Grain orientation, texture, and internal stress optically evaluated by micro-Raman spectroscopy

Abstract

We present a method to experimentally determine the components of stress tensors within grains of multicrystalline materials by micro-Raman spectroscopy. This method is applied to multicrystalline silicon wafers as they are produced for solar cells. Currently, μ-Raman spectroscopy is intensively used to measure stresses in silicon wafers, structures, and devices of known crystallographic orientations. For these cases, the determination of stresses from Raman peak shifts is straightforward. In multicrystalline silicon, however, arbitrary grain orientations complicate the determination of stress tensor components, which depend on the crystallographic orientations of the particular grains. The Raman intensities depend on the polarization direction of the incident and scattered laser light and again on the crystallographic grain orientations. This intensity dependence is used to determine the crystallographic grain orientations. Once the orientation is determined, the components of the stress tensor (with respect to a fixed reference coordinate system—the sample stage), can be calculated numerically from the Raman peak shifts. As examples, we determine (i) the stress components of a nearly plane stress state around the tip of a microcrack and (ii) the stress components at a grain boundary in a multicrystalline silicon wafer.

Measurement of the Euler Angles of Wurtzitic ZnO by Raman Spectroscopy

“…Munisso et al also employed this method to determine the crystallographic orientation of polycrystalline alumina [13]. The Euler angles of multicrystalline silicon have been determined by Becker et al with Raman spectroscopy during the stress measurement, though this method involves complicated formulas and tedious calculations [14]. The validity of the Raman polarization analysis for the crystallographic orientation determination of the diamond and sapphire crystal has been demonstrated.…”

“…In any coordinate system, the Raman intensity can be expressed as [14] I α, β, φ, θ, ψ = C e i ⋅ Φ xyz R j Φ xyz ⋅ e s In order to simplify f ij , the values of θ c and ψ c are substituted into the expression f ij . Thus, we can explicitly obtain a set of general expressions that depend on φ.…”

“…The mirrors and the notch filter will also affect the polarization direction of the scattering light. The effective polarization vector e s of the scattering beam can be written as [14] e s = m ⋅ cos β, sin β, 0 T , 23…”

“…Suppose the primary optical axis of the λ/2 wave plate is initially parallel to the polarization direction of incident light. Then, the polarization vector of the incident beam depends on the λ/2 wave plate's rotation angle (γ) and can be written as [14] e s = cos α, r ⋅ sin α, 0 , 22…”

Raman Study of Multicrystalline Silicon Wafers Produced by the RST Process

“…An iterative method described in a previous work was used to take into account the occurrence of asymmetrical growth [6]. Due to the lack of data on the A detailed calculation of the stress from the Raman shift would require the knowledge of the crystal orientation [8];…”