model for bond pad corrosion is required, which is capable of predicting the lifetime of products from test performed at temperatures above glass transition temperature. In this work we will show the merits of electrochemical cell modeling on the understanding of corrosion failures in microelectronics. The model is based on the Poisson-Nernst-Planck equation for the transport of ions coupled to a generalized Frumkin corrected Butler-Volmer equation for the kinetics of the electrochemical reactions. We present results as an example to clarify our approach.@en

We analyze the steady-state behavior of a general mathematical model for reversible galvanic cells, such as redox flow cells, reversible solid oxide fuel cells, and rechargeable batteries. We consider not only operation in the galvanic discharging mode, spontaneously generating a positive current against an external load, but also operation in two modes which require a net input of electrical energy: (i) the electrolytic charging mode, where a negative current is imposed to generate a voltage exceeding the open-circuit voltage, and (ii) the ¿super-galvanic¿ discharging mode, where a positive current exceeding the short-circuit current is imposed to generate a negative voltage. Analysis of the various (dis-) charging modes of galvanic cells is important to predict the efficiency of electrical to chemical energy conversion and to provide sensitive tests for experimental validation of fuel cell models. In the model, we consider effects of diffuse charge on electrochemical charge-transfer rates by combining a generalized Frumkin-Butler-Volmer equation for reaction kinetics across thecompact Stern layer with the full Poisson-Nernst-Planck transport theory, without assuming local electroneutrality. Since this approach is rare in the literature, we provide a brief historical review. To illustrate the general theory, we present results for a monovalent binary electrolyte, consisting of cations, which react at the electrodes, and non-reactive anions, which are either fixed in space (as in a solid electrolyte) or are mobile (as in a liquid electrolyte). The full model is solved numerically and compared to analytical results in the limit of thin diffuse layers, relative to the membrane thickness. The spatial profiles of the ion concentrations and electrostatic potential reveal a complex dependence on the kinetic parameters and the imposed current, in which the diffuse charge at each electrode and the total membrane charge can have either sign, contrary perhaps to intuition. For thin diffuse layers, simple analytical expressions are presented for galvanic cells valid in all three (dis-)charging modes in the two subsequent limits of the ratio ¿ of the effective thicknesses of the compact and diffuse layers: (i) the ¿Helmholtz limit¿ (¿¿¿) where the compact layer carries the double layer voltage as in standard Butler-Volmer models, and (ii) the opposite ¿Gouy-Chapman limit¿ (¿¿0) where the diffuse layer fully determines the charge-transfer kinetics. In these limits, the model predicts both reaction-limited and diffusion-limited currents, which can be surpassed for finite positive values of the compact layer, diffuse layer and membrane thickness.@en

Plastic encapsulations will absorb moisture in humid environments due to their hydrophilic nature, this in combination with the inherent ionic contamination of the plastic will result in an electrolyte. This electrolyte might pose several reliability issues for the package and the encapsulated microelectronic circuit, such as electrochemical migration and bond pad corrosion. The corresponding failure mechanisms are associated with ionic currents through the package and electrochemical processes at e.g. the leads or bond wires. In this paper we present a generic mathematical framework for modeling ionic currents and electrochemical processes. We will apply this framework to electrochemical migration of metal between the leads of a plastic encapsulation, and show results for the transient formation of migration fluxes through the plastic encapsulation.@en

We present a numerical method to describe the transport of ions through polymeric electrolytes under the influence of an applied electrostatic field. The transport of ions results in an ion concentration profile with a large gradient near charged interfaces, the so-called diffuse layer. We show that the Poisson-Nernst-Planck theory, which generally describes the transport of ions, can be simplified significantly if the dimensions of the bulk material are much larger than the thickness of the diffuse layer. In this case, charge transport through the bulk of the material is driven by the electric field only (Ohm's law). At all interfaces an analytical mathematical relation between the surface charge and the voltage difference over the diffuse layer can be used. Several of these relations are used, including relations that account for ion volume effects. We use experimental data from literature [J.A. van der Pol, R.T.H. Rongen, H.J. Bruggers, Microelectron.Reliab.40 (2000) 1267] of charge accumulation at the surface of an integrated circuit (IC) resulting from the transport of ions through the polymeric material encapsulating the device. The data are very well described by a two-dimensional finite element model based on the simplified Poisson-Nernst-Planck theory. In addition, the theory predicts that the accumulated charge at the circuit interface will slowly drain away after having reached the experimentally observed maximum.@en

When high electrical fields are applied, and especially above the glass transition temperature, ion transport through the epoxy molding compounds that encapsulate the integrated circuit (die) strongly increases, leading to the accumulation of charge at the passivation-epoxy interface, and possibly to leakage currents because of the formation of parasitic transistors. Recovery from this failure mechanism is possible after annealing the package in the absence of the applied voltage, at sufficiently high temperature. The high electrical fields originate either from within the package due to high-voltage bondpads or are due to an external high-voltage source. We have developed a numerical transport model that is able to describe ion transport through IC packages including the formation of 'ionic diffuse layers', or 'polarisation layers', at the passivation-epoxy interface. In these layers the ion concentration strongly increases leading to a modification of the electrostatic boundary conditions (Gauss' law), as well as to a voltage step over the passivation-epoxy interface. The exact distribution of the ions in this diffuse layer is a very important quantity as it strongly influences the voltage profiles in the bulk of the material via the boundary conditions, and therefore the ion transport rates. We will briefly outline how the relation between charge and voltage (integral capacitance) can be obtained experimentally from the dielectric response when a DC voltage is applied across a thin polymer sample. The data that are obtained can be used to derive realistic microscopic models for the ion distribution in the diffuse layer formed within an epoxy resin next to electrodes and passivation layers.@en

The supply current of plastic encapsulated microelectronic devices in the presence of a high potential source can increase abnormally due to parasitic gate leakage. According to reliability qualification standards, stress during a parasitic gate leakage test is applied by a corona discharge at a thin tungsten needle placed a few centimeters above the devices under test. The gate leakage sensitivity factor obtained from this test lacks any physical basis and is therefore not believed to be useful. Here we show that this sensitivity factor can be replaced by a physical model for charge transport through the encapsulation material. The model is used to explain why devices encapsulated by a molding compound with a low volume resistivity of 6x10(11) Ohm.cm, at high temperature, 150º C, are more prone to fail the test on an increased current, compared to devices encapsulated by a compound having a high resistivity of 4x10(13) Ohm.cm at the same temperature. Furthermore, we discuss an alternative test setup where the potential difference between two parallel electrodes sandwiching the devices is used as the source of stress. It is suggested in literature that this setup yields identical results as the current setup. However, using both setups on the same product did not result in an equal outcome, which indicates that both tests do not trigger the same failure mechanism to the same extent.@en

When a monolayer of negatively charged surfactant molecules is brought in contact with an aqueous solution containing mixtures of counterions of different size and valency, very large deviations from Poisson-Boltzmann theory (PBT) develop at a high surface charge, with the smaller counterion outcompeting the larger one (even if divalent) near the interface, leading to counterion segregation [V.L. Shapovalov, G. Brezesinski, J. Phys. Chem. B 110 (2006) 10032]. We use a modified PBT that empirically includes an extended Carnahan-Starling equation-of-state to describe hard-sphere interactions in electrical double layers containing ions of different size and charge. Model calculations are made for ion concentration profiles, free energies, surface pressures, and differential capacities. At high surface charge, volume interactions become important, leading to significant deviations from PBT. In contrast to PBT, at high surface charge, contributions to energy and pressure are no longer mainly entropic, but instead volume and electrostatic field effects now dominate. When the hydrated size of the divalent ion is used as an adjustable parameter, the theory is in good agreement with the experimental data. Keywords: Poisson-Boltzmann theory; Electrostatic double layer; Surfactant monolayer; Volume effects@en

Due to the ongoing increase of the transistor density on a chip, industry has replaced the silicon oxide dielectric layers, traditionally used in the back-end interconnect stack, by low-K polymer films with a thickness down to several hundred nanometers. The use of these polymer dielectric films has introduced new failure modes. To have a better understanding of these failures, knowledge of the mechanical properties is necessary. Due to surface effects, the material properties of thin films may differ in the in-plane modulus. To have an in situ measurement of the through-plane modulus, a parallel plate capacitor (PPC) under hydrostatic pressure is used in combination with an interdigitated electrode (IDE) to capture the change in dielectric constant. Since it is believed to be mechanical isotropic, a benzocyclobutene (BCB) film is used to provide a reference measurement. The through-plane elastic modulus and change in permittivity for a 1 µm thick film sandwiched by two aluminum electrodes on a silicon wafer are reported. Two circular PPCs and four IDEs were tested at a pressure of 0, 5, 7.5 and 10 MPa. An initial relative dielectric constant of the film of 2.66 ± 0.05 was obtained. This yields a linear elastic behavior equal to 4.73 ± 0.46, 4.11 ± 0.39 and 3.64 ± 0.31 GPa for 20°. 50° and 75°C respectively. The modulus at room temperature is in good agreement with the values found in literature.@en

The miniaturization of microelectronics has led to the use of polmer dielectric films with a thickness less than a micrometer. The use of polymer dielectric films has introduced new failure modes. To have a better understanding of these failures, knowledge of the mechanical properties is necessary.@en