^{1}

We theoretically investigate the effect of a defect at the interface between a conductor and reservoirs in an atomic-scale device. Since fabrication of atomic-scale contacts is a complex task, there could be defects at the interface between the conductor and reservoirs. Such defective contacts will make it difficult to measure currents properly. In this paper, we calculate current-voltage characteristics in two-dimensional devices with a defective connection to reservoirs by using the nonequilibrium Green’s function method. Results show that the magnitude of resistance change depends on the amplitude of quantized wave functions at the position of the defect.

Atomic-scale conductors such as nanowires and nanoribbons are attracting much attention. There are many studies motivated by a prospect that smaller devices would show superior performance: higher speed, higher sensitivity, and less power consumption. Not only carbon (graphene) [

In exploiting transport phenomena in the atomic-scale devices, connection to reservoirs is indispensable. Since fabrication of such a small contact is a complex task, defects will be easily introduced at the interface between the conductor and reservoirs. Even if characteristics of the conductor are interesting and useful, improper connection to reservoirs will rectify the current and will smear out the features that we want to observe. Therefore, connection to reservoirs is of special importance for transport measurements in atomic-scale devices. The effect of a defect at the interface, however, has not been well understood.

In this paper, by using the nonequilibrium Green’s function method [

Figure

Model of the device studied in this paper. Virtual atoms, denoted by dots, are associated with an s-like orbital, and neighboring orbitals are connected by hopping interaction “

Considering that each atom is associated with a single s-like orbital, we introduce a hopping interaction between neighboring atoms denoted by “

In the present calculations, we set the spacing between the virtual atoms to

We note that we consider a square array of the atoms as shown in Figure

Green’s function is a matrix defined by an equation:

In Figure

Current-voltage characteristics calculated for size of the conductor

The defect gives rise to decrease in current, that is, increase in resistance. The resistance increase occurs simply because a defect prevents electrons from flowing through the device. A defect located in the middle of the device gives rise to a larger increase in resistance than that near the edge of the device. In the inset (left up) of Figure

In Figure

Current-voltage characteristics calculated for

Considering that discrete energy levels are formed due to confinement of electron in the lateral direction, we understand the defect position dependence of the resistance. Since each of the discrete levels is associated with a sinusoidal wave function, we can attribute the behavior of resistance against defect position to the amplitude of the quantized lateral wave functions. Current injection from the cathode into the conductor is prevented by the defect. The strength of the current flowing from the cathode into the conductor depends on the amplitude of the wave function in the conductor. The amplitude of the lateral wave function is small at the edge of the device. Therefore, the effect of the defect at the edge is small. On the contrary, when the defect locates at the middle of the interface, current injection is largely affected, and resistance change is also large.

To ascertain the role of the wave functions of the lateral modes, we calculated charge densities in the conductor as shown in Figure

(a) Charge densities calculated for structures without defect and with a defect at the first, third, and fifth positions, respectively. (b) Charge densities along the interface between the cathode and conductor. The large dots indicate the position adjacent to the defect. In (a) and (b), we set

In Figure

To examine further the role of the quantized lateral wave functions, we carried out calculations for wider devices. We show the results in Figure

Change in resistance

Considering that a wave function confined in

The enrolment of the second state appears more clearly when the electron effective mass is larger because the higher levels lie in lower energies. Figure

Change in resistance

The defect position dependence of the resistance described so far might be difficult to be observed because of difficulty in preparing samples containing position-controlled defects. We would realize similar situations by using the scanning tunneling microscopy (STM) technique. In Figure

Current-voltage characteristics for structures containing defects except for a single point as schematically shown in the inset.

We note that these calculations were carried out at the temperature

We have to note that the present model for the defect is a much simplified one. In an atomistic point of view, dislocation or vacancy of atoms in reservoirs may be generated in the fabrication process. If there is a vacancy in the reservoir, many (four) bonds are disconnected. In the calculations, we found that disconnection of a bond apart from interface reduces conductivity a little. This is because, within this model, we consider that equilibrium is always satisfied in the reservoirs. We also ascertained that disconnection of a bond along

The author declares that there are no conflicts of interest regarding the publication of this paper.

The author is grateful to Mr. Y. Hanashiro for his help in developing the program code for the current calculations.