Machine Design

FEA makes short work of optimization studies

FEA software lets users quickly analyze a variety of problems for deflections, stress, thermal, and other characteristics.

A power module

A cross section of a power module shows its different layers. The thicknesses of the device solder and substrate solder are to be optimized.

Solder thickness versus resistance and stress

Blue curves correspond to three thicknesses of substrate solder. Resistance increases with an increase in device-solder thickness. Similarly, tan curves correspond to mechanical stress in the power device. Thicken the device solder and mechanical stresses drops. Where the tan and blue curves cross indicates a best compromise between thermal resistance and mechanical stress.

Setting up an optimization study is done by dragging and dropping defined characteristics from the part tree on the left to the design table at the bottom. Other values in the Constraint Type column identify discrete values or a range of them.

The FEA mesh shows the relative thickness of layers in the power controller.

Solder thickness optimization

The software has finished its 30 runs and plotted results.

The software makes all this easy, has the advantage of importing CAD models, and it finds more than just maximum stress locations. The best way to tour the software is to work through an optimization study such as finding the solder thickness that minimizes thermal resistance and mechanical stresses in a semiconductor. But first, a little explanation of the problem.

The semiconductor industry builds devices to switch and process power, which are subjected to demanding physical environments. For reliability, the thermal and structural performance of single and multichip modules must be analyzed and understood. The circuit substrate of these products is made of a ceramic isolation layer sandwiched between two copper layers and attached to a copper baseplate. Power devices are soldered to the top side of the substrate. Thermal conditions call for solder alloys to make these mechanical and electrical attachments.

Because solder has only a fraction of the thermal conductivity of copper, it plays an important role in the thermal resistance of the entire structure, despite the relatively small thicknesses used for these layers. The device and substrate solder contribute to the mechanical residual stresses of the assembly, which are generated as the module cools after soldering.

The solder layers in most powermodule structures are necessary to bond the device, circuit substrate, and baseplate together into a thermally efficient and mechanically robust structure. However, designing these systems becomes increasingly difficult as applications demand higher power densities and reliabilities. Solder layers range in thicknesses from 0.001 to 0.010 in. But although thin solder helps reduce thermal resistance, thicker solder lowers mechanical stress. Solder also acts as a buffer between other materials, absorbing energy through elastic and plastic deformation. So what thickness meets the requirements of each layer?

Now, back to 3G.Author. For the model, the thicknesses of the device and substrate solder are specified as extrusion dimensions of their respective parts. After importing a quartersymmetry model from SolidWorks into the program, these two thicknesses are easily parameterized by dragging them from the Feature Tree to the Design Table below the graphics. Required simulation ranges are typed into the Values column to define different configurations. Three different thicknesses (0.003, 0.006, and 0.010 in.) are chosen for the substrate solder. These values represent real-world assembly processes in the power-module industry. For the device solder, five thickness values are chosen from 0.001 to 0.005 in. The two ranges define 15 (3 5) total combinations of solder thicknesses.

Next, define the types of analyses. calls these Function Studies and they appear below the Feature Tree. Adding a new Function Study is straightforward: Right click on the model name, select Function Study, and appropriate options. The software also allows "cloning" Function Studies when a similar analysis is needed. This saves much of the setup time.

Setting proper boundary conditions is essential for meaningful analyses. The software makes the process clear and simple. For the Thermal Resistance Function Study, heat is generated on top of the power device. The baseplate backside has a constant temperature. Right clicking on the Function Study name and selecting Thermal Load prompts users for appropriate values. Similar steps specify boundary conditions in the Stress Function Study.

A useful capability lets handle contact between differing materials. The software assumes interfaces are bonded. Other options include sliding, separation, or no contact. Regardless of the interface, the software seamlessly processes meshes at this boundary.

Before executing the simulations, results of interest must be specified in the Design Table. They can be a maximum temperature, stress, or displacement. (This is also done with a simple right click in the "Constraint Name" box.) For this study, the device maximum temperature is selected for the "Resistance" Function Study, and maximum Von Mises Stress is selected for the Thermal Stress Function Study.

Selecting Simulate prompts the software to ask if it should run a Base configuration, a "Smart set" of runs, or an Exhaustive set. For this study, the Exhaustive set of 15 runs is selected to generate the full range of solutions.

The process includes building the geometry and solving each set of 15 runs for each of the two function studies, a total of 30 simulations. For this problem, the entire simulation takes about 20 min on a Pentium 4 processor with 1 Gbyte of RAM.

The three thick curves in Solder thickness optimization represent thermal resistances for the three substrate solder thicknesses. As expected, these values increase as device solder-thickness increases from 0.001 to 0.005 in. The thinner curves show mechanical stress in the device for the same range of substrate and device solder thicknesses. These values decrease as device solder thickens, consistent stress-strain theory. The design engineer would now decide on optimal solder thicknesses, depending in part on whether thermal resistance or mechanical stress is more important. Since mechanical stress appears to depend more heavily on solder thicknesses, a substrate solder thickness of 0.003 in. and device solder thickness of 0.005 in. offers good mechanical stress and reasonable thermal resistance. It would be straightforward to clone the analysis for this problem by modifying a dimension, such as device length or width, and rerunning simulations with minimal model setup.

The software comes from PlassoTech Inc., 16255 Ventura Blvd., Suite 615, Encino, CA 91436, (818) 788-8026,
Guillermo Romero

Guillermo Romero is a senior staff IC design engineer at Motorola Inc. in Phoenix.

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