Emissivity of silicon at elevated temperatures

The temperature dependences of the spectral and total hemispherical emissivities of silicon have been experimentally determined, by using a technique which combines isothermal electron beam heating with in situ optical measurements. Emission spectra were used to deduce the absorption coefficient for phosphorus-doped silicon samples for wavelengths between 1.1 and 1.6 μm, in the temperature range from 330 to 800 °C. For lightly doped samples, the data show good agreement with a model which includes the effects of the various phonon-assisted processes involved in interband transitions in silicon, as well as the free-carrier absorption. For heavily doped samples the agreement was less satisfactory, possibly because of inadequacies in the model for free-carrier absorption. It was shown that reflection spectra can also be used to determine the absorption spectrum, for the range where the absorption coefficient lies between 1 and ∼70 cm−1. By fitting the theoretical model to the absorption coefficients derived from the reflection spectrum, it is possible to deduce the temperature of a sample, which is especially useful for temperatures less than 300 °C, where the thermal emission is very weak. The total hemispherical emissivity of the specimens was determined from the input electron-beam power densities and the measured temperatures. The total emissivity of a 390-μm-thick specimen of lightly doped silicon rises from 0.12 at 280 °C to a limiting value of 0.7 at 650 °C. This behavior is a consequence of the increase in the free-carrier concentration with the temperature. For heavily doped specimens the total emissivity remains approximately constant at ∼0.7 between 200 and 800 °C because the carrier concentration is high even at room temperature, and the additional thermal generation of carriers produces an insignificant change in the total emissivity.