We design and fabricate shallow-etched periodically poled lithium niobate waveguides to realize highly efficient broadband spontaneous parametric down-conversion (SPDC) on nanophotonic chips. The shallow-etched waveguide can tolerate the non-uniformities of waveguide width induced by fabrication imperfections, enabling the generation of photon pairs with high count rate and bandwidth. We demonstrate photon-pair generation with a high brightness of 11.7 GHz/mW and bandwidth of 22 THz in a 5.7-mm-long PPLN waveguide. The generated photon pairs exhibit a strong temporal correlation with a coincidence-to-accidental ratio of up to 16262±850. Our results confirm the feasibility of shallow etching in the fabrication of an efficient SPDC device on the platform of lithium niobate on an insulator, and benefit quantum information processing with a broadband photon source.