1. INTRODUCTION

Most electronic appliances are based on digital electronics, which in essence just require a lot of switches working together in an organized fashion. Recently, much research has been aimed at finding novel switches that can replace conventional silicon-based technology and permit ever smaller and even more powerful electronics. A lot of nanoscale switches have already been fabricated. However, most of the switches involve non-nanoscale components, which makes such switches useful for fundamental researches, but far from potential applications as an actual device.

To solve the problem, Terabe et al. proposed a novel atomic switch using mixed ionic conductor Ag2S.1 This atomic switch has the advantages of bearing simple structure, stability, reliability and operability, and being easy to transfer to real electronic circuit. In their research, an Ag2S layer is connected to battery through two metallic leads (at least one is silver). They speculated that Ag atoms are first accumulated at the interface between silver sulfide and a negative silver electrode, and then diffused into the inner part of silver sulfide and finally, a conductive Ag bridge inside the Ag2S is generated to make the system switch ON. Switch OFF can be fulfilled through reversing polarity of the applied voltages. Though a lot of intriguing results have already been obtained concerning this switch, its working mechanism has not been well clarified yet. Understanding the mechanism of switching will be vital for controlling and fully exploiting this nanoscale switch as functional electronic components.

The ultimate goal of our study, considering the above situation, is to clarify the switching mechanism of the Ag2S atomic switch from first principles. To this end, we have examined several aspects of atomic and electronic structures in both bulk Ag2S and Ag-Ag2S-Ag heterostructure. Here, we first report results on migration energetics and pathways of an Ag ion in low-temperature Ag2S. After that, we examine atomic structure, electronic states and electron transport properties of the Ag-Ag2S (beta-phase)-Ag system. Note that hereafter Ag2S designates the beta-phase Ag2S. Finally, we examine transport property of the systems with excess Ag atoms.

2. SYSTEM INVESTIGATED AND COMPUTATIIONAL DETAILS

In the Ag2S, the anions (S) forms a distorted body-centered-cubic lattice, while the cations (Ag) are located in sites close to the centers of the octahedral (O) and tetrahedral (T) sites within the anion sublattice. We investigated diffusions of Ag ion from a T (O) site to its neighboring T (O) vacancy by performing calculations using a 48-atom supercell, adopting the nudge elastic-band (NEB) method in the VASP code. 2 After that, molecular dynamics simulations were carried out using a 96-atom supercell.2

As for Ag-Ag2S-Ag system, our model is shown in Fig. 1. The model can be divided into left semi-infinite electrode, scattering region, and right semi-infinite electrode. The scattering region consists of Ag2S layers and four or eight surface layers of the left and right electrodes. Two different kinds of interface orientations are considered, and several models within these orientations are constructed, as will be described later.

The electron transport properties of the heterostructure are explored with fully self-consistent nonequilibrium Green's function method implemented in Atomistix ToolKit code.3 This method has been applied to many systems successfully, but was applied to heterostructures of metal and solid electrolyte for the first time in this study. The local density approximation and the Troullier-Matrins nonlocal pseudopotential are adopted, and the valence electrons are expanded in a numerical atomic-orbital basis set of single zeta plus polarization (SZP).

3. RESULTS AND DISCUSSION

3.1 Migration of Ag Ions in Low-temperature Ag2S

We investigated four essential migrations of an Ag ion from two types of lattice sites to their nearest-neighbor vacancies of two kinds in low-temperature Ag2S, namely, from T site to T vacancy, T to O vacancy, O to T vacancy, and O to O vacancy by the NEB. The calculated diffusion energy barriers of the corresponding four cases are 0.46, 0.22, 0.32, and 0.67 eV, respectively, which are comparable to experimental values of 0.43-0.48 eV.4 These results suggest that direct diffusions from T to T and O to O are not energetically preferable to indirect ones from T to O and from O to T, and that indirect T-O-T and O-T-O migrations are more likely than direct ones, T-T and O-O.

Figure 2 illustrates the evolution of trajectory of a focused Ag ion migrating from a T to its nearest-neighbor O vacancy in Ag2S at 700K calculated by the MD. We observed from Fig. 2(b) to Fig. 2(d) that a T Ag migrates directly from its original T site to its neighbor O vacancy through a triangle constructed by three S ions, as denoted in Fig. 2(b). The entire evolution trajectories for an Ag ion migrating from an O to its nearest-neighbor T vacancy are analogous to those migrating from T to its nearest-neighbor O vacancy, which are not shown here. These supports the results obtained from the NEB calculation, that is, the preferential migration of Ag ions between nonequivalent sites.

3.2 Atomic and Electronic Transport Properties of Ag-Ag2S-Ag

Based on the experimentally observed orientation relationships of (0-12)Ag2S//(001)Ag and [100]Ag2S//[100]Ag,5 we constructed three models of the interface structure, where S atoms in the Ag2S layer proximal to the interface are located on the On-top, Bridge, and Hollow sites of the outmost layer of Ag electrode, respectively. Our calculations show that the Bridge case is the most stable one , irrespective of the structural relaxation and applied bias voltages. The Ag2S lattice constant is elongated by 15.2% along x direction and compressed by 7.1% along y direction.

The transmission spectra for structures of the Bridge case with and without relaxation are shown in Fig. 3. The transmission coefficient at EF increases from 0.04 before structural relaxation to 0.455 after relaxation, which shows the opening of a conduction channel in the relaxed structure. Investigation into its atomic arrangement reveals that a zigzag Ag atomic chain is formed in the Ag2S, whose atomic configuration is illustrated in Fig. 4. The neighboring Ag-Ag distances along the chain range from 2.84 angstrom to 3.07 angstrom (see numbers in Fig. 4), which are very close to the nearest neighbor distance in Ag bulk, 2.89 angstrom, but deviate severely from Ag-Ag separation in the Ag2S bulk, 3.08-3.74 angstrom.6

We also investigated electronic and electric properties of the system under applied bias voltages. First, we calculated currents (I) under voltages (V) ranged from -3.0V to 3.0V using the relaxed Bridge structure. The I-V curve is nearly linear, showing metallic nature of this system, which can be explained by the formation of the zigzag atomic chain. Next, we examined how the applied bias voltages drop along the Ag chain plane. Figure 5 illustrates the difference of the effective potential in the plane including the Ag chain between the case where the bias voltage of 0.5V is applied and the case of 0.0V, for both unrelaxed and relaxed Bridge cases. One can see that intensive voltage drop takes place mainly around the negative bias end of the interface region for both cases, which suggests that changes in the Ag2S layer by applying bias voltage should commence from this area.

3.3 Toward the Understanding of the Silver Sulfide Atomic Switch

In view of the large mismatch in the above model, here, we construct a new model having the orientation relationships of (001)Ag //(010)Ag2S and [010]Ag//[100]Ag2S instead. In this model, S atoms in the Ag2S layer proximal to the interface are located at the bridge sites of the outmost layer of Ag electrode. We have confirmed that this model has lower total energy than another possible model with the same orientation relationships. Compared with the previous model, this one has the advantage of smaller lattice mismatch despite relatively small sizes. The Ag2S lattice constant is elongated by 3.75% along x direction and contracted by 3.56% along y direction to match the Ag electrodes.

The transmission coefficient at EF increases slightly from 0.03 before structural relaxation to 0.09 after relaxation, which shows no opening of conduction channel in the relaxed structure in contrast with the model examined in the previous section. Then, nine excess Ag atoms were inserted into the Ag2S in turn from the right electrode side. The transmission coefficient at EF increases to 0.215, 0.358, 0.561, and 0.575 through introduction of two, four, six, and eight excess Ag atoms. Finally, it enhances sharply to 0.909 by introducing nine excess Ag. The change of transmission spectra with the insertions is illustrated in Fig. 6, where we present six representative cases. The valley around EF in Fig. 6(a) disappears after the insertion of nine excess Ag, which means the system changes its nature from semiconducting to metallic.

Investigation into atomic configurations of the systems reveals that a conductive Ag bridge is generated gradually as excess Ag are introduced, and finally bridged over the entire Ag2S when nine excess Ag are inserted, as shown in Fig. 7. The most interesting feature seen in this figure is that the atomic arrangement of the bridge is quite similar to the close-packed Ag (111) faces that have the lowest energy in Ag bulk. As shown from Fig. 8, the neighboring Ag-Ag distances in the face vary from 2.76 angstrom to 2.99 angstrom (see numbers between Ag atoms in Fig. 8), which are very close to the nearest neighbor distance in (111) face of Ag bulk, 2.89 angstrom, but deviate severely from Ag-Ag separation in the Ag2S bulk, 3.08-3.74 angstrom. In addition, analysis of Mulliken population shows that the electron loss of respective Ag atoms in the (111) face is smaller than that in Ag2S bulk, -0.13, but near the value of Ag bulk, 0, for some of Ag atoms (see numbers on each atoms in Fig. 8). This means that Ag atoms along the bridge exhibit more nature of metal Ag than that of Ag in the Ag2S bulk.

4. CONCLUSIONS

We have performed first-principles calculations toward the understanding of the switching mechanism of the Ag2S atomic switch. First, we investigated migration pathways and estimated corresponding activation energy barriers in the low-temperature Ag2S. The calculated energy barriers for the four essential migrations are between 0.21 to 0.67 eV, which are comparable to the experimental values. Migrations between the nearest equivalent positions are not energetically preferable to nonequivalent ones.

Then, we examined electron transport and structural properties of the Ag-Ag2S-Ag heterostructure. We find that an Ag atomic conductance channel in the Ag2S is generated after structure optimization, resulting in large enhancement of transmission and the metallic behavior of the heterostructure.

Finally, we find, through insertion of excess Ag atoms, that a conductive Ag bridge is generated inside the Ag2S, whose structure is similar to that of Ag (111), leading to sharp enhancement of transmission when connected to the two electrodes.

Fig.1. Schematic illustration of the Ag-Ag2S-Ag system. The Smaller balls represent S atoms while the larger ones represent Ag atoms.

Fig.2. (a) Time evolution of distance d, between the focused Ag ion and the triangle formed by three S ions for migration from T to 0 vacancy at T = 700K. The evolution of the diffusion trajectory at (b) t=0.0 ps; (c) t=0.5 ps; and (d) t=1.0 ps. The S atoms are all de noted with "S", and the focused mobile Ag atom and the 0 vacancy are marked with 'T' and 'V0', respectively. For clarity, the tetrah edron and octahedron constituted by S ions are connected with lines.

Fig.3. Transmission spectra for the Bridge case without and with structural relaxation under OV.

Fig.4. Atomic arrangement of the relaxed structure of the Bridge case under OV. The numbers denote the neighboring Ag-Ag distances along the chain in the Ag2S.

Fig.5. Difference of effective potential along the Ag chain plane by an applied bias voltage of 0.5V for (a) unrelaxed Bridge case, and (b) relaxed Bridge case.

Fig.6. Transmission spectra for the Bridge cases with excess Ag atoms under OV.

Fig.7. Simulated formation of a conductive Ag bridge inside the Ag2S with insertion of excess Ag.

Fig.8. Atomic configuration of one of Ag (111) faces.

固体電解質を用いた原子スイッチは、再構成可能LSI中のスイッチや次世代演算素子としての可能性が期待されている。そのスイッチング機構は印加バイアス電圧による固体電解質中の伝導経路生成消滅と推測されているが、微視的な詳細は不明である。最適な素子構造材料の設計に向け、スイッチングの微視的機構の解明が望まれている。本論文は、原子スイッチの中でも特に研究が進んでいる硫化銀原子スイッチに焦点を当て、硫化銀および銀-硫化銀-銀接合系における原子移動と電子伝導を第一原理計算によって解析し、原子スイッチのスイッチングの微視的機構の手がかりを得ようとしたものである、本論文は6章からなる。

第1章は緒言である、電子デバイスの微細化の流れの中での新規スイッチの研究の意義を述べ、量子点接触とこれを用いた原子スケールスイッチの研究について概観した後に、硫化銀を含む固体電解質原子スイッチに関するこれまでの実験および理論研究をまとめている。そして、固体電解質原子スイッチのスイッチング機構の微視的な素過程およびスイッチオン状態で形成されていると推測されている固体電解質内の伝導経路の微視的構造がまだ明らかになっていないことを指摘して、本研究の目的を明確にした。

第2章では、本研究の計算方法を述べている。本研究の計算全ての基盤となる密度汎関数法について概説した後、原子移動経路とその際のエネルギー障壁を計算するためのnudged elastic band法、原子移動を確認する目的で用いた第一原理分子動力学および半無限電極と接合した非平衡開放系の電子状態および電子伝導特性計算に用いた非平衡グリーン関数法の概要を述べている。

第3章では、バルク硫化銀の室温相における、空孔を介した銀原子の移動過程を解析した結果を述べている。銀原子に四面体位置と八面体位置の2種類のサイトがあることから、隣接空孔位置への移動には計4種類のケースがある。その全てについて移動経路とその際のエネルギー障壁を計算し、例えば四面体位置の原子が四面体位置空孔へ移動するといった、同じ対称性の位置間の移動よりも、異なる対称性の位置間の移動の方が起こりやすいことを明らかにした。さらに、これを第一原理分子動力学計算により確認した。硫化銀は超イオン伝導体として注目され活発に研究されてきたが、その対象は専ら高温相であり、原子スイッチの舞台となる室温相に対しては研究が少なかったため、本章で得られた原子移動素過程の知見は基礎的情報として有用である。

第4章では、銀-硫化銀-銀接合系の構造と電子状態、電気特性について、硫化銀層の組成が化学量論比の場合に焦点を当てて解析した結果を述べている。界面の原子構造の詳細に関する実験データがないことから、まず実験から知られている銀-硫化銀界面の方位関係をもとに、界面原子構造のモデルを構築した。構築したモデルに対し系全体の構造緩和を行った結果、フェルミ準位における電子透過率が構造緩和によって大きく上昇することを見出した。解析の結果、構造緩和により硫化銀層内に二つの銀電極を架橋する銀原子の鎖状構造が生成していることが透過率上昇の原因であることがわかった。実際の原子スイッチにおいては低抵抗(スイッチオン)状態を作るのにバイアス電圧印加が不可欠であることから、ここで得られた自発的原子鎖構造形成は実験と直接は対応しないが、予想外の現像であり、また現実の系においても界面の近傍でこのような伝導経路がある程度形成されている可能性を示唆する点で興味深い。また、バイアス電圧印加計算を行い、印加バイアスによるポテンシャル降下が硫化銀層内で一様ではなく、負極側界面に集中することを明らかにした。これは、バイアス電圧による系の原子配置が負極側界面付近から始まることを示唆しており、スイッチング過程の解明に有用な知見である。

第5章では、スイッチング現象は硫化銀層が銀過剰の条件においてのみ顕著に見られるという実験結果を踏まえ、硫化銀層における過剰銀原子の影響に焦点をあてて解析している。この際には、計算量を勘案して実験とは方位関係が異なるが格子歪が小さいモデルを新たに構築した。このモデルではバイアスゼロで4章の自発的原子鎖構造形成が生じないことを明らかにするとともに、この鎖構造形成が格子歪に起こすることを明らかにした。次に過剰原子の安定サイトを詳細に検討し、過剰原子数を増すとともに銀原子の橋状構造が成長し伝導性が増していくこと、そしてこの橋状構造がバルク銀結晶中の(111)面に対応する正六角形型の銀7原子構造をユニットとしたジグザグリボン構造をとっていることを明らかにした。さらに、この橋状構造が原子間距離、電子価数の点でもバルク銀と同様の性質を有することと、この構造の生成とともに硫原子位置も大きく歪むことを明らかにした。これらの結果は、スイッチング機構の解明に有用であるとともに、原子スイッチの微細化を進める上で有用な知見である。

第6章は総括である。

以上のように、本論文は、硫化銀および銀-硫化銀-銀接合系における銀原子移動と原子状態電子伝導を第一原理計算により解析した。室温相硫化銀内の銀原子移動過程および銀-硫化銀-銀接合系の原子構造電子状態電子伝導特性を微視的に解析設計する上で有用な知見を得た。よって本論文のナノ構造物性工学、計算マテリアル工学への寄与はおおきい。

よって本論文は博士(工学)の学位請求論文として合格と認められる。