Undoped (ND) semi-insulating (SI) liquid encapsulated Czochralski (LEC) GaAs crystals were investigated by photocurrent and temperature-dependent Hall measurements. It is indicated that strong nonuniformities in the distributions of impurities and defects can occur for the NDSILEC GaAs crystal grown under a condition with strong constitutional supercooling. In such case, the deep level that dominates Fermi level is spacial location dependent, and the GaAs crystal becomes a composite consisting of a large number of elementary domains with different conductivities. The sub-bandgap photocurrent response and the carrier transport properties for this kind of composite are quite different from those for homogeneous NDSILEC GaAs.