Simplified Thermal Stress Analysis. Reference: Sergent, J., and Krum, A., Thermal Management Handbook for Electronic Assemblies , McGraw-Hill, New York, 1998. Chapter 7
Reference: Sergent, J., and Krum, A., Thermal Management Handbook for Electronic Assemblies, McGraw-Hill, New York, 1998. Chapter 7
Another helpful source: Vaynman, S., Mavoori, H., Chin, J., Fine, M.E., Moran, B, and Keer, L.M., Stress management and reliability assessment in electronic packaging, National Electronic Packaging and Production Conference--Proceedings of the Technical Program (West and East), v 3, 1996, p 1711-1726.
Problem: when one material is bonded to another with a much smaller temperature coefficient of expansion (TCE)
DT=temperature differential across sample
S=stress (psi/in or Pa/m)
Y=modulus of elasticity (lb/in2 or Pa)
When total stress (S*max dimension of sample) exceeds tensile strength, cracks will form
Note that this analysis is simplified (Dr. Yee might not approve.)
The stress can cause displacement in the tangential direction.
Poisson’s ratio n=strain in tangential direction /strain in normal direction =eT/ eN
Shear modulus G=E/2/(1+n)
Two types of problems caused by TCE die<TCE substrate
where D=die, S=substrate, A=ambient with power off
Experimental results will usually be somewhat less than this. However, note that there are other causes of stress, too, such as vibrations or material faults.
*Note again that this is simplified, so other sources may have a somewhat different version of this equation.
Processing temps are usually higher than operating temps, so they may cause the maximum stress. The stress maximum in this case is at the corners.
During manufacturing, small stress concentrations often occur – small cracks when a semiconductor die is sawed, small voids formed. When external stress is applied, these concentrations amplify the stress and may cause a fracture.
For an elliptical microcrack with major axis perpendicular to applied stress, max stress at crack tip
KIC=plain strain fracture toughness in psi-in1/2 or MPa-m1/2
Z=dimensionless constant, usually 1.2