Hall Effect in Gray Tin Filaments

The measurement of the Hall coefficient of gray tin filaments in the temperature range from 70 to 270°K is described. It is found that electron and hole mobilities given by the expressions ${\mu }_n=3.02\mathrm{}\times {10}^7{T}^{-1.65\mathrm{}}$ ${\mathrm{cm}}^2$/volt sec and ${\mu }_p=2.18\mathrm{}\times {10}^8{T}^{-2.0\mathrm{}}$ ${\mathrm{cm}}^2$/volt sec combined with an impurity concentration of 2.5×${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$ give a good fit to the conductivity and Hall data for pure material in the range extending 110 degrees down from the highest measurement temperature. The intrinsic energy gap at absolute zero is 0.094 ev. If one assumes a temperature dependence of -5×${10}^{-5\mathrm{}}$ ev/deg, the high-temperature value of the energy gap remains substantially unaltered from that previously reported and the effective masses of charge carriers have the value 0.68 electron masse. Data for the lower temperature range indicate slight degeneracy and impurity scattering of charge carriers. Similar computations and results are discussed for other samples doped with $n$-type impurities. In contradiction to the results for $n$-type samples, $p$-type samples indicate mobility ratios slightly higher than unity. There is no indication, however, of extremely high mobility ratios such as those found in InSb. The field dependence of the Hall coefficient of $p$-type specimens shows a shift of the crossover to higher temperatures with increasing magnetic field, qualitatively in agreement with isotropic theory.