Elastic strains and coherency stresses in Mo/Ni multilayers

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Abstract
The observed expansion in the out-of-plane lattice parameter in metal multilayers can be produced by elastic strains, bulk relaxation, or interface dilatation. Each can produce the observed out-of-plane result but will differ in their in-plane lattice-parameter behavior. We perform a complete strain determination in Mo/Ni multilayers, using grazing-incidence and asymmetric x-ray diffraction as well as substrate-curvature-stress measurements, and determine that elastic strains dominate. Assuming Nishiyama-Wasserman epitaxial orientation, we were able to calculate the complete stress state in both materials. The stresses, which arise from substrate interaction and coherency between the bcc Mo and fcc Ni layers, increase as the bilayer period is decreased. We find remarkable agreement between the substrate-interaction stresses calculated from x-ray strain measurements and those measured using wafer-curvature techniques; this shows that interface contraction stresses are not significant. We found no evidence for interface dilatation strains. Furthermore, the small changes that are observed in the unstrained lattice parameters can be ascribed to alloying rather than bulk relaxation.