  We have elaborately studied the electronic structure of 555-777 divacancy
(DV) defected armchair edged graphene nanoribbon (AGNR) and transport
properties of AGNR based two-terminal device constructed with one defected
electrode and one N doped electrode, by using density functional theory and
non-equilibrium Green's function based approach. The introduction of 555-777 DV
defect into AGNRs, results in a shifting of the {\pi} and {\pi}* bands towards
the higher energy value which indicates a shifting of the Fermi level towards
the lower energy. Formation of a potential barrier, very similar to that of
conventional p-n junction, has been observed across the junction of defected
and N doped AGNR. The prominent asymmetric feature of the current in the
positive and negative bias indicates the diode like property of the device with
high rectifying efficiency within wide range of bias voltages. The device also
shows robust negative differential resistance (NDR) with very high
peak-to-valley ratio. The analysis of the shifting of the energy states of the
electrodes and the modification of the transmission function with applied bias
provides an insight into the nonlinearity and asymmetry observed in the I-V
characteristics. Variation of the transport properties on the width of the
ribbon has also been discussed.
