IMPROVED ANALYTICAL ESTIMATE OF GLOBAL CTE MISMATCH DISPLACEMENT IN AREAL-ARRAY SOLDER JOINTS

An analytical expression is derived for determining the maximum solder joint shearing displacement occurring in an areal-array interconnect under global CTE mismatch loading. The result may be viewed as a ''loa d correction factor'' to be applied to the commonly used estimate whic h is based on the free thermal expansion of component and substrate. T he new expression for the correction factor includes the following par ameters: (a) dimensions and material properties of component and subst rate; (b) array size and population; (c) material properties of solder ; and (d) geometric parameters of the individual joints. The theoretic al result is based on modeling the assembly as two circular elastic di sks connected by a shear-type ''elastic foundation'' whose distributed shear stiffness is related to the joint/array characteristics. The an alytical expression and the graphical aids presented herein may provid e convenient alternatives to performing time-consuming and expensive f inite element ''macro-analyses'' on the assembly for the purpose of sp ecifying boundary conditions for a subsequent ''micro-analysis'' on a single joint.