An emissivity-invariant condition for a silicon wafer was determined by simulation modeling and it was confirmed experimentally. The p-polarized spectral emissivity at a wavelength of 900 nm and at temperatures over 900 K was constant at 0.83 at an angle of about 55.4° irrespective of large variations in the oxide layer thickness and the resistivity due to the different impurity doping concentrations of the silicon wafer. The expanded uncertainty, U(c) = ku(c) (k = 2), of the temperature measurement is estimated to be 4.9 K. This result is expected to significantly enhance the accuracy of radiometric temperature measurements of silicon wafers in actual manufacturing processes.

The temperature dependence of silicon wafer transmittance is well understood, and is caused by various absorption mechanisms over a wide spectral range. As the wavelength increases, the photon energy decreases until it becomes lower than the minimum energy gap in the silicon band structure. At this point, which is often referred to as the absorption edge wavelength, there is a rapid drop in absorption. The absorption edge shifts to a longer wavelength with increasing temperature, because the bandgap narrows with increasing temperature. Experiments were carried out with varying wavelength (900 nm to 1700 nm), polarization (p-and s-polarized), and direction (from normal to 80 • ), using specimens with different resistivities (0.01 · cm to 2000 · cm). A characteristic curve relating the absorption edge wavelength and temperature was obtained for all of the silicon wafers, despite their differing resistivity. This method enables in situ temperature measurements of silicon wafers from room temperature to 900 K, using wavelengths to which the wafer is semitransparent. In this article, an experimental apparatus and measurement results are described in detail, and several remaining problems are discussed.

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We studied the spectral and directional emissivities of silicon wafers using an optical polarization technique. Based on simulation and experimental results, we developed two radiation thermometry methods for silicon wafers: one is based on the polarized emissivity-invariant condition and the other is based on the relationship between the ratio of the p- and s-polarized radiance and the polarized emissivity. These methods can be performed at temperatures above 600 °C and over a wide wavelength range (0.9-4.8 μm), irrespective of the dielectric film thickness and the substrate resistivity, which depends on the dopant concentration. The temperature measurements were estimated to have expanded uncertainties (k = 2) of less than 5 °C. With a view to practically applying these methods, we investigated a method to reduce the intense background radiance produced by high-intensity heating lamps. We found that the background radiance can be greatly reduced by using a radiometer that is sensitive to wavelengths of 4.5 or 4.8 μm and suitable geometrical arrangements of a quartz plate. This opens up the possibility of using the two proposed radiation thermometry methods in practical applications.

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