Mechanical Stress Gradients in Thin Films Analyzed Employing X-Ray Diffraction Measurements at Constant Penetration/Information Depths


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Stress gradients have been investigated employing a measurement strategy for diffraction measurements at constant penetration/information depths. Two examples have been considered: (i) sputter-deposited copper thin films on silicon wafers and (ii) γ’-Fe4N1-x layers on α-Fe substrates obtained by gaseous nitriding. In the Cu thin films rather low tensile stresses, increasing in magnitude with increasing penetration/information depth have been found. An evaluation of the measured lattice strains has been performed on the basis of the f(ψ) method, where the X-ray elastic constants (XEC’s) have been calculated as weighed averages of the corresponding Voigt and Reuss XEC’s and the weighing parameter has been taken as a fitting parameter. This evaluation reveals that the grain interaction changes with increasing penetration/information depth from near-Reuss type towards Neerfeld-Hill type. In the γ’-Fe4N1-x layers stress gradients occur due to surface relaxation near the surface and deeper in the layer due to a nitrogen concentration gradient which is built up during nitriding. First measurements in a laboratory diffractometer show the effect of surface relaxation on the stress-depth profile near the surface. As no single-crystal elastic constants are available for γ’-Fe4N1-x, the mechanical elastic constants have been employed in diffraction stress analysis. The results indicated that single-crystal elastic anisotropy occurs. From the measured data also a concentration – depth profile has been deduced.



Materials Science Forum (Volumes 524-525)

Edited by:

W. Reimers and S. Quander






M. Wohlschlögel et al., "Mechanical Stress Gradients in Thin Films Analyzed Employing X-Ray Diffraction Measurements at Constant Penetration/Information Depths ", Materials Science Forum, Vols. 524-525, pp. 19-24, 2006

Online since:

September 2006




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