Anti-site defect e ﬀ ect on the electronic structure of a Bi 2 Te 3 topological insulator

Tuning the Fermi level ( E F ) in Bi 2 Te 3 topological-insulator (TI) ﬁ lms is demonstrated on controlling the temperature of growth with molecular-beam epitaxy (MBE). Angle-resolved photoemission spectra (ARPES) reveal that E F of Bi 2 Te 3 thin ﬁ lms shifts systematically with the growth temperature ( T g ). The key role that a Bi-on-Te(1) (Bi Te1 ) antisite defect plays in the electronic structure is identi ﬁ ed through extended X-ray-absorption ﬁ ne-structure (EXAFS) spectra at the Bi L 3 -edge. Calculations of electronic structure support the results of ﬁ tting the EXAFS, indicating that the variation of E F is due to the formation and suppression of Bi Te1 that is tunable with the growth temperature. Our ﬁ ndings provide not only insight into the correlation between the defect structure and electronic properties but also a simple route to control the intrinsic topological surface states, which could be useful for applications in TI-based advanced electronic and spintronic devices.


Introduction
Topological insulators (TI) are novel quantum materials with promising applications in advanced spintronic devices. A threedimensional (3D) TI is a gapped bulk insulator, but possesses gapless conducting surface states. 1,2 These topological surface states in 3D TI arise from a band inversion of the valence and conduction bands due to strong spin-orbit interactions. 3,4 This inversion makes the surface state topologically nontrivial, being protected by the time-reversal symmetry. The surface state in 3D TI shows a helical Dirac-type dispersion, in which the spin is tightly coupled to the momentum, so called spin-momentum locking. 5 V 2 -VI 3 -type 3D TIs, such as Bi 2 Se 3 , Bi 2 Te 3 and Sb 2 Te 3 , have been theoretically predicted and experimentally conrmed. 4,6,7 Bi 2 Te 3 belongs to the V 2 -VI 3 TI family and has a rhombohedral crystal structure that can be considered to consist of the stacking of -Te(1)-Bi-Te(2)-Bi-Te(1)quintiple layers (QL). 8 Within a QL unit, the interaction between Bi and Te is a chemical force whereas the interaction between two QL involves a van der Waals force. The surface states of Bi-based TI families are widely regarded as ideal systems for applications in spintronic and quantum devices, but a large bulk charge-carrier contribution generally originates from intrinsic defects, such as anion vacancies and antisite defects in Bi-based TI. 9 When the charge carrier is dominated by bulk donors, the Dirac point (DP) is located deep below the Fermi level, making it difficult to utilize the unique property of the topological surface states. Understanding and manipulating the electronic structure during the growth of a thin lm of TI becomes a crucial problem, especially for the effect of key parameters such as the growth temperature on the electronic structure of TI.
For a Bi 2 Te 3 single crystal near the solid-liquid equilibrium composition for Te ranging from 58 to 62.8 atomic per cent, a substitution of Bi for a Te(1) site (Bi Te1 ) is energetically favored and hole charge carriers dominate. In contrast, electron carriers dominate the behavior in the case of substitution of Te for Bi (Te Bi ) for Te in a range from 62.8 to 66 atomic per cent. For single-crystalline Bi 2 Te 3 , the p-type and n-type charge-carrier concentration can range from 3 Â 10 17 to 5 Â 10 19 cm À3 , depending on the initial growth condition with excess either Bi or Te. [10][11][12][13][14] For bulk Bi 2 Te 3 crystal growth near the solid-liquid equilibrium temperature, anti-site defects can be simply described by element compositions. In comparison, thin lm growth is far from the equilibrium conditions, so that the composition of Bi/Te can be tuned by growth temperature. In the present work, we report a systematic study of the crystal structure and electronic properties of epitaxial Bi 2 Te 3 lms upon tuning the growth temperature. A correlation between the position of the Dirac point of Bi 2 Te 3 lms via angle-resolved photoemission spectra (ARPES) and the coordination number of Bi-Bi Te1 via extended X-ray-absorption ne structure (EXAFS) spectra is clearly identied. To compare with the experimental results, we conducted a simulation on Bi Te and Te Bi antisite defects with density-functional theory (DFT); the results support the conclusion that the variation of the electronic structure of Bi 2 Te 3 lms is highly correlated with the antisite defects that vary with the growth temperature. Our ndings provide also a simple route to manipulate the Dirac point and topological surface states that can yield applications in electronic and spintronic devices.

Sample preparation
The TI lms were grown on c-plane Al 2 O 3 (0001) substrates with a MBE system (AdNaNo Corporation, model MBE-9). The sapphire substrates were chemically cleaned with standard procedures before being loaded into the growth chamber. To remove any possible contaminant from the surface, we heated the sapphire substrates to 1000 C for 1 h under a ultrahighvacuum (UHV) environment. Highly pure Bi (99.99%) and Te (99.999%) were evaporated from Knudsen cells; the ux rate was calibrated in situ with a quartz crystal microbalance. The base pressure of the MBE system was less than 2 Â 10 À10 Torr; the pressure during growth was kept below 1 Â 10 À9 Torr. The Bi 2 Te 3 thin lms were prepared with a stable beam-ux ratio Te/ Bi (F Te/Bi ) $ 15; the substrate temperature was varied from 310 C to 430 C. The crystallinity of Bi 2 Te 3 lms was monitored in situ with reection high-energy diffraction (RHEED); additional structural characterization was performed with X-ray diffraction (XRD).

XPS and ARPES characterization
The stoichiometry and electronic structure of the Bi 2 Te 3 lms were characterized with X-ray photoemission spectra (XPS) and ARPES. The XPS and ARPES experiments were conducted at beamlines 24A and 21B1 at Taiwan Light Source in National Synchrotron Radiation Research Center. The MBE-grown Bi 2 Te 3 lms with a Te capping layer of thickness $20Å were annealed at 260 C about 1 h in an UHV environment to remove the capping layer before XPS and ARPES measurements. XPS were recorded with an energy analyzer (SPEC Phoiboss150); the core levels of Bi 4f and Te 3d were recorded with photon energy 800 eV. The incident photon energy for XPS measurements was calibrated with Au 4f levels. ARPES were recorded for samples in an UHV chamber equipped with a hemispherical analyzer (Scienta R4000, collection angle AE15 ). The ARPES were recorded for samples at 83 K, base pressure 5 Â 10 À11 Torr and photon energy 22 eV; the angular resolution was 0.2 and overall energy resolution was better than 12 meV. The position of the Dirac point was determined from an analysis of momentum distribution curves (MDC).

EXAFS characterization
The local structure of Bi 2 Te 3 thin lms was determined with EXAFS spectra. The L 3 -edge spectra of Bi (13 419 eV) were recorded near 296 K at beamline 07 A of NSRRC and Taiwan beamline SP12B2 of SPring-8. The uorescence mode was implemented with the beam incident at 54.7 with respect to the sample plane; the signal was collected with a Lytle detector. The measured energy resolution of the used double-crystal Si(111) monochromator was better than 0.6 eV.

Computational
In this work we used spin-polarized density-functional calculations as implemented in the Vienna ab initio simulation package (VASP) 15,16 to derive the electronic band structure. The local-density approximation was selected for the exchangecorrelation potential including spin-orbit interaction (SOI). The electron-ion interaction was represented by the projectoraugmented wave potential. 17 The cutoff energy for the expansion of wave functions and potentials in the plane-wave basis was chosen to be 300 eV. A 9 Â 9 Â 1 sampling of k points in the rst Brillouin zone was adopted. A vacuum space in the supercell was allocated on setting a minimum height 15Å above the lm in the cell, which was proved to be sufficient to minimize articial interactions between supercells.  (015) lattice plane that can be attributed to the rhombohedral Bi 2 Te 3 structure is also observed. 18 The main feature of the XRD patterns of these Bi 2 Te 3 samples is clearly close to that of Bi 2 Te 3 (0001) single crystal.

Results and discussion
ARPES were measured to probe the quality and electronic structure of MBE-grown Bi 2 Te 3 lms. Fig. 2 shows the band structure recorded along direction G-K. In addition to the broad M-shaped valence-band (VB) feature located at binding energy 0.3 eV, a linear band dispersion associated with the topological surface state (TSS) was clearly observed in each sample. ARPES in a series in Fig. 2(a)-(d) show that the Fermi level varied with the growth temperature, T g . At T g ¼ 310 C, the Dirac point is located at the binding energy (E B ) ¼ À0.320 eV; the bottom of the conduction band appears below the Fermi level. On increasing T g to 370 C and 390 C, the position of the Dirac point shied to E B ¼ À0.305 eV and À0.295 eV, respectively. A similar tendency of the position variation of the Dirac point with increasing T g below 400 C was reported by Guang Wang et al., 19 but when T g was further increased to 410 C and 430 C, we observed an opposite trend in which the position of the Dirac point shied further to E B ¼ À0.315 eV and À0.335 eV, respectively. The ARPES result shows a turning point of the position of the Dirac point that occurred at T g $ 390 C. As E F was located above DP for all samples, the result indicates that the charge carriers of the Bi 2 Te 3 lms were dominantly n-type so that E F became tunable on varying growth temperature T g .
Hole-dominated carriers with E F located within the bandgap is expected if the electronic structure were determined mainly by the antisite defects in Bi 2 Te 3 , but the lm growth occurred far from the equilibrium growth conditions of a bulk single crystal. The formation of Te vacancies can hence not be avoided during the growth of a Bi 2 Te 3 lm. Te vacancies likely provide ntype carriers as the majority carriers for all Bi 2 Te 3 lms. It is difficult to perform quantitative analysis on the Te vacancies although they play an important role in the electronic structure. Besides point defects in Bi 2 Te 3 , antisite defects, substitutional Bi on Te site (Bi Te ) or substitutional Te on Bi site (Te Bi ) are energetically favored. 10,20,21 The tendency of Fermi level shi in the Bi 2 Te 3 lms observed by ARPES suggests the major defects are Te vacancies and/or Bi Te . Note that the Te vacancies acts as double donors while the Bi Te as triple acceptors. Therefore, ntype behavior in the Bi 2 Te 3 lms can be attributed to Te vacancies that donate electrons to the conduction band. 22,23 This is consistent with the ARPES observation that the positions of the Fermi level are close to the conduction band. However, the ARPES data show clearly that E F varies with growth temperature T g , which indicates that antisite defects also play a role in this case. According to the previous reports, 19,24 a shi of the Fermi level in Bi 2 Te 3 depends strongly on the native point of antisite defects (Bi Te and Te Bi ) in the Bi-Te compound. Near a stoichiometric Bi 2 Te 3 with Te fraction about 62.8 at%, acceptor-like Bi Te antisite defects can dominate the carrier behavior. Donor-like Te Bi antisite defects are energetically favored at a larger Te composition, above 63%. The ratio of Bi and Te can be estimated qualitatively from XPS measurements with a peak analysis of the core level spectra of Bi 4f and Te 3d; the secondary electron background is removed with the Shirley background subtraction, as shown in Fig. 3(a) and (b). [25][26][27][28] The tendency that the Fermi level shied toward the Dirac point in APRES as T g increased from 310 to 390 C implies that the concentration of Bi Te antisite defects increased with increasing T g , as shown in Fig. 3(d). The highest Te fraction at 390 C as revealed in XPS might indicate the diffusion of Te atoms towards the outermost surface. The reduction of Te fraction at T g >390 C can be attributed to the desorption of Te from the surface. 29 Nevertheless, a shi of E F away from the DP at T g > 390 C indicates a redistribution of the Bi Te /Te Bi ratio at the elevated growth temperatures. Detailed studies regarding the antisite defects dependent on growth temperature enable a quantitative analysis with EXAFS in the following.
To verify our deductions about the antisite defects, we performed Fourier transformation of the X-ray absorption spectra (XAS) at the Bi-L 3 edge; the radial distribution function is shown in Fig. 4(a). The tted results of extended X-ray-absorption nestructure (EXAFS) spectra enable a direct identication of the antisite defects in Bi 2 Te 3 lms. In this EXAFS work we took Bi instead of Te as the central atom, because the two Te sites in each unit cell make the analysis difficult. Herein, EXAFS spectra were recorded with the background subtraction of the XAS data m(E) and conversion of m(E) to c(k); both processes were performed with ATHENA using the IFEFFIT XAS package. 30 The Fourier transforms (FT) of k-weighted EXAFS spectra use Hann windows with k ranging from 1.2 to 10Å À1 , as shown in Fig. 4(b). The rhombohedral primitive and hexagonal unit cell of Bi 2 Te 3 consists of a ve-layer lamellar structure of one quintuple layer (QL). The schematic diagram in Fig. 4(c) shows that a -Te(1)-Bi-Te(2)-Bi-Te(1)-ve-layer structure; one Bi atom coordinates three Te atoms at each Te site. According to calculations that provided predictions for the Bi-rich condition, Bi Te1 has the least formation energy, 0.4 eV and 0.9 eV, which is less than for Bi Te2 and Te Bi , respectively. For a Te-rich condition, Te Bi has the least formation energy, 0.7 eV and 1.1 eV, which is less than for Bi Te1 and Bi Te2 , respectively. 23 The coordination relevant for Bi and Te(1) and the bond length of quantitative analysis is indicated in Table 1. At growth temperatures T g ¼ 310, 370 and 390 C, the coordination numbers of Bi-Bi Te1 (N Bi-BiTe1 ) that correspond to the substitution of Bi for Te(1) are 1.05 AE 0.11, 1.312 AE 0.47 and 2.725 AE 0.35, respectively. Accordingly, the length of the Bi-Te(1) bond decreased to 3.04 AE 0.31Å, 3.02 AE 1.07Å, and 2.88 AE 0.37Å, as more Te(1) sites became occupied with Bi atoms. When the growth temperature exceeded 390 C, the coordination number of Bi-Bi Te1 (N Bi-BiTe1 ) decreased to 0.77 AE 0.06 at T g ¼ 410 C. Moreover, no Bi substitution was observed at T g ¼ 430 C. The length of the Bi-Te(1) bond increased to 3.06 AE 0.23Å and 3.04 AE 0.36Å at T g ¼ 410 and 430 C respectively.
On increasing growth temperature T g to 390 C, the tted results of EXAFS clearly show the substitution of a Te(1) site by a Bi atom with increased coordination number of Bi-Bi Te1 . Because of the extra holes created from antisite Bi Te , a smaller Fermi level crossing k F was observed from ARPES, 31 indicating a decreased concentration of electron carriers. For a growth temperature above T g ¼ 390 C, the coordination number of Bi-Bi Te1 decreased, accompanied with an incremented concentration of electron carriers as shown in Fig. 4(d). The evolution of the DP (E F ) as a function of growth temperature T g exhibits a trend similar to that of the coordination number of Bi-Bi Te1 , as displayed in Fig. 4(e). Both the T g -dependent DP and Bi-Bi Te1 coincide with the variation in the concentration of electron carriers.
To conrm the above experimental studies and analyses, we calculated the electronic band structure of Bi 2 Te 3 considering varied chemical composition. Four quintuple layers of pristine Bi 2 Te 3 were used; one Te in the structure was replaced with a Bi atom and vice versa. The concentration of Bi was increased from 40% to 41.7% (Bi 23 Te 37 ) in the former case and decreased from 40% to 38.3% in the latter. Drawn in Fig. 5(a) is the band structure of the pristine Bi 2 Te 3 with red circles representing the contribution of the surface states of Bi 2 Te 3 . Fig. 5(b) shows the    Fig. 5(c), however, the Dirac point in the Te-rich structure shis downward in energy. The calculated energy-band structures are consistent with the T g -dependent DP (E F ) and Bi-Bi Te1 . As Fig. 5(d) shows, the formation of Bi-Te(1) produces a shi of the E F towards the maximum of valence band. With decreased substitution of Bi in Te(1), Te Bi became the dominant defects, resulting in an increased concentration of electron carriers so that the E F shied away from the maximum of valence band.

Conclusions
On controlling the growth temperature using a MBE method, we fabricated Bi 2 Te 3 TI thin lms with a varied Fermi level. ARPES and EXAFS results reveal direct evidence for the substitution of Bi for the Te(1) site, which is the key origin for the shi of the Fermi level or the position of the Dirac point in Bi 2 Te 3 .
Calculations of the electronic structure support these experiments. The calculated structure of the energy band that took into account the existence of Bi Te and Te Bi antisite defects with Bi-rich and Te-rich conditions further revealed that the variation of the electronic structure in Bi 2 Te 3 lms can be attributed to the antisite defects that are tunable with the growth temperature. Our approaches and results demonstrated the growth of homogenous n-type Bi 2 Te 3 lms, showing the potential for topological insulator-based device applications.

Conflicts of interest
There are no conicts to declare.