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Determination of Strain and Stress in Thin Films Using Curvature MeasermentsExperiment
Si (001) wafer (5", 180 µm thick) with 1000 Å film of deposited gold was cut along (100) direction. A radius of curvature of each sample was measured in (010) direction with two different setups (fig. 1).
First one (fig. 1a) consists of focusing lenses, manually positioned mirror, main lens, video camera and PC. As a source of light we used a laser diode. The laser beam reflects from the mirror and goes through the main lens. Reflected from the surface of a sample goes again through the main lens and finally hits the CCD camera. The image from the camera is forwarded through a video capture card to the computer. A program processes the image and determines a position of a spot of the laser beam on the CCD. The lenses focus a laser beam on the CCD in order to obtain the highest accuracy of the spot position. The second setup (fig. 1b) [1, 2] uses a position sensitive detector (PSD) instead of CCD, and a computer positioned mirror.
Fig. 2: Optic system of both setups.
Both setups are based on the optic system shown in fig. 2. One can deduce a relation for all parameters of the optic system using basic laws of optics. When a and b are equal to a focal length of lens f we get the simple relation:
Thus the displacement of the spot when the angle q is changing determines a radius of curvature R of investigated surface. For flat surface focal point is in the same plane as a mirror and a movement of the spot is not observed. Concave and convex surfaces shift this point from the focal plane and move the spot on the detector. A type of bending (a sign of a radius of curvature) is determined by the direction of movement of a spot on the detector.
The radius of curvature corresponds to the biaxial stress s in agreement with Stoney's formula:
Fig. 3: Positions of the spot on CCD and PSD for sample 1.
Positions of the spot on CCD and PSD for sample 1 are shown in fig. 3. We calculated average displacements using a linear fit. The radius of curvature and stress for each sample were calculated from equations 1, 2 and are shown in fig. 4. Results from both setups are in a very good agreement. One should take into account that a measured radius of curvature depends very strongly on area of a scan. A strain of the wafer is not homogeneous. Even sign of radius of curvature changes for investigated wafer. Stress in the samples changes from -0.17 Gpa to 0.3 GPa. Analysis of plot from fig. 3 gives also information about irregularity of a bend of the sample. Inhomogeneous strain of the wafer may be caused by structure imperfections in substrate as well as in the deposited layer.
Fig. 4: Radiuses of curvature and corresponding stresses of the samples obtained with two setups. At the bottom: the placement of the samples in a silicon wafer.
First setup (fig. 1a) provides possibility of biaxial measuring of the displacement of a spot. It enables more detailed analysis of the investigated surface. On the other hand it requires more time to process or to store an image from CCD. A signal form PSD corresponds to a position of the spot and it is available at once. This feature allows increase a number of measurements in a time unit.Acknowledgements
We would like to thank O. Thomas, P. Gergaud and Ola from MATOP  for the access to the setup 2.References
 S. Labat, Diplome d'Etudes Approfondies, UniversitÚ Aix-Marseille III, 1994.
 MATOP, URA CNRS 1530, FacultÚ de St JÚr˘me F-13397 Marseille Cedex 20, France.