Spectral Emissivity & Emittance

by N.M. RAVINDRA,(1,5) KRSHNA RAVINDRA,(1,2) SUNDARESH MAHENDRA,(1,3) BHUSHAN SOPORI,(4) and ANTHONY T. FIORY(1)
1.—Department of Physics, New Jersey Institute of Technology, Newark, NJ 07102. 2.—Intern atNJIT from Union County Magnet High School, Scotch Plains, NJ 07076. 3.—Intern at NJIT fromMillburn High School, Millburn, NJ 07041. 4.—National Renewable Energy Laboratory, Golden, CO 80401. Journal of ELECTRONIC MATERIALS, Vol. 32, No. 10, 2003, (Downloadable PDF Format)

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 ?m, and its emissivity is almost temperature independent; and (5) SIMOX exhibits significant changes in emissivity in the wavelength range of 1–20 um.”

by Curt H. Liebert and Ralph D. Thomas, NASA Lewis Research Center (Downloadable PDF File), APRIL 1968.

SUMMARY
“Measurements were made at temperatures of 300°, 882′, and 1074′ K of the normal was doped with a r s e n i c spectral emissivity of opaque, highly doped silicon. The silicon and boron to electron carrier concentrations of 2. 2X101′, 3. %lo1′, and 8 . 5 ~ 1 0 ~ ‘ electrons per cubic centimeter and hole carrier concentrationsof 6. 2X101′ and 1 . 4 ~ 1 0 holes per cubic centimeter. The 30 K emissivity data were obtained at wavelengths from 2.5 to 35 microns. The high temperature emissivities were measured from 3.5 to 1 4 . 8 microns. Carrier concentrations and direct-current resistivity of the silicon were also measured. The carrier concentrations were determined from Hall measurements made at 30 K. The direct-current resistivity was measured at temperatures from 30 to 1200′ K. These quantities (among others) were used in analytical calculations of the emissivities. Agreement of the Hagan-Rubens theory with experiment was found at wavelengths greater than 12 microns and at 30 K. Good agreement of the free carrier absorption theory with experiment w a s achieved at all wavelengths and temperatures investigated. The free carrier absorption theory predicts the emissivity in terms of the index of of these quantities are presented. A refraction and the absorption index. The values comparison of the values of the absorption index obtained herein with those obtained from the literature showed good qualitative agreement.”

By P. J. Timans , Microelectronics Research Centre, Cavendish Laboratory, Cambridge University, Madingley Road, Cambridge CB3 0HE, United Kingdom Journal of Applied Physics — November 15, 1993 — Volume 74, Issue 10, pp. 6353-6364