Study on the Photoelastic Constant of 4H-SiC +
PAM-XIAMEN is able to offer conductive and semi-insulating 4H-SiC substrates for experimental research. For more specifications, please contact [email protected]
As the diameter of silicon carbide (SiC) substrates continues to increase, the uniformity of residual strain inside them becomes a key factor affecting device performance and reliability. Traditional strain detection methods such as X-ray diffraction and Raman spectroscopy have high accuracy, but their measurement speed is slow and the area is limited, making them unsuitable for large-sized substrates. In contrast, photoelastic technology has the advantages of fast and full field measurement, especially suitable for residual strain imaging of SiC substrates.
The core of photoelastic technology lies in the accurate acquisition of the photoelastic constant. This constant describes the sensitivity of a material to changes in refractive index under stress, and is the physical basis for achieving quantitative conversion from birefringence measurement to stress measurement. However, the study of the photoelastic constant of 4H-SiC is still insufficient, especially its variation with wavelength has not been systematically explored.
1. Fundamentals and Constant Definitions of Photoelastic Technology
The photoelastic effect can be described by the stress optical law. For hexagonal crystals such as 4H-SiC, they exhibit optical isotropy in the (0001) plane, and the photoelastic effect can be simplified as:
In the formula, Δn is birefringence, σ1−σ2 is the main stress difference, π11− π12 is the piezoelectric coefficient, which can also be converted into the photoelastic constant Cσ. In practical applications, ∣p11−p12∣ is often used as a characterization parameter for the photoelastic coefficient.
2. Experimental Methods and Determination of Photoelastic Constants
The accurate determination of the photoelastic constant is the key to achieving quantitative analysis of residual stress. Researchers have developed different experimental methods for 4H-SiC materials, ranging from traditional three-point bending testing to advanced wafer level scanning technology, providing diversified solutions for obtaining reliable photoelastic parameters.
2.1 Three Point Bending Method and Multi Wavelength Measurement
Fukuzawa et al. conducted three-point bending experiments on 4H-SiC substrate using a self-developed imaging polarizer (xIPS) at three wavelengths of 630nm, 940nm, and 1200nm. By measuring the birefringence distribution ∣Δn∣ and combining it with the ∣σ1−σ2∣ distribution obtained from finite element simulation, regression analysis is performed to obtain ∣p11−p12∣.
Fig. 1 Linear relationship between Δn and σ1−σ2
The experimental results showed that ∣p11−p12∣ were 0.040, 0.090, and 0.13 at 630nm, 940nm, and 1200nm, respectively, indicating that the coefficient increases with wavelength.
2.2 SIRD System and Centrifugal Loading Method
Hermes et al. conducted radial loading experiments on (0001) 4H SiC substrates using a scanning infrared depolarizer (SIRD) at a wavelength of 1300 nm. By adjusting the loading force by changing the rotation frequency, the equivalent value of shear stress G is measured, and the compression coefficient (π11−π12)=(−3.3±0.5)×10-13Pa−1 and the photoelastic constant Cσ=(−2.8±0.4)×10-12 Pa−1 are derived. Although the high defect density and non-uniformity of the studied material result in relatively large errors, the obtained values are in good agreement with a few existing data in the literature and are suitable as standard parameters for quantitative stress analysis of similar wafers.
Fig. 2 Linear relationship with (G-G0) and the square of the rotation frequency
By combining the three-point bending method with SIRD centrifugal loading method, researchers not only obtained the key photoelastic parameters of 4H-SiC in the visible to infrared wavelength range, but also established a complete stress quantitative analysis capability from laboratory samples to industrial grade wafers.
3. Wavelength Dispersion Phenomenon and Technological Trade-Offs
Fukuzawa et al. first systematically revealed the significant wavelength dispersion behavior of the photoelastic coefficient ∣p11−p12∣ in the visible to near-infrared wavelength range. The research results indicate that the value of this coefficient increases monotonically with wavelength, and this trend is inversely proportional to photon energy, which is a common physical phenomenon in cubic and hexagonal crystals, and is consistent with Adachi’s theoretical and experimental research conclusions on III-V semiconductors.
Fig. 3 Trend of ∣p11−p12∣ with wavelength variation
More importantly, the dispersion curve strongly suggests that the value of ∣p11−p12∣ may approach zero at a wavelength shorter than 630nm. This discovery has had a profound impact on the practical application of photoelastic imaging technology, as it directly introduces the core trade-off between photoelastic sensitivity and measurement signal-to-noise ratio (SNR). This discovery has important guiding significance for wavelength selection in photoelastic imaging:
Short wavelength: Photon energy is high, SNR is excellent, which helps detect weaker signals; However, the sensitivity of photoelasticity is low, and the optical response generated under the same stress is very small, which is not conducive to accurately quantifying strain;
Long wavelength: high sensitivity to photoelasticity, greatly improving the sensitivity of stress/strain detection; But the SNR is poor, and in order to obtain measurable signals, longer exposure times or higher power light sources may be required, which may affect measurement speed or cause thermal effects on the sample.
Therefore, a balance needs to be struck between sensitivity and signal-to-noise ratio in practical applications. Future research can be further expanded to shorter or longer wavelength ranges, combined with low defect density samples, to improve measurement accuracy and optimize wavelength selection strategies for imaging systems.
Whether you need 4H-SiC wafer for research or for industrial applications, please contact us email at [email protected] and [email protected].
References:
- Fukuzawa, M., & Kudo, N. (2023). Experimental study on the photoelastic coefficient and its wavelength dispersion for quantitative imaging of residual strain in commercial sic substrates. Journal of Electronic Materials, 52(8), 5172-5177.
- Herms, M., Irmer, G., Spira, S., & Wagner, M. (2021). The photoelastic constant of (0001) 4H silicon carbide determined by scanning infrared polariscopy. physica status solidi (a), 218(23), 2100198.