Transverse Hall and Magnetoresistance Effects in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi></mml:math>-Type Germanium

Abstract

Modification of the two-band model to include existence of a small number of high-mobility holes permits calculations of the magnitude, temperature dependence, and magnetic-field dependence of Hall and magnetoresistance effects in high-purity $p$-type germanium, which are in excellent quantitative agreement with experimental data. For a specimen containing 4.3\ifmmode\times\else\texttimes\fi{}${10}^{13}$ acceptors/${\mathrm{cm}}^{3}$, the data indicate at 300\ifmmode^\circ\else\textdegree\fi{}K the presence of 1.1\ifmmode\times\else\texttimes\fi{}${10}^{12}$ positive carriers/${\mathrm{cm}}^{3}$ with a mobility of 15 000 ${\mathrm{cm}}^{2}$/volt-sec. At 205\ifmmode^\circ\else\textdegree\fi{}K these high-mobility holes increase the magnetoresistance at weak fields by a factor of 25 and the Hall coefficient by 1.6. Results indicate that Hall mobilities computed by taking the product $R\ensuremath{\sigma}$ must be interpreted with caution, or unwarranted inferences may be drawn. For the specimens studied, mobilities computed from the Hall data, by using equations based on spherical energy surfaces but taking into account the fast holes and the values of the magnetic fields, agree within experimental error with the values obtained by other methods. Discussion of the fast holes in connection with valence band degeneracy, cyclotron resonance observations, and interband optical transitions is given. The desirability of using data taken at large and at very small magnetic fields in analyzing galvanomagnetic phenomena is emphasized.