Determine extent of strain that occurred at the interface

Question

How to solve the following

1) For integrated circuits, Al lines are commonly placed on Si to act as electrical conductors between different parts of the device. Assuming that the Al is deposited at a temperature of 300oC, determine the CTE (Coefficient of Thermal Expansion) mismatch at the Al-Si interface as follows:

a) First, determine the % change in length of the Al upon cooling to room temperature, 20^oC (assume

CTE = 22 x 10-6/oC).

b) Next, determine the % change in length of the Si upon cooling (assume CTE = 3 x 10-6/oC).

c) determine the extent of the strain (% difference) that has occurred at the interface? Do you think this is enough to cause the interface to fail?