Sc. Jain et al., EDGE-INDUCED STRESS AND STRAIN IN STRIPE FILMS AND SUBSTRATES - A 2-DIMENSIONAL FINITE-ELEMENT CALCULATION, Journal of applied physics, 78(3), 1995, pp. 1630-1637
Finite element calculations of stresses and strains in substrates and
stripe films of thickness h and width 2l are reported. Both variation
of the stress in the vertical direction (away from the interface) in t
he film and distortion of the substrate are taken into account. The ca
lculations show that both the horizontal and vertical lattice planes a
re curved in the film as well as in the substrate. If the thickness of
the substrate is infinite, the curvature in the substrate is maximum
near the interface and decays rapidly with depth. Furthermore, the edg
es near the top are over-relaxed, i.e., if the film is originally unde
r compression, the stress becomes tensile because the free edge surfac
es affect the relaxation. For a film with h/l=1 or greater, the stress
is reversed throughout the top layer. The change from compression to
tension takes place partly because of the Poisson effect and partly du
e to the bending of the lattice planes. The approximations made in the
existing analytical models were examined and the conditions under whi
ch the models describe the stresses in the film or in the substrate we
re determined to a good approximation. Our finite element calculations
agree with the available experimental data. Ours are the only theoret
ical results with which measured substrate stresses agree qualitativel
y. (C) 1995 American Institute of Physics.