Residual strain and texture in free-standing nanoscale Cu-Nb multilayers

Abstract

We investigate the residual strains in a free-standing Cu/Nb multilayer of 30 nm nominal layer thickness with synchrotron x-rays. This material system is characterized by columnar grains of Cu and Nb with incoherent interfaces and a sharp physical-vapor-deposition texture. High energy x-rays were used with an area detector along with multiple sample rotations to yield diffraction strain components in a very large number of directions. Due to the texture and the elastic anisotropy of constituents, observed diffraction strains cannot be derived from a single strain tensor (also known as linear sin2 ψ). Orientation-dependent diffraction strain modeling is utilized with a Vook–Witt micromechanical model. Obtained phase-resolved in-plane stress magnitudes are −515 MPa in Nb and +513 MPa in Cu, satisfying force equilibrium within experimental errors. The stresses of this magnitude will certainly influence the mechanical behavior of the multilayer upon further loading. The Vook–Witt model describes the Nb diffraction strains very well, and thereby provides information on the stress distribution in crystallites as a function of their orientation. On the other hand, the same level of agreement with the Vook–Witt model has not been achieved for Cu diffraction strains.