November- December 1998
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Finite Element Modeling of Chip - Scale Packages
Computer simulations of mechanical behavior can help identify IC package design issues early in the design process, which minimizes the number of prototypes needed later.
-Dr. John C. Muskivitch, Pacific Consultants LLC, Mountain View, Calif.
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| Figure 1. Bimetallic strip model graphically illustrates how CTE mismatches can cause stress in a system. The aluminum-copper in the bimetal strip model (A) expand disproportionately when heated (as shown) or cooled causing the strip to warp (B). |
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| Figure 2. The elastic modulus of most materials diminishes with increases in temperature. These subtle but important effects can easily be and should be accounted for in finite element modeling. |
The most obvious of the mechanical properties of concern in electronic packaging is the coefficient of thermal expansion (CTE). The CTE is a measure of how much a material will expand or contract when subjected to a temperature change. If all the materials in a package had the same CTE, the effects of differential thermal motion would, generally, be minimal. This is because in a true, free thermal expansion, there are no displacement differentials and, thus, no stresses. In reality, however, it is the difference in the CTE of the various elements of an IC package that can lead to stress problems. By way of example, consider a simple bimetallic bar of aluminum (CTE~24) and copper (CTE~18) shownin Figure la. Asitis heated or cooled, the differential expansion between the two materials causes the sample bar to bend in one direction or the other (Fig. lb). If we, for the moment, assume that the other mechanical properties (elastic modulus, Poisson's ratio, etc.) are the same in both materials, then thermal displacement may cause a symmetric stress pattern about the center axis of the bending bar.
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| Figure 3. The CTE will often vary with the temperature of the material This is especially true for plastic materials which are fundamental to IC packaging. |
The mechanical behavior of the IC package is further complicated by the fact that the key package component material properties will also normally vary with temperature and time. Heating, for example, typically results in a softening of the material as the elastic modulus is reduced (Figure 2). In addition, significant heating of a material will reduce its yield and ultimate strength and make the material behave in a more nonlinear fashion. A lower yield strength will result in a redistribution of the internal forces and possibly relieve some of the stress in the system. In turn, this redistribution can also lead to a shift in high stress areas and changes in both the failure mode and location within the package.
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| Figure 4. This illustration shows an example of meshing lor a finite element model. For symmetrical constructions, fractional models, such as this one, can be used. |
When performing finite element modeling, it is necessary to remain alert to the possibilities of secondary effects related to the materials used. For example, a shift in the material CTE due to temperature difference (Figure 3) can also change the mechanical behavior of the package. If the temperature-dependent influences of CTE are overlooked, the designer may also overlook potential stress problems, and may overlook possible areas of benefit from this behavior as well. In addition to the ternperature-dependent effects covered earlier, certain package materials change with time, either in the manufacturing process or under thermal cycling. These time- dependent effects are due to such phenomena as the curing of encapsulant material or strength degradation due to creep. The interaction between the encapsulant and the other components of the chip package is very complex. At first glance, it appears as if we are confronted with a similar issue of matching CTEs and strengths of the encapsulant with the surrounding materials. However, the determination of encapulant stresses is compounded by its change in material behavior as it cures and as it is influenced by temperature changes. The mechanical properties of the encapsulant can change with time as the material cures.
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| Figure 5. This stress map shows a flip -chip CSP with underfill. Note that the underfill helps to protect the solder joints. |
The curing process typically results in CTE and strength mismatches caused by material stratification due to differential curing. To facilitate understanding of complex behaviors, as described, the modeling engineer will frequently break down the complex behavior into components of simple behavior that are both more easily characterized and more easily understood. Nevertheless, many times the modeling engineer arrives at a point where simple assumptions do not provide adequate resolution of the problem. It is then necessary to look to tools and methods that will expand understanding of the behavior by providing the opportunity and capability to study most, if not all, of the complexities together.
Predictive Engineering, An Exereise in Cost Savings
Using predictive engineering tools, such as finite element analysis (FEA), the influence of manufacturing issues and material variations can be studied and quantified. FEA models can be for mutated to simulate package behavior under any variety of conditions, to practically any level of detail. The results of FEA can be used by mechanical specialists to better understand the physical behavior behind the interaction of the components and the various materials. This can greatly reduce the cost of developing a new product by helping to define the properties required more precisely to assure the product's structural integrity and reliability.
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| Figure 6. This figure shows a stress map of a flip-chip CSP without underfill. Note that the highest stress (shown in red) is concentrated on the solder joints. |
A Chip-Scale Package Example
The following general problem for a chip-scale package is illustrative of how FEA can be used to solve complex problems. First, a sample cross-section of the package design is selected (Figure 4). The fundamental constituents of the package are represented by a collection of interconnected elements, each with the mechanical properties of its respective constituent material. In a simple sense, it is possible to study the influence of the encapsulant by considering models with and without encapsulant. Figure 5 shows a representative stress pattern and exaggerated deformation pattern in a heated package with encapsulant. Peak stresses are found to occur on the outer solder ball, at its interface with the chip.
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| Figure 7. Shrinkage of encapsulant can result in a steady strain condition on the outermost solder joints. |
Phenomena of potential importance can be investigated very easily using a finite element model. For example, as a typical encapsulant cures, it also shrinks. Because of the bond of the encapsulant with the surrounding elements of the sample CSP construction, differential stresses are induced into the system by the shrinkage contraction as shown in Figure 7. The shrinkage stresses form an initial stress state or "pre-stress." When the operational thermal loading is applied, these "pre-stress" stresses are reversed as expansion in the encapsulant occurs.
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| Figure 8. Thermal cycling tests are commonly used in reliability tests Finite element models can be used to approximate the life of a electronic package by calculating the cumulative strain on the solder joints resulting from thermal cycling. |
With a more complete understanding of the interaction of the different materials on a simple cross-section, the model can easily be extended to model larger portions of the package to incorporate three-dimensional effects.
Many materials have different properties in different directions and sometimes are most accurately represented in 3-D. For example, Figure 9 shows a model of a detailed region of a CSP used to study the behavior of the leads. Nonsymmetric configurations that can cause excessive differential stresses and strains, but can be easily modeled, are visible.
Summary
Finite element modeling is an important tool for analyzing complex systems, such as chip-scale packages. By providing a more thorough understanding of the complex behavior associated with chip-scale packages and their constituent materials, it is be possible to create and optimize designs that can take advantage of variable material properties such as CTE and elastic modulus. Moreover, computer simulations of mechanical behavior help to identify design issues early in the design cycle and minimize the number of prototypes needed for tests. In short, finite element modeling is a cost-effective method for rapidly moving products from concept to production while minimizing risk and increasing understanding of the overall system. FEA is a tool and a technique that should not be ignored if one hopes to keep pace in today's competitive electronics market.
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| Figure 9. An example of an EEA model for a CSP constructed with leads fanning away in opposite directions from a central bonding land area. |