Methods for in-plane strain measurement of a substrate
Methods for measuring and/or mapping in-plane strain of a surface of a substrate. A grating is formed on at least a portion of the surface of the substrate. A laser is then used focused onto the grating to determine the strain on the surface by determining the variation of the grating wavelength due to the strain on the surface. The strain information is essentially carried by the grating, in terms of grating wavelength, because it varies according to the volume change of the underlying substrates. By scanning the surface grating with the small laser size, a high resolution strain map of the surface can be produced. The induced strain is related to the grating wavelength variation, which leads to the diffraction angle variation that is captured by the strain sensing measurements.
1. A method for determining a strain on a surface of a substrate, the method comprising:
providing a grating pattern on at least part of the surface;
scanning a laser beam over the grating pattern, the laser beam having a spatial resolution between 1 μm and 200 μm;
capturing, with a camera, light from the laser beam that is reflected from the grating pattern;
measuring a diffraction pattern of the reflected light;
determining a wavelength variation of the grating pattern based on the diffraction pattern;
generating a diffraction light intensity map based on the wavelength variation of the grating pattern; and
generating a strain distribution map of the substrate based on the diffraction light intensity map.
2. The method of claim 1 , wherein the laser beam has a spot diameter of about 1 μm to about 100 μm.
3. The method of claim 1 , wherein the grating pattern has a period of about 750 nm to about 850 nm.
4. The method of claim 1 , wherein the grating pattern occupies the entire surface.
5. The method of claim 1 , wherein the grating pattern has a constant period or a varying period.
6. The method of claim 1 , wherein the grating pattern is formed directly on the substrate.
7. The method of claim 1 , wherein the grating pattern is formed separately and adhered to the surface of the substrate.
8. The method of claim 1 , wherein the grating pattern is formed by soft contact lithography or electron beam lithography.
9. The method of claim 1 , wherein the substrate contains at least two different materials having different coefficients of thermoexpansion.
10. A method for producing a strain map of a surface of a substrate comprising the steps of
providing a grating pattern on at least part of the surface;
scanning a laser beam over the grating pattern;
capturing, with a camera, light from the laser beam that is reflected from the grating pattern;
generating a contour plot of grating wavelength versus position of the surface by combining a series of columns having a plurality of pixels defining a diffraction light intensity profile based on the reflected light;
extracting a grating wavelength value from a greatest peak at each position to generate a strain distribution map of the surface.
11. The method of claim 10 , wherein the laser beam has a spot diameter of about 1 μm to about 200 μm.
12. The method of claim 10 , wherein the grating pattern has a period of 750 nm to about 850 nm.
13. The method of claim 10 , wherein the grating pattern occupies the entire surface.
14. The method of claim 10 , wherein the grating pattern has a constant period or a varying period.
15. The method of claim 10 , wherein the grating pattern is formed directly on the substrate.
16. The method of claim 10 , wherein the grating is formed separately and adhered to the surface of the substrate.
17. The method of claim 10 , wherein the grating is formed by soft contact lithography or electron beam lithography.
18. The method of claim 10 , wherein the substrate contains at least two different materials having different coefficients of thermoexpansion.
19. A method for determining a strain on a surface of a substrate, the method comprising:
providing a grating pattern on at least part of the surface;
scanning a laser beam over the grating pattern;
capturing, with a camera, light from the laser beam that is reflected from the grating pattern;
measuring a diffraction pattern of the reflected light;
determining a wavelength variation of the grating pattern based on the diffraction pattern;
generating a diffraction light intensity map based on the wavelength variation of the grating pattern; and
generating a strain distribution map of the substrate based on the diffraction light intensity map.