Development of effective compact models for depopulated ball grid array packages

This paper describes the development of compact models that represent the thermal features of depopulated ball grid array packages. The test vehicles consist of an enhanced ball grid array (EBGA) with 352 solder balls and a plastic ball grid array (PBGA) with 388 solder balls. Two types of compact model are developed for each using CFD software. Fine geometrical features, such as the solder balls, are further verified with a finite element program. The first model is a straightforward use of an equivalent contact area, whereby the solder ball array is modeled as flat cuboidal blocks with the contact area equal to the sum of contact areas of all the solder balls, and with the thermal conductivity of solder. The centerline of the cuboidal blocks is placed at the geometric center of the area that is occupied by the solder balls. In the second model, the solder ball array is also modeled as flat cuboidal blocks but with a contact area equal to the solder balls as well as the spacing between them, i.e. the entire solder ball array area. To ensure correct thermal performance, an equivalent thermal conductivity for this layer is determined by an analysis using the concepts of spreading and constriction resistance. The simulation results of the two types of compact models are compared with experimental measurements using thermal test chips set up in accordance to JEDEC standards. The results compare well to within about 10% in terms of junction temperature, with the equivalent thermal conductivity model showing the more consistent results