Silicon emissivity as a function of temperature

In this paper we present the temperature-dependent emissivity of a silicon sample, estimated from its cool-down curve in a constant low temperature environment ($approx$ 82K). The emissivity value follow a linear dependency in the 120-260 K temperature range. This result is of great interest to the LIGO Voyager gravitational wave interferometer project since it would mean that no extra high thermal emissivity coating on the test masses would be required in order to cool them down to 123 K. The results presented here indicate that bulk silicon itself can have sufficient thermal emissivity in order to cool the 200 kg LIGO Voyager test masses only by radiation in a reasonable short amount of time (less than a week). However, it is still not clear if the natural emissivity of silicon will be sufficient to maintain the LIGO Voyager test masses at the desired temperature (123 K) while removing power absorbed by the test masses. With the present results, a black coating on the barrel surface of the test masses would be necessary if power in excess of 6 W is delivered. However, the agreement we found between the hemispherical emissivity obtained by a theory of semi-transparent Silicon and the obtained experimental results makes us believe that the LIGO Voyager test masses, because of their dimensions, will have effective emissivities around 0.7, which would be enough to remove about 8.6 W (7.5 W) for a shield at 60 K (80K). This hypothesis may be confirmed in the near future with new measurements.