Ab Initio Study of Al Atomic Chains with Na Impurity Atom

We have carried out ab initio calculations on the electrical properties of Al chains with a substitutional Na impurity, focusing on the potential drop due to the applied bias voltage. Besides the expected electric current reduction by the introduction of Na impurity, we have found that the effective potential almost drops at the Na atom position wherever Na atom is located. This behavior is maintained when the applied bias voltage is increased. These results can be understood from the strength of interactions between atoms and between atom and electrode. [DOI: 10.1380/ejssnt.2006.570]

The remarkable progress in fabrication technology enables us to shrink the size of electronic devices to nanometer scale. In this scale, the electron conduction mechanism is different from that in large-scale conductors. For example, it is reported that the conductance of atomic point contact has been quantized in the unit of G 0 (=2e 2 /h, where e is the electron charge and h is Planck's constant) [1][2][3]. Further, it is reported that the conductance of single row of Au atomic chain between electrodes has also been quantized [4,5]. There are also several reports of conductance quantization for other atom species such as Al [6,7].
Many theoretical studies have been performed concerning electrical properties of the atomic chains, too. Their current(I)-voltage(V ) characteristics is one of the focused topics of the theoretical studies on the atomic chains. One of the important behaviors which may provide a clue to understand their electric properties is the potential drop due to the bias voltages between electrodes. However, there are only few reports focused on the potential drop. Moreover, different behaviors of the potential drop are seen among the reported studies. In a carbon atomic chain, Brandbyge et al. reported that the potential drop concentrates at one of the ends of the chain [8]. On the other hand, Lang et al. reported that the potential drop is spread over the chain and also into the electrodes by examining another carbon atomic chain [9]. In the case of Al atomic chains between jellium electrodes, the potential drop is reported to concentrate at a certain position in the chain [10,11]. Further, in the case of a Na atomic chain between jellium electrodes, the potential drop concentrates at one of the ends of the chain [12]. In the above investigations, all the atomic chains were constructed by * Corresponding author: furuya@cello.t.u-tokyo.ac.jp the same atomic species. On the contrary, Hirose et al. examined Al atomic chains where the Al atom next to a jellium electrode was replaced by a Na atom, and found that the potential drop concentrates at the Na atom [13]. Although their results clearly show that the replacement of the Al atom with Na enhances the degree of localization of the potential drop region, the effects of the Na impurity are not well separated from those of the contact between chain and electrode. To investigate the potential drop behavior in more detail including this point would be of great interest not only from the view point of fundamental science, but also from technological application: the understanding, control and design of the potential drop lead to the control and design of the electrical properties of nanostructure, and thus we may be able to obtain guiding principles to design nanoscale devices.
In this letter, we report the impurity effects on the electrical properties of the Al atomic chains, focusing on the behavior of the effective potential drop. In the present analysis, we carried out ab initio calculations using the boundary-matching scattering-state density functional (BSDF) method developed by our group [10,14,15]. This method is based on the density functional theory [16,17] incorporating scattering states, and can calculate electronic states including semi-infinite electrodes under applied bias voltage self-consistently. We used the local density approximations for the exchange-correlation potential [18,19], and local pseudopotentials suggested by Chelikowsky et al. for Al [20] and Ashcroft for Na [21] for the ionic potentials.
In the calculation, we examined an Al atomic chain consisting of six atoms between jellium electrodes, and substitute one of the atoms with a Na atom. The Al 6 chain without Na impurity was also examined as a reference. The Al chains with a substitutional Na impurity may be difficult to be fabricated, but we expect that the essence of the behavior of the potential drop can be seen in these  systems easily and clearly. Hereafter, we use the notation given in Table I: for example, the AlNaAl 4 chain denotes a chain where Al, Na, Al, Al, Al and Al atoms are placed between electrodes with this order. The Wigner-Seitz radius of the jellium is set to be 2.0 atomic units (a.u.), which is the same as that of bulk aluminum. In principle, we choose the geometrical parameters referring to the bulk crystal: the distances of jellium-Al, jellum-Na, Al-Al and Al-Na are set to be 2.5 a.u., 2.9 a.u., 5.4 a.u. and 6.2 a.u., respectively. The positions of atoms are fixed throughout the calculations. We impose the periodic boundary condition in the directions parallel to the surface, and the size of supercell is set to be 15.0 a.u×15.0 a.u. Figure 1 shows the calculated I-V characteristics of the NaAl 5 , AlNaAl 4 , Al 2 NaAl 3 and Al 6 chains. From this figure, we can see that the existence of Na atom much reduces the electric current. We can also see that the electric current through the NaAl 5 chain is slightly higher than the other chains which include Na atom. This can be understood by the difference in electronic states of Na atom: Na atom of NaAl 5 is located between Al atom and jellium, while that of AlNaAl 4 and Al 2 NaAl 3 is located between Al atoms. It should be noted that these I-V characteristics hardly depend on the applied bias voltage within the range that we examined. It should also be noted that the I-V characteristics is nonlinear in the Al 6 and NaAl 5 chains but not in others. The appearance of such nonlinear characteristics has already been reported [11], and can be understood from density of states: there are two energy peaks in local density of states within the range of 0.4 eV from the Fermi level in the Al 6 and NaAl 5 but not in others. Figure 2 shows the shift in effective potential by an applied bias voltage of 0.1 V along the chain axis. From this figure, we can see that the effective potential drop due to the applied bias voltage always concentrates at the Na atom wherever it is placed. From the dependence of the effective potential on the applied bias voltage shown in Fig. 3, we can see that the features of the above concentration of potential drop do not depend on the bias voltage within the examined range. Further, all the chains show the common feature of the potential shift: the potential shifts of the atoms at the left of the Na hardly change, while those of the atoms at the right of the Na shift nearly the same amount of the applied bias voltage.
We also examined the shift in the local density of states (LDOS) around each atom of the Al 2 NaAl 3 chain as shown in Fig. 4. From this figure, we notice that the peak of LDOS hardly changes by the applied bias voltage for the atom located just at the left of the Na, while the peak of LDOS shifts about 0.5 eV for the atoms located at the right of the Na. This means that the atoms at the left of the Na behaves as if they do not feel the applied bias voltage, while the atoms at the right of the Na behave as if they feel the applied bias voltage fully.
On the basis of the above results, we can speculate the trend of the effective potential drop as follows. In the Al 6 chain, there are strongly hybridized states between the Al atoms, and also Al atom and electrode. However, in the case of the Al atomic chain which includes Na impurity atom, the hybridization between the Al and Na atoms is less weaker than that between Al atoms. In this case, to maintain the hybridization between the Al atoms is more energetically favorable than to maintain that between the Al and Na atoms when the bias voltage is applied. In consequence, the energy level of the LDOS peak remain the same as much as possible in respective regions when the applied bias voltage varies. This leads to the LDOS peak shift in Fig. 4, and causes the concentration of the effective potential drop in Fig. 2.
As mentioned before, we neglected the structural relaxation in the present analysis. However, preliminary calculation considering the structural relaxation is performed using the BSDF method [22]. We confirmed that the above features does not change when the optimized geometries are used in the cases of the AlNaAl 4 and Al 2 NaAl 3 atomic chains. That is, the concentration of the potential drop and the linear I-V characteristics appears similarly, though the electric current decreases by half. It should be noted that we have not obtained the optimized geometries of the NaAl 5 atomic chain yet, which may imply that this chain is unstable at the present distance between the electrodes.
In summary, we report the impurity effects on the electrical properties of the Al atomic chains, focusing on the concentration of the effective potential drop. We found that the shift in effective potential due to the applied bias voltage concentrates at the substitutional Na impurity atom wherever the Na atom is located. The analysis of the local density of states around each atom shows that the electronic states behave as if the bias voltage is absent at one side of the Na atom, while they behave as if they feel the bias voltage fully on the other side. We expect that the potential drop concentration also appears in more complicated nanostructures, and thus the present findings would be useful in controlling and designing electric properties of nanoscale devices.