Anti-site defect effect on the electronic structure of a Bi₂Te₃ topological insulator

Abstract

Tuning the Fermi level (E_F) in Bi₂Te₃ topological-insulator (TI) films is demonstrated on controlling the temperature of growth with molecular-beam epitaxy (MBE). Angle-resolved photoemission spectra (ARPES) reveal that E_F of Bi₂Te₃ thin films 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 identified through extended X-ray-absorption fine-structure (EXAFS) spectra at the Bi L₃-edge. Calculations of electronic structure support the results of fitting 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 findings 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.

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1. Introduction

Topological insulators (TI) are novel quantum materials with promising applications in advanced spintronic devices. A three-dimensional (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 V₂–VI₃-type 3D TIs, such as Bi₂Se₃, Bi₂Te₃ and Sb₂Te₃, have been theoretically predicted and experimentally confirmed.^4,6,7 Bi₂Te₃ belongs to the V₂–VI₃ 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 film 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 Bi₂Te₃ 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 Bi₂Te₃, the p-type and n-type charge-carrier concentration can range from 3 × 10¹⁷ to 5 × 10¹⁹ cm⁻³, depending on the initial growth condition with excess either Bi or Te.^10–14 For bulk Bi₂Te₃ crystal growth near the solid–liquid equilibrium temperature, anti-site defects can be simply described by element compositions. In comparison, thin film 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 Bi₂Te₃ films upon tuning the growth temperature. A correlation between the position of the Dirac point of Bi₂Te₃ films via angle-resolved photoemission spectra (ARPES) and the coordination number of Bi–Bi_Te1 via extended X-ray-absorption fine structure (EXAFS) spectra is clearly identified. 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 Bi₂Te₃ films is highly correlated with the antisite defects that vary with the growth temperature. Our findings provide also a simple route to manipulate the Dirac point and topological surface states that can yield applications in electronic and spintronic devices.

2. Experimental

2.1 Sample preparation

The TI films were grown on c-plane Al₂O₃(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 ultrahigh-vacuum (UHV) environment. Highly pure Bi (99.99%) and Te (99.999%) were evaporated from Knudsen cells; the flux rate was calibrated in situ with a quartz crystal microbalance. The base pressure of the MBE system was less than 2 × 10⁻¹⁰ Torr; the pressure during growth was kept below 1 × 10⁻⁹ Torr. The Bi₂Te₃ thin films were prepared with a stable beam-flux ratio Te/Bi (Φ_Te/Bi) ∼ 15; the substrate temperature was varied from 310 °C to 430 °C. The crystallinity of Bi₂Te₃ films was monitored in situ with reflection high-energy diffraction (RHEED); additional structural characterization was performed with X-ray diffraction (XRD).

2.2 XPS and ARPES characterization

The stoichiometry and electronic structure of the Bi₂Te₃ films 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 Bi₂Te₃ films with a Te capping layer of thickness ∼20 Å 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 ±15°). The ARPES were recorded for samples at 83 K, base pressure 5 × 10⁻¹¹ 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).

2.3 EXAFS characterization

The local structure of Bi₂Te₃ thin films was determined with EXAFS spectra. The L₃-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 fluorescence 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.

2.4 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 exchange–correlation potential including spin–orbit interaction (SOI). The electron–ion interaction was represented by the projector-augmented 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 × 9 × 1 sampling of k points in the first Brillouin zone was adopted. A vacuum space in the supercell was allocated on setting a minimum height 15 Å above the film in the cell, which was proved to be sufficient to minimize artificial interactions between supercells.

3. Results and discussion

Fig. 1 depicts the XRD pattern of the MBE-grown Bi₂Te₃ films at substrate temperature T_g ranging from 310 °C to 430 °C. For the films grown at lower substrate temperature of T_g = 310 °C, the (015) lattice plane that can be attributed to the rhombohedral Bi₂Te₃ structure is also observed.¹⁸ The main feature of the XRD patterns of these Bi₂Te₃ samples is clearly close to that of Bi₂Te₃ (0001) single crystal.

Fig. 1 XRD curves of several Bi₂Te₃ epilayers grown with MBE at substrate temperature T_g from 310 to 430 °C. In this T_g range, XRD curves of Bi₂Te₃ samples clearly show features related to a single-crystal Bi₂Te₃ epilayer that is (0001)-oriented on the sapphire (0001) substrate (indicated by *).

ARPES were measured to probe the quality and electronic structure of MBE-grown Bi₂Te₃ films. Fig. 2 shows the band structure recorded along direction Γ–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 = 310 °C, the Dirac point is located at the binding energy (E_B) = −0.320 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 shifted to E_B = −0.305 eV and −0.295 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 shifted further to E_B = −0.315 eV and −0.335 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 Bi₂Te₃ films were dominantly n-type so that E_F became tunable on varying growth temperature T_g.

Fig. 2 Band structure of Bi₂Te₃ at various T_g: (a) 310 °C (DP = −0.32 eV). (b) 370 °C (DP = −0.305 eV). (c) 390 °C (DP = −0.295 eV). (d) 410 °C (DP = −0.315 eV). (e) 430 °C (DP = −0.335 eV). All spectra were recorded along the Γ–K direction. The panels show the ARPES intensity maps. The surface states, valence band and conduction band of the bulk states are denoted SS, VB and CB, respectively.

Hole-dominated carriers with E_F located within the bandgap is expected if the electronic structure were determined mainly by the antisite defects in Bi₂Te₃, but the film 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 Bi₂Te₃ film. Te vacancies likely provide n-type carriers as the majority carriers for all Bi₂Te₃ films. 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 Bi₂Te₃, 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 shift in the Bi₂Te₃ films 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, n-type behavior in the Bi₂Te₃ films 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 shift of the Fermi level in Bi₂Te₃ depends strongly on the native point of antisite defects (Bi_Te and Te_Bi) in the Bi–Te compound. Near a stoichiometric Bi₂Te₃ 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).^25–28

Fig. 3 XPS of (a) Bi-4f core-level spectra and (b) Te-3d core-level spectra of the Bi₂Te₃ thin film grown at 390 °C. (c) Total carrier concentration of the Bi₂Te₃ films as a function of the growth temperature measured by Hall measurement. (d) The Te/Bi ratio of the Bi₂Te₃ thin films as a function of the growth temperature.

The tendency that the Fermi level shifted 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 shift 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-L₃ edge; the radial distribution function is shown in Fig. 4(a). The fitted results of extended X-ray-absorption fine-structure (EXAFS) spectra enable a direct identification of the antisite defects in Bi₂Te₃ films. 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 μ(E) and conversion of μ(E) to χ(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 10 Å⁻¹, as shown in Fig. 4(b). The rhombohedral primitive and hexagonal unit cell of Bi₂Te₃ consists of a five-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)– five-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 = 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 ± 0.11, 1.312 ± 0.47 and 2.725 ± 0.35, respectively. Accordingly, the length of the Bi–Te(1) bond decreased to 3.04 ± 0.31 Å, 3.02 ± 1.07 Å, and 2.88 ± 0.37 Å, 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 ± 0.06 at T_g = 410 °C. Moreover, no Bi substitution was observed at T_g = 430 °C. The length of the Bi–Te(1) bond increased to 3.06 ± 0.23 Å and 3.04 ± 0.36 Å at T_g = 410 and 430 °C respectively.

Fig. 4 EXAFS spectra at the Bi L₃-edge of the Bi₂Te₃ thin films. The curves are vertically shifted for the substrate temperature. (a) Fourier transform of the R-space (symbols) together with the theoretical fit to the first shells (solid line). (b) k-Space (symbols) together with the best fit (solid line). (c) Hexagonal conventional unit cells of Bi₂Te₃; schematic diagram of one QL of the mechanism of the antisite defect in Bi-rich and Te-rich conditions, respectively. (d) Bi_Te antisite of Bi–Bi averaged coordination number and surface carrier concentration (estimated from the Fermi level crossing k_F) plotted versus T_g. (e) Bi_Te antisite of Bi–Bi averaged coordination number and Dirac point at binding energy plotted versus T_g.

Table 1 Rhombohedral primitive of first-shell EXAFS fitted results for Bi₂Te₃ TI thin films. N_Bi–Te1 is the Bi–Te(1) average coordination number, BL_Bi–Te1 is the Bi–Te(1) bond length, and N_Bi–BiTe1 is the Bi_Te antisite of the Bi–Bi average coordination number, BL_Bi–BiTe1 is the Bi_Te antisite of the Bi–Bi bond length

Sample	NBi–Te1	BLBi–Te1 (Å)	NBi–BiTe1	BLBi–BiTe1 (Å)
Tg = 310 °C	1.67 ± 0.17	3.04 ± 0.31	1.05 ± 0.11	3.13 ± 0.32
Tg = 370 °C	1.6 ± 0.57	3.02 ± 1.07	1.312 ± 0.47	3.11 ± 1.1
Tg = 390 °C	2.39 ± 0.31	2.88 ± 0.37	2.725 ± 0.35	3.11 ± 0.4
Tg = 410 °C	1.06 ± 0.08	3.06 ± 0.23	0.77 ± 0.06	3.17 ± 0.24
Tg = 430 °C	1.3 ± 0.16	3.04 ± 0.36	None	None

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On increasing growth temperature T_g to 390 °C, the fitted 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 = 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 confirm the above experimental studies and analyses, we calculated the electronic band structure of Bi₂Te₃ considering varied chemical composition. Four quintuple layers of pristine Bi₂Te₃ 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% (Bi₂₃Te₃₇) 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 Bi₂Te₃ with red circles representing the contribution of the surface states of Bi₂Te₃. Fig. 5(b) shows the energy bands for the Bi-rich structure, with its Dirac point shifting upward in energy. In Fig. 5(c), however, the Dirac point in the Te-rich structure shifts 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 shift 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 shifted away from the maximum of valence band.

Fig. 5 Band structure of Bi₂Te₃ from calculations of electronic structure for Bi-rich and Te-rich conditions. The direct coordinates of high symmetry points in the Brillouin zone are K, Γ and M as the Dirac point of Bi₂Te₃. (a) Electronic structure of four quintuple layers of pristine Bi₂Te₃ near the Γ point. The band structure is shown with (b) replacement of one Bi atom with a Te atom and (c) replacement of one Te atom with a Bi atom in 4 QL Bi₂Te₃. The size of the red circle indicates a contribution of the surface state in the low-energy band structure. (d) Theoretical Dirac points with Bi-rich and Te-rich antisite defect concentrations are compared with the ARPES-measured Dirac points.

4. Conclusions

On controlling the growth temperature using a MBE method, we fabricated Bi₂Te₃ TI thin films 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 shift of the Fermi level or the position of the Dirac point in Bi₂Te₃. 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 Bi₂Te₃ films 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 Bi₂Te₃ films, showing the potential for topological insulator-based device applications.

Author contributions

S. H. Su, C. W. Chong and J. C. A. Huang designed and prepared the experiment. P. Y. Chuang, W. C. Chen, C.-M. Cheng and K.-D. Tsuei performed ARPES measurements. The thin-film growth was performed by Y. F. Chen, Y. H. Chou, and P. Y. Chuang, for C.-H. Wang, Y. F. Liao, S. C. Weng, J. F. Lee, and Y.-W. Yang characterized samples with XPS and EXAFS. Y. K. Lan, S. L. Chang, C. H. Lee, C. K. Yang provided theoretical support. All authors have given approval to the final version of the manuscript.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Ministry of Science and Technology Republic of China, Taiwan supported this research under contract MOST 103-2119-M-006-015 and 105-2112-M-213-006-MY2. Funding was received also from the headquarters of University Advancement at NCKU, which is sponsored by the Ministry of Education, Taiwan ROC. The National Synchrotron Radiation Research Center (NSRRC) is operated under the Ministry of Science and Technology of Taiwan.

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