Fig 1. The stress strain curve for a ductile material shows the elastic modulus, E (a), the elastic limit (b), the ultimate strength (c), and the rupture strength (b).
Fig 2. Shown is a simple three-point bend structure for flexural modulus testing.
Fig 3. This out of axis contraction is described by Poisson’s ratio, which in this would be calculated as n = ?T/2?T.
Fig 4. This image of stud shear test samples for adhesion testing shows studs of mold compound (black studs) and die attach (silver studs) on special test leadframes.
We’ve all heard the adage “garbage in, garbage out.” This truism applies directly to co-design, which uses the outputs of modeling tools to ensure first-time success of complex designs. Carefully selecting the data that’s input to the tools is crucial. Otherwise, the outputs become meaningless.
Unfortunately, engineers often believe in computer simulation outputs even when they’re wrong. This can lead to a false sense of security. The wrong results can be more hazardous to a project’s success than skipping modeling altogether, when erroneous results overrule the designer’s skilled intuition. As a result, the co-designer must take responsibility to ensure the inputs are correct and track down the right values if they’re unknown.
This article offers some guidelines to help co-design engineers determine what data is needed for correct analyses, and identify the most common characterization techniques used to generate the data and pitfalls that may occur. The next article in this series will further explore validation approaches to prove the correctness of the results.
Stress Analysis
Three primary properties are used for stress and thermomechanical analysis: coefficient of thermal expansion (CTE), modulus (E), and Poisson’s ratio (n). These temperature-dependent properties must be measured across the range of temperature experienced by the system. However, because they’re often nonlinear, simple linear approximations of temperature dependency usually are insufficient.
CTE determines how much the length of a material changes as the temperature changes. A thermomechanical analyzer (TMA) tool is typically used to measure CTE (in ppm/°C). If a material has a CTE of 100 ppm/°C, the length would change by 1% over 100°C.
The material’s modulus is a measure of its resistance to stretching (Fig. 1). Rubber bands, for example, have low modulus values compared to steel. The units of modulus are pressure, such as N/m2.
The modulus of electronic materials is measured with a tensile tester (elastic modulus), three-point or four-point bend tester (flexural modulus) (Fig. 2), or a dynamic mechanical analyzer (DMA). In the case of DMAs, the reported value is often flexural modulus rather than the elastic modulus (or Young’s modulus) that’s characteristic with most modeling tools.
Two common standards are employed when measuring these properties for plastics: ASTM D638 for the elastic modulus and ASTM D790 for the flexural modulus. The two moduli are not necessarily the same, though. For example, an online datasheet for perfluoroalkoxy shows an average tensile modulus of 80 kPSI, with an average flexural modulus of 96 kPSI. Since a 10% to 30% difference sometimes exists between flexural modulus and Young’s modulus, it’s important to be sure which is being reported.
Poisson’s ratio describes the tendency of a material to shrink in the X or Y directions when being pulled in the Z direction (Fig. 3). It’s a similar in concept to pulling on a rubber band or sponge—the length increases while the width decreases. Poisson’s ratio, which is dimensionless, ranges between 0.2 and 0.4 for many electronic materials. It’s often measured with strain gauges or optical techniques.
Other important mechanical properties for electronic materials include:
- Tensile strength—the stress point at which brittle materials will break
- Elastic limit—the stress at which plastic deformation begins in ductile materials
- Viscoelastic properties for plastics
- Any plastic or creep model for the solder alloy being applied
Plastics used in electronics often exhibit viscoelastic properties, wherein the observed modulus is a function of the rate at which the load is applied. The stress developed initially for a viscoelastic material may decay over time as molecules within the material slide against each other. Alternately, under a fixed stress load, the deformation, or strain, of the material may increase with time. DMA tools are usually employed to determine the viscoelastic properties of plastics. Solders exhibit complex time-dependent creep and plastic deformation characteristics.
The most common solder model is the Anand model, though many others exist in literature. Each solder alloy will have its own set of properties, so it’s important that the co-designer find or measure the right set for the materials being used.
Recently, some articles highlighted changes that occur in solder properties as a function of a sample’s aging time, or the time between solder solidification and the characterization test. The solder ages as a result of crystal growth (grain coarsening) that occurs even at room temperatures. This tendency leads to the finding that reliability phenomenon (e.g., drop test performance) depends on the time between the fabrication of the electronic system and the drop.
There are two primary failure modes for solder: brittle intermetallic fracture, which often occurs during an impulse stress (e.g., dropping a phone on a floor), and fatigue failure, which occurs after repeated application of cyclical stresses (e.g., temperature cycles or key push bend testing). Solder joint reliability is usually calculated by correlating a modeled parameter, such as the inelastic strain energy density per cycle to the number of cycles to fail for a particular assembly. However, adoption of newer techniques, including cohesive zone modeling approaches, is on the rise.
Adhesion values are important for reliability prediction, since most electronics consist of laminated materials. For example, a printed-circuit board (PCB) is a laminate of glass, polymer, and copper layers. An IC package is a laminate of epoxy, adhesives, silicon, and metals.
Predicting the reliability of an interface involves comparing the energy that’s available to drive a crack at the interface (the energy release rate, or ERR) to the critical energy that’s required to experimentally propagate a crack under specific measurement conditions (Gc). Correlation is performed between the modeled value of ERR to the measured value of Gc and observed reliability behavior to build confidence in stress-related interfacial reliability calculations. Gc is typically measured with four-point bend tests, or double cantilever bend tests. A more recent method that’s gaining traction uses laser spallation.
Stud shear test values are commonly reported by vendors of various materials (Fig. 4). These tests give qualitative values for adhesion, but don’t provide the fracture mechanics properties such as Gc. Still, with sufficient correlation, it’s possible to obtain some predictability between stud shear values and modeled ERR.1
When comparing vendor-reported values for stud shear testing, it’s important that the same technique is used among the vendors. For example, if one vendor uses a different stud geometry compared to another, or a different shear tool height, the results won’t be comparable. A stud shear test standard exists to minimize these test variations (Semi G69-0996). For any adhesion test, the test surfaces must be the same as those of the final product. For instance, a stud test of a mold compound against a lead-frame finish that differs from the production finish will not be valid.
Evaluating chip-package interactions requires knowledge of all the aforementioned properties for the thin-film materials produced on the die surface. These films, usually measuring less than a micron thick, can’t be handled in typical mechanical analyzers. Characterization techniques ranging from X-ray to bulge testing, to nano-indentation testing, to wafer bow measurements, to capacitance monitoring have been created to characterize these film properties.2 Co-design engineers will find a wealth of enrichment opportunities while indoctrinating themselves in the field of thin-film characterization.
Thermal Analysis
The number of material properties to collect for thermal analysis pales in comparison to stress analysis. The three primary thermal properties are thermal conductivity, specific heat, and density. They should be known as a function of temperature, just as with properties for mechanical analysis. If computational fluid dynamics is used, numerous properties are required to describe the fluid such as viscosity and temperature-dependent expansion. But when air is the gas surrounding the electronics, these properties are usually built into the tool with other defaults like wall functions and turbulence models.
On the whole, specific heat is measured using differential scanning calorimeters. A divided bar approach is common for measuring thermal conductivities of polymers. In this method, a material sample with a known thickness is sandwiched between two bars of known conductivity. The temperature immediately above and below the sample is measured, as is the temperature gradient developed across one of the bars at a set distance. The temperature gradient on the bar is used to back-calculate the heat passing through the sample, while the temperature gradient across the sample calculates the conductivity using the equation:
where Q is the heat through the sample, t is the sample thickness, A is the sample area, and ?T is the temperature gradient over the sample.
It should be noted that many filled materials, such as lid-attach and die-attach epoxies, won’t possess the same thermal conductivity at an interface when compared to the bulk. For these types of materials, characterization of the effective thermal conductivity as a function of bond line thickness must be determined through appropriate sample preparation and measurements. Plotting the observed thermal conductivity versus thickness enables the backing out of thermal interfacial resistance. JEDEC defined thermal test die that are adequate for measuring these thermal interfacial resistances.
Electrical Analysis
Co-design’s four fundamental electrical properties are electrical conductivity, dielectric constant (or relative permittivity), loss tangent, and permeability. These properties may vary with both frequency and temperature, requiring careful characterization. Electrical conductivity determines how easily current will flow in a conductor, and the dielectric constant calculates capacitance between structures. The permeability calculates the magnetic fields generated in a medium for a given current, while the loss tangent provides a measure of energy lost as heat when signals propagate through lossy mediums like silicon.
Electrical conductivity is often measured for thin-film materials like copper (Cu) via specific test structures or van der Pauw measurements. Depending on the frequency of interest, the dielectric constant can be measured using a number of different approaches.
For higher-frequency applications, microstrip line tests are typically performed with the material at a known thickness. The material’s dielectric constant can be backed out from the measured impedance of the line. To measure loss tangent, a number of techniques are available.3,4 They involve testing either of transmission-line characteristics or resonant cavity performance. Finally, magnetic permeability is measured with simple inductor structures whose inductance is perturbed by the presence of the magnetic material.
Similar to the dielectric measurements, the presence of a magnetic material will affect a transmission-line’s impedance. Therefore, the permeability as a function of frequency can be backed out from this behavior. The structure of the materials under investigation can also play a significant role in the material properties; i.e., surface roughness plays a big role in a conductor’s conductivity versus frequency performance. As a result, the standard skin-effect conductor loss deviates from the inverse square root of frequency relationship.
Pitfalls
Unfortunately, the properties supplied in many datasheets indicate only specification limits. For example, measurements often show the thermal conductivity of mold compounds to be 20% or 30% higher than the values of these properties published in the datasheets. In these instances, the datasheet might show a lower spec limit, and not the accurate value that’s needed for modeling.
Other pitfalls occur when datasheets don’t list properties as a function of temperature, but rather give only one value. Or, a datasheet might list shear modulus, but not tensile or flexural modulus.
Many material properties change somewhat after exposure to high temperatures, such as those experienced during solder reflow, or they’re a function of the degree of polymer cure. Moisture absorption can also change a material’s properties, impacting the dielectric constant, modulus, and adhesion strength.
A critical parameter required for most warpage models is polymer cure shrinkage. However, datasheets often omit cure shrinkage altogether. When confronted with these gaps, the co-design engineer can turn to a number of available solutions. The most reliable path is to use a well-equipped materials characterization lab with a trained staff capable of measuring the missing characteristic.
A trusted internal lab offers another advantage—all measurements of a particular type will be conducted using the same technique across material suppliers, reducing unknowns and variability. This resource is a luxury often unavailable to the co-design engineer. If a good relationship exists between the engineer’s company and materials supplier, communiqués are often sufficient to initiate a required measurement. In other instances, external labs may be used to gather the data. Whatever sources are used, it’s important that they employ a standardized method in all cases. Supplying them with standard samples for calibration measurements helps along these lines.
Some material properties are anisotropic, meaning they vary in the X, Y, and Z direction. A good example is the thermal conductivity of a PCB, which exhibits higher conductivity in the direction of the glass weave versus perpendicular to the weave. The CTE as well as the modulus of PCBs and materials that are cast in place, such as polyimides, are anisotropic, too. Tin is quite anisotropic due to its crystal structure, but since it’s not possible to ascertain the crystalline orientation of each lead-free solder joint, some scatter will be expected in the actual stress data compared to the model results.
Co-design engineers should never just guess a property value. For example, the strength behind many co-design studies is the comparison of trends. Co-design engineers may say that one option is better than another. Guessing a material input can result in a meaningless trend. Gathering the required materials inputs may be time-consuming, so it’s important for engineers to ensure that their inputs are in place well in advance of the time critical modeling need. Storing and sharing these inputs with others can also be beneficial. Thus, a database should be built to make the properties available to all.
Another pitfall occurs when a modeling engineer isn’t careful with the units of the materials properties. The units must be consistent when doing models. Moreover, it’s important to have a good working knowledge of the units being reported in a datasheet. If the units don’t appear, contact the vendor. Unfortunately, a vendor may use an unusual set of units to make a material look better, so ensure everything is up to snuff.
Summary
Along with geometrical descriptions, material properties are the most important inputs to co-design tools. It’s critical that properties be correct. Otherwise, the modeling results will be meaningless and misleading. This short article isn’t adequate to cover the depth and breadth of every characteristic needed to perform co-design. Co-design engineers must pursue a process of continuous learning to improve their capabilities. The study of materials properties and the measurement techniques used to generate the characteristics is a ripe field for personal enrichment.
References
- V. Srinivasan, et al, “Delamination Prediction in Lead frame Packages using Adhesion Measurements and Interfacial Fracture Modeling,” Electronic Components and Technology Conference, 2011.
- V. Gupta, et al, “Ultra Low-K Dielectric Mechanical Property Characterization,” ITHERM, 2008.
- A. Ege Engin, et al, “Dielectric Constant and Loss Tangent Characterization of Thin High-K Dielectrics Using Corner-to-Corner Plane Probing,” IEEE Electrical Performance of Electronic Packaging, 2006.
- D. Li, et al, “A Simple Method for Accurate Loss Tangent Measurement of Dielectrics Using Microwave Resonant Cavity,” IEEE Microwave and Wireless Components Letters, Vol. 11, No. 3, March 2001.