n (where, n ¼ 1, 2, 3, . . .) participating in an atomic point contact. Observations of
filament growth processes in a planar Ag/PEO/Pt device evidenced that the metal
filament is made up of small Ag clusters that are unevenly precipitated in the PEO
matrix [20]. Based on this result, we consider an atomic point contact structure as
consisting of Ag atom chains between Ag electrode blocks. Under these circumstances, the transmission eigenvalues and eigenstates of the entire structure, and the
conductance states, were evaluated from first-principles DFT simulations.
We divided the situation into two parts; below and above 1G 0 . For below 1G 0 , we
first considered a channel consisting of two Ag atoms in a symmetric three-to-one
atom chain configuration, which is connected to linked three-atom chain structures
on both sides. This is shown as the top structure in Fig. 8a. The transmission
eigenvalues and the corresponding transmission eigenstates were analyzed under a
bias voltage of 0.25 V between the electrode blocks, and the conductance was
calculated as a function of the energy relative to the Fermi energy (E F ) at 0 eV.
The top structure of Fig. 8a has one transmission channel of 1G 0 , in the energy range
of between À0.5 and 0.5 V, as shown by the black curve in Fig. 8b, and a
transmission eigenvalue at E F is estimated to be 0.999. This suggests that electrons
incoming from the left electrode are negligibly scattered and reach the right electrode
without any loss. The channel length was calculated to be 7.58 Å, which length is
defined as the distance between the tips of the two electrode blocks.
The conductance was calculated by extending the channel length up to 2.5 Å in
steps of 0.5 Å. In the calculations, the two in-line atoms were relaxed to minimize the
total energy, while atoms in the electrode blocks were fixed in position. The resulting
relaxed structures are presented in Fig. 8a for three extended distances of 0.5, 1, and
2 Å. The channel lengths are estimated to be 8.08, 8.58, and 9.08 Å, respectively.
With extending the channel length, the center region breaks easily and a small gap
appears, even at the extended distance of 0.5 Å. This gap becomes larger as the
channel length is increased, and the corresponding conductance is substantially
reduced, as shown in Fig. 8b. The result shows that such a single-atom point contact
is unstable and breaks easily under small or no bias conditions. Thus, the volatile
switching behavior that occurs below 1G 0 originates from the change of the gap
distance at the atomic point contact, where electron tunneling through Ag clusters
dominates.
For conductance states above 1G 0 , we next considered the addition of Ag atoms
into the channel with the same electrode configuration. DFT calculations were
performed by adding different numbers of Ag atoms (n ¼ 2–5) to the atom chains,
as shown by the dotted circles in Fig. 9a. The channel length was fixed at 7.58 Å in
all the calculations. Figure 9a represents the final (relaxed) structures for the given
number of Ag atoms in the channel. The corresponding conductance is plotted as a
function of the energy in Fig. 9b. The three-atom chain exhibits conductance slightly
higher than 1G 0 at E F . This suggests that a three-atom chain forms almost a singleatom point contact after structural relaxation. In contrast, the four- and five-atom
chains exhibit conductance values slightly lower than 2G 0 at E F , indicating the
formation of a two-atom point contact. Atomic contacts that have more than three
atoms are deformed and twisted, and lose translational invariance along the channel.
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T. Tsuruoka et al.
filament growth processes in a planar Ag/PEO/Pt device evidenced that the metal
filament is made up of small Ag clusters that are unevenly precipitated in the PEO
matrix [20]. Based on this result, we consider an atomic point contact structure as
consisting of Ag atom chains between Ag electrode blocks. Under these circumstances, the transmission eigenvalues and eigenstates of the entire structure, and the
conductance states, were evaluated from first-principles DFT simulations.
We divided the situation into two parts; below and above 1G 0 . For below 1G 0 , we
first considered a channel consisting of two Ag atoms in a symmetric three-to-one
atom chain configuration, which is connected to linked three-atom chain structures
on both sides. This is shown as the top structure in Fig. 8a. The transmission
eigenvalues and the corresponding transmission eigenstates were analyzed under a
bias voltage of 0.25 V between the electrode blocks, and the conductance was
calculated as a function of the energy relative to the Fermi energy (E F ) at 0 eV.
The top structure of Fig. 8a has one transmission channel of 1G 0 , in the energy range
of between À0.5 and 0.5 V, as shown by the black curve in Fig. 8b, and a
transmission eigenvalue at E F is estimated to be 0.999. This suggests that electrons
incoming from the left electrode are negligibly scattered and reach the right electrode
without any loss. The channel length was calculated to be 7.58 Å, which length is
defined as the distance between the tips of the two electrode blocks.
The conductance was calculated by extending the channel length up to 2.5 Å in
steps of 0.5 Å. In the calculations, the two in-line atoms were relaxed to minimize the
total energy, while atoms in the electrode blocks were fixed in position. The resulting
relaxed structures are presented in Fig. 8a for three extended distances of 0.5, 1, and
2 Å. The channel lengths are estimated to be 8.08, 8.58, and 9.08 Å, respectively.
With extending the channel length, the center region breaks easily and a small gap
appears, even at the extended distance of 0.5 Å. This gap becomes larger as the
channel length is increased, and the corresponding conductance is substantially
reduced, as shown in Fig. 8b. The result shows that such a single-atom point contact
is unstable and breaks easily under small or no bias conditions. Thus, the volatile
switching behavior that occurs below 1G 0 originates from the change of the gap
distance at the atomic point contact, where electron tunneling through Ag clusters
dominates.
For conductance states above 1G 0 , we next considered the addition of Ag atoms
into the channel with the same electrode configuration. DFT calculations were
performed by adding different numbers of Ag atoms (n ¼ 2–5) to the atom chains,
as shown by the dotted circles in Fig. 9a. The channel length was fixed at 7.58 Å in
all the calculations. Figure 9a represents the final (relaxed) structures for the given
number of Ag atoms in the channel. The corresponding conductance is plotted as a
function of the energy in Fig. 9b. The three-atom chain exhibits conductance slightly
higher than 1G 0 at E F . This suggests that a three-atom chain forms almost a singleatom point contact after structural relaxation. In contrast, the four- and five-atom
chains exhibit conductance values slightly lower than 2G 0 at E F , indicating the
formation of a two-atom point contact. Atomic contacts that have more than three
atoms are deformed and twisted, and lose translational invariance along the channel.
152
T. Tsuruoka et al.