Abstract
Monocrystalline silicon (c-Si) is still an important material related to microelectronics/optoelectronics. The nondestructive measurement of the c-Si material and its microstructure is commonly required in scientific research and industrial applications, for which Raman spectroscopy is an indispensable method. However, Raman measurements based on the specific fixed Raman geometry/polarization configuration are limited for the quantified analysis of c-Si performance, which makes it difficult to meet the high-end requirements of advanced silicon-based microelectronics and optoelectronics. Angle-resolved Raman measurements have become a new trend of experimental analysis in the field of materials, physics, mechanics, and optics. In this paper, the characteristics of the angle-resolved polarized Raman scattering of c-Si under the in-axis and off-axis configurations are systematically analyzed. A general theoretical model of the angle-resolved Raman intensity is established, which includes several alterable angle parameters, including the inclination angle, rotation angle of the sample, and polarization directions of the incident laser and scattered light. The diversification of the Raman intensity is given at different angles for various geometries and polarization configurations. The theoretical model is verified and calibrated by typical experiments. In addition, this work provides a reliable basis for the analysis of complex polarized Raman experiments on silicon-based structures.
Highlights
Monocrystalline silicon (c-Si) plays a core role in the advanced manufacturing of optoelectronic and microelectronic devices, with microelectromechanical system (MEMS) being an important semiconductor material [1, 2]
Using the Raman tensors given by Loudon [16], Anastassakis [17] set up a theoretical model of Raman mechanics
According to (20) and (21), Figure 19 shows the distribution of the Raman intensity with the polarization direction, which clearly indicates that neither refraction nor depolarization is ignorable in the angle-resolved Raman measurement: INRND ∝ sin22φ + 0.75 cos4 φ, IND ∝ sin22φ + 0.06 cos4 φ, (20)
Summary
Monocrystalline silicon (c-Si) plays a core role in the advanced manufacturing of optoelectronic and microelectronic devices, with microelectromechanical system (MEMS) being an important semiconductor material [1, 2]. To reveal the influence of the inclination angle β on the Raman intensity for different sample rotation angles α and polarization directions φ, several three-dimensional diagrams are achieved based on (15), as shown in Figures 5 to 7. E trend and period of the change in Raman intensity with the polarization direction and sample rotation angle are different due to the visible TO modes. Different from those under the vertical backscattering configuration, the TO1 and TO2 Raman modes are visible (nonzero) under the oblique backscattering configuration. TO1 mode TO2 mode LO mode Figure 4: Raman intensity distribution of vertical backscattering without an analyzer
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