Impurity Conduction in Transmutation-Dopedp-Type Germanium

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×{}10¹⁴ to 5×{}10¹⁷ 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 $a=40$ 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 to 5.9×{}10^-4 ev and agrees well with the predictions of Miller's theory for gallium concentration below 5×{}10¹⁵ per cc. Measurements on samples which contain different dislocation densities but identical impurity concentrations show that up to 10⁴ dislocations per cm² do not affect impurity conduction.