(a) Mohr’s circle and (b) the quantities , , and . The quantities in (b) can be measured by a single IBI measurement, whereas quantities in (a) can be determined by comparing IBI measurements before and after stress relief (Fig. 2).
IBI measurements of a single-crystalline silicon ribbon wafer before cleaving (a) and after cleaving along the dashed line (c) demonstrate the characteristic crosshatch pattern attributed to dislocations, as confirmed by the etch pit density map (b). This crosshatch pattern is not evident in the difference images [(d)–(f)], which illustrate the residual stress relieved by cleaving. Coordinate system shown in (a).
Normal absolute stress evaluation of the ribbon sample shown in Fig. 2, by comparing IBI measurements before and after cleaving.
Silicon carbide and nitride inclusions in ingot mc-Si. Large tensile stresses, which decay in the radial direction, are observed surrounding the inclusions.
FEA of a model structure (a) predicts the stress field surrounding a sphere and a rod due to CTE mismatches (b). Large stresses are predicted at the particle, as seen experimentally in Fig. 4(c). The stress magnitude linescans starting at the interface (c) compare experimental IBI data (red dots) to FEA simulations using three different sets of material parameters given in Table I.
IBI and dislocation etch pit density measurements for three different silicon materials: dislocated single-crystalline silicon (dendritic web), and two types of mc-Si (string ribbon and ingot mc-Si). Band-like features in IBI measurements correlate well with dislocation bands.
The strong IR birefringence signal in (a) is attributed to nanotwinned regions, as confirmed by (b) dislocation etch pit density and (d) lifetime maps. The direction of the first principal stress in (c) is usually perpendicular to the direction of twin propagation.
IBI image of nontwinned GBs. Some GBs exhibit periodic localized stresses, while others are largely stress-free. Arrows denote the two GBs in the image above.
(a) Comparison of IBI-measured retardation values and (b) conversion to stress values among defect types.
(a) IBI and (b) dislocation etch pit measurements on a ribbon silicon wafer. Two distinct regions can be observed: higher-stress, dislocation-free nanotwinned regions (such as those featured in Fig. 7) shown in gray (red online) in (c); and lower-stress, nontwinned, dislocated regions (such as that featured in Fig. 6) shown in black in (c). A correlation plot highlights this distinction (d).
Millimeter-thick vertical slice of mc-Si ingot material examined with IBI. Unpolarized infrared transmission imaging (a) reveals inclusions, while an IBI measurement [(b)–(d)] reveals dislocation bands in addition to microdefects.
The dark features in the X-Y plane represent a microdefect [IR transmission image, from Fig. 4(a)]. The colored spikes represent metal clusters detected by . These metal clusters are visibly located at or near the microdefect, within the region of highest stress evidenced in Fig. 4(c).
Sets of material parameters used to simulate radial birefringence linescans shown in Fig. 5(c). From Refs. 43, 78, and 79.
Summary of piezo-optical coefficients from literature, and corresponding stress-optic coefficients calculated from Eq. (A1) for different crystal orientations. For light with 1100 nm wavelength, (from Ref. 124).
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