Modeling the radiative properties of microscale random roughness surfaces

The radiative properties of engineering surfaces with microscale surface texture or topography (patterned or random roughness and coating or multi-layer) are of fundamental and practical importance. In the rapid thermal processing or arc/flash-assisted heating of silicon wafers, the control of thermal energy deposition through radiation and the surface temperature measurement using optical pyrometry require in-depth knowledge of the surface radiative properties. These properties are temperature, wavelength, doping level, and surface topography dependent. It is important that these properties can be modeled and predicted with high accuracy to meet very stringent temperature control and monitor requirements. This study solves the Maxwell equations that describe the electromagnetic wave reflection from the one-dimensional random roughness surfaces. The surface height conforms to the normal distribution, i.e., a Gaussian probability density function distribution. The numerical algorithm of Maxwell equations' solution is based on the well-developed finite difference time domain (FDTD) scheme and near-to-far-field transformation. Various computational modeling issues that affect the accuracy of the predicted properties are quantified and discussed. The model produces the bi-directional reflectivity and is in good agreement with the ray tracing and integral equation solutions. The predicted properties of a perfectly electric conductor and silicon surfaces are compared and discussed.