Interface Properties of Dielectric Oxides
電介質氧化物的界面特性

1.1 Dielectric Oxides 1.1 電介質氧化物

Dielectric materials are technologically important for electrical insulation, charge storage in capacitors, and for modification of electric fields. In contrast to electrically conducting materials such as metals or semiconductors, which screen the penetration of electric fields by free carriers, electric fields penetrate dielectric materials. An ideal dielectric has no free charges and is therefore also a perfect electrical insulator.
介電材料對於電絕緣、電容器中的電荷儲存以及電場的改變具有重要的技術意義。與金屬或半導體等屏蔽自由載子對電場的穿透的導電材料相比，電場會穿透介電材料。理想的電介質沒有自由電荷，因此也是完美的電絕緣體。

The electrical conductivity of a material is given by:
材料的電導率由下式給出：

(1)

where q_i, n_i, and μ_i are the charge, concentration, and mobility of the different charge carriers. Electrons, holes (unoccupied electronic states in the valence band), and ions can contribute to the overall conductivity. Since mobility of electrons and holes are typically orders of magnitude higher than those of ions at not too high temperatures, their concentration must be low enough to ensure the insulating nature of a material. The concentration of electrons n (holes p) is determined by the distance between the Fermi energy and the minimum of the conduction band E_CB (maximum of the valence band E_VB) via:
其中 q、n 和 μ 是不同電荷載子的電荷、濃度和遷移率。電子、電導率（價帶中未佔據的電子態）和離子可以對整體電導率做出貢獻。由於電子和電洞的遷移率在不太高的溫度下通常比離子的遷移率高幾個數量級，因此它們的濃度必須足夠低，以確保材料的絕緣性質。電子濃度 n（電洞 p）由費米能階與導帶最小值 E _CB （價帶最大值 E _VB ）之間的距離決定：

(2)

where N_CB and N_VB are the density of states in the conduction and valence band and f(E) is the Fermi distribution function. In order to ensure low carrier concentrations, the Fermi energy should remain > 1 eV above E_VB and below E_CB. This is typically considered to be achieved by an energy gap, which separates the highest occupied electronic states in the material from the lowest unoccupied states, of ≥ 3 eV. Here, it must be emphasized, however, that the magnitude of the energy gap is not a sufficient criterion for an electrical insulator. Diamond, for example, which has an energy gap of 5.5 eV,1 can be a p-type semiconductor when doped with boron.2 On the other hand, Ga₂O₃, which has an energy gap of 4.9 eV, becomes an n-type conductor upon doping with tin.3, 4 The origin of the different behavior is related to the defect properties of the materials, which limits the variation of the Fermi energy in the energy gap, and the absolute energy position of the valence band maximum E_VB and conduction minimum E_CB. This will be described in detail in Section IV of this contribution. The different electronic structures are illustrated in Fig. 1.
其中 N _CB 和 N _VB 是導帶和價帶中的態密度，f(E) 是費米分佈函數。為了確保低載子濃度，費米能量應保持高於 E _VB 且低於 E _CB > 1 eV。這通常被認為是透過 ≥ 3 eV 的能隙來實現的，該能隙將材料中最高佔據電子態與最低未佔據電子態分開。然而，這裡必須強調的是，能隙的大小並不是電絕緣體的充分標準。以鑽石為例，它的能隙為5.5 eV，摻雜硼後可以成為p型半導體。 2 另一方面，Ga ₂ O ₃ 的能隙為4.9 eV，摻雜錫後成為n型導體。 3, 4 不同行為的根源與材料的缺陷性質有關，限制了能隙內費米能的變化，以及價帶最大值E _VB 的絕對能量位置和傳導最小值E _CB 。這將在本貢獻的第四節中詳細描述。不同的電子結構如圖1所示。

Materials with lower energy gaps can also be good insulators if undoped. However, it becomes increasingly difficult to prevent charge injection from the electrodes with decreasing energy gap, by which the structure will loose its insulating properties.
如果未摻雜，具有較低能隙的材料也可以是良好的絕緣體。然而，隨著能隙的減小，防止電荷從電極注入變得越來越困難，結構將失去其絕緣性能。

An important parameter for dielectrics is their relative permittivity. Dielectric oxides have relative permittivities from 3.9 for SiO₂ up to several thousands for ferroelectric materials such as BaTiO₃ and Pb(Zr,Ti)O₃.5 The very high values in ferroelectrics are caused by the domain structure, particularly by the movement of domain walls.6 High permittivities are superior for charge storage. Multilayer ceramic capacitors (MLCC), for example, use polycrystalline BaTiO₃ ceramics as dielectric.7 High permittivity (high-k) dielectrics are also relevant for transistor applications, for example to reduce leakage currents in Si MOSFET.8 The role of the high-permittivity dielectric here is to maintain the electric field at the Si/dielectric interface with higher oxide thickness. For Si MOSFET, HfO₂ is the material of choice as it provides sufficiently high permittivity and energy gap as well as low density of interface states due to the formation of Hf–Si oxides and a good compatibility with Si microelectronic processing.9 Dielectrics with permittivity lower than that of SiO₂ are employed as so-called low-k materials, for example in Si microelectronic back-end technology.10 Corresponding materials are, however, no pure metal oxides, but typically organic–inorganic hybrid materials. The interface properties of such materials are not considered in this article.
電介質的一個重要參數是它們的相對介電常數。介電氧化物的相對介電常數從SiO ₂ 的3.9 到鐵電材料（例如BaTiO ₃ 和Pb(Zr,Ti)O ₃ 的數千）。 5 鐵電體中非常高的值是由磁疇結構造成的，特別是由磁疇壁的移動所造成的。 6 高介電常數有利於電荷儲存。例如，多層陶瓷電容器 (MLCC) 使用多晶 BaTiO ₃ 陶瓷作為電介質。 7 高介電常數（高 k）電介質也與電晶體應用相關，例如減少 Si MOSFET 中的漏電流。 8 高介電常數電介質的作用是在具有較高氧化物厚度的 Si/電介質界面處維持電場。對於Si MOSFET，HfO ₂ 是首選材料，因為它提供足夠高的介電常數和能隙，以及由於形成Hf-Si 氧化物而提供的低界面態密度以及與Si 微電子的良好相容性加工。 9 介電常數低於 SiO ₂ 的電介質被用作所謂的低 k 材料，例如在矽微電子後端技術中。 10 然而，相應的材料不是純金屬氧化物，而是典型的有機-無機雜化材料。本文不考慮此類材料的界面特性。

The permittivity of dielectrics is connected to their energy gap, as illustrated in Fig. 2. Permittivities ε ≳ 40 are only obtained with oxides having energy gaps of < 4 eV. With such energy gaps, the barriers for charge injection may become quite small, increasing the importance of leakage. Dielectrics in Si MOSFETs, for example, should have barrier heights > 1 eV to avoid high leakage.8 This usually requires dielectrics with energy gaps ≳ 5 eV which limits the maximum permittivity of suitable dielectrics.
電介質的介電常數與其能隙有關，如圖 2 所示。有了這樣的能隙，電荷注入的障礙可能會變得相當小，增加了洩漏的重要性。例如，Si MOSFET 中的電介質的勢壘高度應 > 1 eV，以避免高洩漏。 8 這通常需要電介質的能隙 ≳ 5 eV，這限制了適當電介質的最大介電常數。

1.2 The Role of Interfaces
1.2 接口的作用

In almost all cases, dielectrics are used in conjunction with metallic electrodes. The fundamental processes at these interfaces are therefore of particular importance. Probably, the most important property is the position of the metal's Fermi energy E_F with respect to the valence band and conduction band edges (E_VB and E_CB) of the dielectric at the interface, which is illustrated in Fig. 3. The differences E_F – E_VB and E_CB – E_F are known as Schottky barrier heights (Φ_B,p and Φ_B,n).
在幾乎所有情況下，電介質都與金屬電極結合使用。因此，這些介面的基本流程尤其重要。也許，最重要的屬性是金屬費米能 E _F 相對於價帶和導帶邊緣（E _VB 和 E _CB ) 的界面電介質，如圖3 所示。基勢壘高度（Φ _B,p 和Φ _B,n ）。

The magnitude of these barriers determines whether charges are injected into the dielectric when a voltage is applied across the opposing electrodes. In the case of thermionic emission (thermal excitation and transport across the barrier), which is often the dominating transport mechanism in the case of dielectrics, the current density depends exponentially on the barrier height Φ_B via the Richardson–Dushman equation (also referred to as Schottky equation)11
這些勢壘的大小決定了當在相對的電極上施加電壓時電荷是否注入電介質中。在熱電子發射（熱激發和穿過勢壘的傳輸）的情況下，這通常是電介質情況下的主要傳輸機制，電流密度透過 Richardson- 指數依賴勢壘高度 Φ _B 杜什曼方程式（也稱為肖特基方程式）11

(3)

where is the effective Richardson constant with the effective mass m*, the elementary charge q, the Boltzmann constant k_B and Planck's constant h. It should be mentioned that the Schottky barrier heights are reduced under applied high electric fields due to the image force effect. This leads to reduction in barrier height with the square root of the electric field.11 There are also additional mechanisms contributing to electronic charge transport across the interface:11 Thermionic field emission, which involves tunneling, is particularly important for highly doped semiconductors and at very high applied voltages. Defect-mediated transport through the space charge region may occur in materials with a high defect concentration. Minority carrier injection and recombination can be safely neglected in dielectric materials due to the high-energy gap.
其中 是有效理查森常數，具有有效質量 m*、基本電荷 q、玻爾茲曼常數 k _B 和普朗克常數 h。應該要提到的是，由於鏡像力效應，在施加高電場的情況下肖特基勢壘高度會降低。這導致勢壘高度隨著電場的平方根而減少。 11 還有其他機制有助於電子電荷在界面上的傳輸： 11 涉及隧道效應的熱離子場發射對於高摻雜半導體和在非常高的外加電壓下尤其重要。透過空間電荷區域的缺陷介導的傳輸可能發生在具有高缺陷濃度的材料中。由於高能隙，介電材料中的少數載子注入和複合可以安全地忽略。

The leakage current through dielectric thin films with blocking electrodes is often limited by charge injection at the electrodes and therefore strongly dependent on electrode material.12-16 For lower barrier heights, the transport through thin films may also become bulk limited by the mobility of the carriers. A recent review of transport through dielectric thin films has been given by Chiu.16
通過具有阻擋電極的介電薄膜的漏電流通常受到電極處的電荷注入的限制，因此強烈依賴電極材料。 12-16 對於較低的勢壘高度，通過薄膜的傳輸也可能受到載子遷移率的限制。 Chiu 最近對介電薄膜的傳輸進行了綜述。 16

Aside from its strong influence on leakage current, the barrier height at a dielectric/metal1 interface can strongly change the electric and dielectric behavior of a device. An example is illustrated in Fig. 4(a), where the current–voltage characteristic of two (Ba,Sr)TiO₃ (BST) thin films with either Pt- or Sn-doped In₂O₃ (ITO) top electrode are compared. Both films were grown under identical conditions on Pt bottom electrodes and are nominally insulating. The current through the Pt/BST/Pt structure is more or less symmetric with a low magnitude, as expected for a dielectric material with blocking electrodes. In contrast, the Pt/BST/ITO structure exhibits a strongly rectifying behavior with a high current density when the ITO electrode is used as cathode (negative voltage polarity). This is a typical behavior for a semiconductor diode. It therefore appears that the top electrode determines whether the BST film is an insulator or a semiconductor. The different behavior can be explained by a negligible barrier for electron injection at the BST/ITO interface, which has been determined by photoelectron spectroscopy.17 Considerably higher barriers are found at the BST/Pt contact.18 The resulting energy band diagrams for the Pt/BST/Pt and the Pt/BST/ITO structures are shown in the inset of Fig. 4(b).
除了對漏電流的強烈影響之外，電介質/金屬 1 界面處的勢壘高度還可以強烈改變裝置的電氣和介電行為。圖 4(a) 顯示了一個範例，其中兩個摻雜 Pt 或 Sn 的 In ₂ (BST) 薄膜的電流-電壓特性 O ₃ (ITO) 頂部電極進行了比較。兩種薄膜都是在相同的條件下在 Pt 底部電極上生長的，並且名義上是絕緣的。通過 Pt/BST/Pt 結構的電流或多或少是對稱的且幅度較低，正如對於具有阻擋電極的介電材料所預期的那樣。相較之下，當ITO電極用作陰極（負電壓極性）時，Pt/BST/ITO結構表現出強整流行為和高電流密度。這是半導體二極體的典型行為。因此看來頂部電極決定了BST膜是絕緣體還是半導體。這種不同的行為可以透過 BST/ITO 介面上電子注入的勢壘可以忽略不計來解釋，這已透過光電子能譜確定。 17 在 BST/Pt 接觸處發現了相當高的勢壘。 18 Pt/BST/Pt 和 Pt/BST/ITO 結構的能帶圖如圖 4(b) 的插圖所示。

The electron injection through the ITO electrode is also apparent in the capacitance–voltage measurements shown in Fig. 4(b). The increased capacitance at low measurement frequency and negative sample bias is caused by the electrons injected from the ohmic ITO contact. The barrier height at the interface therefore affects not only the electric, but also the dielectric behavior of the BST film.
透過 ITO 電極的電子注入在圖 4(b) 所示的電容電壓測量中也很明顯。低測量頻率和負樣品偏壓下電容的增加是由從歐姆 ITO 接觸注入的電子引起的。因此，界面處的勢壘高度不僅影響 BST 薄膜的電學行為，也影響其介電行為。

An alternative explanation for the different behavior of Pt/BST/Pt and Pt/BST/ITO might be a modification of the BST film by the ITO deposition. During deposition of an oxide onto an oxide substrate, oxygen may diffuse from the substrate to oxidize the growing film. This has been reported, for example, during deposition of SrTiO₃ by PLD at 750°C onto different substrates.19-22 While such effects may contribute to the different behavior, they are not expected to be dominant due to the lower deposition temperature of ITO (400°C) and the abundance of oxygen in the sputter deposition process. The presence of a significant amount of excess interstitial oxygen in ITO23 also makes the opposite effect, oxidation of the films during ITO deposition, more likely.
Pt/BST/Pt 和 Pt/BST/ITO 不同行為的另一種解釋可能是透過 ITO 沉積對 BST 薄膜進行修改。在將氧化物沉積到氧化物基板上的過程中，氧可以從基板擴散以氧化生長的膜。例如，在 750°C 下透過 PLD 將 SrTiO ₃ 沉積到不同基材上時就已報道過這一點。 19-22 雖然這些效應可能會導致不同的行為，但由於 ITO 的沉積溫度較低 (400°C) 和濺鍍沉積過程中氧氣含量豐富，因此預計它們不會占主導地位。 ITO 23中大量過量間隙氧的存在也更可能產生相反的效果，即在ITO沉積期間膜的氧化。

Charge injection into (Ba,Sr)TiO₃ thin films is not only possible with ITO electrodes, but has also been reported for films grown on Nb-doped SrTiO₃ single crystals.24 Apparently, and as shown in the inset of Fig. 4(b), ITO and Nb-doped SrTiO₃ form an ohmic contact to (Ba,Sr)TiO₃, which enables charge injection. The formation of ohmic contacts to covalent semiconductors such as Si and GaAs requires a high doping of the interface region as Fermi level pinning by induced gap states is preventing the formation of small barriers (see Section I (C) and Refs. [11, 25]). The BST/ITO example clearly shows that direct ohmic contact formation by small Schottky barrier heights, are possible for oxide semiconductors. Ohmic contacts are, of course, undesirable for dielectric applications, but are required for other applications of such materials, such as the positive temperature coefficient resistors (PTCR).26
(Ba,Sr)TiO ₃ 薄膜的電荷注入不僅可以使用ITO 電極實現，而且也有報導在Nb 摻雜的SrTiO ₃ 單晶上生長的薄膜是可能的。 24 顯然，如圖 4(b) 插圖所示，ITO 和 Nb 摻雜 SrTiO ₃ 與 (Ba,Sr)TiO ₃ 形成歐姆接觸，這啟用電荷注入。與共價半導體（例如Si 和GaAs）形成歐姆接觸需要對界面區域進行高摻雜，因為誘導間隙態的費米能階釘扎會阻止小勢壘的形成（參見第I 節(C) 和參考文獻[11, 25] ]）。 BST/ITO 範例清楚地表明，對於氧化物半導體，透過小蕭特基勢壘高度形成直接歐姆接觸是可能的。當然，歐姆接觸對於介電應用來說是不受歡迎的，但對於此類材料的其他應用是必需的，例如正溫度係數電阻器（PTCR）。 26

Interfaces between two dielectrics can also modify the (di-)electric behavior of a material in a device considerably. Such interfaces occur, for example, in sintered doped ceramics in the case of segregation of secondary phases as in varistors,27 or in ceramics sintered from core–shell particle structures.28 Interfaces between dielectrics are inherent in thin film heterostructures. The most prominent example is that provided by the SrTiO₃/LaAlO₃ interface, which shows a two-dimensional electron gas (2DEG) if the LaAlO₃ thickness is four unit cells or more.29, 30 The origin of the 2DEG has been intensively discussed in the last decade.31 Most popular is the polar catastrophe model, which is based on the internal potential drop in the LaAlO₃ layer due to the polar nature of the LaAlO₃.29, 30, 32
兩種電介質之間的界面還可以顯著改變裝置中材料的（介）電行為。例如，在壓敏電阻中二次相偏析的燒結摻雜陶瓷中，27 或由核殼顆粒結構燒結而成的陶瓷中，就會出現這種界面。 28 電介質之間的界面是薄膜異質結構所固有的。最突出的例子是 SrTiO ₃ /LaAlO ₃ 界面提供的，如果 LaAlO ₃ 厚度，則顯示二維電子氣 (2DEG)是四個單元電池或更多。 29, 30 2DEG 的起源在過去十年中得到了廣泛的討論。 31 最受歡迎的是極地災難模型，該模型基於由於 LaAlO ₃ 的極性而導致 LaAlO ₃ 層內部電位下降。 29、30、32

Charges will naturally accumulate at interfaces between two dielectrics when a current is flowing across it. The reason is the mismatch of electrical conductivity and dielectric permittivity. The electric current density is the same in both materials, hence where σ_1,2 are electric conductivities of the materials and E_1,2 the respective electric fields. On the other hand, the dielectric displacements must fulfill , where ε_1,2 are the dielectric constants of the materials and Σ is the interface charge density. As σ₁/σ₂ is generally different from ε₁/ε₂, both conditions can only be satisfied if Σ ≠ 0. Due to the low conductivity of dielectrics, the charges may remain at the interface for a considerable time even after the electrical current is switched off.
當電流流經兩個電介質時，電荷會自然地累積在兩個電介質之間的界面。原因是電導率和介電常數不符。兩種材料中的電流密度相同，因此 其中 σ _1,2 是材料的電導率，E _1,2 是各自的電場。另一方面，介電位移必須滿足 ，其中 ε _1,2 是材料的介電常數，Σ 是界面電荷密度。由於σ ₁ /σ ₂ 通常與ε ₁ /ε ₂ 不同，因此只有當Σ ≠ 0 時才能滿足這兩個條件由於電介質的電導率較低，即使在電流關閉後，電荷仍可能在界面上保留相當長的時間。

An example for interface charging has been reported for (Ba,Sr)TiO₃/Al₂O₃ thin film heterostructures.33 In these structures, the thin (< 5 nm) Al₂O₃ layer facilitates tunnel injection of charges from the electrode through the Al₂O₃ into the (Ba,Sr)TiO₃ as it has a much lower permittivity than (Ba,Sr)TiO₃.34, 35 Dielectric measurements revealed that both negative and positive charges can be stored at the (Ba,Sr)TiO₃/Al₂O₃ interface.33 This is evident from a striking modification of the capacitance–voltage dependence, which was changing from that of a field -dependent (tunable) dielectric as observed for high frequencies in Fig. 4 to a ferroelectric-like hysteresis behavior shown in Fig. 5. The hysteresis is not only observed for (Ba,Sr)TiO₃, but also for pure SrTiO₃ layers. As the Al₂O₃ is deposited on top of the (Ba,Sr)TiO₃ or SrTiO₃, strain effects, which can also induce ferroelectric behavior,36 can also be ruled out as origin for this phenomenon, making interface charges the most likely explanation for the behavior observed in Fig. 5
(Ba,Sr)TiO ₃ /Al ₂ O ₃ 薄膜異質結構的界面充電範例已被通報。 33 在這些結構中，薄 (< 5 nm) Al ₂ O ₃ 層有助於電荷從電極通過 Al ₂ O ₃ 進入(Ba,Sr)TiO ₃ ，因為它的介電常數比(Ba,Sr)TiO ₃ 低很多。 34, 35 介電測量表明，(Ba,Sr)TiO ₃ /Al ₂ O ₃ 界面上可以儲存負電荷和正電荷。 33 這從電容電壓依賴性的顯著變化中可以明顯看出，電容電壓依賴性從圖 4 中高頻觀察到的場相關（可調諧）電介質變化為圖 5 中所示的類鐵電磁滯行為不僅在(Ba,Sr)TiO ₃ 中觀察到滯後現象，在純SrTiO ₃ 層中也觀察到滯後現象。由於 Al ₂ O ₃ 沉積在 (Ba,Sr)TiO ₃ 或 SrTiO ₃ 頂部，應變效應，這也可以誘導鐵電行為，36也可以被排除為這種現象的起源，使得界面電荷成為圖5中觀察到的行為最可能的解釋

At interfaces between two dielectrics, the relative position of the valence band maxima and the conduction band minima of the respective materials, which is called energy band alignment, is one of the fundamental properties of the interface affecting electrical device behavior. In addition, the energy band alignment provides a comparison of the absolute values of E_VB and E_CB, which can be used to rationalize different electrical properties of materials. 37-42 The discontinuities (offsets) in the valence and conduction band, ΔE_VB and ΔE_CB (see Fig. 3), form barriers for electronic charge transport comparable to the situation at dielectric/metal interfaces. The energy band alignment at dielectric/metal- and dielectric-heterointerfaces, i.e., the magnitudes of Schottky barrier heights and band discontinuities, is affected by the choice of dielectric and electrode material.
在兩種電介質之間的界面處，各自材料的價帶最大值和導帶最小值的相對位置（稱為能帶排列）是影響電氣裝置行為的界面的基本屬性之一。此外，能帶排列提供了E _VB 和E _CB 絕對值的比較，可用於合理化材料的不同電氣特性。 37- 42 價帶與導帶的不連續性（偏移）ΔE _VB 和 ΔE _CB （見圖 3）形成電子電荷傳輸的勢壘，與電介質/金屬介面.電介質/金屬和電介質異質界面的能帶排列，即肖特基勢壘高度和能帶不連續性的大小，受到電介質和電極材料選擇的影響。

Interfaces not only affect the (di)electric properties of dielectric oxides, but also the long-term behavior. It is well-known that the electrical fatigue of Pb(Zr,Ti)O₃ thin films, which can limit the application considerably, is strongly affected by the electrode material.43-46 The relation of dielectric breakdown to defect properties47 and the potential generation of defects by the electrode processing26, 48, 49 also provide a connection between dielectric breakdown and interface properties. Furthermore, dielectric/metal interfaces are highly relevant for resistive switching, a promising new memory concept based on electrically switchable electronic conductance.50-53
界面不僅影響介電氧化物的（介電性能，也影響其長期行為。眾所周知，Pb(Zr,Ti)O ₃ 薄膜的電疲勞受到電極材料的強烈影響，大大限制了其應用。 43-46 介電擊穿與缺陷特性47的關係以及電極處理26、48、49可能產生的缺陷也提供了介電擊穿與界面特性之間的連結。此外，電介質/金屬介面與電阻開關高度相關，電阻開關是一種基於電可開關電子電導的有前途的新儲存概念。 50-53

1.3 Physical Models for Interfaces of Semiconductors and Dielectrics
1.3 半導體和電介質界面的物理模型

This section summarizes briefly the physical understanding of semiconductor/metal interfaces and semiconductor heterointerfaces. A more extensive description of the different models of semiconductor interface formation has been given by Tung.25
本節簡要總結了半導體/金屬界面和半導體異質界面的物理理解。 Tung 對半導體界面形成的不同模型進行了更廣泛的描述。 25

Semiconductors and dielectrics are, with respect to the fundamental description of barrier formation, identical materials as long as perfect crystalline structures are under consideration. The differences, for example in band gaps, permittivity and conductivity, are only quantitative and in principle, the same physical concepts should be valid for both. However, technologically important semiconductors such as Si and the III–V compounds are more covalently bonded than dielectric oxides. The physical models developed to describe the properties of semiconductor interfaces are mostly related to covalently bonded materials. On the contrary, dielectric oxides are, like the II–VI semiconductors, more ionically bonded. To the understanding of the author of this article, the main difference between “semiconductors” and “dielectrics” is related to the different ionicity of the chemical bonds and the respective different defect properties. Formation of point defects generally requires higher energies in covalent than in ionic materials, which is related to the higher defect charge. This is why point defects are neglected in many physical models on semiconductor interfaces, although interface defect formation or reactions have been shown to affect barrier formation considerably.48, 49, 54-56 There are nevertheless some fundamental differences between interfaces of covalent and ionic semiconductors, which can be explained without involving defects. The influence of defects on interface properties has been summarized recently for chalcogenide semiconductors, which are important for thin-film solar cells.57
就勢壘形成的基本描述而言，只要考慮完美的晶體結構，半導體和電介質就是相同的材料。帶隙、介電常數和電導率等方面的差異只是定量的，原則上，相同的物理概念應該對兩者都有效。然而，技術上重要的半導體（例如矽和 III-V 族化合物）比電介質氧化物的共價鍵更強。為描述半導體界面特性而開發的物理模型大多與共價鍵結材料有關。相反，介電氧化物與 II-VI 族半導體一樣，離子鍵結程度較高。根據本文作者的理解，「半導體」和「電介質」之間的主要差異與化學鍵的離子性不同以及各自不同的缺陷性質有關。點缺陷的形成通常需要共價材料比離子材料更高的能量，這與較高的缺陷電荷有關。這就是為什麼在半導體界面的許多物理模型中點缺陷被忽略的原因，儘管界面缺陷的形成或反應已被證明會顯著影響勢壘的形成。 48, 49, 54- 56 儘管如此，共價半導體和離子半導體的界面之間仍然存在一些基本差異，可以在不涉及缺陷的情況下對其進行解釋。最近總結了硫族化物半導體的缺陷對界面性質的影響，這對薄膜太陽能電池很重要。 57

In the early physical models on barrier formation, barrier heights and band offsets were derived from a vacuum level alignment as illustrated for doped and undoped semiconductors in Figs. 3(b) and (c). The vacuum level alignment is known as electron affinity rule (EAR), as the barrier height for electrons Φ_B,n and the conduction band discontinuity ΔE_CB are obtained directly from the difference of electron affinities χ. Here, the electron affinity of a metal is the same as its work function. For semiconductor/metal interfaces and semiconductor heterointerfaces, the EAR is more generally known as Schottky–Mott58, 59- and Anderson60- rule, respectively.
在關於勢壘形成的早期物理模型中，勢壘高度和能帶偏移源自真空能階對準，如圖 1 和 2 中摻雜和未摻雜半導體所示。 3(b)和(c)。真空能階排列稱為電子親和力規則（EAR），因為電子的勢壘高度 Φ _B,n 和導帶不連續性 ΔE _CB 直接從電子親和力的差異獲得χ 。這裡，金屬的電子親和勢與其功函數相同。對於半導體/金屬界面和半導體異質界面，EAR 通常分別稱為肖特基-莫特 58、59 和安德森 60 規則。

It has early been recognized in semiconductor interface science that the EAR does not properly describe the dependence of Schottky barrier heights on the metal's function.61 On the contrary to what is suggested by the Schottky–Mott rule, the barrier heights at the interfaces of the more covalently semiconductors are rather independent on the contact material. As the barrier heights correspond with the Fermi level position at the contact (see Fig. 3), the independence of barrier height on metal has been coined Fermi level pinning. Fermi level pinning is related to the formation of interface states in the semiconductor band gap. The charges trapped in the interface states, together with the charges at the metal surface, form an interface dipole, which modifies the barrier height as illustrated in Fig. 3(d).62 In the limit of a high concentration of interface trap states (≥1014 eV⁻¹ cm⁻²), the so-called Bardeen limit, the Fermi level position at the interface is determined by the charge neutrality level E_CNL, which is associated with the interface states.
半導體界面科學界很早就意識到，EAR 並沒有正確描述肖特基勢壘高度對金屬功能的依賴。 61 與肖特基-莫特規則所建議的相反，共價半導體界面上的勢壘高度相當獨立於接觸材料。由於勢壘高度與接觸處的費米能階位置相對應（見圖 3），勢壘高度對金屬的獨立性稱為費米能階釘扎。費米能階釘扎與半導體帶隙中界面態的形成有關。界面態中捕獲的電荷與金屬表面的電荷一起形成界面偶極子，它改變了勢壘高度，如圖 3(d) 所示。 62 在界面陷阱態高濃度的極限下（≥10 14 eV ⁻¹ cm ⁻² ），即所謂的巴丁極限，界面處的費米能階位置被決定電荷中性水平E _CNL ，其與界面態相關。

Interface states are intrinsic to all semiconductor/metal interface. A physical description of the situation is based on Metal-Induced Gap States (MIGS), which result from the coupling of the metal's wave function with the virtual gap states2 of the semiconductor.63 The existence of such states is evident from density functional theory calculations of a Si/Al interface by Louie and coworkers.64
界面態是所有半導體/金屬界面所固有的。這種情況的物理描述是基於金屬感應能隙態 (MIGS)，它是金屬波函數與半導體虛擬能隙態 2 耦合的結果。 63 Louie 及其同事對 Si/Al 界面的密度泛函理論計算證明了這種狀態的存在。 64

The fact that the induced gap states are intimately related to the virtual gap states of the semiconductor and hence to its electronic band structure has the consequence that the induced gap states and the related charge neutrality level do not depend on the contact material. In the case of strongly pinned semiconductors such as Si, one would therefore expect that the barrier height does not depend on interface orientation. This is not generally true. Epitaxial Si/silicide junctions show a considerable dependence of barrier height on interface preparation and termination, for example.65
感應帶隙態與半導體的虛擬帶隙態密切相關並因此與其電子能帶結構密切相關的事實導致感應帶隙態和相關的電荷中性水平不依賴接觸材料。因此，在強釘扎半導體（例如 Si）的情況下，人們會期望勢壘高度不依賴界面取向。這通常不是真的。例如，外延矽/矽化物結顯示勢壘高度對界面製備和終止有相當大的依賴。 65

Charge neutrality levels of a number of semiconductors have been calculated using a Greens function approach for the electronic structure of semiconductors by Tersoff.66 These revealed the so-called branch point energies, which correspond to the transition between dominating valence and dominating conduction band character of the gap states. Tersoff also emphasized that the same approach is valid not only at semiconductor/metal interfaces, but also at semiconductor heterointerfaces. In the case of a high density of induced interface states, the energy band alignment is then determined by alignment of the charge neutrality levels, rather than of the vacuum level.67 Cardona and Christensen later used dielectric midgap energies as an alternative way for deriving charge neutrality levels.68 An additonal approach based on linear combination of atomic orbital (LCAO) theory for semiconductor band structures69 to determine charge neutrality levels has been put forward by Harrison and Tersoff and by Mönch.70, 71 A summary of charge neutrality levels calculated using the different approaches can be found in the article of Tung.25
Tersoff 使用半導體電子結構的格林函數方法計算了許多半導體的電荷中性水平。 66 這些揭示了所謂的分支點能量，它對應於能隙態的主導價態和主導導帶特徵之間的轉變。 Tersoff 也強調，同樣的方法不僅適用於半導體/金屬界面，也適用於半導體異質界面。在誘導界面態密度高的情況下，能帶排列是由電荷中性能階的排列而非真空能階的排列決定。 67 Cardona 和 Christensen 後來使用介電中帶隙能量作為推導電荷中性水平的替代方法。 68 Harrison 和 Tersoff 以及 Mönch 提出了一種基於半導體能帶結構的原子軌道線性組合 (LCAO) 理論的附加方法 69 以確定電荷中性水平。 70, 71 使用不同方法計算的電荷中性水平的摘要可以在 Tung 的文章中找到。 25

Induced gap states provide the physical basis for understanding Fermi level pinning at semiconductor interfaces. Fermi level pinning is, however, not a general phenomenon. It is particularly pronounced for more covalently bonded semiconductors and less effective in ionically bonded materials (see Fig. 6).72 In principle, dielectric oxides belong to the latter group of materials as evident from Fig. 6. The difference between covalent and ionic semiconductors becomes clear when the barrier heights are plotted versus the work function (or the related electron affinity71) of the contact materials. The dependence of barrier height on the metal's work function reveals the interface index S, which can vary between 0 and 1 as illustrated in Fig. 6.72 The barrier height for electrons is then given by:
感應間隙態為理解半導體介面上的費米能階釘扎提供了物理基礎。然而，費米能階釘扎並不是普遍現象。對於共價鍵結較多的半導體尤其明顯，而對於離子鍵結材料則效果較差（見圖 6）。 72 原則上，電介質氧化物屬於後一組材料，如圖6 所示。的差異變得清晰材料。勢壘高度對金屬功函數的依賴性揭示了界面指數 S，它可以在 0 和 1 之間變化，如圖 6 所示。

(4)

Cowley and Sze62 described the various degrees of Fermi level pinning using a phenomenological model where the interface states in the semiconductor are separated from the metal surface by an interface layer of thickness d_int and permittivity ϵ_int, as illustrated in Fig. 6. They obtained a dependence of the interface index S on the density of interface states in the semiconductor as
Cowley 和Sze 62 使用唯像模型描述了不同程度的費米能階釘扎，其中半導體中的界面態透過厚度為d _int 和介電常數ϵ _int

(5)

where N_int is the areal density of interface states per electron volt. The dependence of S on N_int for two different values of ϵ_int is also included in Fig. 6. The interface layer adds a serial capacitance to the space charge or bulk capacitance and is comparable to a dead layer, which reduces the effective capacitance in thin high permittivity capacitors.73
其中 N _int 是每電子伏特界面態的面密度。對於兩個不同的 ϵ _int 值，S 對 N _int 的依賴性也包含在圖 6 中。死層相當，它降低了薄型高介電常數電容器的有效電容。 73

The dependence of the interface index S on the ionicity of the semiconductor can also be regarded as a dependence on semiconductor energy gap. Higher energy gaps generally lead to a higher S, as the induced gap states decay faster away from the interface.64 This relation is not surprising when recalling that the energy gap, at least for tetrahedrally coordinated semiconductors, increases with ionicity.1
界面指數S對半導體離子性的依賴性也可以被視為對半導體能隙的依賴性。較高的能隙通常會導致較高的 S，因為感應間隙態在遠離界面時衰減得更快。 64 當回想起能隙（至少對四面體配位半導體而言）隨著離子性增加而增加時，這種關係並不奇怪。 1

Mönch has found an empirical relation for the interface index S:74, 75
Mönch 發現了界面指數 S 的經驗關係：74, 75

(6)

This relation has been used by Robertson to derive the interface index of number of dielectric oxides,76 which range from 0.18 for TiO₂ to 0.86 for SiO₂. According to this work, dielectric oxides may therefore also show a pronounced Fermi level pinning. The low S for TiO₂ is, however, not consistent with interface experiments using nonreactive contact partners [for a more detailed description see Section III (A)].
Robertson 使用這種關係推導了介電氧化物數量的界面指數 76，其範圍從 TiO ₂ 的 0.18 到 SiO ₂ 的 0.86。根據這項工作，介電氧化物也可能表現出明顯的費米能階釘扎。然而，TiO ₂ 的低 S 與使用非反應性接觸夥伴的界面實驗不一致[更詳細的描述請參閱第 III (A) 節]。

Using experimental electron affinities, the S values calculated using Eq. 6, and charge neutrality levels calculated using the Greens function approach, Robertson has further derived a number of band alignments of dielectric oxides and other semiconductors.76 An explicit comparison between calculation and experiment is given for Ta₂O₅, which exhibits an interface index of S ≈ 0.5.77
使用實驗電子親和力，使用方程式計算 S 值。如圖6所示，並使用格林函數方法計算電荷中性水平，羅伯遜進一步推導出電介質氧化物和其他半導體的許多能帶排列。 76 對 Ta ₂ O ₅ 給出了計算與實驗之間的明確比較，其界面指數為 S ≈ 0.5。 77

The determination of Schottky barrier heights and band discontinuities from Eq. 4 requires electron affinities or ionization potentials of the semiconductors (dielectrics), which are not a unique number for a given material. This is the case even for nonpolar materials such as Si78 or only slightly polar materials such as GaAs.79 In general, the electron affinity depends on surface orientation and surface termination and can vary by more than 1 eV in the case of oxides. The dependencies have been studied explicitly for ZnO, SnO₂, and In₂O₃,80-82 but are mostly unknown for other oxides. Studies on a number of oxides are currently ongoing in our laboratory. The surface structures of different oxides have been studied extensively using theoretical techniques by Noguera and coworkers.83, 84
根據方程式確定肖特基勢壘高度和能帶不連續性。 4 需要半導體（電介質）的電子親和勢或電離勢，這對於給定材料來說不是唯一的數字。即使對於 Si 78 等非極性材料或 GaAs 等微極性材料也是如此。 79 一般來說，電子親和勢取決於表面取向和表面終止，在氧化物的情況下變化可能超過 1 eV。已經明確研究了 ZnO、SnO ₂ 和 In ₂ O ₃ 、 80- 82 的依賴性，但對於其他氧化物大多未知。我們的實驗室目前正在進行多種氧化物的研究。諾格拉及其同事利用理論技術對不同氧化物的表面結構進行了廣泛的研究。 83, 84

1.4 Scope of the Article
1.4 本條的範圍

The focus will be on the underlying physical and chemical factors governing interface formation and how they might be manipulated by sample processing rather than provide a comprehensive summary of experimental data. Examples for the observed phenomena will be provided using SrTiO₃, (Ba,Sr)TiO₃, BaTiO₃, Pb(Zr,Ti)O₃, ZrO₂, and TiO₂.
重點將放在控制界面形成的潛在物理和化學因素以及如何透過樣品處理來操縱它們，而不是提供實驗數據的全面總結。將使用 SrTiO ₃ 、(Ba,Sr)TiO ₃ 、BaTiO ₃ 、Pb(Zr,Ti)O ₃ 、ZrO ₂ 和TiO ₂ 。

3.1 Deposition of Metals onto Dielectric Oxides
3.1 金屬在電介質氧化物上的沉積

Interface studies in which semiconductors have been used as substrates for metal deposition are quite abundant in literature. Dielectrics are less frequently used due to their low conductivity. Studies of dielectric interfaces therefore use mostly thin films or electrically conducting bulk material. The latter is feasible for such dielectrics, which can be made conductive by doping or reduction/oxidation. Examples for such materials are TiO₂, SrTiO₃, or BaTiO₃, which become n-type conductors upon donor doping with Nb or La or by chemical reduction.101-106 Why some dielectrics become conducting upon doping and others not will be discussed in Section IV.
使用半導體作為金屬沉積基底的界面研究在文獻中相當豐富。由於電介質的電導率較低，因此較少使用。因此，介電界面的研究主要使用薄膜或導電塊體材料。後者對於此類電介質是可行的，可以透過摻雜或還原/氧化使其導電。此類材料的例子有TiO ₂ 、SrTiO ₃ 或BaTiO ₃ ，它們在用Nb 或La 施主摻雜或經由化學還原後變成n型導體。 101- 106 為什麼有些電介質在摻雜後會導電而有些電介質不會導電，將在第四節中討論。

The deposition of metals onto a dielectric oxide very often leads to a partial chemical reaction with the substrate. Such reactions are often evident from the observation of a metallic species formed by the cation of the substrate. This is not surprising if metals are deposited, which form a stable oxide like Al, but quite unexpected for deposition of inert metals such as Pt or Au.18, 96, 99, 107, 110 An example for such reactions is given in Fig. 10, which displays the Pb 4f spectra of three PZT thin films in the course of stepwise deposition of Cu, Ag, and Pt, respectively.109 The samples were cleaned by heating in 0.5 Pa O₂ before metal deposition. In all cases, a metallic Pb species appeared in the course of deposition.
金屬在介電氧化物上的沉積經常導致與基材發生部分化學反應。透過觀察由基材的陽離子形成的金屬物質，這種反應通常是顯而易見的。如果金屬沉積形成穩定的氧化物（如 Al），這並不奇怪，但對於惰性金屬（如 Pt 或 Au）的沉積則完全出乎意料。 18, 96, 99, 107, 110 圖10給出了這種反應的一個例子，它分別顯示了在逐步沉積Cu、Ag和Pt的過程中三個PZT薄膜的Pb 4f光譜。 109 在金屬沉積之前，透過在 0.5 Pa O ₂ 中加熱來清潔樣品。在所有情況下，沉積過程中都會出現金屬鉛物質。

In principle, thermodynamic reactions at a metal–oxide interface can be predicted from the relation111

(7)

where the formation of a solution A_xM_y of the substrate cation and the deposited metal is taken into account. Metallic phases of the substrate's cation and the deposited metal are not considered in this reaction as they do not constitute a thermodynamic driving force for the reaction because their standard heat of formation is 0. The standard heat of reaction for (7) is:

(8)

where is the standard heat of formation of the compound XY. ΔH_r should, in principle, be negative for the reaction to occur spontaneously if entropy contributions can be neglected.

Taking the above into account, one would not expect that the deposition of Pt or Au leads to an interface reaction as the heat of formation of PtO₂ or AuO_x are low. The reactivity observed in Fig. 10 and at other oxide/Pt or oxide/Au interfaces is clearly not related to the kinetic energy of the deposited particles, as they are also observed if the metals are deposited by thermal evaporation.108, 112, 113 An additional energy input, which is not considered in (8), is the heat of condensation of the metal atoms, which has been suggested by Spicer et al. to be a potential source of defect formation at an interface.54 The heat of condensation of Pt on BaTiO₃, for example, has been calculated to be ~4 eV,114 which is sufficient to cause defect formation at the surface of most metal oxides. It is expected, however, that the effect is not present when inert metals are deposited onto metal oxides with a high heat of formation, such as Al₂O₃, Ga₂O₃, or SiO₂. This agrees with the observation that flat band potential in Si/SiO₂/metal diodes can be adjusted by the metal's work function.1 In contrast, the Schottky barriers in Si/HfO₂/metal diodes exhibit Fermi level pinning for the more reactive interfaces.115

The deposition-induced defects lead to a Fermi level pinning at the interface. This is evident from the barrier heights of metals on PZT, which are displayed in the lower part of Fig. 10. Despite the considerable differences in work function of Cu (φ = 4.9 eV), Ag (φ = 4.5 eV), and Pt (φ= 5.6 eV), all three metals result in similar barrier heights at the interface of Φ_B,p = 1.7 ± 0.1 eV.

Brillson has emphasized that the barrier heights are correlated with the interface reaction.48, 49 Heats of formation for oxides of potential gate metals for high-k dielectrics are given by Robertson et al.115 These metals exhibit a clear correlation between their work function and the heat of formation of their oxide. The higher work function metals, which should form high Schottky barriers for electrons, show less interface reactions. As the interface reaction generates defects, in the case of dielectric oxides mostly oxygen vacancies,26, 48 the Fermi level at the interface becomes pinned at the energy level associated with the defect (oxygen vacancy). The barrier heights of low work function (reactive) metals are therefore mostly insensitive to the metal's work function, as they are dominated by defect formation. In the case of ZnO, the assignment of Fermi level pinning to oxygen vacancies is furthermore supported by the Fermi level position at the pinned interfaces, which corresponds well with the energy level of the oxygen vacancy in ZnO.99, 116

A way to overcome defect formation by metal deposition is by depositing metal oxides. Examples for high and low work function metal oxides are RuO₂ and ITO. The former is a metal with a work function of ~6 eV117 and the latter a degenerately doped semiconductor with a work function of ~4.5 eV.95 No substrate reduction during deposition of these materials is expected. The Fermi level positions at the interfaces of Pb(Zr,Ti)O₃ and (Ba,Sr)TiO₃ with RuO₂ and ITO vary by more than one electronvolt.93 There is hence no Fermi level pinning at these interfaces, which further supports the conclusion that deposition-induced defect formation is the origin of the Fermi level pinning at oxide/metal interfaces and not intrinsic interface states. This is also strongly indicated by the observation that the barrier heights can be changed dramatically by postdeposition treatments, which will be presented in Section III (C). To which extend oxygen exchange between substrate and film during formation of heterostructures between two metal oxides,19-22 which changes defect concentrations in the substrate and the film, can also be an origin of Fermi level pinning is not yet elucidated.

Barrier heights of ITO and RuO₂ on anatase and rutile TiO₂ differ by only ~0.7 eV.118 This is less than for SrTiO₃ and Pb(Zr,Ti)O₃  indicating a lower S value for TiO₂. Nevertheless, the difference is considerably higher than what would be expected for , which has been calculated by Robertson.76

The barrier heights of reactive and nonreactive interfaces of PZT and SrTiO₃ are displayed in Fig. 11. Here, a reactive interface is identified by the appearance of reduced cation species of the oxides in the XPS core level spectra. It should be mentioned, however, that the reduction in the oxide is not always evident from the formation of a metallic species of a substrate cation as in the case of PZT (see Fig. 10 and Refs. [96, 107, 109]) or SnO₂.110, 119 No metallic species are observed during metal deposition on SrTiO₃, for example.18, 109 In the case of SrTiO₃, reduction in the substrate can be evident either directly from the formation of Ti³⁺ species18, 109 or indirectly from the observation of oxygen on the deposited metal's surfaces.108 It will be shown later in Section III (C), that oxidation/reduction of a SrTiO₃ surface is not necessarily related to the observation of Ti³⁺. The pinning of the Fermi level by deposition induced defects is evident in Fig. 11 for the strongly reactive interfaces.

As in the case of ZnO, one could estimate the oxygen vacancy level in SrTiO₃ and Pb(Zr,Ti)O₃ from the Schottky barrier heights for the strongly reactive interfaces. According to Fig. 11 the oxygen vacancy level in SrTiO₃ should be slightly above the conduction band minimum and that of Pb(Zr,Ti)O₃ approximately in the middle of the band gap. For SrTiO₃, this is consistent with the postdeposition treatments discussed in Section III (C), as the Fermi level position for the most reduced sample is inside the conduction band. An oxygen vacancy level inside the conduction band is furthermore indicated by the observation that room-temperature electron concentrations above 1020 cm⁻³ can be achieved with reduced SrTiO₃,102, 103 and by the fact that surface oxygen vacancies can induce a two-dimensional electron gas at the surface.120 Defect calculations also indicate that the doubly charged oxygen vacancy provides electrons with energy above the conduction band minimum.31, 121 In addition, reactive interfaces form ohmic contacts to BaTiO₃.26 No comparable studies are available for Pb(Zr,Ti)O₃. The observation that the pinning level in Pb(Zr,Ti)O₃ is deeper in energy than that of SrTiO₃ is, however, consistent with the fact that the band egdes in Pb(Zr,Ti)O₃ are higher in energy than those of SrTiO₃, which is derived from energy band alignment measurements37 (see Section IV).

Allen and Durbin have used a modified pulsed laser deposition technique and a high Ar pressure of 100 mbar to deposit metals on ZnO surfaces.116 With this techniques, it has also been possible to overcome deposition-induced oxygen vacancy formation and obtain higher Schottky barriers.99 Von Wenckstern et al. and Hirose et al. could also prepare high Schottky barriers on n-type conducting In₂O₃ and SrTiO₃, which indicates absence of oxygen vacancy formation, by depositing Pt in an oxygen ambient.100, 122 Such deposition leads, however, to the formation of Pt-oxide,123 which results naturally in a different barrier compared to that of Pt due to its different work function [see also Section III (B)].

Deposition-induced defect formation should be particularly pronounced if the metal deposition is performed by condensation of atomic species from the gas phase, like in evaporation, sputtering, or pulsed laser deposition. The effects may not be present when chemical vapor deposition or solution-based deposition techniques are applied. In these cases, the metal atoms in the gas phase are already coordinated by ligands or solvents and do therefore release only a fraction of the condensation energy directly to the oxide surface. In case the surface of the material is contaminated, for example by adsorbed water or hydrocarbons, the reduction in the surface may be prevented as the metals are condensing on the adsorbates and not directly on the substrate surface. To obtain particular electrode properties, it is therefore important to consider not only the work function and reactivity of the contact metal, but also to choose appropriate deposition techniques and surface pretreatments.

3.2 Growth of Dielectric Oxides on Metals

In contrast to metal deposition onto dielectrics, studies of interface formation with photoelectron spectroscopy in which dielectric oxides are deposited onto metal substrates are scarce. It is immediately clear, however, that the conditions during preparation of the interface are substantially different from those during deposition of metals onto dielectric oxides. The deposition of metals corresponds to a more reducing situation while the deposition of oxides requires a minimum oxygen activity, which corresponds to more oxidizing conditions. The formation of interfacial oxygen vacancies is therefore suppressed when dielectric oxides are grown on metal surfaces. The asymmetric deposition conditions can result in different barrier heights at a metal/dielectric as compared to a dielectric/metal interface. This has been explicitly demonstrated for Pt/(Ba,Sr)TiO₃/Pt thin film structures, where Φ_B,n = 1 eV at the bottom Pt/(Ba,Sr)TiO₃ interface and Φ_B,n = 0.4 eV at the top (Ba,Sr)TiO₃/Pt interface. This difference explains the often reported polarity-dependent leakage current of such structures.

Due to the higher oxygen activity during deposition of dielectrics, the metal substrate may oxidize during growth. This is clear if reactive metal substrates are used, which easily form oxides. Formation of oxides may also occur on inert substrates such as Pt. This is particularly observed at lower deposition temperatures. An example for the formation of PtO₂ after deposition of ~4 nm thick ZrO₂ films is shown in Fig. 12. The films were deposited by reactive magnetron sputtering, i.e., by sputtering from a metallic Zr target in an Ar/O₂ gas mixture.124 During this process, the ionized oxygen in the sputter gas is accelerated toward the substrate. The oxygen ions can have energies corresponding to the discharge voltage, which, in the case DC excitation used in the presented experiments, is ~400 eV.125 This oxygen bombardment during film growth is the source of Pt oxidation.

The oxidation of the Pt is evident from the Pt 4f spectra shown in Fig. 12, which are dominated by PtO₂ emissions when the ZrO₂ films were grown at room temperature or at 200°C. The characteristic Fermi edge emission of metallic Pt is also absent in the corresponding valence band spectra. It is mentioned that the Pt substrate, which has been grown by magnetron sputtering on a sapphire substrate before ZrO₂ deposition, shows no evidence for PtO₂. The PtO₂ signatures are still present, although considerably reduced, if the ZrO₂ is grown at 400°C. A metallic Pt 4f doublet and the characteristic Fermi edge of metallic Pt are now clearly observed. No PtO₂ is observed for higher deposition temperatures.18 The reason for the absence of PtO₂ at higher growth temperature is the limited thermal stability of this compound.123 Annealing of the room temperature grown Pt/ZrO₂ sample at 400°C also removes the PtO₂ (see top spectra in Fig. 12). After annealing, the Pt intensity has increased and the Zr intensity decreased slightly, indicating formation of ZrO₂ islands. Whether the PtO₂ can also be removed by annealing of thicker ZrO₂ films is not clear, as in this case oxygen diffusion in ZrO₂ will be suppressed.

The different binding energies of the Zr 3d emission and of the O 2p derived valence band states indicate different Schottky barrier heights at the interfaces. The lower the binding energy, the lower the Fermi energy in the band gap. In Fig. 12, the binding energies of the valence band maximum and the Zr 3d level increase from bottom to top, corresponding to hole Schottky barriers of Φ_B,p = 2.15 ± 0.15, 2.35 ± 0.1, 2.68 ± 0.1, and 3.27 ± 0.1 eV for the RT, the 200°C, the 400°C, and the annealed film, respectively. This huge variation of more than 1 eV emphasizes again the importance of interface processing on barrier height. The difference might be related to the difference in work function between PtO₂ (φ = 6.55 ± 0.1 eV) and Pt (φ = 5.6 ± 0.1 eV), which also is about 1 eV.

Impurities at interfaces can also affect Schottky barriers at metal/dielectric interfaces quite significantly. One example is the presence of submonolayer Ag at Pt/(Ba,Sr)TiO₃ interfaces, which modifies the barrier height by about 1 eV.126 In this example, the Ag originates from the attachment of the substrate to the sample holder during high-temperature (Ba,Sr)TiO₃ deposition using Ag paste. This is a common practice in pulsed laser deposition, as it guarantees a good thermal contact. At the Pt/(Ba,Sr)TiO₃ interface, the Ag impurities raise the Fermi level to a position close to the conduction band, similar to the (Ba,Sr)TiO₃/ITO contact. Films grown with such contacts can no more be applied as capacitors due to a too high leakage current.126 Ag is not observed on a pure SrTiO₃ surface, despite the same sample mounting and temperature treatment. The difference between Pt and SrTiO₃ is supposed to be related to a higher surface energy of Pt, which can effectively be lowered by Ag adsorbates.

3.3 Postdeposition Treatments

As discussed above, the barrier heights are strongly dependent on the presence of defects, particularly to defects related to the oxygen sublattice. It is therefore to be expected that postdeposition treatments with varying oxygen activity affect interface chemistry and barrier heights. Such treatments have been carried out for SnO₂/Rh,119 SnO₂/Pt,110, SrTiO₃/Pt,18 and PZT/Pt.96 In all cases, a reversible oxidation/reduction of the substrate surface has been observed, which is related to changes of Fermi level positions at the interface, i.e., Schottky barrier heights, by up to 1 eV. The changes of barrier heights are more pronounced for SrTiO₃ and PZT than for SnO₂.

An example for such a treatment of a PZT/Pt sample is shown in Fig. 13.96 At the beginning of the experiment, a 10-nm thick Pt layer has been deposited onto a PZT thin film, which was deposited by pulsed laser deposition onto a platinized Si wafer and heated prior to Pt deposition to remove hydrocarbon and water adsorbates. The samples show no substrate, but only Pt emission. After the first heating in oxygen, the substrate emissions reappear. This is related to islands formation of the Pt film, which is not uncommon for such low film thickness.18, 110, 127

After the substrate emissions reappeared, the Pb 4f emission shows two species as during Pt deposition (see Fig. 10): A high binding energy species related to Pb bonded in PZT (Pb²⁺) and a low binding energy species related to metallic Pb. In the following, an additional heating with a higher oxygen pressure, a storage under vacuum for 1 week, and a heating under vacuum have been performed. The following changes occur during these treatments: (i) the Pb²⁺ emissions shift in parallel with the Ti 2p emissions. These shifts can therefore be associated to changes of the Fermi level position at the surface, which is covered with Pt islands; (ii) the intensity of the metallic species is reduced upon oxidation (lower binding energy of Pb²⁺ and Ti) and increases upon reduction. The most reducing situation (highest binding energy of Ti 2p) is obtained after storing the sample under vacuum for 1 week. Due to the presence of H₂ and H₂O in the residual gas and the catalytic activity of Pt, ultrahigh vacuum is apparently a strongly reducing environment, even at room temperature; (iii) the Pt peak also shows binding energy changes, which are the same as those of the metallic Pb component. Such shifts can be associated with a photovoltage induced by the X-ray source and have to be subtracted from the PZT emissions in order to obtain the proper Fermi level position.18, 128

Taking the binding energy shifts of the PZT and metallic species together, the Fermi level at the PZT surface changes by more than 1 eV during oxidation and reduction.96 As the metallic Pb species is not completely removed during oxidation, even higher changes can be expected. The variation in the Fermi level at the Pb(Zr,Ti)O₃/Pt interface upon oxidation/reduction is within the range defined by the Schottky barriers with RuO₂ and ITO, given in Fig. 11.

A more detailed approach for studying the changes of interface properties upon oxidation/reduction is provided by near-ambient pressure XPS,129, 130 which allows to measure XPS in a pressure of up to ~1 kPa. Such measurements have been performed at the Berlin electron storage ring BESSY II using the ISISS beamline and endstation. A Nb-doped SrTiO₃ single crystal coated with 3 nm of Pt was used. The sample was heated in steps of 100°C up to 400°C. At each temperature, the pressure was changed between vacuum (10⁻⁵ Pa) and 100 Pa by control of pumping speed and O₂ gas inlet. Photon energy calibration was performed by measuring the kinetic energy difference of the Pt 4f emission peak excited by the first and by the second harmonic of the bending magnet beamline. The Pt 4f binding energy follows the changes of photon energy, indicating that the binding energies are not affected by photovoltage shifts as in comparable laboratory experiments.18

Temperature, pressure, Sr 3d/Pt 4f intensity ratio, and binding energies of Sr 3d and Ti 2p recorded during the measurements are displayed in Figs. 14(a)-(d), respectively. It is emphasized that the gas composition in the chamber is dominated by the residual gas at lower pressures. Only at pressures ≳ 10⁻⁴ Pa, the pressure corresponds to the oxygen pressure.

The Sr 3d/Pt 4f intensity ratio increases with time, which can be associated with formation of Pt islands. The strongest changes are observed when the temperature is increased from 200°C to 300°C. At lower temperatures, the increase in the intensity ratio does not appear directly after the temperature increase, but only when the pressure is reduced. A higher oxygen pressure apparently stabilizes the film, while islands formation is promoted preferentially under reducing conditions.

The main result in Fig. 14 is that the valence band maximum binding energy derived from the Sr 3d and the Ti 2p core levels follows the oxygen pressure. A higher oxygen pressure reduces E_VB, which can be interpreted as an increase in the electron Schottky barrier height Φ_B,n. The highest variation in Φ_B,n of ~1 eV is observed at 200°C and 300°C, but considerable variation is already observed at 100°C. Within the time required to perform the measurements, the changes occur without delay. The reduced amplitude of binding energy variation after the sample has reached a temperature of 400°C can be attributed to islands formation.18, 131, 132 The change in the barrier height occurs at the STO/Pt interfaces under the Pt islands while the Sr 3d and Ti 3d signals originate mainly from the areas between the islands, where the surface potential is also affected by the doping of the substrate. This may particularly be the reason that the lowest binding energy achieved under oxidizing conditions increases with increasing temperature.

A striking feature is that the Fermi level raises above the conducting band minimum under reducing conditions. Here, the temperature dependence of the energy gap as reported by Denk et al.133 was taken into account. Whether the high Fermi level is related to the formation of oxygen vacancies only at the STO/Pt interface or also in the SrTiO₃ bulk is not clear at present. It may also be related to the used Nb-doped substrate (0.05 wt% Nb, corresponding to n = 1.6 · 10¹⁹ cm⁻³), which should exhibit a Fermi level inside the conduction band. Formation of bulk oxygen vacancies in SrTiO₃ is also not likely at the lower temperatures used as the surface oxygen exchange should not be enabled at such low temperatures even in the presence of Pt on the surface. As the Fermi energy remains within the energy gap at lower temperatures, formation of bulk oxygen vacancies at higher temperatures is not excluded. Further experiments using undoped SrTiO₃ will be useful to understand the role of dopants and oxygen vacancies on the surface Fermi level position. Avoiding island formation would also be important in obtaining more detailed knowledge about chemical and electronic interfacial processes. This might be achieved by different oxide/metal combinations, different surface orientation, or higher metal film thickness. For the latter, high-energy excitation in combination with near-ambient pressure XPS is a promising experimental approach.

It is often reported that a reduction in SrTiO₃ by formation of oxygen vacancies is accompanied by the observation of not fully oxidized Ti species like Ti³⁺.120, 134-137 We do not observe any Ti³⁺ during the experiment as shown in Fig. 15. Defect calculation for TiO₂ also shows that oxygen vacancies do not necessarily lead to charge localization at neighboring Ti atoms.138

The Ti 2p spectra shown in Fig. 15 are taken from reducing and oxidizing experimental conditions at 100°C and at 300°C. The spectra are selected to represent lowest and highest Fermi level positions at the STO surface. Other Ti 2p spectra also showed no evidence for Ti³⁺ species. In contrast to literature,120 irradiation with synchrotron light for several hours does not lead to formation of Ti³⁺. The difference might be the higher temperature and probably the different vacuum conditions. At the ISISS endstation, the vacuum (see Fig. 14) is not as low as that in a conventional ultrahigh vacuum system (10⁻⁸ Pa).

3.4 Influence of Polarization on Barrier Height

Polarization, particularly ferroelectric polarization, can modulate Schottky barrier heights.73, 139-142 This is caused by an imperfect screening of the polarization charges by the corresponding screening charges in the metal electrodes. The difference in barrier height between polarization pointing toward and away from the interface can then be written as:139

(9)

where λ_eff is the effective screening length and D_S the spontaneous polarization of the ferroelectric. Stengel has calculated ΔΦ_B for BaTiO₃ to be 1.8 eV with SrRuO₃ electrodes139, 143 and 0.03 eV for a particular arrangement of Pt atoms at the electrode interface.143

Variation of barrier heights with ferroelectric polarization can be obtained from electrical measurements,142, 144 but are difficult to relate to absolute values of the barrier heights and further assumptions concerning the charge transport mechanism are required. On the other hand, XPS measurements of Schottky barrier heights of as-prepared ferroelectric/metal interfaces show no evidence for a dependence on polarization. A clear example is that of a polycrystalline PZT ceramic with grain size of several micrometers. The polarization perpendicular to the electrode interface should depend on the surface orientation of the crystallites and also vary along the interface due to the domain structure of the ferroelectric. If the barrier height depends on polarization, one has to expect a lateral variation in the Schottky barrier height in such a situation. This should show up in the XPS core level emissions of the substrate as a broadening of the peaks. In contrast, the substrate peaks of the PZT ceramic after RuO₂ deposition are as sharp as those measured using epitaxial PZT thin films, indicating a homogeneous barrier height.93

In order to resolve the issue of polarization dependence of barrier heights, dedicated experiments with in situ control of polarization have been developed.145 The experimental sample setup is illustrated in Fig. 16. A BaTiO₃ single crystal has been used for the experiments. The top electrode is made thin enough that substrate core levels can still be observed through the electrode, but thick enough that polarization can be reversed with applied voltage. The sample is then mounted in the spectrometer with the top electrode connected to ground.

With this arrangement, XPS measurements have been first performed before any voltage has been applied to the bottom electrode. Thereafter, the voltage at the bottom electrode has been set to 200, 0, −200, and 0 V during XPS measurements, respectively. The voltage cycle has been repeated to check for reproducibility. While the binding energies of the top electrode, either RuO₂ or Pt, do not change with voltage as expected for a grounded metal, those of the Ba 3d and Ti 2p change reversibly when the polarization is reversed [see Fig. 16(e)].145 The changes are remanent, i.e., the peaks remain at the same value when the voltage at the bottom electrode is set to 0.

The changes in binding energy of the BaTiO₃ core levels are directly related to changes of the barrier height at the interface, which exhibit a magnitude of the order of 1 eV. This is in the range expected from the calculations of Stengel et al.139, 143 The barrier changes with Pt electrodes of ~0.7 eV are slightly higher than those obtained in a similar measurement on a BaTiO₃ thin film with Pt electrodes performed by Rault et al.146

It is mentioned that more recent measurements on BaTiO₃ single crystals with different crystallographic orientation revealed much smaller variation in Schottky barrier heights than those observed in the original experiment displayed in Fig. 16 (A. H. Hubmann, S. Li, and A. Klein, in preparation). Concurrently, the polarization of the crystal is much higher than that measured with the crystals used in the original experiment. This suggests that the polarization dependence of the barrier height is directly related to the polarization hysteresis behavior. Small changes of barrier height with polarization, which are related to a good screening of the polarization charge (a low λ_eff) correspond to high polarization. This is not contradicting Eq. 9, as the screening length is strongly affected by the interface quality.

The polarization dependence of Schottky barriers can have a strong effect on charge injection. A negative voltage polarity at an electrode shifts the Fermi level at this electrode toward the conduction band. It thereby decreases the barrier for electron injection. For positive voltage polarity, the barrier for hole injection is reduced. In both cases, the polarization dependence of barrier height potentially increases the current through the device.

4.1 Band Alignment, Electrical, and Contact Properties

The energy band alignment, i.e., the relative position of the valence band maximum and conduction band minimum of two materials at an interface, is directly related to their electrical properties. This is clearly demonstrated in Fig. 17, which displays the Fermi level positions of a number of (Ba,Sr)TiO₃ and Pb(Zr,Ti)O₃ films. The energy bands of (Ba,Sr)TiO₃ and Pb(Zr,Ti)O₃ are aligned according to the experimental determination using photoelectron spectroscopy. The valence band of Pb(Zr,Ti)O₃ is ~1.1 eV higher than of (Ba,Sr)TiO₃, which is obtained with concording result (i) from a comparison of ionization potentials, (ii) from a comparison of Schottky barrier heights (see also Fig. 11), and (iii) from a direct measurements using deposition of SrTiO₃ onto a PbTiO₃ thin film.37 Additional experiments and literature show no noticeable influence of the Ba/Sr ratio in (Ba,Sr)TiO₃ and of the Zr/Ti ratio in Pb(Zr,Ti)O₃ on the energy band alignment.39, 150

Regardless of the defects involved, Fig. 17 provides a guideline for dopability of materials. Electron (n-type) conduction can be achieved in a material which exhibits a low conduction band minimum on an absolute energy scale and hole (p-type) conduction can be achieved in materials exhibiting a high valence band maximum energy. Different energy scales for the absolute alignment of energy bands will be discussed in Section IV (B). Materials exhibiting both a low valence band maximum and a high conduction band minimum, i.e., materials with high-energy gaps, will remain insulators regardless of doping. However, it is emphasized that it is not the magnitude of the band gap, which determines whether a material will become electronically conducting upon doping or not, but the absolute position of E_VB and E_CB with respect to the allowed range of Fermi energies. The latter is defined by the range in which defect formation energies are positive, as illustrated in Fig. 18. Coming back to the explicit example shown in Fig. 17, it should now be clear that it is not the range of Fermi level which explains the differences between (Ba,Sr)TiO₃ and Pb(Zr,Ti)O₃ but the different band edge energies.

4.2 Band Alignment of Dielectric Oxides

Due to the importance of energy band alignment for electrical and contact properties, is important to find a proper “absolute” energy scale for aligning the valence and conduction bands of dielectric oxides. Robertson and Clark have addressed this issue by aligning several oxides according to their electron affinities and according to their charge neutrality levels.40, 161 It has already been mentioned in Section I (C) that the electron affinity is not a unique value, but depends on surface orientation and surface termination.80-82 The experimentally determined electron affinities can therefore hardly be used for aligning energy bands.

In a previous work, the vacuum level and charge neutrality level alignment have been compared with experimentally determined energy band alignment at heterointerfaces for a few oxides (see Fig. 15 in Ref. [161]). It is clear that neither an alignment of vacuum energies nor that of charge neutrality levels can be used to predict the energy band alignment at intimate contacts between oxides. The charge neutrality levels of SrTiO₃ and Pb(Zr,Ti)O₃161 are included in Fig. 17 as an example. It is mentioned explicitly that charge neutrality levels appear particularly inappropriate for oxides. Other materials show different behavior. On one hand, energy band alignment of covalently bonded semiconductors is well represented by charge neutrality level alignment.71, 86 On the other hand, organic semiconductors162, 163 or van der Waals bonded layered chalcogenides164, 165 are close to a vacuum level alignment. A more extensive discussion of this has been given previously.166

An extensive study of energy band alignment at oxide heterointerfaces using photoelectron spectroscopy has been reported recently by Li et al.39 Based on a series of interface experiments at oxide interfaces and proofing transitivity of energy band alignment, a general arrangement of valence and conduction band edges could be given (see Fig. 19).

Transitivity means that the band discontinuities ΔE_VB and ΔE_CB at the interface between two materials A/C are given by the sum of the discontinuities at the interfaces A/B and B/C. Transitivity is not always fulfilled at oxide heterointerfaces,167 but valid for a large number of interfaces.39 A possible origin of nontransitivity are time-dependent charging effects, which occur at some interfaces and which make the evaluation of band alignment more difficult.147-149 It is therefore important to check the validity of transitivity in order to obtain an intrinsic, i.e., an undistorted, alignment of energy bands of oxides. The general band alignment presented in Fig. 1939 is in good agreement with studies on oxide heterointerfaces reported by other groups.150, 168-170

As a first observation from Fig. 19, it can be noted that E_VB is at a very similar energy if the valence band states are mostly derived from O 2p orbitals. These materials follow the so-called common-anion-rule, which states that the valence band offset ΔE_VB between two materials sharing the same anion is small.171 Such an alignment is also closely fulfilled by binary Zn and Cd chalcogenides.57, 172 The common-anion-rule alignment clearly fails for the more covalent III–V compounds56, 172 and also if other orbitals than those of the anion are contributing to the valence band states.38 An example is that given in Fig. 17. The only exception, where a higher valence band maximum is observed for an oxide where the valence bands are dominated by O 2p states is rutile TiO₂. The higher valence band maximum in rutile TiO₂ compared to anatase TiO₂173 can be explained by the different overlap of the nonbonding O 2p_z orbitals.118 This is stronger in rutile, leading to a broader energy band, which forms the valence band maximum in rutile.

The valence band maxima of Cu₂O, those of the oxides containing occupied s-orbitals (Pb or Bi), and those of the oxides with partially filled d-shells have higher valence band maxima than the oxides where the valence bands are formed only by O 2p orbitals. The difference is strongest for Cu₂O, resulting in the highest valence band maximum of all investigated oxides. This is explained by the hybridization between the Cu 3d and the O 2p states. The effect is also known for chalcogenides, where it is referred to as p-d-repulsion.174 The higher valence band maxima of oxides with contributions of Cu 3d states to the valence bands is consistent with the observation of p-type conductivity in such compounds.175-179

The effect of the occupied s-orbitals is less evident, as the majority of electronic states of the 6s electrons of Pb and Bi are found at the bottom of the valence band.180 Nevertheless, hybridization of the Bi 6s states with Bi 6p and O 2p states causes the upward shift of the valence band maximum.38, 181 This shift can be of comparable magnitude to the one caused by hybridization with the shallow Cu 3d (or Ag 4d) states. The contribution of occupied metal s-orbitals to the valence band maximum energy is also evident for the binary Sn chalcogenides and oxides. Both SnS and SnO show quite high valence band maximum energies.182-184 The high valence band maximum energy of these compounds corresponds well with their p-type conductivity. The higher E_VB of oxides where Bi 6s or Pb 6s states contribute to the states at the valence band maximum also holds if the respective cations are diluted as in Bi_1/2Na_1/2TiO₃, where only half of the A-site cations in the perovskite lattice are occupied by the Bi ion with its occupied 6s orbitals. Bi_1/2Na_1/2TiO₃ has a similar valence band maximum energy as Bi₂O₃ and BiFeO₃.38

The effect of partially filled d-shells on the valence band maximum energies is even more subtle. The arrangement of electronic states depends on the magnitude of the exchange and the crystal field splitting. Due to the lack of systematic data and potential issues of Fermi level pinning by defects, there are not yet enough data about absolute values of the valence and conduction band energies of such oxides. Some insight is provided by the BiFeO₃ compound, which can be considered as a 1:1 mixture of Bi₂O₃ and Fe₂O₃. The valence band maxima of the two binary compounds are both at similar energies as the ternary BiFeO₃ mixture, as evidenced by band alignment measurements.38

Summarizing the observations given above, it is straightforward to conclude that the valence band maximum energy in oxides is determined by the orbital contributions to the states at the valence band maximum. Due to the dependence of the electron affinity on surface orientation and termination, the vacuum level is not a proper reference energy. Also, charge neutrality levels are not a proper reference for oxides, as the pinning by induced interface states is not very strong [see Section III (B)]. For a comparison of band edge energies of oxides, the valence band maximum of any oxide can be used as reference as done in Fig. 19, where SnO₂ has been choosen as reference. With such a reference, the valence band discontinuity between any two oxides can be directly obtained by assuming transitivity of band alignment.

It is furthermore noted that the energy band alignment given in Fig. 19, which is obtained from a series of interface formation between two oxides, partially differs considerably from the alignment obtained using electrochemical measurements of oxides in contact with liquid electrolytes.185 The origin of the deviations and their consequences are not yet understood.