Heavily Ge-doped GaAs single crystals were grown by the liquid-encapsulated Czochralski technique in the absence and the presence of a magnetic field of 4000 G. Three photoluminescence emission bands A, B, and C were observed in the as-grown crystals. Bands A and B were explained by a deep acceptor and self-activated center emissions, respectively. The central energy and half width of band C increased with increasing Ge-doped concentration. The photoluminescence excitation spectrum of band C was observed to be broad. The temperature dependence of the full width at half maximum of band C was analyzed. The results were considered to be caused by distributed states with different energy positions and electron-lattice couplings due to the impurity concentration effect on the unknown Ge-related complexes responsible for band C. The emission intensity of band C was markedly weaker in the magnetic-field growth crystals where both donor and acceptor concentrations were higher than those in traditional growth crystals, which showed that the formation of the unknown Ge-related complex can be reduced and the Ge doping efficiency can be improved during crystal growth by applying a magnetic field to suppress the temperature fluctuations in molten GaAs.