Solid-state nanopores attract widespread interest, owning to outstanding robustness, extensive material availability, as well as capability for flexible manufacturing. Bioinspired solid-state nanopores further emerge as potential nanofluidic diodes for mimicking the rectification progress of unidirectional ionic transport in biological K⁺ channels. However, challenges that remain in rectification are over-reliance on complicated surface modifications and limited control accuracy in size and morphology. In this study, suspended Si₃N₄ films of only 100 nm thickness are used as substrate and funnel-shaped nanopores are controllably etched on that with single-nanometer precision, by focused ion beam (FIB) equipped with a flexibly programmable ion dose at any position. A small diameter 7 nm nanopore can be accurately and efficiently fabricated in only 20 ms and verified by a self-designed mathematical model. Without additional modification, funnel-shaped Si₃N₄ nanopores functioned as bipolar nanofluidic diodes achieve high rectification by simply filling each side with acidic and basic solution, respectively. Main factors are finely tuned experimentally and simulatively to enhance the controllability. Moreover, nanopore arrays are efficiently prepared to further improve rectification performance, which has great potential for high-throughput practical applications such as extended release of drugs, nanofluidic logic systems, and sensing for environmental monitoring and clinical diagnosis.