We experimentally demonstrate efficient broadband self-powered photo-detection and power generation in thin films of polycrystalline bismuth telluride (Bi2Te3) semiconductors under inhomogeneous strain. The developed simple, junction-free, lightweight, and flexible photo-detectors are composed of a thin active layer and Ohmic contacts on a flexible plastic substrate, and can operate at room temperature and without application of an external bias voltage. We attribute the observed phenomena to the generation of an electric field due to a spontaneous polarization produced by strain gradient, which can separate both photo-generated and thermally-generated charge carriers in bulk of the semiconductor material, without a semiconductor junction. We show that the developed photo-detectors can generate electric power during both the daytime and the nighttime, by either harnessing solar and thermal radiation or by emitting thermal radiation into the cold sky. To the best of our knowledge, this is the first demonstration of the power generation in a simple junction-free device under negative illumination, which exhibits higher voltage than the previously used expensive commercial HgCdTe photo-diode. Significant improvements in the photo-detector performance are expected if the low-charge-mobility polycrystalline active layer is replaced with high-quality single-crystal material. The technology is not limited to Bi2Te3 as the active material, and offers many potential applications in night vision, wearable sensors, long-range LIDAR, and daytime/nighttime energy generation technologies.