Precision improvement study of thermal warpage prediction technology for LSI packages

A finer interconnection pitch of LSI packages has enhanced the importance of precise prediction technology of temperature-dependent warpage. In our research, we prepared a model package with minute wiring and vias, and examined a method of improving the agreement accuracy between numerical analysis and measurement of temperature-dependent warpage. To improve the precision of warpage prediction technology, we paid attention to warpage measurement technology, especially the temperature distribution in a sample, in addition to improving the accuracy of the numerical analysis model and material properties. We succeeded in heating a substrate with a temperature difference of 20degC or 3degC between the top side and bottom side, by controlling the heating conditions. Furthermore, the numerical analysis with a fine wiring model was performed under conditions where the temperature varied in consideration of the thermal conductivity of the substrate. The material properties for the numerical analysis, such as Coefficient of Thermal Expansion and Relaxation Modulus were measured very carefully with original setups, because they are essential for improving the accuracy of our numerical analysis. As a result, we found that substrate warpage with an uneven temperature distribution is quite different from such warpage with uniform temperature. To predict the temperature-dependent warpage with a high accuracy, we found that the temperature distribution in a substrate should be considered in the numerical analysis, besides applying the precise model and material properties.