Adsorption-controlled growth of La-doped BaSnO3 by molecular-beam epitaxy

Epitaxial La doped BaSnO3 films were grown in an adsorption controlled regime by molecular beam epitaxy, where the excess volatile SnOx desorbs from the film surface. A film grown on a (001) DyScO3 substrate exhibited a mobility of 183 cm^2 V^-1 s^-1 at room temperature and 400 cm^2 V^-1 s^-1 at 10 K, despite the high concentration (1.2x10^11 cm^-2) of threading dislocations present. In comparison to other reports, we observe a much lower concentration of (BaO)2 Ruddlesden Popper crystallographic shear faults. This suggests that in addition to threading dislocations that other defects possibly (BaO)2 crystallographic shear defects or point defects significantly reduce the electron mobility.

Transparent conducting oxides with high mobility are being studied in hopes of realizing high-performance transparent electronics. 1 La-doped BaSnO 3 has emerged as a material of interest in this arena due to its high mobility at room temperature, transparency, and stability. Ladoped BaSnO 3 single crystals are reported to have mobilities as high as 320 cm 2 ·V -1 ·s -1 at room temperature at a mobile electron concentration of n=8×10 19 cm -3 . 2 Indeed, La-doped BaSnO 3 has a higher mobility than all mainstream semiconductors (Si, GaAs, GaN, etc.) at doping concentrations above about n=10 19 cm -3 , where it is degenerately doped; 3 CdO is the only transparent semiconductor with higher mobility in this doping range. 4 Another advantage of BaSnO 3 is its excellent structural match to ferroelectric and antiferroelectric oxides with the perovskite structure, e.g., Pb(Zr,Ti)O 3 . This could enable La-doped BaSnO 3 to serve as a high mobility channel for smart transistors 5 including ferroelectric field-effect transistors [6][7][8][9][10][11][12][13][14][15][16] and yield a subthreshold slope beating the 60 mV/decade Boltzmann limit of conventional field-effect transistors by fabricating negative capacitance field-effect transistors (NCFET). 17,18 Two major deficiencies of today's epitaxially grown La-doped BaSnO 3 films that impact the performance of field-effect devices are (1) their mobility is significantly lower 2,3,[19][20][21][22][23][24] than what has been demonstrated in La-doped BaSnO 3 single crystals 2,24,25 and (2) when doped below about 1×10 19 cm -3 they are no longer conductive. 2,3,[19][20][21][22][23][24] This latter point also applies to La-doped BaSnO 3 single crystals. 2,24 Both of these issues relate to the presence of significant concentrations of defects. The low mobility has been attributed to the high density of threading dislocations in epitaxial BaSnO 3 films that arise because they are grown on substrates to which they are poorly lattice matched. 2,[19][20][21][22][23][24] High concentrations of threading dislocations are known to limit the mobility of other semiconductors including Ge, 26 (In,Ga)As, 27 In(As,Sb), 28 SiGe, 29 and GaN. 30 Indeed the mobilities of epitaxial GaN and BaSnO 3 films with threading dislocation 4 densities in the 10 10 -10 11 cm -2 range have been observed to scale with the square root of the mobile carrier concentration, 2,19,30 in agreement with theory. 26,30 In addition to the ability of dislocations to trap charge, nonstoichiometry, i.e., the ratio of (La+Ba):Sn deviating from 1 in La-doped BaSnO 3 films and the point defects it leads to, could also be responsible for the insulating behavior seen in lightly La-doped BaSnO 3 thin films. The inability to lightly dope Ladoped BaSnO 3 layers is an obstacle to the fabrication of depletion-mode field-effect transistors.
The cutoff at about 1×10 19 cm -3 in mobile electron concentration, below which doped films are insulating, is indicative of the concentration of electron traps in BaSnO 3 thin films. If nonstoichiometry is the root of the traps, then insulating behavior below a lanthanum concentration of 1×10 19 cm -3 implies that the films deviate by 0.07% or more from being stoichiometric. This value is comparable to state-of-the-art stoichiometry control in the deposition of multicomponent films by physical vapor deposition methods. 31-39 A way to circumvent this limit is to exploit thermodynamics by entering an adsorption-controlled growth regime where the volatile constituents are provided in excess, but film composition is controlled automatically and locally through the volatility of those constituents to produce single-phase films. [40][41][42][43][44][45][46][47][48][49] Adsorption-control has been extensively used for the growth of oxides [50][51][52] including, most recently, for the growth of epitaxial BaSnO 3 films utilizing metalorganic precursors. 53 In this Letter, we utilize adsorption-controlled growth with inorganic precursors to achieve La-doped BaSnO 3 thin films with (1) higher mobility and (2) that are conductive to lower carrier concentrations than have been reported to date. Room-temperature mobilities in excess of 150 cm 2 ·V -1 ·s -1 , the prior mobility record, 22 are achieved in fully relaxed La-doped BaSnO 3 thin films on substrates with mismatches ranging from -5.1% (SrTiO 3 ) to -2.3% (PrScO 3 ). Our result 5 demonstrates that dislocations are not the only defect that limit the mobility in La-doped BaSnO 3 thin films and emphasizes the importance of precisely controlling film stoichiometry.
La-doped BaSnO 3 thin films were grown in a Veeco GEN10 MBE system from molecular beams emanating from separate effusion cells containing lanthanum (99.996% purity, Ames Lab), barium (99.99% purity, Sigma-Aldrich), and SnO 2 (99.996% purity, Alfa Aesar), respectively, in combination with a molecular beam of oxidant (the ~10% ozone + oxygen output of a commercial ozone generator). 54 The fluxes emanating from the effusion cells were determined by a quartz crystal microbalance (QCM) before growth. To achieve the desired doping concentration, the lanthanum flux was adjusted from the temperature at which its flux was measured by the QCM to a lower temperature, where accurate QCM measurements are not possible, by extrapolating its flux using the known activation energy of the vapor pressure of lanthanum, 55 i.e., a linear extrapolation of a plot of lanthanum vapor pressure vs. 1/T. According to vapor pressure calculations, multiple species evaporate from SnO 2 under our growth conditions, with the major species being SnO. 56 In the supplementary material (S1) the calculated vapor pressure of species over solid SnO 2 are plotted at a fixed oxygen partial pressure of 7.6×10 -7 Torr (10 -9 atm). We used an excess of SnO x -flux (above 9.0×10 13 atoms·cm -2 ⋅s -1 ) during growth, which is approximately three times greater than the barium flux relationship. The substrate temperature was maintained between 830-850 °C, as measured by an optical pyrometer. To determine the optimal single-phase growth window, we used in situ reflection high-energy electron diffraction (RHEED) as described below. The RHEED intensity oscillation period was used to estimate the film thickness and growth rate. The film growth rate was about 0.3 Å/s. The phase purity and structural perfection of the films were assessed using four-circle x-ray diffraction (XRD) utilizing Cu K α radiation with a high-resolution diffractometer (Panalytical X'Pert Pro MRD with a PreFix hybrid 4×Ge 220 monochromator on the incident beam side and a triple axis/rocking curve attachment (Ge 220) on the diffracted beam side). The microstructure and defects in the film were studied by cross-sectional and plan-view high (low)angle annular dark field scanning transmission electron microscopy (HAADF-STEM and LAADF-STEM) with an FEI Titan Themis with a probe aberration corrector at 300 kV.
Temperature-dependent electrical transport and Hall effect were measured in a van der Pauw geometry with contacts made by wire bonding. Figure 1 shows the calculated oxygen partial pressure (P O 2 ) vs. temperature (T) diagram for the Ba-Sn-O system with the tin partial pressure fixed at 7.6×10 -8 Torr (10 -10 atm). It is constructed using the CALPHAD method and first-principles calculations (see supplementary material for additional details (S2)). 58 The reaction enthalpy (ΔH) values shown in Table I  Within region III stoichiometric BaSnO 3 films grow free of any surface reconstruction, i.e., with a 1×1 RHEED pattern. This can be clearly seen in Fig. 2(a) from the sharp 1×1 LEED image of a La-doped BaSnO 3 film. In contrast, we observe a 2×1 RHEED pattern, with the 2× reconstruction along the [110] azimuth of BaSnO 3 when the film growth conditions become slightly Ba-rich and move toward the boundary between region III and region II by either (1) increasing the substrate temperature, (2) lowering the flux supplied from the SnO 2 source, or (3) lowering the ozone partial pressure. Exiting region III and moving into region II is manifested by a more diffuse RHEED pattern with spots corresponding to the growth of a disordered   Fig. 3. The θ-2θ scan is shown in Fig. 3(a). The total film thickness is calculated based on the Kiessig fringes 67 around the 002 Bragg peak of the BaSnO 3 , as shown in Fig. 3(b). The θ-2θ scan exhibits solely the 00ℓ reflections of BaSnO 3 without any impurity phase. From these reflections 9 the c-axis of this La-doped BaSnO 3 film is calculated to be c = 4.116 ± 0.001 Å using a Nelson-Riley fit; 68 this is in agreement with the bulk lattice constant of BaSnO 3 , a = 4.116 Å. 66 A comparison of the structural perfection of this same La-doped BaSnO 3 film and the underlying DyScO 3 substrate it was grown upon are shown in Fig. 3(c). Here, the rocking curve of the 002 peak of the La-doped BaSnO 3 film is overlaid upon the 004 peak of the DyScO 3 substrate. The full width at half maximum (FWHM) of the film peak is 0.016°, which is far broader than the 0.0062° FWHM of the substrate. Although narrower than all prior reported FWHM for as-grown  resistivity at room temperature is 2.3×10 -4 Ω⋅cm and its temperature dependence exhibits metallic behavior down to 10 K with a resistivity ratio, ρ 300 K / ρ 10 K , of 2.15. The concentration of negatively charged mobile carriers (n) is temperature independent, as shown in Fig. 4(b).
Assuming that all of the mobile carriers are attributable to the 60-nm-thick La-doped BaSnO 3 layer, the Hall resistance implies that n is 1.2×10 20 cm -3 . The mobility (µ) of this same sample was 183 cm 2 ·V -1 ·s -1 at room temperature and reached 400 cm 2 ·V -1 ·s -1 at 10 K as can be seen in Fig. 4(c). This room-temperature mobility is 20% higher than the previous record, 150 cm 2 ·V -1 ·s -1 , which was achieved on a (110) PrScO 3 substrate. 22 The sample described in detail so far, is our highest mobility sample. The roomtemperature mobility of other La-doped BaSnO 3 samples grown using the same adsorptioncontrolled growth conditions on a variety of substrates and with differing doping concentrations are shown in Fig. 4(d). These substrates ranged from SrTiO 3 to PrScO 3 , with lattice matches to BaSnO 3 ranging from -5.1% to -2.3%, respectively. Note that the room-temperature mobility of La-doped BaSnO 3 films on all of these substrates was higher than 160 cm 2 ·V -1 ·s -1 for doping concentrations in the (2-30)×10 19 cm -3 range. Additionally, our growth conditions enable films with mobile carrier concentrations all the way down to 1×10 18 cm -3 to be achieved; 69 this is an order of magnitude lower than prior reports. 2,3,[19][20][21][22][23][24] The ability to dope BaSnO 3 at lower levels is consistent with the improved stoichiometry control that can accompany adsorption-controlled growth, leading to a reduction in the concentration of traps.
We investigated the defect structure of the La-doped BaSnO 3 sample with the highest mobility, the same sample whose other characteristics appear in Figs. 2-4, by STEM. A crosssectional LAADF-STEM image of the entire film thickness is shown in Fig. 5(a). The high sensitivity of LAADF to strain and dislocations 70 makes it easy to see the threading dislocations.
They are the vertically running defects with dark contrast in the BaSnO 3 film; one is indicated by a yellow arrow on Fig. 5(a). The HAADF-STEM images in Figs. 5(b) and 5(c) characterize the fully relaxed interface between the DyScO 3 substrate and the BaSnO 3 film. The spacing between the edge dislocations is on average 23 unit cells of DyScO 3 vs. 22 unit cells BaSnO 3 , which is consistent with that calculated from the ratio of the relaxed lattice parameters. Extended dislocations can also be seen, as indicated by the yellow arrow in Fig. 5(b).
The density of threading dislocations in the same high-mobility sample characterized in Figs. 2-5 was determined by plan-view STEM measurements (Fig. 6) to be 1.2×10 11 cm -2 . A high-resolution HAADF-STEM image is shown in Fig. 6(d)  This could be because the out-of-plane component of the Burgers vectors of these two dislocations are not identical; they could have mixed character rather than being pure edge dislocations. Another possibility is that the adsorption controlled growth conditions lead to excess SnO x species on the film surface during growth, which acts as a flux that lowers γ. 71 The amount that γ is lowered depends on the concentration of flux and could vary spatially, leading to dislocations that are hollow or not hollow even though they have identical magnitudes of their Burgers vectors.
The huge density of dislocations observed in this film with record mobility (1.2×10 11 cm -2 ) led us to question if there might be some other defects besides dislocations that currently limit mobility in BaSnO 3 films. After all, our films are grown on the same substrates and have comparable dislocation densities to prior studies, 19 yet the mobilities are far higher. How is it that our films have higher mobility? We do not know the answer to this question and are studying it further; what little we do know is mentioned below.
A potential culprit is Ruddlesden-Popper 60-62 (BaO) 2 crystallographic shear defects, which have been reported to be a dominant structural defect in La-doped BaSnO 3 films grown by pulsed-laser deposition. 74 The TEM images in the study of Wang et al. 74  Differences in point defect concentrations could also be responsible for our films exhibiting higher mobility than other BaSnO 3 films with comparable dislocation densities.
Vacancies on the barium site !" !! or on the tin site !" !!!! are low-energy acceptor defects 75,76 in BaSnO 3 that could be responsible for the lack of conductivity in lightly La-doped BaSnO 3 films as well as the reduction in mobility when sufficient La is added to achieve conductivity.
The local and automatic composition control provided by thermodynamics under adsorptioncontrolled growth conditions, could significantly reduce the concentration of !" !! , !" !!!! , and other point defects, thus enhancing mobility. Note that adsorption-control is not synonymous with perfect composition control. Adsorption-control accesses the single-phase region of BaSnO 3 , but 13 depending on how wide that region is and from which side it is approached (in our case the SnO x -rich side)-things that change with temperature and chemical potentials-the stoichiometry of the resulting film will change though it will always remain single phase. This is fully analogous to the growth of III-V compounds, where this behavior is well understood and utilized to controllably alter point defect concentrations, e.g., the EL2 defect in GaAs. 77 In summary, using adsorption-controlled MBE growth, La-doped BaSnO 3 thin films with room-temperature mobilities as high as 183 cm 2 ·V -1 ·s -1 were achieved on highly mismatched   with Perdew-Burke-Ernzerhof revised for solids (PBEsol) functional, predicted the enthalpy of BaSnO 3 formation to be -107.5 kJ/mol per formula unit for the BaO+SnO 2 =BaSnO 3 reaction (see Table I).   Kim et al. 2,24 at SNU (purple diamond), Shiogai et al. 21 at Tohoku University (orange upside down triangle), and Prakash et al. 23 at the University of Minnesota (cyan sideways triangle).