The electron transport properties of ZnO nano-wires coupled by two aluminium electrodes were studied by {\it ab initio} method based on non-equilibrium Green’s function approach and density functional theory. A clearly rectifying current-voltage characteristics was observed. It was found that the contact interfaces between Al-O and Al-Zn play important roles in the charge transport at low bias voltage and give very asymmetric I-V characteristics. When the bias voltage increases, the negative differential resistance occurs at negative bias voltage. The charge accumulation was calculated and its behavior was found to be well correlated with the I-V characteristics. We have also calculated the electrochemical capacitance which exhibits three plateaus at different bias voltages which may have potential device application.

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