Modeling and simulation of emissivity of silicon-related materials and structures

Abstract

A brief review of the models that have been proposed in the literature to simulate the emissivity of silicon-related materials and structures is presented. The models discussed in this paper include ray tracing, numerical, phenomenological, and semi-quantitative approaches. A semi-empirical model, known as Multi-Rad, based on the matrix method of multilayers is used to evaluate the reflectance, transmittance, and emittance for Si, SiO₂/Si, Si₃N₄/SiO₂/Si/SiO₂/Si₃N₄ (Hotliner), and separation by implantation of oxygen (SIMOX) wafers. The influence of doping concentration and dopant type as well as the effect of the angle of incidence on the radiative properties of silicon is examined. The results of these simulations lead to the following conclusions: (1) at least within the limitations of the Multi-Rad model, near the absorption edge, the radiative properties of Si are not affected significantly by the angle of incidence unless the angle is very steep; (2) at low temperatures, the emissivity of silicon shows complex structure as a function of wavelength; (3) for SiO₂/Si, changes in emissivity are dominated by substrate effects; (4) Hotliner has peak transmittance at 1.25 µm, and its emissivity is almost temperature independent; and (5) SIMOX exhibits significant changes in emissivity in the wavelength range of 1–20 µm.