Measurement and modeling of the emittance of silicon wafers with anisotropic roughness

The unpolished surface of crystalline silicon wafers often exhibits non-Gaussian and anisotropic roughness characteristics, as evidenced by the side peaks in the slope distribution. This work investigates the effect of anisotropy on the emittance. The directional-hemispherical reflectance of slightly and strongly anisotropic silicon wafers was measured at room temperature using a center-mount integrating sphere. A monochromator with a lamp was used for near-normal incidence in the wavelength region from 400-1000 nm, and a continuous-wave diode laser at the wavelength of 635 nm was used for measurements at zenith angles up to 60 degrees. The directional emittance was deduced from the measured reflectance based on Kirchhoff's law. The geometric-optics-based Monte Carlo model that incorporates the measured surface topography is in good agreement with the experiment. Both the experimental and modeling results suggest that anisotropic roughness increases multiple scattering, thereby enhancing the emittance. On the other hand, if the wafer with strongly anisotropic roughness were modeled as a Gaussian surface with the same roughness parameters, the predicted emittance near the normal direction would be lower by approximately 0.05, or up to 10% at a wavelength of 400 nm. Comparisons also suggest that the Gaussian surface assumption is questionable in calculating the emittance at large emission angles with s polarization, even for the slightly anisotropic wafer. This work demonstrates that anisotropy plays a significant role in the emittance enhancement of rough surfaces. Hence, it is imperative to obtain precise surface microstructure information in order to accurately predict the emittance, a critical parameter for non-contact temperature measurements and radiative transfer analysis.