26.1 Introduction

Metal oxides are the most abundant of all compounds found on Earth, many of which serve as ores for the extraction of pure elements. Initially thought to be passive, oxides are now ubiquitous, finding applications in numerous hand‐held electronic devices – either in the form of display screens or gate dielectrics in transistors. These oxides can be binary (A_mO_x), ternary (A_mB_nO_x), or quaternary. Some of the commonly used binary oxides include silicon dioxide (SiO₂) in field‐effect devices [1] and indium–tin oxide (ITO) as transparent conductors [2]. Over the years, beta‐gallium oxide (β‐Ga₂O₃) has also become popular, owing to its wide bandgap, high room‐temperature electron mobility, and high breakdown voltage [3,4]. Ternary oxides, on the other hand, like barium titanate or lead–zirconium titanate, find applications in transducers due to their piezoelectric properties [5,6]. Recently, alkaline earth stannates have garnered much interest due to their optical transparency, wide bandgap, and high conductivity at room temperature [7–9].

26.2 Structure–Property Relationship in Perovskite Oxides

Among various oxides, one class of materials that has emerged as being of great importance is perovskite oxides. These compounds have a general chemical formula of ABO₃, where the A‐site is usually occupied by alkaline‐earth (Ca, Sr, Ba, etc.) or rare‐earth elements (La, Gd, Nd, etc.) and the B‐site by transition metals (Ti, Mn, Ru, etc.) or some of the p‐block elements (Al, Sn, Ga, etc.). They have a simple crystal structure, wherein the A‐site refers to the corners of a unit cell and the B‐site refers to the body‐centered position. Six oxygen ions that sit at the face centers form a three‐dimensional network of BO₆ octahedra, as illustrated in Figure 26.1. The stability of the crystal is given by Goldschmidt's tolerance factor [10]:

where r_A, r_B, and r_O are ionic radii of elements A, B, and oxygen. For the perovskite structure to be stable, t should typically lie between 0.8 and 1.1. A broad range of acceptable tolerance factors that hold the atomic arrangement suggests that the BO₆ octahedra can withstand a large amount of strain. The crystal prefers to be cubic if the tolerance factor is close to 1 [11,12]. Deviations in t can occur due to differences in ionic radii of various cations that can be accommodated in the perovskite structure [13]. As t starts to deviate from 1, the structure undergoes symmetry‐lowering changes and no longer remains cubic. These structural changes can exist in the form of octahedral tilts, or distortions, or both [14]. Octahedral tilts and distortions lead to changes in the bond lengths and the B–O–B bond angle, which in turn affects the orbital overlap and hence the bandwidth. Bandwidth W, being coupled with the electronic structure, has a strong influence on the properties of perovskite oxides. In addition to the flexibility provided by the crystal structure, there are several other degrees of freedom that can be exploited to engineer the physical properties of the system.

26.2.1 Lattice Degrees of Freedom

26.2.1.1 Point Defects

Due to their flexible structure, perovskite oxides can adapt to a combination of cation oxidation states if the charge‐neutrality condition is satisfied (sum of the oxidation states for cations = 6). Further modifications to the crystal and electronic structures of perovskite oxides can be achieved by alloying or doping at the A or B‐sites. Structural changes are discernible in oxides when they are alloyed above a certain limit due to changes in the tolerance factor. Lattice parameters of the alloyed compound can vary linearly between the two parent compounds following Vegard's Law. However, Vegard's Law is not strictly followed, with deviations observed in alloyed compounds such as Sn‐alloyed SrTiO₃ [15] or Sr‐alloyed BaSnO₃ [16]. Doping concentrations, on the other hand, are usually smaller to cause global structural changes. But, aliovalent substitutional doping introduces extra electrons or holes in the lattice, resulting in discernable changes to the electronic structure. Depending on whether the dopant acts as an acceptor or donor, p‐type (hole) or n‐type (electron) carrier transport can be observed, respectively. For instance, in SrTiO₃, p‐type conduction is observed if it is doped with Sc on the B‐site, whereas La doping at the A‐site results in electronic transport [17,18]. Some of the oxides can also withstand oxygen vacancies to a certain extent, which provides another route to alter the electronic properties. This is one of the simplest ways of making a film conducting, as creating oxygen vacancies only requires heating the material to high temperatures in moderate vacuum. At such temperatures, oxygen diffuses out of the lattice and leaves as molecular oxygen. It can be visualized from a simple defect reaction, which also shows that oxygen vacancies can dope the material with electrons [19]:

The ability to create oxygen vacancies in a perovskite structure depends on the activation energy associated with the formation of oxygen vacancies and the oxygen diffusion coefficient [20]. For instance, in BaSnO₃, although the enthalpy of vacancy formation is low [21], the oxygen diffusion coefficient is known to be orders of magnitude smaller than other perovskite oxides such as SrTiO₃ [22], which makes the creation of oxygen vacancies in BaSnO₃ relatively difficult. In many oxides, mainly those having high oxygen diffusivity, oxygen vacancies can be suppressed by annealing in oxygen atmosphere at high temperatures [23,24].

26.2.1.2 Strain

When perovskite oxides exist in the form of thin films, strain provides another tuning knob for controlling their properties. The availability of commercial substrates with lattice parameters close to many of the perovskite oxides makes the growth of single‐crystalline, epitaxial thin films possible. Below a critical thickness, films can grow commensurately (completely strained), taking the in‐plane lattice parameter of the underlying substrate. The constraint induced by the substrate can play important roles and can affect the structural, electronic, and magnetic properties significantly. Structurally, substrate‐induced strain and coupling effects have been observed to affect the octahedral tilts in perovskite oxides such as LaNiO₃ [25], for instance. In the case of SrTiO₃, which is an incipient ferroelectric, tensile strain can stabilize the ferroelectric phase even at room temperature [26].

26.2.1.3 d‐Orbital Splitting

Many of the perovskite oxides are transition‐metal oxides (TMOs), where the B‐site is occupied by transition metals. The physical and electronic properties in TMOs are mostly governed by the electrons in the d‐orbitals. Due to the directional nature of d‐orbitals and the system's propensity to minimize the total energy, several other effects have been observed that are unique to TMOs. Therefore, it is important to review some of the factors relevant to TMOs, such as crystal field splitting, Hund's coupling, and Jahn–Teller distortion. Crystal field splitting in TMOs refers to the splitting of the otherwise degenerate d‐orbitals into different energy levels in the presence of the crystal's static electric field, as shown in Figure 26.2. In the octahedral coordination geometry of the perovskite structure, and orbitals (called e_g orbitals) are directed toward the oxygen ions and therefore electrons in these orbitals experience greater coulombic repulsion. This increases their energies relative to the other three d_xy, d_yz, and d_xz orbitals (called t_2g orbitals). The energy difference between the e_g and t_2g orbitals is called the crystal field splitting parameter (Δ_o). When filling these orbitals, electrons first occupy the lower‐energy t_2g orbitals. Once all three orbitals are filled with one electron each, Δ_o prevents the occupancy of higher‐energy e_g orbitals and favors pairing of electrons with opposite spins. The overall spin angular momentum is therefore reduced in such a configuration. This is known as the low‐spin state. However, when electrons with opposite spins are paired, there exists an energy penalty called the Hund's rule coupling energy (H_ex) due to electrostatic repulsion. When H_ex > Δ_o, it is energetically favorable for the electrons to occupy e_g orbitals before pairing with t_2g electrons, thus maximizing the total spin angular momentum (Hund's Rule). This configuration is known as the high‐spin state. The ground state in TMOs, therefore, may result from a competition between crystal field splitting and Hund's coupling. When H_ex and Δ_o are comparable, the electronic and magnetic properties of TMOs can be tuned by driving the system from a low‐spin ground state to a high‐spin state or vice versa.

For certain electronic configurations, perovskite oxides can further lower their total energy by undergoing Jahn–Teller distortions. These distortions are accompanied by splitting of the e_g and t_2g orbitals, further depending on the type of distortion (elongation vs. compression), as depicted in Figure 26.2. Since two electrons with different spin can occupy d orbitals, degeneracy can further be lifted in TMOs where strong spin–orbit coupling exists.

Several degrees of freedom, discussed above, provided by the amenable crystal structure of perovskite oxides are responsible for the existence of a wide range of novel functionalities. Some of the intriguing properties that have been discovered include high‐temperature superconductivity (e.g. Ba_xLa_5−xCu₅O_5(3−y)) [27], room‐temperature ferromagnetism (e.g. La_0.7Sr_0.3MnO₃) [28], multiferroicity (e.g. BiFeO₃, BiMnO₃) [29,30], colossal magnetoresistance (e.g. La_0.67Ca_0.33MnO₃) [31], and so on.

26.2.3 Thin‐Film Growth Approaches

Thin‐film growth techniques for oxides can be classified into two broad categories – solution and vapor‐based approaches.

26.2.3.1 Solution‐Phase Synthesis

Solution‐phase methods are perhaps the oldest known way of depositing films on a substrate. This is illustrated in Figure 26.3. In step 1, a mixture of solutes is first dispersed in a solution to form colloids, also known as precursors. The solutes react with each other during the aging step, either at room temperature or moderately high temperature, to form the desired material to be deposited. In step 2, the precursor is then transferred to the substrate using a coating technique such as spin‐coating or dip‐coating. The next step involves removal of the liquid phase, either by baking at high temperature or using a centrifuge. This leaves a layer of film on the substrate, which is usually amorphous. Annealing at high temperature improves the crystallinity of the films, however, grain boundaries exist with grain sizes on the order of a few nanometers. These steps can be repeated to achieve a desired thickness of the film. The simplicity with which films can be deposited with this approach makes it one of the most popular, cost‐effective, and energy‐efficient thin‐film deposition methods, albeit not providing atomic‐layer control over film thickness, with the properties being limited by structural imperfections such as grain boundaries and impurity in solutes [71].

26.2.3.2 Vapor‐Phase Synthesis

Vapor‐phase deposition techniques differ from solution‐based approaches in a way that involves a phase change, where the starting material (originally existing as a solid or liquid) is transformed to vapors before encountering the substrate. Vapor deposition can be further classified into chemical and physical deposition approaches. Chemical deposition includes a chemical reaction taking place at the surface of the substrate, whereas in physical deposition methods, films are directly transferred onto the substrate by evaporation or sublimation. Three of the widely used physical vapor deposition methods are discussed below.

26.2.3.2.1 Sputtering

In sputtering, the source material is a bulk sintered target of the film that is being deposited on a substrate. Sputtering of the target is carried out using a plasma source – typically a mixture of an inert gas like argon with oxygen for oxide materials. The ionized species of plasma with positive charges bombard the surface of the target, removing some of the material. The materials coming off the target are also charged and travel toward the substrate due to the applied potential difference between the target and the substrate. The voltage difference can be either DC or AC, depending on the electrical property of the target. Insulating targets require an AC source to avoid charge build‐up at the surface, which would suppress the kinetic energy with which the ionized plasma travels toward the target [72]. Cost‐effectiveness and high throughput of sputter deposition make it one of the preferred industrial growth techniques. However, there are certain challenges, including high defect densities that limit the study of intrinsic properties of thin films.

26.2.3.2.2 Pulsed Laser Deposition

Pulsed laser deposition (PLD) is similar to the sputtering approach, except that instead of an argon plasma, a laser beam is used to ablate the target [73]. The target material should have a high optical absorption coefficient at laser wavelength. Due to ionization by the high‐energy laser beam, the material creates its own plasma, which is directed toward the substrate. The flux of the plume is responsible for film deposition. The film growth can be controlled using the laser pulse. The growth rate is dependent on the laser energy, distance between the substrate and the target, and the background gas pressure. By proper choice of these parameters, each laser pulse can be used to deposit a submonolayer of material at a time. Growth rates are typically below 1 Å per pulse. PLD is usually equipped with in‐situ reflection high‐energy electron diffraction (RHEED), which helps in monitoring the surface crystallinity and growth mode. RHEED intensity oscillations can provide information about the growth rate also for layer‐by‐layer growth [74].

Sputtering and PLD have been used to create some of the structurally superior‐quality thin films and heterostructures with properties not observable in films grown with solution‐based approaches [ 32, 42]. One of the main advantages of sputtering and PLD is their applicability to a wide range of materials. The processes are cheap and can be scaled up to meet industry requirements. In both these methods, the stoichiometry of the target can be preserved (“congruent material transfer”) under proper choice of growth conditions. However, if laser fluence is not selected appropriately, stoichiometry has been found to vary considerably during PLD growth [75]. Even for the same growth parameters, sample‐to‐sample variation has been observed. Sputtering and PLD are both high‐energy deposition techniques, where the high kinetic energy of particles leaving the target can re‐sputter the film. The re‐sputtering effect can create defects which are deleterious to the properties of the films. This can, however, be minimized by a modified sputtering technique called high‐pressure sputtering, in which the oxygen is supplied at relatively high pressure to decrease the kinetic energy of the particles [76–78]. Film properties are also limited by the composition control and purity of the target [79,80]. Sometimes single‐crystalline targets are used to overcome this issue, which, however, increases the total cost of production [81].

26.2.3.2.3 Molecular Beam Epitaxy

In the late 1960s, another thin‐film growth technique known as molecular beam epitaxy (MBE) was devised by A. Y. Cho and J. R. Arthur, which overcame some of the challenges with other deposition methods [82–84]. MBE is a low‐energy, UHV thin‐film deposition technique which employs a molecular beam of source materials impinging at the substrate kept at high temperature. Molecular beam means that the mean free paths of atoms or molecules are larger than the source‐to‐substrate distance (due to the UHV environment). As a result, no inter‐atomic/molecular collision occurs before they reach the substrate. High temperature promotes formation of single‐crystalline films. MBE can be thought of as a combination of chemical and physical vapor deposition, where individual species are either evaporated using an effusion Knudsen cell or an electron beam. These species react with each other to form a layer of material at the surface of the substrate. MBE offers atomic‐layer control over film composition, thickness, and roughness. Films can be grown with low defect densities due to the molecular growth regime. MBE also comes equipped with other in‐situ tools in addition to RHEED, such as a quartz crystal microbalance (QCM) and/or beam flux monitor (BFM), to precisely control the flux of individual beams for better stoichiometry control [83,85,86].

26.3 Oxide Molecular Beam Epitaxy

26.3.2 Design of Oxide MBE

26.3.2.1 Oxygen Plasma‐Assisted MBE

Figure 26.4(a) shows a typical design of a radio‐frequency (rf) plasma source consisting of a water‐cooled rf coil inductively coupled with the rf source operating at 13.56 MHz. It is supplemented with an external matching unit for optimum plasma coupling and to minimize the reflected power. The efficiency of plasma sources is argued to vary anywhere between 10% and 70%, depending on the choice of oxygen pressure and plasma power [Figure 26.4(b)] [102]. Additionally, rf plasma sources are often equipped with ion deflection plates to prevent electrons and high‐energy ions from reaching the growth surface. An atomic source of oxygen has also proved effective in substrate cleaning prior to growth, and to remove any carbon contamination from the surface [103,104]. This ensures that the interface between the film and the substrate is clean, which is essential for studying novel interfacial phenomena.

26.3.2.2 Ozone‐Assisted MBE

The ozone delivery system, on the other hand, consists of a silent discharge ozone generator and a temperature‐controlled ozone trap/still (Figure 26.5). Ozone is either stored in the trap in liquid form or adsorbed on silica gel in gaseous form. Silica gel is supposed to be safer, as liquified ozone is prone to explosions due to abrupt changes in temperature. Cases of explosions have been reported even with the use of silica gel due to the presence of a small amount of liquid ozone. A region of flowing nitrogen gas between the trap and the liquid nitrogen panel keeps the temperature above the liquefaction temperature of ozone, and has proved useful in avoiding these explosions [106,107].

26.3.2.3 NO₂ and H₂O₂ Assisted MBE

Besides molecular oxygen, oxygen plasma and ozone, nitrogen dioxide (NO₂) and hydrogen peroxide (H₂O₂) have been shown to work as oxidizing agents. Growth using NO₂ was carried out even at pressures as low as 10⁻⁷ Torr [108–111]. However, the reactivity of NO₂ was found to be lower than ozone [109]. NO₂ is not a preferred oxidant when substitutional defects become detrimental to the properties of thin films [112], due to the incorporation of nitrogen ions at oxygen sites. A H₂O₂/H₂O mixture was also demonstrated to be a good source of oxygen for oxide film growth [113]. Since water vapor is undesirable for UHV synthesis, the use of H₂O₂/H₂O mixtures is limited.

26.3.3 Challenges with Oxide MBE

With oxygen sources, either in the form of molecular oxygen, rf plasma, ozone, NO₂, or H₂O₂/H₂O mixtures, practical compatibility issues in a UHV environment need to be considered. In what follows, we discuss potential issues associated with the use of oxygen in MBE, along with possible remedies.

26.3.3.1 Issues with the Substrate Heater Filament

The lifetime of the substrate heater filament, generally operating at high temperature, is severely reduced in the presence of high oxygen pressure. With the introduction of more efficient oxygen sources, although the life span was improved as a result of the use of lower oxygen partial pressure, the operating temperature was still limited by filament oxidation [107]. Nowadays, oxygen‐resistant heater filaments made from SiC or noble‐metal alloys (Ni or Pt) have replaced tungsten filaments in oxide MBE systems to achieve higher operating temperatures. The working temperature of SiC filaments can be as high as 1000 °C, depending on the partial pressure of oxygen during growth. Besides the filaments, shields that prevent radiative loss of heat should be compatible with oxygen. Tantalum and stainless steel are most common. Their performance at high temperature and high oxygen pressure can be further enhanced with coatings of oxidation‐resistant nickel alloys, or by replacing them with Ni‐based alloys such as Inconel. Vapor pressure and cross contaminations are always important considerations in choosing parts consisting of non‐refractory materials.

26.3.3.2 Issues with Substrate Holders and Cell Crucibles

Substrate holders made from molybdenum may oxidize in plasma or ozone. Molybdenum oxides having higher vapor pressure than molybdenum itself can get incorporated in the film, which is undesirable [ 106,114]. This type of contamination can be avoided by choosing holders made of materials that are oxidation‐resistant (such as stainless steel, Inconel alloy, etc.), or materials whose oxides have a much lower vapor pressure (such as tantalum). Use of oxygen‐resistant materials recently led to the discovery of the highest mobility (>10⁶ cm² V⁻¹ s⁻¹) ever reported in MgZnO/ZnO heterostructures [115]. The choice of crucible should also be considered, in terms of wettability and reactivity with the source material, and reactivity with an oxidizing atmosphere. Pyrolytic boron nitride is a widely used crucible in MBE growth. However, its reactivity in oxygen‐rich environments results in the formation of B₂O₃, which may contaminate the films [107].

26.3.3.3 Issues with Effusion Cells and Flux Instability

Oxidation of the filaments used in the effusion cell is critical for sources that operate at high temperature. Filament oxidation leads to instability in the flux due to temperature fluctuations, which has undesirable effects on the stoichiometry of the films. Filament materials are, therefore, chosen such that stable fluxes are achievable in high oxygen background. Perhaps an even more severe concern than the filament oxidation is that there is a greater risk of oxidation of the source material in oxide MBE, which again leads to flux instabilities. This issue becomes especially important for high‐oxidation‐potential elements, such as Sr, Ba, Ca, and so on, and for elements with low vapor pressure, such as Ti, Sn, and so on, that require high cell temperatures [116–118]. At high effusion‐cell temperatures, the reactivity of elements with oxygen is enhanced, which can result in oxidation of the charge and flux instability. A significant change in flux is observed when an oxygen source is introduced (Figure 26.6) [ 116,119], due to partial oxidation of the sources. Time‐dependent flux measurements for Ti have shown that flux monotonically decreases in high‐pressure oxygen [117]. This is attributed to the formation of titanium dioxide and its low vapor pressure. In case of ternary oxides, flux instabilities often result in non‐stoichiometric defects. On the other hand, for binary oxides, although stoichiometry can be maintained, lower flux causes a decrease in the growth rate. Growth rates become important when dopants are used, because the doping concentration varies with the growth rate [120].

The oxidation of source elements can be minimized, either by use of differential pumping through a port aperture [121], or a crucible aperture to minimize the charge exposure to oxygen environment [122]. The use of a ceramic aperture, however, also decreased the growth rate. For elements that readily oxidize, it is critical to protect them when they are not in use. Retractable effusion cells are designed to prevent oxidation of such elements during venting of the growth chamber or while growing other oxides. Moreover, they also facilitate replacement of charge without breaking the vacuum of the growth chamber.

Flux instabilities due to source or filament oxidation make beam flux calibration very critical in oxide MBE. Popular ways of measuring fluxes include QCM and BFM. These two techniques allow for measuring the growth rate and flux, respectively, directly below the substrate using a linear travel mechanism. While QCM relies on the change in mass of the quartz crystal and can be used with oxygen, BFM is a type of ionization gauge that is prone to oxidation. Therefore, flux measurements using BFM are usually done prior to growth. On the other hand, the quartz crystal in the QCM needs to be replaced more often than the BFM. To overcome these challenges, sometime real‐time flux‐monitoring systems such as atomic absorption spectroscopy are utilized, which improve the accuracy of flux calibration [123].

One of the advantages of MBE is the availability of in‐situ diagnostic tools for surface characterization, such as RHEED. Apart from providing information about the surface morphology, growth modes, and growth rates (for layer‐by‐layer growth mode) [124], RHEED can be used to adjust the fluxes so as to achieve stoichiometric growth conditions [125,126]. It should be noted that RHEED cannot be used as a standalone method for optimizing the stoichiometry, as it is a surface‐sensitive technique. Stoichiometry needs to be simultaneously confirmed by other composition characterization methods such as X‐ray diffraction and Rutherford backscattering spectrometry (RBS), for example. However, during prolonged exposure to oxygen, RHEED filament oxidation is inevitable if proper caution is not taken. One way to minimize the effect of oxygen is by using differential pumping near the filament, which helps in increasing its lifetime.

26.4 Recent Developments in Oxide MBE

26.4.1 Adsorption‐Controlled Growth

The existence of adsorption‐controlled growth in some ternary perovskite oxides helps in eliminating the disadvantages of flux instabilities and unreliability in growth. The first study of adsorption‐controlled growth was reported by Arthur, where the growth of GaAs was studied using MBE [82] following the work of Gunther [127]. Theis and Schlom were the first to demonstrate adsorption‐controlled growth in the perovskite oxide PbTiO₃ [128,129]. In this kind of growth mode, non‐stoichiometry resulting from small fluctuations in the beam flux of Pb or Ti is compensated by excess Pb desorbing from the surface in the form of PbO. The deposition rate in the adsorption‐limited regime is determined by the non‐volatile component – in this case TiO₂ (Figure 26.7).

Although adsorption‐controlled growth has been demonstrated for many perovskite oxides including PbTiO₃, Bi₂Sr₂CuO_y, Bi₄Ti₃O₁₂, BiFeO₃, BiMnO₃, and LuFe₂O₄ [132–136], to access such a growth regime or “MBE growth window” as it is now called, certain conditions should be satisfied. First, at a given temperature, the equilibrium partial pressure of the volatile oxide should be high enough to enable deposition of perovskite oxide with practically achievable growth rates. Second, the growth window should be accessible at realistic temperatures.

However, it is not possible to satisfy these criteria for all perovskite oxides. For example, in the case of MBE growth of SrTiO₃ using solid sources for Sr and Ti, it has been found that a growth window may exist at much lower vapor pressures (in this case SrO), as illustrated in Figure 26.7. To achieve practical fluxes, much higher substrate temperatures are required, which may not be feasible for oxide MBE. Besides an inaccessible growth window, several other challenges exist for the growth of SrTiO₃.

1. One issue is the low vapor pressure of titanium. As a result, the growth rate of SrTiO₃ is limited by titanium. Higher growth rates are required for practical applications.
2. Titanium flux is unstable in the presence of oxygen, as previously shown in Figure 26.6(b), which can result in high defect concentrations in the film in the form of cation non‐stoichiometry. Beam fluctuation in the range of 0.1–1.0% can introduce a defect density of ∼10²⁰ cm⁻³ in films [137].
3. To maintain the desired mean free path of atomic species, and due to the limitations put on the system by pumps, oxygen pressure is usually kept low. At the same time, high substrate temperatures are necessary for better crystallinity of films. As a result, oxygen vacancies are prone to form in the film during growth. These oxygen vacancies often tend to make the film conducting, which may be undesirable for some applications such as dielectrics. Post‐oxygen annealing, therefore, becomes necessary, adding an extra processing step. In fact, the post‐oxygen annealing step may or may not work in some cases.

These issues are not just pertinent to titanium, but also apply to other elements that have low vapor pressures (e.g. vanadium, ruthenium, etc.). To achieve a balance between elemental flux stability and the need for high oxygen pressure, an alternative MBE approach was devised, known as hybrid MBE (conventionally known as metal–organic MBE or MOMBE [138,139]).

26.4.2 Hybrid Molecular Beam Epitaxy

As the name suggests, hybrid MBE is a combination of conventional MBE and metal–organic MBE. The method, first introduced by Jalan et al. in 2009 for SrTiO₃ films, used a conventional effusion cell for strontium and a metal–organic precursor – titanium tetraisopropoxide (TTIP) – for titanium [ 137,140,141]. TTIP was supplied through a gas inlet system, as illustrated in Figure 26.8. The precursor was thermally evaporated from a stainless‐steel bubbler. The gas lines were maintained at higher temperature than the bubbler to prevent any condensation and subsequent blockage. The pressure of the gas precursor was controlled using a linear leak valve that receives feedback from a capacitive manometer (Baratron^®). Unlike metal–organic chemical vapor deposition (MOCVD), no carrier gases were used. The shower head nozzle design of the gas injector provides an effusive beam of TTIP. The way a TTIP precursor works is that at high growth temperatures (>400 °C), it decomposes into TiO₂ via the following reaction [143,144], thereby forming TiO₂ at the surface of the substrate:

The hybrid MBE approach offers several advantages over the conventional MBE approach:

1. TTIP has a much higher vapor pressure than solid titanium, allowing for growth rates to be scalable. Due to its high vapor pressure, no carrier gas is needed, thereby reducing the load on vacuum pumps [140].
2. The beam flux remains stable in the presence of oxygen as the precursor does not come into direct contact with oxygen. This also facilitates refilling the metal–organic source without venting the growth chamber [ 140, 141].
3. Since the precursor comes already bonded with oxygen, the oxidation state of Ti is preserved. The use of TTIP with oxygen plasma also helps maintain the oxygen stoichiometry and the insulating nature of SrTiO₃ films [141].
4. TTIP enables an adsorption‐controlled growth window to be accessible at reasonable growth temperatures [137].

Using this precursor, several perovskite oxides have been grown, including SrTiO₃, CaTiO₃, and BaTiO₃ [ 141,145,146]. Figure 26.9(a–c) shows the out‐of‐plane lattice parameters for SrTiO₃ films grown at different Ti:Sr beam equivalent pressure (BEP) ratio and different growth temperatures. For all three temperatures, there was a range of Ti:Sr ratio for which the lattice parameter was identical to the bulk value. This suggested that a self‐regulated growth window exists for SrTiO₃ when TTIP is used as a Ti source. With increasing temperature, the lower boundary of the growth window shifted to a higher TTIP flux because of the increased rate of TTIP desorption. Moreover, higher growth temperatures also resulted in broadening of the growth window [148,149]. Outside the growth window, the lattice parameter showed an increasing trend due to cation non‐stoichiometry. Non‐stoichiometry is generally incorporated in thin films as vacancies, due to their ease of formation as opposed to other defects such as interstitials. Therefore, the expanded lattice parameter is a result of increased interaction between two negatively charged oxygen ions.

Point defects, either in the form of vacancies or interstitials, strongly affect the physical properties. Having an accessible growth window for SrTiO₃ eliminates non‐stoichiometry due to fluctuations in the beam flux, thus minimizing defect concentrations in thin films. As a result, electron mobilities exceeding 50 000 cm² V⁻¹ s⁻¹ (n = 8 × 10¹⁷ cm⁻³) have been achieved in La‐doped SrTiO₃ films at 2 K [150]. This value is higher than those reported in the bulk single crystals (22 000 cm² V⁻¹ s⁻¹) [151] by more than twice, and much higher than those reported for films grown by PLD (6600 cm² V⁻¹ s⁻¹) [152] or any other techniques. This suggests that hybrid MBE provides excellent control over defects [18]. Electron mobility can be further enhanced by 300% under strain [Figure 26.9(d–f)] [147]. High mobilities at low temperature also allow for quantum effects such as Shubnikov–de Haas oscillations to be observable in magnetic fields, enabling direct measurement of electron effective mass [ 18,153]. Recently, the use of a hybrid MBE approach has led to the discovery of quantum Hall effects for the first time in perovskite oxides [154].

Similar growth windows have been shown to exist for vanadium precursor – vanadium‐oxy‐triisopropoxide (VTIP) – during the growth of SrVO₃, LaVO₃, and CaVO₃ [155–158]. Both TTIP and VTIP precursors, having the same isopropoxide (C₃H₇O–) group bonded with the metal ion, are expected to show similar growth kinetics at the substrate surface. Oxygen‐containing precursor has now been successfully employed for zirconates (zirconium tert‐butoxide) as well ruthenates (ruthenium tetroxide) [159,160].

26.4.2.1 Challenges with Hybrid MBE

26.4.2.1.1 Carbon Contamination

As with any other approaches, hybrid MBE also has its limitations. Metal–organic precursors contain carbon, which can potentially result in contaminations within the film or at the film surface. Below 725 °C, carbon contaminations exceeding 2 × 10¹⁸ cm⁻³ have been detected in SrTiO₃ films using dynamic secondary ion mass spectroscopy (SIMS). Carbon contamination was found to be negligible (<1 × 10¹⁷ cm⁻³) at higher substrate temperatures (≥800 °C), likely due to dissociation of the C–O bond in TTIP [161].

26.4.2.1.2 Volatility and By‐products

In conventional MBE, most of the source elements or species formed during reaction in the growth chamber have low vapor pressure. Therefore, they get permanently attached to the chamber walls. They desorb during high‐temperature bake out if their vapor pressure is sufficiently high. Meanwhile in hybrid MBE, precursors that stick to the cryo‐panel during growth also desorb during warm‐up due to their high vapor pressure, even at room temperature. As a result, the pressure inside the growth chamber may rise over time to as high as 1 × 10⁻⁴ Torr. This can put a tremendous load on the vacuum pumps if proper caution is not taken during regeneration [162]. At the same time, intercell contamination should also be considered due to the high volatility of these by‐products.

26.4.2.1.3 Availability of UHV Compatible Precursors

While precursors already bonded with oxygen is desirable, it may not be trivial to find such precursors for every element for which conventional MBE may be problematic. So, one must resort to the idea of using other available precursors. Several precursors exist for various elements and have been shown to work in atomic layer deposition (ALD) and/or chemical vapor deposition (CVD). However, they may not be compatible with the UHV MBE approach. Many of these precursors that have been successfully used for depositing metals and their oxides contain halogen atoms, or sulfur, or nitrogen, which can potentially react with residual water vapors in the chamber to form corrosive acids. Other considerations when choosing appropriate precursors include their vapor pressures, thermal decomposition temperatures, and reactivity with oxygen at growth temperatures.

26.4.3 Radical‐Based Molecular Beam Epitaxy

As stated earlier, the flexible perovskite crystal structure can accommodate a variety of elements at A and B‐sites. Since both the elements need to be oxidized, there is competition for the limited oxygen available during UHV growth. When the oxidation potential of the two elements is similar, both elements will be oxidized without preference. However, a serious problem can arise for MBE growers when they have very different affinities toward oxygen. Figure 26.10 shows the values of standard half‐cell oxidation potentials for some of the elements commonly present in perovskite oxides. The ones with higher oxidation potentials are easier to oxidize than those with lower oxidation potentials. For example, in the case of nickel, which has a low oxidation potential, it was shown that oxidation of nickel is challenging during MBE growth of PrNiO₃ using conventional solid sources [164]. At oxygen pressure ∼1 × 10⁻⁶ Torr, binary oxides of Ni and Pr were stabilized. Nickel was present in a reduced +2 state in the form of NiO, instead of the desired +3 state. Even at higher oxygen pressures, Ni +2 was not eliminated.

Several routes have been proposed to circumvent this challenge, such as high substrate temperature, high oxygen pressure, and/or use of reactive gases like ozone [ 100, 164]. However, these approaches may not be feasible for all the elements with low oxidation potential. For example, in case of tin (Sn), at high substrate temperatures, the growth rate of SnO₂ is dramatically reduced due to the formation and simultaneous desorption of highly volatile SnO [165]. The use of high oxygen pressure or ozone, on the other hand, can lead to flux instabilities if a conventional effusion cell is used. Alternatively, a hybrid MBE method can be employed as shown earlier for titanates and vanadates, which supplies metal–organic precursors already bonded with oxygen to maintain the stoichiometry and oxidation states. Although an oxygen‐containing precursor exists for many of these low‐oxidation‐potential metals, they may not be feasible for MBE growth. For example, in case of tin, tin tert‐butoxide (TTB) is an oxygen‐containing precursor but was found to have low vapor pressure and be thermally unstable for MBE growth of Sn‐based compounds [166,167].

Recently, Jalan's group at the University of Minnesota has shown that a novel radical‐based MBE approach can be exploited to increase the reactivity of the metal toward oxygen. The unique aspect of this approach is that it does not rely on improving the reactivity of oxidants but rather on making the metal itself more reactive by forming its radicals. This approach, demonstrated for Sn, used hexamethylditin (HMDT)–(CH₃)₃Sn–Sn(CH₃)₃ as the tin precursor. HMDT provides several advantages over a solid Sn source. First, it has a much higher vapor pressure than solid tin, which permits high and scalable growth rates. Second, the dissociation of the Sn–Sn bond with lower bond energy than the Sn–C bond results in the formation of (CH₃)₃Sn^• radicals that have higher reactivity than metallic Sn. Better reactivity of these radicals helps in maintaining the correct oxidation state (+4) of Sn, even in low oxygen pressures. The formation of highly reactive radicals also allows for this approach to work with the less reactive molecular oxygen for the growth of binary and ternary tin oxides such as SnO₂ and BaSnO₃, respectively [ 163,168]. Use of HMDT also allows oxygen stoichiometry to be maintained [169].

The high volatility of HMDT precursor also facilitated a growth window during MBE of BaSnO₃ films, allowing for highly reproducible film structures. Figure 26.11 shows the variation of out‐of‐plane lattice parameter and cation ratio measured using RBS as a function of cation flux ratios. There was a range of Sn:Ba ratio for which cation stoichiometry was maintained as 1:1, suggesting a self‐regulated growth regime. Within the growth window, nominally same thickness of the films is indicative of adsorption‐controlled growth mode [142]. Unexpectedly, lattice parameters for Ba‐deficient (or Sn‐rich) films were the same as stoichiometric films, irrespective of the flux ratio. It was hypothesized that the presence of anti‐site defects, where Ba sites are occupied by excess Sn, likely in the +2 state, may cause this unusual trend [142].

Non‐stoichiometry‐related defects (vacancies, interstitials, anti‐site defects, etc.) are found to have a strong influence on the electronic properties of La‐doped stannates (BaSnO₃ and SrSnO₃) [ 7, 9, 142]. These defects neutralize some of the charge carriers, resulting in a smaller carrier density and increased scattering, thus leading to lower carrier mobility as shown in Figure 26.11 [ 7, 9,170]. For example, compensation due to point defects can be visualized in terms of a simple defect reaction [142].

Ba‐deficient conditions:

Overall defect reaction:

26.1

Sn‐deficient conditions:

Overall defect reaction:

26.2

Having an assessible growth window using the radical‐MBE approach helps in minimizing defects in BaSnO₃. This has led to the highest reported conductivity, to date, in BaSnO₃ (>10⁴ S cm⁻¹) amongst all semiconducting perovskite oxides at room temperature [7]. This method has now been extended to SrSnO₃. The highest reported mobility in La‐doped SrSnO₃ was achieved with this approach [9]. Although growth of BaSnO₃ has not been possible so far with the conventional MBE approach, use of SnO₂ instead of metallic Sn as a source for tin has been successful in producing films with good structural quality and high mobility [8,171]. However, growth of conductive SrSnO₃ film using SnO₂ remains elusive [16].

26.5 Outlook

Given the important role of III–V MBE in developing new device applications, it is reasonable to discuss the important current (and potential) role of oxide MBE in bringing oxide electronics a step closer to reality. To put our discussion in context, we show a timeline in Figure 26.12(a) indicating how mobility of the GaAs/AlGaAs system (as a measure of materials quality) has improved over the years. For instance, the extreme level of atomic layer control with improved defect concentrations afforded by III–V MBE led to the discovery of the fractional quantum Hall effect in AlGaAs/GaAs heterostructures, which later went on to receive a Nobel Prize in Physics in the year 1998 [172–174]. Spanning almost four decades since the first report of modulation doping in AlGaAs/GaAs heterostructures [175], the highest low‐temperature mobility in this system has increased more than four orders of magnitude during this time. While much effort was initially directed toward optimizing the structure in order to enhance mobility [ 175–182], the major increment in the mobility values came only with improvements in the level of purity achievable inside the growth chamber [183–193]. III–V MBE with better vacuum and ultra‐high‐purity sources played a key role in this process.

Taking analogy from III–V MBE, a similar trend has been observed for Mg(Mn)ZnO/ZnO heterostructures [Figure 26.12(b)]. Modifications to the growth chamber and amendments to the film structure have resulted in an almost four orders of magnitude increase in low‐temperature mobility [ 42, 115194–200]. Enhanced mobility has also guided the discovery of novel quantum phenomena never seen in oxide systems. Importantly, this remarkable growth has been achieved in less than two decades [201]. Similarly, in perovskite oxides such as doped SrTiO₃ (see Figure 26.13), in just over a decade, a significant improvement in low‐temperature mobility, by over three orders of magnitude, has been observed [ 18, 147, 152, 154202–205].

The aforementioned high mobility value in SrTiO₃ is at 2 K, which has led to the discovery of new physics and also validated theoretical models that otherwise could not have been validated without these high‐quality materials. It is noteworthy that oxide MBE including the development of a novel hybrid MBE has played a significant role in this impressive achievement. However, at room temperature, SrTiO₃ possesses mobility <10 cm² Vs⁻¹, which on the other hand has limited their use in electronics operated at room temperature.

Only recently, the discovery of high mobility at room temperature in doped‐BaSnO₃ has projected perovskite oxides for the first time onto an equal footing with conventional semiconductors for applications in oxide electronics. In addition, BaSnO₃ is also a wide‐bandgap material [169], making it optically transparent [206] and relevant for power electronic applications. For instance, the room‐temperature conductivity in BaSnO₃ has already attained values comparable to commercially available transparent conductors (Figure 26.14).

The question that remains to be answered, however, is: can the mobilities of stannate films be further improved? One of the main challenges with the thin‐film BaSnO₃ films is the unavailability of lattice‐matched substrates. Due to large lattice mismatch between the substrate and BaSnO₃ (Figure 26.15), films relax within a nanometer thickness via formation of misfit dislocations [163]. In addition to these misfit dislocations at the interface, threading dislocations also exist, which can propagate through the entire film thickness.

Prior reports have argued that dislocation cores can be comprised of Ba vacancies which can also compensate for charge carriers similar to non‐stoichiometric defects [7]. Inspection of individual electron‐scattering mechanisms using first‐principle calculations also revealed that at low carrier concentrations, dislocation scattering is the primary mobility‐limiting scattering mechanism. At higher concentrations, mobility is mostly limited by ionized impurity scattering and/or phonon scattering [ 7,212]. Therefore, efforts need to be made to minimize the effect of dislocations on electronic properties. Once the issue of lattice mismatch is addressed, attention should move toward developing modulation‐doped structures in addition to improving the vacuum and purity level in the MBE growth chamber.

26.6 Summary

Oxide MBE has come a long way since its introduction in the late 1970s. Significant progress in the growth and controlled doping (both extrinsic and intrinsic) of oxide semiconductors has been made. For example, low‐temperature electron mobility in SrTiO₃ or ZnO‐based heterostructures has improved by several orders of magnitude over the last decade, owing to the advancements made in the design of the MBE chamber, choice of materials for vacuum components, vacuum level, purity of sources, and modifications made to growth processes as well. The major bottleneck still exists in preparing device‐quality films of stannate compounds suitable for room‐temperature electronic applications. To date, the known limiting factor is largely substrate‐induced defects. Intrinsic defects, extrinsic impurities, and reproducibility are expected to play an important role in realizing the full potential of stannate compounds, once the issues related to substrate‐induced defects are addressed. In this context, it is perhaps reasonable to say that oxide MBE has yet to reach its pinnacle for oxide electronics operating at room temperature.

Acknowledgments

We acknowledge support from the Air Force Office of Scientific Research (AFOSR) through Grant FA9550‐16‐1‐0205, the National Science Foundation through award numbers DMR‐1410888, DMR‐1607318, and DMR‐1741801, the UMN MRSEC program under award number DMR‐1420013, the DOE Center for Quantum Materials (CQM) under DE‐SC0016371, and the RDF Fund of the Institute on the Environment (UMN). A. P. would like to acknowledge support from a UMN Doctoral Dissertation Fellowship. The authors would also like to thank Steve May for careful reading of the manuscript.

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