Raman microprobe measurements of residual strains at the interfaces of Si on quartz
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F. Adar Instruments S. A., Inc., 6 Olsen Avenue, Edison, New Jersey 08820-2419 (Received 12 February 1987; accepted 20 July 1987) In order to quantitatively determine the residual stresses at the interfaces of laminate composite materials, a model involving exponential stress gradient in the substrate and no stress gradient in the film was derived. The measurements of residual strains at the Si/quartz interfaces using the Raman microprobe were compared to expected strains by the model. The model shows that a small volume of substrate near the interface about 2 times the film thickness was affected by the thermal mismatch of the two regions. Approximately 5-10 times higher residual strains were expected at the substrate-side interfaces compared to the measured results. This is explained by the experiments averaging along the probe thickness of about 10/im resolution. The recrystallization process of Si film by thermal annealing was also investigated using Raman spectroscopy.
I. INTRODUCTION When a composite material, consisting offibersor films that are chemically bonded to associated matrices or substrate, is processed, residual stresses are often developed at the interfaces. Unfortunately, it is not easy to measure the residual stresses at the interfaces experimentally, due to heterogeneity at the interfaces. Furthermore, the residual stress distribution that is associated with zero resultant forces when a body is in equilibrium and has no applied external forces is very complex. In this article a residual stress pattern in laminate composites was modeled based on the thermal mismatch at an interface. The model was tested on a thin film of Si deposited on a quartz substrate. Residual stresses were monitored by measuring shifts of Raman bands. Because the Raman frequency shifts are proportional to the strain and because the laser beam can be focused at an interface with axial spatial resolution of approximately 10 jam, it is possible to investigate the residual strains in small regions of the film and the substrate in the region near the interface. Measured residual strains at the interfaces were compared to the theoretically predicted strains that were calculated assuming an exponential stress gradient in the substrate and no gradient in the film.
substrate (i.e., infinite thickness or rigidity of substrate). Thus on cooling from elevated temperature, where the stress is assumed to be zero, to ambient temperature, the difference of the thermal expansion coefficients Aa = af-as results in a total stress in the film. The amounts of bending or curvature of the system can be calculated as a result of these thermal stresses using the equations of equilibrium of forces and momentum in the system.3 However, if we consider the very small volume near the film-substrate interface and assume finite rigidity of the substrate, a difference of thermal expansion or contraction yields residual stresses or strains in both film and substrate. The state of residual stresses and strains in a film and substrate at the interface can
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