Coulomb Screening in Intrinsic Medium-Gap Semiconductors and the Electrical Conductivity of Silicon at Elevated Temperatures

As the temperature of medium-gap intrinsic semiconductors is raised and the concentration of charge carriers increases beyond ${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$, the average distance between the charges will have decreased sufficiently for the electrostatic interaction energy between each charge and its neighbors to be an appreciable fraction of the width of the forbidden energy region. From this point onwards, and through the onset of degeneracy, the temperature dependence of the concentration and of the width of the energy gap will depend appreciably upon this energy. It is the object of this paper to give an account of this phenomenon; to compute the temperature variation of the concentration, of the energy gap, and of the Herring screening length; and to compare these results to experimental values deduced from the measurement of the electrical conductivity of silicon from 500°K up to about 50° away from the melting point. An estimate of the effective conductivity mobility for the high-temperature range is also presented.