An aluminum film, 1 urn in thickness, is deposited onto a silicon substrate which is 500 fim thick and 100 mm in diameter. The isotropic properties of
perature, this thin-film/substrate system is flat (i.e. zero curvature). This bilayer is now uniformly cooled by 50 °C.
(a) What is the average stress in the aluminum film?
(b) Is it tensile or compressive?
(c) Describe the direction in which the bilayer bends during the above thermal excursion.
(d) If the yield strength of the thin aluminum film is 140 MPa, what is the temperature change needed to cause plastic yielding in the aluminum film?
(e) If the thin-film/substrate system is thermally cycled between the stressfree initial temperature and some high temperature Tcycle what is the minimum value of Tcycle needed to induce fully reversed plastic flow in the entire aluminum film?