Measuring the tensor nature of stress in silicon using polarized off-axis Raman spectroscopy

Abstract

Polarized off-axis Raman spectroscopy is a technique for measuring the complete tensor nature of stress fields in semiconductors. By combining incident light tilted away from the normal axis with polarization of the incident and scattered beams, any Raman-active optical phonon mode can be selectively studied. Once the frequencies and intensities of these phonons are measured, the complete stress tensor can be uniquely determined. This technique has been applied macroscopically to mechanically deformed silicon wafers under biaxial tension. The results of this approach compare favorably with the stress calculated by means of the theory of elasticity.

Relation between Raman frequency and triaxial stress in Si for surface and cross-sectional experiments in microelectronics components

“…One way to obtain additional information on stress in Si is using off-axes micro-Raman spectroscopy, as demonstrated in Ref. 38. An easier option allowing measurements with higher spatial resolution is by using a large numerical aperture objective lens, as was mentioned in the discussion about the deformation potentials of Si.…”

Investigations of the ionizing radiation induced effects in ultra-thin strained-silicon layers on insulator using confocal microscopy measurements

“…We then choose to split this spectrum into two Gaussian bands (dashed blue lines): the first one, associated to the relaxed silicon, is fixed at a wavelength ω = 520 cm − 1 . The second one is centered on ω = 512.5 cm − 1 , a typical response of a biaxial tensile strained silicon layer [26][27][28]. The sum of these two Gaussian bands fits the experimental spectrum of the strained-SOI device demonstrating the suitability of this characterization technique on such a "complex" stacked device.…”

Combining high resolution and tensorial analysis in Raman stress measurements of silicon

“…It is generally possible to measure all phonon polarizations with Raman spectroscopy, but, up to the present, it has been done only by sacrificing the high spatial resolution. 2,3 This article presents the detailed explanation of the method we recently proposed 4 for the measurement of other phonon polarizations without renouncing high spatial resolution. The method does not completely solve the problem of making assumptions about the shape of the stress tensor, however, because it still requires an estimation of three degrees of freedom out of six.…”