Memristor crossbar arrays without selector devices, such as complementary-metal oxide semiconductor (CMOS) devices, are a potential for realizing neuromorphic computing systems. However, wire resistance of metal wires is one of the factors that degrade the performance of memristor crossbar circuits. In this work, we propose a wire resistance modeling method and a parasitic resistance-adapted programming scheme to reduce the impact of wire resistance in a memristor crossbar-based neuromorphic computing system. The equivalent wire resistances for the cells are estimated by analyzing the crossbar circuit using the superposition theorem. For the conventional programming scheme, the connection matrix composed of the target memristance values is used for crossbar array programming. In the proposed parasitic resistance-adapted programming scheme, the connection matrix is updated before it is used for crossbar array programming to compensate the equivalent wire resistance. The updated connection matrix is obtained by subtracting the equivalent connection matrix from the original connection matrix. The circuit simulations are performed to test the proposed wire resistance modeling method and the parasitic resistance-adapted programming scheme. The simulation results showed that the discrepancy of the output voltages of the crossbar between the conventional wire resistance modeling method and the proposed wire resistance modeling method is as low as 2.9% when wire resistance varied from 0.5 to 3.0 ohm. The recognition rate of the memristor crossbar with the conventional programming scheme is 99%, 95%, 81%, and 65% when wire resistance is set to be 1.5, 2.0, 2.5, and 3.0 ohm, respectively. By contrast, the memristor crossbar with the proposed parasitic resistance-adapted programming scheme can maintain the recognition as high as 100% when wire resistance is as high as 3.0 ohm.
