Do you know the thermal conductivity of paper? This was the start of a phone call a few years ago. The conversation continued and the reason for the question became apparent. A thermal analysis of a printed circuit board had determined that a thermal interface material was needed under some hotter components to provide a better conduction path. The circuit card was edge cooled which meant that the thermal coupling between the component and the board was significant. In the course of the design, a thermal pad material had been identified, dimensional tolerances considered, and sheets of the thermal pad material obtained that were precut to fit. The boards were assembled and because these cards were subjected to a harsh environment, a conformal coating was applied for corrosion resistance.
The question related to the thermal properties of paper became relevant when it was discovered that the individual placing the thermal pads under the parts had confused the paper and the gap pad material and had placed the paper backing where the gap pad material was designed to go and threw away the gap pad portion. The hope was that the thermal properties of the paper backing were good enough to allow the boards to be used but ultimately, the boards had to be replaced because they were not compliant to the design specifications. In fairness to the assembly person, the thickness of the pad and paper were similar.
The reason for starting this column with this type of example is that I have been asked over the years for an accuracy assessment of both predictive thermal models and thermal measurements. Answering this question nearly always requires gathering additional information, especially when reviewing the work of others. What follows are some of my personal observations related to numerical simulation and the most common sources of uncertainty in thermal model predictions. A well-documented analysis should provide the reviewer with information related to these items as well as assist the analyst with providing a credible response related to accuracy concerns.
Physical Description, Motivation for Analysis
Understanding why the analysis was performed provides a necessary basis for evaluating the need for accuracy. Revisiting the reason the analysis was performed can reveal that the larger objective was lost in generating the details. The physical description should include the heat source terms and the information used to determine the dissipation.
If the analysis included an estimate of a convection heat transfer coefficient as a boundary condition, the accuracy of this portion of the thermal model can be difficult to assess [1] and at a minimum should have some rationale as to the applicability of the method used to predict the convection coefficient. It can be difficult to determine the range of the tested data which is needed to avoid extrapolation. This creates the risk that the situation analyzed is outside the range of applicability of the correlations, leading to excessive error.
Material Properties
Document the material properties and the source of the information. Adhesives and solders property data usually have wider variation. In addition, the thermal properties of adhesives and solders can vary with processing conditions which usually requires obtaining data consistent with the manner in which they will be used. ElectronicsCooling’s past columns on technical data provide one source of information in this area.
Discretization and Meshing
Determining that predictions are not sensitive to meshing density reduces part of the uncertainty but unfortunately, grid-density convergence studies do not seem to be the norm. It is not enough that the mesh simply represent the geometry. A simple example is provided by considering a small heat source on the surface of a rectangular shape, such as might be encountered with developing thermal models at the semiconductor die level. Resolving the surface metallization features provides a starting point for mesh density along the top surface of the die. However, there are not any geometric driven reasons for a higher mesh density through the thickness. Temperature gradients near heat sources such as FET gates are concentrated and providing an accurate solution requires a higher mesh density than would be anticipated from geometric considerations alone [2]. Given the significant computer memory and processing speed available today, performing some level of a grid convergence study is a reasonable request.
An additional source of uncertainty related to thermal models is making sure that the geometry modeled actually represents the end product. For example, layout tools used to create the geometry may be sized to yield a different feature when processed. A certain width trace in an IC database may result in a different physical width after processing. The diligent thermal analyst will check for these types of potential discrepancies.
While this list is by no means exhaustive, my personal experience is that careful attention to these items significantly increases confidence in model predictions. Having information to answer these items also makes it much easier on others to review your work as well.
* For a list of references, go to www.electronics-cooling.com
