A Model for the High Temperature Transport Properties of Heavily Doped P-Type Silicon-Germanium Alloys
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A MODEL FOR THE HIGH TEMPERATURE TRANSPORT PROPERTIES OF HEAVILY DOPED P-TYPE SILICON-GERMANIUM ALLOYS. CRONIN B. VINING Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 ABSTRACT A model is presented for the high temperature transport properties of large grain size, heavily doped p-type silicon-germanium alloys. Good agreement with experiment (±10%) is found by considering acoustic phonon and ionized impurity scattering for holes and phonon-phonon, point defect and hole-phonon scattering for phonons. Phonon scattering by holes is found to be substantially weaker than phonon scattering by electrons, which accounts for the larger thermal conductivity values of ptype silicon-germanium alloys compared to similarly doped n-type silicongermanium alloys. The relatively weak scattering of long-wavelength phonons by holes raises the possibility that p-type silicon-germanium alloys may be improved for thermoelectric applications by the addition of an additional phonon scattering mechanism which is effective on intermediate and long-wavelength phonons. Calculations indicate improvements in the thermoelectric figure of merit up to 40% may be possible by incorporating several volume percent of 20 A radius inclusions into p-type silicon-germanium alloys. INTRODUCTION Silicon-germanium (SiGe) alloys are the current material of choice for the active elements in radioisotope thermoelectric generators (RTG's)1 which provide reliable electrical power for the Voyager and Galileo spacecrafts. Recent improvements in thermoelectric figure of merit values 2 ensure that these materials will play a vital role in space power systems for some time to come. Since even modest improvements in thermoelectric performance can result in substantial savings due to the high cost of fuels for RTGs, better theoretical models for their transport properties would be very useful. The purpose of this study is to develop a physically reasonable model for the high temperature properties of p-type SiGe alloys which treats all of the transport properties on a reasonably consistent footing. An essentially similar model has been recently developed for n-type SiGe alloys 3, and the present model is closely patterned after that work. Such Mat. Res. Soc. Symp. Proc. Vol. 234. 01991 Materials Research Society
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models provide a baseline for examining the potential for improving the performance of the material through various modifications, such as doping optimization and by the incorporation of phonon scattering centers. Fortunately, the physical understanding of transport in silicon and SiGe alloys is relatively mature. A model is available for the mobility of ptype silicon"'5 which accurately reproduces the mobility and resistivity of p-type silicon over a wide range of temperature and doping levels. Some calculations are available for the mobility of SiGe alloys as well.6'7'8 Detailed models for the thermal conductivity of SiGe alloys are available 0 for low temperatures, 9 high temperatures and high doping levels,1' 11 and hav
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