Stresses in Cu Thin Films and Ag/Ni Multilayers - Harvard School of ...

List of Figures x
3.1 Diagram showing the nucleation and propagation of dislocations along a
slip plane from the surface to the grain boundaries and film/substrate interface.
...................................... 55
3.2 Schematic showing the predicted dislocation behavior at different points
on the stress-temperature profile. Based on the diagram by Weihnacht and
Brückner [245]. . . .............................. 57
3.3 The scattering geometry for the GID measurements. As shown in (a), the
2θ value is not the same as the motor position for the detector, 2θ ′ . The correction
can be made using the well known formulas for the right-spherical
triangle shown in (b). ............................. 67
3.4 Cross-sectional views of an as-deposited (a) and annealed (b) 0.87 µm
thick copper film................................ 69
3.5 Deposition stress for ion beam sputtered Cu films as a function of total film
thickness. ................................... 70
3.6 Room temperature flow strength as a function of inverse thickness for Cu
samples thermally cycled to 660 ◦ C. ..................... 71
3.7 The stress-temperature profiles for the Cu films used in the strain gradient
studies. .................................... 71
3.8 Lattice parameter of CeO2 as a function of incidence angle, α. The lattice
parameters were measured with the (331) reflection. ............. 72
3.9 Elastic strain gradients in Cu films. The solid and dotted curves refer to the
thermally cycled films and as-deposited films, respectively. The reflection
is denoted by different markers, as shown in the legend. The plastic strain
is given by 0.9% minus the elastic strain. ................... 73
3.10 sin 2 ψ-plot for an as-deposited Cu film. ................... 74
3.11 sin 2 ψ-plot for a thermally cycled Cu film................... 75
3.12 Hypothetical strain profiles and their normalized finite thickness Laplace
transforms for a 1.8 µm thick Cu film. .................... 77
4.1 The Ag/Ni phase diagram [149]. ....................... 85
4.2 Top view of the Ag/Ni {111} interface, with Ag and Ni denoted by closed
and open circles, respectively. After relaxation, misfit dislocations are
formed, as delineated by the dark lines. The coherent areas and intrinsic
stacking fault areas lie in the centers of the white and shaded triangles,
respectively. .................................. 86
4.3 An edge-on view of the Ag/Ni {111} interface along the [110] direction,
with the Ag and Ni atoms denoted by closed and open circles, respectively.
The large circles are atoms in the plane of the diagram; the small circles are
atoms in the planes immediately above and below the plane of the figure.
Two distinct dislocation nodes can be seen and associated with the different
stacking conditions. Adapted from Gao and Merkle [75]. . . ........ 87