Multi-beam optical stress sensor

If (j) is the angle of reflection of the laser beams, L is the distance between the specimen and the CCD camera, D is the average spacing between adjacent reflected beams, and Dq is the average initial spacing, the substrate 

A typical resolution of 15 km is achieved for the radius of curvature p, for an array consisting of four or five parallel laser beams. Prom the substrate curvature, the film stress is calculated using the Stoney formula as a function of film thickness, thereby providing a complete history of intrinsic stress evolution during the deposition of the film on a substrate. For a typical setup, the deposition of a 1 nm thick Sii a,Gej film with a stress of 50 MPa (i.e., a membrane force of 50 MPa-nm) on a 100-nm thick Si substrate is routinely detected (Floro et al. 1997). 

A limitation of the serial and parallel laser scanning methods and multi-beam optical stress sensor is that they employ monochromatic beams, which would lead to difficulties in measuring the curvature of transparent films with thicknesses of one-fourth the wavelength. These optical methods also require reflective surfaces for curvature determination. 

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Fig. 2.9. Schematic of the setup of multi-beam optical stress sensor.

Since substrate curvature can be accurately measured, even in the presence of rigid body motion or vibration, by use of the multi-beam optical stress sensor or the coherent gradient sensor techniques de-... 

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