A polymer electrolyte includes an additive and a crosslinked polymer with a heterogeneous polymer network synthesized from one or more crosslinkers, wherein at least one crosslinker has three or more polymerizable terminals. In another embodiment, the crosslinked polymer has a polymer network with topological defects. In some embodiments, the additive comprises element F and at least one of elements B and P. In some embodiments, the additive comprises F—B, F—P, F—P—O, F—P=O, or any combinations thereof. In one embodiment, the crosslinked polymer is not over-crosslinked. An electrochemical device with the crosslinked polymer as electrolyte exhibits an improved electrochemical and safety performance.