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Memories play a key role in FGPAs in the forms of both programming bits and embedded memory blocks. FPGAs using non-volatile memories have been the focus of attention with zero boot-up delay, real-time reconfigurability, and superior energy efficiency. This paper presents a novel three-dimensional (3D) non-volatile FPGA architecture (3D-Non-FAR) using phase change memory (PCM) and 3D die stacking techniques. Basic structures in a conventional FPGA architecture are renovated with PCM, and components are repartitioned and reorganized in 3D-NonFAR to allow an efficient 3D integration of PCM elements. 3D-NonFAR not only preserves the advantages of existing non-volatile FP-GAs, but also provides high integration density, high performance, and bit-level programmability, which enable PCM as a universal memory replacement in FPGAs. Evaluation results show that 3D-NonFAR has smaller footprint, higher performance, and lower power consumption compared with other FPGA counterparts.