Lab-grown Diamond Retardance Correlates with Thickness: Anisotropic Behaviour Demonstrates Linear and Square Root Relationships

Birefringence, or the splitting of light into two rays, significantly impacts the performance of diamond substrates used in advanced technologies, and a new study investigates how this phenomenon changes with substrate thickness. Thanh Tran, Phuong Vo, and Thomas Sheppard, from Great Lakes Crystal Technologies, Inc., alongside Timothy Grotjohn from Michigan State University and Paul Quayle from Great Lakes Crystal Technologies, Inc., present a detailed analysis of retardance, a measure of this light splitting, in diamond wafers grown using a specialised technique. Their work reveals that retardance behaves differently depending on the direction relative to the growth of the diamond, exhibiting a square root relationship for one orientation and a linear correlation for the other. Crucially, the team demonstrates this anisotropy stems from how stress aligns between layers within the diamond, and they developed a novel model, based on a momentum-drift random walk, to accurately predict and explain these observations, offering a quantitative understanding of birefringence with important implications for thermal management, high-power electronics, and optical applications.

HPHT Diamond Growth, Defect Characterisation and Quantification

This research presents a detailed analysis of defects, specifically dislocations, within single-crystal diamond wafers grown using the High-Pressure/High-Temperature (HPHT) method. Understanding these defects is crucial for improving the performance of diamond-based devices in electronics, optics, and quantum technologies. Scientists employed birefringence imaging, a technique that visualizes strain within the crystal, to map the distribution of these imperfections, exploiting how dislocations alter the polarization of light. Researchers captured images of the diamond wafers using a polarized light microscope and processed them to generate retardance and azimuth maps, revealing the magnitude and orientation of strain at each point.

Analysis involved correlating maps from different layers to understand how dislocations propagate through the material, and a random walk model, simulating dislocation movement, was used to estimate a momentum factor influencing their direction. The model was refined by optimizing its fit to experimental data, achieving strong correlation between simulation and observation. The data demonstrates that dislocation density varies with depth within the wafers, and that dislocations do not propagate equally in all directions, suggesting a preferred orientation for their movement. The optimized momentum factor from the random walk model significantly influences predicted dislocation propagation, validating the model’s accuracy. This research provides a detailed understanding of defect distribution and propagation, offering valuable insights into the HPHT growth process and enabling the development of higher-quality diamond materials.

Retardance and Thickness in Diamond Substrates

Scientists investigated the relationship between mean retardance and thickness in diamond substrates grown via microwave plasma-enhanced chemical vapor deposition. Birefringence measurements revealed that retardance differs depending on the orientation of the measurement relative to the growth direction. Researchers measured phase retardation and azimuth angle to quantify the optical properties of the diamond samples. The experimental design revealed a near-proportional relationship between retardance and the square root of thickness when measured perpendicular to the growth direction. In contrast, measurements parallel to the growth direction exhibited a generally higher retardance and an approximately linear correlation with thickness, indicating a directional dependence of stress within the diamond lattice.

To model this behavior, the team developed a two-dimensional random walk model with momentum drift, designed to capture the tendency of the diamond crystal to maintain a consistent orientation of stress across layers. By optimizing the momentum factor within the model, scientists achieved close agreement with experimental data, demonstrating the model’s ability to accurately simulate the observed retardance behavior. The optimized momentum factor was found to be higher along the growth direction, aligning with calculated correlation coefficients between the azimuth angles of consecutive layers. Both the model and experiments confirmed that retardance-to-thickness ratios converged toward similar base retardances in both orientations for thin samples, establishing a quantitative framework for interpreting birefringence in diamond substrates. This work provides a crucial foundation for material selection and development in applications such as thermal management and high-power electronics, where precise control of stress is paramount.

Retardance Anisotropy Correlates with Diamond Thickness

Researchers investigated the relationship between mean retardance and thickness in diamond substrates grown via microwave plasma-enhanced chemical vapor deposition. They measured retardance in two orientations, perpendicular and parallel to the growth direction, and discovered distinct correlations. When measured perpendicular to the growth direction, the mean retardance exhibited approximate proportionality to the square root of the substrate thickness, while measurements parallel to the growth direction revealed a generally higher mean retardance and an approximately linear correlation with thickness. This anisotropy arises not from variations in stress magnitude, but from differences in the interlayer correlation of the principal stress axes, as evidenced by correlation coefficients between consecutive layers within the diamond crystal.

To model the integrated retardance of diamond wafers, the team developed a two-dimensional random walk model incorporating momentum drift, which effectively captures the diamond crystal’s tendency to maintain the azimuth angle across samples. Optimization of the momentum factor allowed the model to closely match experimental data, with the factor found to be higher along the growth direction, consistent with calculated correlation coefficients. Furthermore, both the model and experiments demonstrate that retardance-to-thickness ratios of thin samples converge toward similar base retardances in both orientations. These findings establish a quantitative framework for interpreting birefringence in diamond substrates, with implications for material selection and development in thermal management, high-power electronics, and optical applications. The research provides a detailed understanding of stress distribution within diamond, crucial for optimizing material quality and performance in advanced technologies.

Birefringence Anisotropy in Diamond Substrates

This work establishes a quantitative understanding of birefringence in diamond substrates grown via microwave plasma-enhanced chemical vapor deposition. Researchers demonstrated that the relationship between mean retardance and substrate thickness differs depending on the measurement orientation relative to the growth direction. Specifically, retardance correlates with the square root of thickness when measured perpendicular to the growth direction, and with thickness itself when measured parallel to it. This anisotropy arises from variations in the correlation of principal stress axes between layers within the diamond crystal, not simply from differences in stress magnitude.

To model this behavior, the team developed a two-dimensional random walk model incorporating a momentum drift, effectively capturing the tendency of the diamond crystal to maintain a consistent azimuth angle across layers. By optimizing the momentum factor within the model, they achieved close agreement with experimental data, further validating the proposed mechanism. Importantly, the research indicates that retardance-to-thickness ratios converge toward similar values in both orientations for thin samples. The authors acknowledge that while processing steps like laser cutting and polishing were carefully controlled to minimize induced stress, some residual effects may be present. Future work could focus on refining the model to account for more complex crystal structures and exploring the impact of different growth conditions on birefringence. These findings provide a crucial framework for material selection and development in applications requiring precise control of light polarization, including thermal management and high-power electronics.