For realizing neural networks with binary memristor crossbars, memristors should be programmed by high-resistance state (HRS) and low-resistance state (LRS), according to the training algorithms like backpropagation. Unfortunately, it takes a very long time and consumes a large amount of power in training the memristor crossbar, because the program-verify scheme of memristor-programming is based on the incremental programming pulses, where many programming and verifying pulses are repeated until the target conductance. Thus, this reduces the programming time and power is very essential for energy-efficient and fast training of memristor networks. In this paper, we compared four different programming schemes, which are F-F, C-F, F-C, and C-C, respectively. C-C means both HRS and LRS are coarse-programmed. C-F has the coarse-programmed HRS and fine LRS, respectively. F-C is vice versa of C-F. In F-F, both HRS and LRS are fine-programmed. Comparing the error-energy products among the four schemes, C-F shows the minimum error with the minimum energy consumption. The asymmetrical coarse HRS and fine LRS can reduce the time and energy during the crossbar training significantly, because only LRS is fine-programmed. Moreover, the asymmetrical C-F can maintain the network’s error as small as F-F, which is due to the coarse-programmed HRS that slightly degrades the error.

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Memristor crossbar arrays were fabricated based on a Ti/HfO2/Ti stack that exhibited electroforming-free behavior and low device variability in a 10 x 10 array size. The binary states of high-resistance-state and low-resistance-state in the bipolar memristor device were used for the synaptic weight representation of a binarized neural network. The electroforming-free memristor was confirmed as being suitable as a binary synaptic device because of its higher device yield, lower variability, and less severe malfunction (for example, hard break-down) than the electroformed memristors based on a Ti/HfO2/Pt structure. The feasibly working binarized neural network adopting the electroforming-free binary memristors was demonstrated through simulation.