Determination of the total emittance of n-type GaAs with application to Czochralski growth

Abstract

We have calculated the total emittance εt of n-type GaAs as a function of doping level and thickness in the temperature range between 300 and 1500 °K. εt is related to the spectral emittance ελ, which in turn depends on the index of refraction, thickness, and absorption coefficient α. To obtain a theoretical representation of α, a model is constructed which includes contributions by the fundamental edge, interconduction band, and free carriers (acoustic and optical phonons and ionized impurities). Since this two-parameter model offers a good description of assorted α measurements with respect to wavelength, impurity level, and temperature, the evaluation of ελ is relatively straightforward. At each temperature, εt is computed by the numerical integration of ελ over a wide wavelength range followed by normalization to σT4. The calculations show that εt increases with temperature and doping level. At 1300 °K, for a 1-cm-thick sample, as the carrier concentration rises from 1016 to 1017 cm−3, εt increases from 0.28 to 0.68, respectively. These results are compared with those for Ge and general comments are made on the εt of p-type and semi-insulating GaAs. Finally, employing εt as one of the parameters in the quasi-steady state heat transfer/thermal stress model for dislocation generation in the Czochralski growth of GaAs, we explain the inherent difficulty encountered in pulling sizable defect-free crystals in terms of the severe thermal strss generation in excess of the critical resolved shear stress. One realistic set of conditions that would lead to a dislocation-free GaAs is small diameter (∼1 cm), light doping concentration (∼1016 cm−3), and shallow ambient temperature gradient (<100 °K).