Measurement and Modeling of the Bidirectional Reflectance of SiO2 Coated Si Surfaces

Abstract

An understanding of the variation of directional radiative properties of rough surfaces with dielectric coatings is important for temperature measurements and heat transfer analysis in many industrial processes. An experimental study has been conducted to investigate the effect of coating thickness on the bidirectional reflectance distribution function (BRDF) of rough silicon surfaces. Silicon dioxide films with thicknesses of 107.2, 216.5, and 324.6 nm were deposited using plasma-enhanced chemical vapor deposition onto the rough side of two Si wafers. The wafer surfaces exhibit distinct anisotropic characteristics as a result of chemical etching during the manufacturing process. A laser scatterometer measures the BRDF at a wavelength of 635 nm, after improvement of the signal-to-noise ratio. The slope distribution function obtained from the measured BRDF of uncoated Si surfaces was used in an analytical model based on geometric optics for rough surface scattering and thin-film optics for microfacet reflectance. The predicted BRDFs are in reasonable agreement with experimental results for a large range of coating thicknesses. The limitations of the geometric optics for modeling the BRDF of coated anisotropic rough surfaces in the specular direction are demonstrated. The results may benefit future radiative transfer analysis involving complicated surface microstructures with thin-film coatings.

Radiative properties of materials with surface scattering or volume scattering: A review

“…(7). Rather than relying on the AFM measurement, Lee and Zhang [50] obtained SDFs from BRDF measurements of rough surfaces by virtue of an inverse method. Their method allows the error reduction due to surface characterization and takes less time compared with the AFM topography measurement.…”

“…Lee and Zhang [50] investigated SiO 2 coating effects on BRDF using the SDF obtained from the BRDF measurement of bare surfaces instead of that from AFM measurement. The BRDF of Si-2 at normal incidence is shown in Fig.…”

“…In-plane BROFs of Si-2 with different coating thicknesses for random polarization at normal incidence[50] (a) h = 0; (b) h = 107.2 nm; (c) h = 216.5 nm; (d) h = 324.6 nm…”

A Hybrid Partial Coherence and Geometry Optics Model of Radiative Property on Coated Rough Surfaces

“…Figure 4 plots comparison of the directional-hemispherical reflectance solved by HPCGO model, micro facet slope method (MSM), and FDTD method, respectively. MSM is one of the raytracing techniques, which was applied for modeling the BRDF using the Monte Carlo method [10,11]. For an incident ray, only the normal vector of a microfacet determines the reflection direction of rays and the reflectivity according to Fresnel's formula.…”

Measurement and Modeling of the Emittance of Silicon Wafers with Anisotropic Roughness

“…Zhu and Zhang [6] incorporated the anisotropic slope distribution function, obtained from the topographic measurements made using an atomic force microscope (AFM), into an analytical model of the bidirectional reflectance distribution function (BRDF). Lee and Zhang [7] extended the model-based approach to silicon wafers with thin-film coatings and studied the combined effect of coating and anisotropic roughness on the BRDF. Using the Monte Carlo method, Lee et al [8] developed ray-tracing techniques and obtained good agreement with measurements for both in-plane and outof-plane BRDFs.…”