The Hall coefficient and resistivity of germanium single crystals bombarded with slow neutrons were measured between 1.2 and 300°K. Slow neutron capture and subsequent nuclear transmutation produce majority impurities, gallium atoms, and compensating impurities, arsenic and selenium atoms. $p$-type samples with a gallium concentration ranging from 8×${10}^{14}$ to 5×${10}^{17}$ per cc with a fixed compensation ratio of 0.40 were thus prepared and the impurity conduction was studied as a function of the average distance between the majority impurities. The effective radius $a$ of the acceptor ground-state wave function is 90.1 A according to Miller's theory of impurity conduction, whereas $a=40\mathrm{}$ A according to Twose's theory. The latter value agrees well with the effective radius of the Kohn-Schechter acceptor wave function. The activation energy of impurity conduction changes slowly with impurity concentration from 3.5×${10}^{-4\mathrm{}}$ to 5.9×${10}^{-4\mathrm{}}$ ev and agrees well with the predictions of Miller's theory for gallium concentration below 5×${10}^{15}$ per cc. Measurements on samples which contain different dislocation densities but identical impurity concentrations show that up to ${10}^4$ dislocations per ${\mathrm{cm}}^2$ do not affect impurity conduction.

• Received 4 April 1960

DOI:https://doi.org/10.1103/PhysRev.119.1238