1 Introduction

Recent advances in fabrication and evaluation techniques have made possible the design and evaluation ofdevices at the nanometer or even sub-nanometer scales. Such devices sometimes exhibit peculiar propertiesthat cannot be explained by the bulk properties of the constituent materials. This is presumably due to themodulation of materials properties at interfaces, which becomes significant with increasing interface to bulkratios in nanodevices. Furthermore, such interface effects are not limited to nanodevices; the properties ofa bulk material can also be altered through the introduction of a sufficient density of interfaces. Thus, thecontrol and active utilization of such interface properties represent an entirely new degree of freedom inmaterials and device design. However, the origins of such interface effects are still unclear in many cases,and design principles for utilization of such effects are in dire need. In this dissertation, we tackle this issueby first principles materials modeling. We present analyses of the mechanisms for modification of dielectricresponse and ion transport at interfaces. We also propose ideas for controlling those effects for obtaining thedesired properties.

2 Ionic space charge layer at metal/oxide interfaces

In bulk materials, the charge neutrality condition must be fulfilled because otherwise, the electrostatic potentialwould diverge. However, at interfaces, this is not the case; in general, a thin charged layer is formedto keep the electrochemical potential constant across the interface. This space charge layer can consist ofthe deficiency or excess of various ionic and/or electronic carriers, which can lead to modification of electricalconductivity. However, few works have dealt with the space charge formation at metal/ionic conductorinterfaces despite their increasing importance in the development of electrochemical devices such as solidoxide fuel cells. To simulate the space charge effect at such interfaces, we took a combined ab initio andcontinuum modeling approach. In this scheme, the relation between defect concentration and the local potentialis first obtained from first principles. This relation is then used to construct a continuum model forsimulating space charge profiles at various atmospheric conditions [1, 2].

Figure 1 shows the simulation results for the oxygen vacancy concentration and valence band profilesin acceptor-doped zirconia adjacent to an interface with metal (oxygen vacancies are the dominant chargecarriers in this system). It is found that oxidizing atmosphere and high valence band offset result in vacancydepletion, while the opposite trend is seen in reducing atmosphere and low valence band offset. The spacecharge region is confined to within 2 nm from the interface. This can be understand in a similar mannerto space charge formation at metal/semiconductor Schottky junctions: ionic space charge is accumulatedat the interface to align the Fermi levels in the metal and ionic conductor, just like electrons or holes areaccumulated to align the Fermi levels at metal/semiconductor interfaces. The important difference is that theFermi level in an oxide can be controlled within a rather wide range by the oxygen atmosphere. The Fermilevel position is higher in the band gap in reducing atmosphere compared to oxidizing atmosphere (ΔEF,bulkin Fig. 1).

3 Orbital separation approach for simulating metal-insulator-metal capacitors under bias voltage

The capacitance is a fundamental variable in the design and operation of devices such as transistors and capacitors.As the dielectric layer is made thinner in order to keep up with Moore's law, it has been found thatthe capacitance often deviates from the classical geometric capacitance C = εS/d, where ε is the bulk dielectricconstant, d is the dielectric thickness, and S is the area of the electrode plates. This is presumed to bedue to the property of the metal-dielectric interface, whose impact on the overall capacitance becomes largerwith increased interface to bulk ratios. Furthermore, it has been pointed out that the total capacitance includescontributions of quantum mechanical origin, which becomes significant as the geometric capacitancebecomes larger as d → 0.

First principles simulation based on the Kohn-Sham (KS) formalism of density functional theory is apowerful tool for examining such effects. However, the calculation of capacitance requires the application ofbias voltage on a metal/insulator/metal (MIM) structure, and this is incompatible with the conventional KSscheme which seeks the global ground state. Although several methods have been proposed to circumventthis problem, they have not seen widespread use due to problems in accuracy and/or efficiency, geometricconstraints, and difficulty in implementation.

To rectify this situation, we propose a new method that is based on the separation of the KS orbitals nearthe Fermi level into each electrode (Fig. 2). The separated orbitals are occupied according to different Fermilevels, allowing for consideration of bias voltage in a straightforward manner. We refer to this method as theorbital separation approach (OSA) [3].

The OSA was implemented in Vienna ab initio Simulation Package, which is a widely-used code for firstprinciples electronic structure calculations. We then tested this method by performing calculations of thecapacitance and dielectric response in Au-vacuum-Au, Au-MgO-Au, and graphene-vacuum-graphene capacitors,and demonstrated that the method is robust, efficient, and reliable. This method is used extensivelyin the following chapter to examine the modulation in dielectric response at metal/high-k oxide interfaces.

4 Countering the intrinsic dead layer effect utilizing ferroelectric negative capacitance

The use of higher-k dielectrics such as SrTiO3 and TiO2 is being explored for further increase in capacitancedensity, particularly for dynamic random access memory applications. When using these materials in thinfilmgeometries, however, it has been found that the capacitance is reduced significantly from nominal values(i.e., those calculated assuming that the dielectric constant is the same as in bulk). First principles simulationhave shown that a large part of this reduction can be explained by an "intrinsic dead layer effect" [4]. Thatis, the dielectric response at interfaces is reduced significantly compared to the bulk, even when the interfaceis atomically sharp with no defects or interdiffusion. Thus, we need to go beyond the conventional wisdomof simply using thinner dielectrics with higher dielectric constant to increase the capacitance further.

One approach to enhancing capacitance is through the use of negative capacitance. A negative capacitor isthermodynamically unstable, but can be stabilized by placing in series with a positive capacitor. Recently, theidea of placing a ferroelectric in series with a paraelectric for negative capacitance stabilization was proposedand then demonstrated experimentally on ferroelectric/paraelectric bilayer structures [5]. However, the effectwas seen only at elevated temperatures over 300℃, limiting its usefulness for device applications. In thiswork, we consider the possibility of using ultra-thin ferroelectric film to counter the dead layer effect atrealistic operating temperatures.

Figure 3 shows the inverse permittivity profile in the SrRuO3/SrTiO3/SrRuO3 (SRO/STO/SRO) capacitorcalculated using the orbital separation approach (OSA). A clear drop in the permittivity is observed at theinterface, reconfirming the dead layer effect mentioned earlier. The calculated capacitance is only 20%of the nominal capacitance, verifying the extremely deleterious effect of the interface on the capacitanceof nanocapacitors. We then sandwiched 3 layers of ferroelectric BaTiO3 (BTO) between SRO and STO.The calculated permittivity profile of this system (Fig. 4) clearly shows that the interfacial dead layer iscountered by the negative capacitance of the ultra-thin BTO film. The capacitance is 70% (40%) larger thanthe SRO/STO/SRO capacitor when negative (positive) bias is applied. We also note that the BTO ultra-thinfilm is centrosymmetric, i.e., the spontaneous polarization is suppressed. The suppression of polarization is,in fact, the prerequisite for ferroelectric negative capacitance [6].

The above results suggest that the utilization of ferroelectric negative capacitance is a viable approachfor capacitance enhancement, especially in view of the problematic intrinsic dead layer. The calculationsperformed are essentially 0 K simulations, so we expect that this effect will be seen at room temperature,rather than at 300℃ reported in the experiment on thicker ferroelectric films [5]. Although we carried outcalculations on capacitors with ultra-thin dielectric films (up to just a few nanometers), the cancellation ofthe dead layer has implications for much thicker capacitors. This is illustrated by the fact that according toour results for the interfacial capacitance, even a 54-nm thick SRO/STO/SRO capacitor is predicted to haveonly 74% of nominal capacitance due to the intrinsic dead layer (such significant impact of the dead layeron the total capacitance was also pointed out in Ref. [4]). Thus, the dead layer cancellation by just three unitcells of BTO at the interface can be expected to enhance the capacitance of capacitors that are much thicker than those explicitly considered in the present simulations.

5 Ferroelectric domain formation in thin-film geometries

We pointed out above that the suppression of spontaneous polarization is required for a ferroelectric toexhibit negative capacitance, and that this is realized for ultra-thin BTO sandwiched between SRO and STO.However, the above calculations only considered the monodomain situation, while it has been pointed outthat even for very thin films, polar distortion can occur by forming 180° striped domains with the polarizationpointing in the out-of-plane direction [7]. If polar distortion occurs, the negative capacitance will not berealized. The literature indicates that domain formation or its suppression depends on the boundary conditionand the specific materials, and no general criteria for spontaneous polarization in ultra-thin films have beenfound.

To help clarify this issue, we performed structural optimization of domain structures in ferroelectric thinfilms to see if spontaneous polarization is stable in various geometries. When considering PbTiO3 in placeof BaTiO3 in the capacitor geometry mentioned above, polarized domains are clearly observed. In contrast,the polarization of BaTiO3 is suppressed in the same geometry, although it is not completely zero as in themonodomain calculation. It is possible that finite temperature effects will reduce the polarization further,although we have not been able to carry out such calculations at the moment.

6 Summary and outlook

We simulated the modulation of ionic carrier concentration and dielectric response at interfaces, and suggestedrecipes for controlling those properties. The understanding obtained here should be helpful in designingnew materials through the active utilization of interfaces that provide better performance or reliabilitycompared to conventional materials. It may even be possible to fabricate materials with novel functionalities.However, ion concentration and dielectric response are semi-static properties of materials. Futureworks on the dynamics of interfaces should have even more impact on the design of interfaces for high performance,reliability, and novel functionalities. We expect that the methodologies and ideas developed inthis dissertation will be instrumental in the future research in that direction.

Fig. 1 Oxygen vacancy concentration and valence band maximum (VBM) profiles calculated in anoxidizing atmosphere (top) and a reducing atmosphere (bottom) for various values of the valence bandoffset(φVBO). The interface with metal is located at z = 0.

Fig. 2 (a) Schematic of the MIM slab structure simulated in this study. The box indicates the boundaries of the periodic boundary condition employed in the calculations. (b) Schematic of the orbital separation procedure within a preset window around the Fermi level.

Fig. 3 The calculated inverse permittivity profile of the SRO/STO/SRO capacitor

Fig. 4 The calculated inverse permittivity profile of the SRO/BTO/STO/SRO capacitor when positive (+) and negative (-) bias is applied on the right electrode.

近年、マテリアルのナノスケール構造制御の技術が進歩するのに伴い、異種マテリアル界面近傍における物性の変調が様々なデバイスの性能に及ぼす影響への関心が高まっている。既に界面近傍での様々な物性変調が報告されているが、物性変調のメカニズムやその制御可能性については、十分明らかにされたとは言い難い。本論文は、第一原理計算をはじめとする計算材料学的手法を用い、酸化物‐金属界面を中心に、異相界面における誘電物性等の変調メカニズムやそのマテリアル依存性を解析し、電子デバイスや電池等の特性を向上させるための設計指針を得ることを目指したものである。本論文は7章からなる。

第1章は緒言であり、異相界面における物性変調に関するこれまでの研究を概観している。特に、燃料電池やリチウムイオン電池におけるイオン輸送および電子デバイスにおける誘電応答に関して異相界面近傍のナノスケール領域における顕著な物性変調が既に報告されていること、しかし実験データ間や計算結果と実験との間に不一致があること等のためにまだその理解は十分とは言え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、本研究の計算手法である密度汎関数法について概説している。密度汎関数法の考え方とその基本方程式であるコーン・シャム方程式について述べた後、交換相関ポテンシャルに対する密度勾配近似、波動関数の平面波展開、および擬ポテンシャル法など、本研究の計算に使用する近似や計算法について概略を述べている。

第3章では、金属‐酸化物界面において生じるイオンキャリアの空間電荷層について解析している。第一原理計算で得られるデータを基に、イオンキャリアの生成と局所ポテンシャルの関係を考慮する連続体モデルを構築し、酸化物としてはイットリア安定化ジルコニウムを具体的な対象として、酸素分圧、温度、および界面の価電子帯オフセットへの空間電荷層分布の依存性を調べた。酸化雰囲気、かつ価電子帯オフセットが大きいほど界面近傍で酸素空孔濃度が減少し、還元雰囲気、かつ価電子帯オフセットが小さいほど逆の傾向を示すことを明らかにした。また、空間電荷層は界面から1 nm 程度の領域に生じるという結果を得たことから、原子層の離散性を陽に考慮した平行薄板モデルを構築し、これを用いた計算も行った。連続体モデルとほぼ同じ結果が得られたことから、本研究の第一原理計算データに基づく連続体モデル計算の妥当性を確認できた。

第4章では、ナノサイズのキャパシタ構造(金属/絶縁体/金属構造)に電圧を印加した状況を第一原理計算によって考慮するために本研究で新たに開発した軌道分離法と、その有用性を確認するために行った計算の結果を述べている。この方法では、フェルミ準位近傍のコーン・シャム軌道を波動関数分布によって2つの金属電極のいずれかに振り分ける。そして、2つの電極に異なるフェルミ準位を与えることにより、電極間にバイアス電圧が印加された状況の第一原理計算を行うことができる。Au/真空/Au、Au/MgO/Auキャパシタについて妥当なキャパシタンス値が得られることを示すと共に、後者では界面近傍での局所誘電率の変調を解析できることも示した。さらに単層グラフェン/真空/単層グラフェンキャパシタについて解析し、グラフェンに特徴的な線形バンド分散からくる量子キャパシタンスに由来するバイアス電圧依存性を再現できることを示した。

第5章では、high-k 材料と金属との界面近傍の誘電応答を調べた結果を述べている。特に、high-k/金属界面の誘電応答特性はバルクに比べて大きく劣ることが知られているのに対し、強誘電体において発現しうる負のキャパシタンスを用いてこれを補う可能性を示した。軌道分離法を用いた計算により、まずSrRuO3/StTiO3/SrRuO3構造において、先行理論研究で指摘された界面近傍での局所誘電率の顕著な低下を再現できることを示した後、SrRuO3/BaTiO3/SrRuO3構造でBaTiO3の層厚が十分薄い場合には負のキャパシタンスが発現することを示した。さらに、SrRuO3/BaTiO3/StTiO3/SrRuO3構造において、膜厚がSrRuO3/StTiO3/SrRuO3構造より厚くなるにもかかわらずキャパシタンスが大きくなること、すなわち負のキャパシタンスによって界面効果を補填できることを示した。

第6章では、強誘電体の自発分極に対するドメイン形成の影響について、第一原理計算により解析している。PbTiO3とBaTiO3の2種類の強誘電体について計算し、分極方向が180度反転したドメイン構造がPbTiO3においてBaTiO3よりも形成されやすいこと、BaTiO3においてはドメイン構造が形成された場合にも分極の大きさがバルクよりずっと小さくなることを示した。これらは絶対零度での計算であり、またドメインサイズについては少数のケースを調べたのみであるので、実験結果との定量的な比較は難しい。しかし、マテリアルによって振舞いに顕著な違いがあることを示した点、およびBaTiO3に関する結果は第5章に述べた負のキャパシタンスによる界面効果の補填がドメイン構造形成の可能性を考慮しても実現しうることを示唆している点で興味深い。

第7章は総括である。

以上のように、本論文は、異相界面近傍のナノスケール領域における物性変調を理論計算により解析した。界面近傍のイオンキャリアの空間電荷層の挙動とその酸素分圧およびバンドオフセットへの依存性を明らかにすると共に、誘電特性解析に関して新たな計算方法を開発し、それを用いてマテリアルおよび積層構造による分極挙動の変化を明らかにして、ナノスケール電気特性を理解する上で有用な知見を得た。よって本論文のナノスケール電子物性学、計算マテリアル工学への寄与は大きい。

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。