What determines the interfacial configuration of Nb/Al2O3 and Nb/MgO interface

Nb films are deposited on single crystal Al2O3 (110) and MgO(111) substrates by e-beam evaporation technique. Structure of Nb films and orientation relationships (ORs) of Nb/Al2O3 and Nb/MgO interface are studied and compared by the combination of experiments and simulations. The experiments show that the Nb films obtain strong (110) texture, and the Nb film on Al2O3(110) substrate shows a higher crystalline quality than that on MgO(111) substrate. First principle calculations show that both the lattice mismatch and the strength of interface bonding play major roles in determining the crystalline perfection of Nb films and ORs between Nb films and single crystal ceramic substrates. The fundamental mechanisms for forming the interfacial configuration in terms of the lattice mismatch and the strength of interface bonding are discussed.

Scientific RepoRts | 6:33931 | DOI: 10.1038/srep33931 In this article, the Nb films were epitaxially grown on Al 2 O 3 (1120) and MgO(111) substrates, respectively, and the fundamental mechanisms for the formation of interfacial configuration were systematically investigated by experiments and simulations. Comparison of the two systems, in terms of crystalline perfection of Nb film and interface orientation, indicates that the lattice mismatch and the strength of interface bonding are dominating factors for the formation of Nb/oxide ORs.

Results
Nb is a body centered cubic (BCC) crystal with the lattice parameter of 0.3307 nm. Al 2 O 3 is a hexagonal close packed (HCP) crystal with the lattice parameters of a = 0.4759 nm and c = 1.2991 nm, and MgO has a face centered cubic (FCC) structure with the lattice parameter of a = 0.4217 nm. Figure 1a shows XRD θ -2θ diffraction pattern of the Nb film on Al 2 O 3 (1120) substrate. The specimen shows a strong diffraction peak of Nb(110) together with a peak of Al 2 O 3 (1120), and a weak diffraction peak of Nb(220) together with a peak of Al 2 O 3 (2240). No other diffraction peaks are present, indicating that the Nb film is strongly textured wherein the Nb(110) plane is parallel to the Al 2 O 3 (1120) plane. Figure 1b shows the XRD θ -2θ diffraction pattern of Nb film on MgO(111) substrate. Despite the deposition substrate difference, both Nb film on Al 2 O 3 (1120) and Nb film on MgO (111) exhibit the strong texture of Nb (110) as evidenced by XRD results.
The interplanar spacing d of Nb (110) can be obtained from the Bragg's law: where λ = 1.5406 Å in this experiment. The peak position of Nb(110) in experimental plots is calibrated by diffraction peak of Al 2 O 3 (1120) and diffraction peak of MgO(111), respectively. If the sample presents uniform strain ε′ at the interface, the modified interplanar spacing of Nb(110) will produce a peak shift to a new position. The uniform strain ε′ is defined as:   High resolution TEM (HRTEM) image of the Nb/Al 2 O 3 interface is shown in Fig. 3a,b. An array of misfit dislocations is observed, which are labeled by the "T" sign in Fig. 3b. The average spacing of misfit dislocations was measured to be 1.9 nm. Also, the average interface dislocation spacing can be given by [36][37][38] : where b is the Burgers vector's absolute value of the misfit dislocation parallel to the interface and δ is the lattice mismatch. By using eq. (4), the average interface dislocation spacing is calculated as     Fig. 3d. The difference in the calculated dislocation spacing along the interface implies the difference of the dislocation density along the interface. The dislocation density of Nb(110)/Al 2 O 3 (1120) interface is lower than that of Nb(110)/MgO(111) interface. As a result, the Nb(110)/Al 2 O 3 (1120) interface has less distortion and thus it is more stable than Nb(110)/MgO(111) interface.
In short, the ORs of Nb/Al 2 O 3 (1120) and Nb/MgO(111) interfaces are observed by TEM. The lattice mismatches along two perpendicular in-plane directions for Nb/Al 2 O 3 interface are 12.5% and 1.8%, while for Nb/MgO interface are 10.1% and 10.2%. HRTEM analysis shows that the measured lattice mismatch is consistent with the calculated value.
Above study shows that both Nb film on Al 2 O 3 (1120) and Nb film MgO (111) exhibit the strong texture of Nb (110) plane, and it is essential to investigate the films crystalline perfection which can be characterized by channeling RBS and XRD rocking curve. Figure 4 illustrates 2 MeV 4 He + RBS spectrums from Nb(110) film on Al 2 O 3 (1120) substrate taken under random and [110] aligned condition. The yield ratio of the aligned spectrum to random spectrum was used to characterize the crystalline perfection along the out-of-plane direction. The peaks of random spectrum line (black line) and aligned spectrum line (red line) correspond to Nb, Al and O atoms with the decrease of the channel, respectively. The aligned spectrum has two shoulders on the Nb peak. The peak at the higher channel side is the surface peak, mainly from the direct collisions of He ions with the surface Nb atoms in the film. The peak at the lower channel side reflects the imperfection of crystal lattice of Nb film near the Nb(110)/Al 2 O 3 (1120) interface [39][40][41] . The yield ratio of the Nb[110] aligned spectrum to random spectrum from Nb at the position just below the surface peak is about 6.8%, demonstrating that the Nb film deposited on Al 2 O 3 substrate has a well aligned crystalline orientation. The same experiments of Nb(110)/MgO(111) interface was done, however, it was too difficult to observe the channeling effect, indicating that the Nb(110) film on MgO(111) substrate has highly mis-oriented crystallites. These results indicate that the crystalline quality of Nb film deposited on MgO(111) substrate is worse than that deposited on Al 2 O 3 (1120).
High resolution X-ray diffraction is used to investigate the crystalline quality of films and evaluate the dislocation density of interfaces [42][43][44][45][46] . The measured full width at half maximum (FWHM) from the XRD rocking curves is obtained by rotating the sample through the Bragg angle after the angle (θ ) and the detector position (2θ ) are fixed at the Bragg angle of the corresponding reflection. The FWHM is used to determine the mean spread (range) in orientation of the different out-of-plane crystalline domains of a perfect crystal with mis-orientation. Defects like mosaicity, misfit dislocations and mis-orientation will create disruptions in the perfect parallelism of atomic planes and thus broaden the width of rocking curve. Figure 5 illustrates the rocking curves of Nb thin films on Al 2 O 3 (1120) substrate (Fig. 5a) and MgO(111) substrate (Fig. 5b). The peaks of both Fig. 5a,b are reflected from Nb(110) lattice planes. The FWHM of the rocking curve is a way to quantify how well the crystallites in the film are ordered along the growth direction, where in general smaller FWHM values indicate better ordering along the growth direction 47 . Measured FWHM for Nb film deposited on Al 2 O 3 (1120) plane is 0.385°, while the value for Nb film deposited on MgO(111) is 1.247°. Thus Fig. 5 indicates that the atomic alignment  (111) shows that Nb(110) film grown on Al 2 O 3 (1120) substrate has higher crystalline quality. Film with higher crystalline quality usually has lower defects, and often dislocations are thought to be the main defects in the epitaxial single crystal thin film. Here the dislocation density of Nb films will be estimated by the FWHM values of rocking curves through the Hirsch model using equation 45,48 : To further understand the difference of crystalline quality, the lattice mismatch of these two interfaces is investigated. It is well known that interface with larger lattice mismatch usually leads to smaller misfit dislocation spacing. The interface misfit dislocation intersections (MDIs) in interface are usually used to characterize the interface dislocation lines' network [49][50][51][52] and the areal density of MDIs is the indication of the misfit dislocation density. From the dislocation spacing of the two perpendicular directions which are parallel to interface, the areal density of MDIs can be defined as: 1 2 where ρ′ is the dislocation density of misfit dislocation, d 1 and d 2 are the dislocation spacings which are perpendicular with each other and can be obtained from Eq. (4). The areal density of MDIs of Nb(110)/Al 2 O 3 (1120) interface is ρ ′ 1 = 2.8 × 10 12 /cm 2 , while the areal density of MDIs of Nb(110)/MgO(111) interface is ρ ′ 2 = 2.9 × 10 13 /cm 2 . This result shows that the MDIs density in Nb/Al 2 O 3 system is much smaller than that in Nb/MgO system, thus the misfit dislocation density of Nb/Al 2 O 3 interface is lower than that of Nb/MgO interface.
Commonly, the occurrence of misfit dislocations in epitaxial films, which further lowers the crystalline quality of single crystal films, is contributed to the decrease of film's strain energy before and after the formation of misfit dislocation. Strain energy change in thin film with the thickness (h) can be written as , where u f and v are the shear modulus and poisson's ratio of film.
Clearly, only the term (δ − b/d) 2 is related to the strain energy difference between Nb film grown on MgO and on Al 2 O 3 substrate. The Nb film grown on MgO substrate has a larger lattice mismatch (δ) and a larger dislocation spacing (d), thus has a larger decrease of strain energy than that grown on Al 2 O 3 substrate, therefore, leading to more dislocations in Nb film in Nb/MgO. As a whole, the Nb/MgO interface has larger lattice mismatch and thus leads to higher density misfit dislocation in the interface. Subsequently, the stress fields of misfit dislocations promote the occurrence of defects during the following film growth. As a result, Nb/MgO has low crystalline quality of Nb film. Orientation relationships of Nb/Al 2 O 3 and Nb/MgO interface. In order to understand the fundamental mechanisms that why these interfacial configurations behave as they are, the first principle calculation through the coherent models was used to understand their orientation relationships. The building process of the interface structure models is shown in Support Information. Work of separation (W Sep ), defined as the reversible energy needed to separate the interface into two free surfaces, is a fundamental quantity to characterize the strength of the metal/oxide interface, thus it was calculated for the six models. W sep is calculated as 25 : where E Nb , E Al O 2 3 is the energy of single Nb slab and single Al 2 O 3 slab, respectively, E Nb/Al O 2 3 is the total energy of the whole coherent structure after energy minimization, and S is the interface area. Two preset cutoff values of lattice strain (ε) and interface mismatch (δ′) are used to reduce the number of interfacial configuration models. The lattice strain is the strain of Nb along a given direction, e.g., ε l = (a′ − a)/a, where a′ and a are the lattice constants after and before deformation along l direction. The interface mismatch (δ′) refers to the strain required to make two unit cells form coherent structure, and is defined as where Ω represents the overlap area of unit cell with the match cell area of S A in the film and the match area of S B in the substrate. It should be noted that the δ′ is commonly used to describe two plane mismatch of heterointerface, different from the lattice mismatch δ in an axial direction. Study shows that there are six potential models of the Nb/Al 2 O 3 (1120) system and these models are shown in Figure S1b. The calculation results for the six potential models are shown in Table 1.
In addition, we also calculated the atomic Mulliken population to check the information about electron transfers along the interface. , m and ′ m is the Mulliken population for oxygen atoms with and without Nb film, respectively. We noted that ∆m is an average value, as there are more than one equivalent position for oxygen atoms in Al 2 O 3 (1120) plane.

ORs of Nb(110)/Al 2 O 3 (1120) interface.
The calculation results for the six types of potential models are shown in Table 1. It shows that model b1 has the biggest work of separation (0.77 eV/Å 2 ) and the biggest ∆m (0.26 e) among the six possible models. This indicates that among all the six potential candidates, the model b1 has the most stable interface structure, and more electrons are transferred from Nb film to Al 2 O 3 substrate in this model than that occurred in other five models, implying stronger chemical bonds are formed along the interface of the model b1.
The detailed lattice structure of the model b1 is shown in Fig. 6. Interestingly, we also noticed from Table 1 that the smallest mismatch at interface does not naturally relate to the interface with the biggest work of separation (the strongest chemical bound), e.g., the result of the model b2. In contrast, model b1 has the largest W sep while the interface mismatch is not the smallest (δ ′(b2) < δ ′(b1)). As

Model
ORs lattice strain (ε l , ε m , ε n )   both TEM and XRD results confirmed that the interfacial configuration of Nb/Al 2 O 3 (1120) favors model b1, this indicates that although misfit is important for the interface structure of metal/oxide system, the work of separation and the formation of chemical bound may be the dominant factors that determine the ORs between the metal/oxide system.  Table 2. First, it is noticed that the interface mismatch (δ′) of Nb(110)/ Al 2 O 3 (1120) system is 0.07 eVÅ −2 , smaller than that in Nb(110)/MgO(111) system (0.10 eVÅ −2 ). This indicates that there is a better interface overlap of Nb/Al 2 O 3 than that of Nb/MgO. Meanwhile, the lattice mismatch for Nb(110)/Al 2 O 3 (1120) at l and m direction (2.0%, 12.9%) is also smaller than that of Nb(110)/MgO(111) (10.0%, 10.2%). A small lattice mismatch means a large distance between misfit dislocations along the interface of Nb/Al 2 O 3 , which is consistent with the dislocation spacing observed in the experiment. Second, it is noticed that the work of separation of Nb(110)/Al 2 O 3 (1120) system (0.77 eV/Å 2 ) is larger than that of Nb(110)/MgO(111) system (0.74 eV/Å 2 ). It means the combined strength between Nb film and Al 2 O 3 substrate is stronger, and defects might be more difficult to form along the interface in this system. In addition, Table 2 also showed that Nb atoms in Nb(110)/Al 2 O 3 (1120) system lose more electrons (0.47 e) than that in Nb(110)/MgO(111) system (0.25 e). This indicates that stronger ionic bonds are formed along the interface Nb/Al 2 O 3 system. In summary, it is concluded that the higher degree of crystal perfection of Nb(110)/Al 2 O 3 (1120) likely arises from the smaller interface mismatch, larger work of separation and stronger ionic bonds.

Comparison of interfaces in Nb
The bonding information can also be visualized by delocalization of atomic charge density. The electron density difference ( ρ ∆ ) maps of the above two interface structures are shown in Fig. 7, where ρ ρ / is the self-consistent electron density of whole relaxed metal/substrate interface structure, ρ A and ρ B are the electron densities of isolated metal and substrate slabs having the same atomic positions in the interface structure. We observed from Fig. 7 that for both systems, Nb atoms lose electrons, and O atoms gain electrons, as the blue and light red color shown. This means electrons are transferred from Nb film to substrate along the interface, and the transfer mainly takes place between the two adjacent layers next to the interface. However, the electrons redistribution in Nb(110)/Al 2 O 3 (1120) is stronger than that in Nb(110)/MgO(111). This indicates that ionic bonds in Nb/Al 2 O 3 are stronger than that in Nb/MgO system. In fact, the electron density difference maps can also be understood as follow: the number of electron suppliers are almost the same Nb(110) in both systems, however, the atomic ratio of the electron supplier(Nb) and electron acceptor (oxygen) is 2:3 in the Nb/Al 2 O 3 system, while this value for Nb/MgO system is 1:1. Thus it is natural that the Nb atoms in Nb/Al 2 O 3 interface will lose more electrons than that in Nb/MgO system.
In conclusion, Nb films were deposited on the Al 2 O 3 (1120) substrate and MgO (111)  . Comparison study shows that the degree of Nb crystalline perfection in Nb(110)/Al 2 O 3 (1120) system is higher than that in Nb(110)/MgO(111). Frist-principle calculations through a coherent interface model showed that the higher crystal perfection of Nb(110)/ Al 2 O 3 (1120) arises from the smaller interface mismatch, larger work of separation and stronger ionic bonds. Although misfit is important for forming the interface configuration of metal/oxide interface system, the work of separation and the strength of chemical bound may be the dominant factors that determine the interface configuration in the metal/oxide interface system.

Methods
Sample preparation and characterization. Nb thin films were deposited on single crystal Al 2 O 3 (1120) substrate and MgO(111) substrate by electron-beam evaporation technique with a deposition rate of 5Å/s at 950 °C under a vacuum of 3.5 × 10 −5 Pa. The purity of the Nb evaporation target was 99.999%. The thickness of Nb thin film is 170 nm. The single crystal Al 2 O 3 substrate has the dimension of 10 mm × 10 mm × 0.5 mm. The detailed deposition conditions of Nb film on single crystal MgO(111) can be found elsewhere 27 . XRD analysis was    used to characterize the Nb film structure and the ORs between the Nb film and the substrates. The cross sectional TEM samples were prepared at room temperature by using conventional thinning-milling process. The FEI Tecnai F30 transmission electron microscope (TEM), which worked at 300 kV with a field-emission gun, was used to characterize the interface structure of Nb film on different substrates. The selected area electron diffraction (SAD) was used to identify the ORs between the Nb films and the substrates. RBS/Channeling measurement was used to characterize the crystal structure of deposited Nb films. The analyzing beam was 2 MeV 4 He + ions and the beam current was about 10 nA with an area of 1 mm 2 .