Numerical simulation tools used to predict the movement of atoms and the resulting deformation in metallic interconnects under the influence of electrical or thermal gradients provide a predictive model for reliability. This finite element drift solver is a software module that integrates with standard engineering platforms to model the phenomenon of electromigration and stress migration in microelectronics. It works by dividing the geometry of a wire or a solder joint into thousands of small elements and solving the governing equations of diffusion for each one.
The solver calculates how the flow of electrons or the variation in temperature drives the transport of metal ions over time. This allows designers to identify potential failure points where voids might form or where hillocks might grow and cause short circuits. The accuracy of the simulation depends on the quality of the material properties and the boundary conditions used in the model.
Application of partial differential equations to describe the transport of mass and momentum within a solid structure provides the basis for the simulation. The finite element drift solver utilizes the nernst planck equation to represent the flux of atoms caused by electrical potential, concentration gradients and mechanical stress. These equations are coupled with the heat transfer and structural mechanics modules to account for the interactions between different physical phenomena.
As the simulation progresses, the solver updates the shape of the elements to reflect the accumulation or depletion of material at each location. This allows for the modeling of the entire lifecycle of a defect, from its initial nucleation to the final failure of the interconnect. The computational intensity of these calculations requires significant hardware resources, especially for large and complex assemblies.
Engineers must balance the level of detail in the mesh with the available processing power to achieve results within a reasonable timeframe.
Selection of the correct physical constants and material coefficients determines the degree to which the simulation reflects the behavior of real world components. For a finite element drift solver to be effective, the user must input accurate values for the effective charge of the ions, the diffusion coefficients and the elastic constants of the materials. These parameters are often obtained through experimental testing under accelerated aging conditions.
For example, the rate of atom movement in a tin silver copper solder joint is different from that in a pure copper wire, and these differences must be captured in the model. If the input data is incorrect, the solver will produce misleading results that could lead to poor design decisions. Many companies maintain internal databases of material properties to ensure consistency across their engineering teams.
The calibration process involves comparing the simulation results with actual failure data from the laboratory to refine the coefficients and improve the accuracy of the model.
Utilization of the simulation results to improve the layout and material selection of electronic packages reduces the risk of field failures and extends the life of the product. The finite element drift solver allows engineers to test different design scenarios without the need for expensive and time consuming physical prototypes. By analyzing the current density and stress distribution in a proposed interconnect, the designer can make adjustments to the width of the traces or the spacing of the solder bumps to minimize the drift of atoms.
This proactive approach is particularly important in the development of high power devices where the electrical and thermal loads are extreme. The solver can also be used to evaluate the impact of different manufacturing processes, such as the effect of reflow temperature on the initial stress state of the joint. The final goal is to create a design that is inherently resistant to the mechanisms of degradation.
This leads to a more robust supply chain and a higher level of customer satisfaction.
Coupled hydrostatic stress models predict thermal shock vacancy voiding across ternary intermetallic joints before thermal cycling failure occurs.
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