Problem 1. You are asked to provide a damage model to estimate the life of a new solder that has been developed at UPRM. For this task, you have decided to use accelerated thermal cycling (ATC) on a set of specimens: (a) 3mm X 3mm Si die (b) 7mm X 7mm Si die (c) 10mm X 10mm Si die Two thermal profiles for the cycling test were developed: (i) T.P. I: Tmax-230°C, Tmin=-40°C (ii) T.P. II: Tmax = 180°C, Tmin = -20°C A total of 20 specimens (of each size) and per thermal profile, were mounted on AIN substrates and tested. (Note that there are 6 different experimental conditions, i.c. 3 die sizes X 2 thermal profiles.) It is known that the maximum shear strain range (Ay) occurs at the corner of the chip, i.e. at a distance (L) that is equal to half of the diagonal length of the die. For this problem, all samples were fabricated under the same conditions and inspected so that the quality of all samples was identical. Given: Bond line thickness (h): 2 mils (0.002 in) CTE of Si: 2.5 X 10 mm/(mm*°C) CTE of AIN: 4.5 X 10 mm/(mm*°C) After performing the thermal cycling test, the following life data was obtained (Note that we are reporting the mean time to 20% failure, i.e. N₁): T.P.I T.P. II 3mm X 3mm 6,000 15,000 7mm x 7mm 1,300 2,800 Using the Coffin-Manson model for low cycle fatigue: ΔΥ, =Y, (2N) 2 10mm X 10mm 150 800 A. Calculate the constants for this new material (i.e. c and 2yr). Use Engelmaier approximation for your analysis assuming complete stress relaxation per cycle. B. Estimate the life (mean time to 20% failure, Nr) of an actual microsystem that consists of an AIN substrate with a 3mm X 3mm Si chip attached with this new alloy. The bondline thickness is 2 mils (0.002 in) and the service temperature in the real application will swing between 0°C and 100°C.