Metrological Technique
An x ray diffraction technique used to determine the residual stress in crystalline materials measures the variation in lattice spacing as a function of specimen tilt. In thin film analysis, the sin2 psi method provides a non destructive means of quantifying the stress within deposited layers. This technique is applied to evaluate the internal forces that develop during the sputtering process.
Measurement Principle
Bragg’s law is used to measure the spacing of specific crystallographic planes at multiple tilt angles with respect to the incident beam. As the tilt angle, represented by psi, is varied, changes in the diffraction peak position reveal the elastic strain in the lattice. This strain is plotted against the square of the sine of the tilt angle to determine the stress state.
A positive slope indicates tensile stress, while a negative slope indicates that the film is in a state of compression.
Analytical Execution
Linear regression of the strain data yields a straight line for isotropic materials in a biaxial stress state. The slope of this line is directly proportional to the residual stress and the elastic properties of the film. Deviations from linearity indicate the presence of stress gradients or texture, which must be analyzed using more complex models.
Stress Calculation
Calibrated diffractometers and precise alignment are necessary to ensure the accuracy of the peak shift measurements. The resulting stress value helps engineers optimize deposition parameters to prevent coating delamination or cracking. This measurement process is verified using standard powder reference materials to check for instrument drift.
