Study of Stresses in Thin Silicon Wafers with Near-infraredphase Stepping Photoelasticity
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This paper reports on a study of stress in thin silicon plates sectioned from wafers by a near-infrared transmission technique. Phase stepping was incorporated to determine the magnitude and orientation of stress from fractional birefringence fringe images. The anisotropic relative optic-stress coefficient of (100) silicon was determined and the limitation of the stress orientation measurement is discussed.
I. INTRODUCTION
It is well known that silicon used in the manufacturing of integrated circuits and photovoltaic cells contains stresses. These stresses are introduced during processing, including the growth of the single crystal, oxidation, thin film deposition, and mechanical handling. Stresses can initiate and propagate dislocations and cracks, and affect electrical properties of silicon devices, so it is critical to understand, minimize, and control these stresses.1–3 Various techniques have been used to determine stresses in silicon. However, optical techniques usually have the advantage of being noncontact and nondestructive. One technique that is of particular benefit is infrared photoelasticity, used by Bond and Andrus (1956),4 Landerhandler (1959), 5 Denicola (1971), 6 Kotake (1980), 7 Shimaoka (1987),8 and others to examine silicon samples of rather large thickness (5–8 mm) using 1100–1500 nm illumination and fringe counting methods. Photoelasticity relies on birefringence effects accumulated through the sample thickness. When the sample becomes less than 1 mm thick and the whole field maximum fringe order is much less than one, traditional photoelasticity techniques will not work. Date reported a synthesized photoelasticity for fractional fringe analysis,9 but the information of stress orientations was not obtained. Another point-by-point fractional fringe analysis was reported by Gorshkov (1988)10 and Niitsu (1994),11,12 but their technique requires scanning to produce a whole field measurement. Patterson et al. (1992) reported a sixstep phase-stepping technique.13–16 As applied to optically transparent materials to visible light, they used digital image processing to obtain the whole-field
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J. Mater. Res., Vol. 17, No. 1, Jan 2002
fractional fringe analysis and found both the stress magnitude and orientation. However, this technique has not yet been applied to silicon. A critical element in the use of photoelasticity to study silicon is the determination of its stress–optic relationship because the single-crystal silicon is anisotropic.17 The stress–optic relationships of silicon have been reported for several specific orientations and light frequencies. For example, Liang et al.18 presented an analysis of the stress–optic relationship of (100) and (111) wafers, but the illumination and observation orientations were in-plane only. This paper incorporates phase stepping with the nearinfrared (NIR) photoelasticity to study stress in thin silicon samples. The stress–optic relationships of (100)Si samples, when the illumination and observation orientatio
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