Sm. Heinrich et al., IMPROVED ANALYTICAL ESTIMATE OF GLOBAL CTE MISMATCH DISPLACEMENT IN AREAL-ARRAY SOLDER JOINTS, Journal of electronic packaging, 119(4), 1997, pp. 218-227
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.