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We studied the topological insulators, Bi2-xSbxTe3-ySey thin films of different thickness and chemical composition. For the first time, a decrease in conductivity in the terahertz range was observed as the chemical composition approached the Ren curve. The obtained temporal dependences of terahertz radiation show that generation of THz waves is more effective in an island film with a total thickness of about tens of nanometres with a composition close to the Ren curve, where the volume contribution to the conductivity is suppressed. This effect can be useful for making photoconductive THz antennas based on topological insulators.