Vibrational Properties of Epitaxial Bi 4 Te 3 Films as Studied by Raman Spectroscopy

Bi 4 Te 3 , as one of the phases of the binary Bi–Te system, shares many similarities with Bi 2 Te 3 , which is known as a topological insulator and thermoelectric material. We report the micro-Raman spectroscopy study of 50 nm Bi 4 Te 3 films on Si substrates prepared by molecular beam epitaxy. Raman spectra of Bi 4 Te 3 films completely resolve the six predicted Raman-active phonon modes for the first time. Structural features and Raman tensors of Bi 4 Te 3 films are introduced. According to the wavenumbers and assignments of the six eigenpeaks in the Raman spectra of Bi 4 Te 3 films, it is found that the Raman-active phonon oscillations in Bi 4 Te 3 films exhibit the vibrational properties of those in both Bi and Bi 2 Te 3 films. C 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.


I. INTRODUCTION
Bi 2 Te 3 has been predicted and experimentally confirmed to be a typical three-dimensional (3D) topological insulator (TI) material, and is expected to possess robust conducting surface states and an insulating gap in the bulk. 1,2The unique surface states originating from strong spin-orbit coupling are topologically protected against backscattering by time reversal symmetry. 3Bi 2 Te 3 can thus potentially be used for quantum computing, magnetic memory and so forth. 4Bi 2 Te 3 is also known as a significant thermoelectric (TE) material owing to the highest figure-of-merit among all bulk materials at room temperature: ZT = 1. 5 This value can be further increased in low dimensional heterostructures 6 or through the thermoelectric superlattices. 7umerous efforts [1][2][3][4][5][6] have been devoted to the study of Bi 2 Te 3 as one phase of the binary Bi-Te system, which has often overshadowed the fact that the Bi-Te system exhibits various different phases, such as BiTe and Bi 4 Te 3 .It has been reported that there exists no less than seven phases of Bi x Te y in a compositional range between 40 and 75 .%Bi. 8 By contrast, all phases have a rhombohedral-or trigonal-layered structure at ambient conditions with very similar a-axis parameters (approximately 4.4 Å) while c-axis parameters vary from 10 Å to above 100 Å. 9 Bi 4 Te 3 , also known as pilsenite, is another representative phase of the binary Bi-Te system.Given the periodical crystal structure, Bi 4 Te 3 can be written as (Bi 2 ) 3 (Bi 2 Te 3 ) 3 . 10Among the widely studied and superior thermoelectric materials are the long known Bi 2 Te 3 and Bi based alloys, thus, it is essential to investigate the (Bi 2 ) m (Bi 2 Te 3 ) n homologous series.Additionally, a heterostructure formed by a Bi bilayer above Bi 2 Te 3 has been shown to exhibit new TI phenomena, 11 thus, it is reasonable to expect Bi 4 Te 3 , whose crystal structure contains almost the same Bi 2 Te 3 /Bi 2 heterostructure, to also be a TI with unique properties.We have found that different flux ratios of Te/Bi can lead to the phases of bismuth telluride between Bi 2 Te 3 and Bi 4 Te 3 when grown by molecular beam epitaxy (MBE). 12he structural and electronic properties of these two phases are significantly different. 12Other properties, for example, phonon scattering and phonon-electron interactions, are of great interest for both TI and TE applications.
Raman spectroscopy can provide useful information about inherent phonon oscillations, phonon-electron interactions and structural features down to the nanoscale, which will aid in the research on Bi 4 Te 3 .Despite the promising TI and TE properties of Bi 4 Te 3 , there has only been one report of the Raman spectra of Bi 4 Te 3 .Russo et al. reported the Raman spectra of Bi 4 Te 3 polycrystalline thin films prepared by pulsed laser deposition, where only one peak was found. 13In this work, we undertook Raman spectroscopy measurements from 50-nm-thick Bi 4 Te 3 and Bi 2 Te 3 films both grown on Si substrates by MBE.In the spectra of the Bi 4 Te 3 films, all the six expected Raman-active phonon modes are observed and are resolved completely for the first time.Phonon oscillations involved in the Raman scattering in Bi 4 Te 3 films are found to display the vibrational properties of those in both Bi and Bi 2 Te 3 films.

II. EXPERIMENTAL DETAILS
The Bi 4 Te 3 and Bi 2 Te 3 thin films were grown on Si (111) substrates by MBE and details of the substrate preparation and growth can be found in Ref. 12.Both materials grew along their c-axis confirmed by X-ray diffraction (XRD), meaning that the quintuple layers (QLs) and the bilayer-Bi (Bi 2 ), which will be described in the next section, are parallel the substrate surface.Raman scattering experiments were conducted at room temperature, using a Horiba HR confocal micro-Raman spectrometer in the backscattering configuration excited with a Nd:YAG 532 nm laser, whose light spot diameter was around 1 µm.The resolution was approximately 1 cm −1 using the 1800 groove/mm grating.Since Bi 4 Te 3 and Bi 2 Te 3 have a low thermal conductivity and a low melting point, it is essential to control the laser power and irradiation time to avoid local heating effects (LHE) and melting-induced oxidation during the measurements.After many trials, the optimum excitation power of 2 mW (the irradiation laser power on the sample surface was much less than 2 mW) together with a 0.1 µm wide slit and exposure time of 100 s were found to provide the best signal-to-noise (S/N) ratio and effectively avoid heating-induced effects.

A. Crystal structure and Raman tensors
Bi 4 Te 3 has a rhombohedral crystal structure, 14 which is composed of double atomic layers of bismuth -Bi-Bi-lying between the QL -Te-Bi-Te-Bi-Te-slabs, as shown in Fig. 1(a).It can be seen that there exist two different Bi atoms with two different symmetry centers.The unit cell contains three Bi 2 slabs and three QL slabs, one third of which is arranged in the following order: -(Te 1 -Bi 1 -Te 2 -Bi 1 -Te 1 )-(Bi 2 -Bi 2 )-.Atoms inside both the Bi 2 slabs and the QL slabs are covalently connected 15,16 whereas the interactions between the Bi 2 and the QL slabs are of a weak covalent nature. 10Assessed by the bond-length-bond-strength concept, the structure of Bi 4 Te 3 has the weakest bonding at the slab boundaries. 17Bi 4 Te 3 , as another phase of the Bi-Te binary system, exhibits many similar properties with Bi 2 Te 3 , which is comprised of almost the same QL slabs, 18 such as a very close a-axis lattice constant (around 4.4 Å) and being assigned to the same space group R3m (D 5 3d ). 14or Bi 4 Te 3 , according to the group theory classification and Raman selection rules, it is expected that there are nine Raman-active modes corresponding to the six different frequencies at the Brillouin zone center: 3(E g + A 1g ). 13 The Raman tensors of the six Raman-active modes are as follow: Here, the letters "E" and "A" related to symmetry represent in-plane and out-plane (C H axis) lattice vibrations, respectively.The subscript "g" standing for gerade denotes Raman-active.The six eigenpeaks can be assigned to E 1 g (TO), E 2 g (TO), E 3 g (TO), A 1 1g (LO), A 2 1g (LO), A 3 1g (LO) modes based on their wavenumbers and corresponding oscillation modes, respectively.
The arrangement of the Bi 2 atoms in Bi 4 Te 3 films have particularly similar properties to those in bismuth films, for example, the symmetry properties, the length of Bi-Bi bond, a-axis lattice constant 19 and so forth.So the structural properties of the Bi 2 slabs in Bi 4 Te 3 could refer to those in bismuth films, which crystallize in a rhombohedral A7 structure and belong to the space group D 5 3d , as well as Bi 2 Te 3 and Bi 4 Te 3 . 20Regarding bismuth films, they have a layered structure like Bi 4 Te 3 , consisting of stacks of Bi 2 atoms (see Fig. 1(b)).Based on the bonding abilities of Bi governed by its 6p orbitals, 15 each Bi atom is bonded to three intra-bilayer partners at 3.07 Å and to three inter-bilayer partners at 3.53 Å.As a result, each Bi atom has three nearest-neighbor bonds, forming the stable Bi 2 slabs with strong intra-bilayer covalent bonds in bismuth films. 15,21i 4 Te 3 films can be considered to have a structure where the Bi 2 slab is inserted into the Bi 2 Te 3 film structure periodically.10,22 Taking into account the properties of the Bi 2 atoms, the Bi 2 slabs in Bi 4 Te 3 can be further viewed as ultrathin Bi films with a thickness of only one bilayer.The equivalent model above suggests that Bi 4 Te 3 is expected to exhibit some of the specific properties arising from both Bi and Bi 2 Te 3 films.increasing excitation power and irradiation time, indicating that no laser-irradiation-induced damage occurred at these powers and irradiation times.23 When the excitation power was increased to 4 mW, the intensity of the peaks in the spectra were all strengthened, together with the appearance of new peaks.Peaks at 88 and 115 cm −1 were both pronounced and assigned to the Raman eigenpeaks of Bi 4 Te 3 films.The reason for these assignments is two-fold. First the peak at 88 cm −1 has been reported and interpreted to arise from the vibrational mode of Bi 4 Te 3 films in Ref. 13, although this peak was observed at 83 cm −1 in that study, probably owing to systemic errors (the peak positions of Bi 2 Te 3 in Ref. 13 all experienced around a five wavenumber redshift compared with the standard values 24 ).Second, Yang et al. 25 predicted theoretically that the phonon dispersions of ultrathin Bi films with only one bilayer thickness have frequencies for the E g (TO) mode and A 1g (LO) mode of 92 cm −1 and 115.3 cm −1 (both are Raman-active), respectively, at the Brillouin zone center, which are listed in Table I.To our best knowledge, there has been no publication reporting the experimental Raman results of ultrathin Bi films whose thickness is down to the atomic layer level, although Ref. 13 reported two measured Raman peaks of Bi films at around 65 cm −1 and 91 cm −1 .It is worth noting that when the thickness of materials decreases from 3D to 2D, the Raman peak positions are expected to be shifted.26 Taking the calculation and experimental errors into account, the theoretical results are consistent with the observed peaks at 88 and 115 cm −1 in Bi 4 Te 3 , indicating that both peaks can be credibly attributed to the vibrational modes of Bi 2 slabs in Bi 4 Te 3 films and are therefore assigned to the E g (TO) and A 1g (LO) modes, respectively.I and are comparable with the previously reported data.24 It is particularly noticeable that the three eigenpeaks at lower frequencies of the Bi 2 Te 3 film can also be directly observed in the spectra of Bi 4 Te 3 films.In Figure 2(a), the E 1 g and the A 1 1g modes are distinct, albeit with a few wavenumber redshift, while the E 2 g mode is obscured when the irradiation power was below 2 mW.When the irradiation power and exposure time was increased to 4 mW and 40 s, respectively, the E 2 g mode can also be pronouncedly observed.The A 2 1g mode of Bi 2 Te 3 films can be distinguished from the spectra of Bi 4 Te 3 films by multiple peak fitting.Figure 3 displays the Raman spectrum of a Bi 4 Te 3 film under 4 mW excitation (the blue curve in Fig. 2(a)), which is analyzed by Gaussian fitting to decompose the overlapped peaks.According to the fitting results, the spectrum consists of nine separate peaks, which are labelled as shown in Fig. 3, whose frequencies are listed in Table I.P1, P2 and P4 correspond to the three Raman-active peaks at lower frequencies of Bi 2 Te 3 films, and P3 and P5 have been analyzed above.As can be seen, the frequency of P6 is very close to that of the A 2 1g mode of Bi 2 Te 3 films.The four Raman peaks of Bi 2 Te 3 films correspond to the Raman-active oscillation modes (E 1 g (TO), A 1 1g (LO), E 2 g (TO), A 2 1g (LO)) involving the QL slabs.Furthermore, the structure of Bi 4 Te 3 contains similar QL slabs, thus, it is reasonable to observe the similar peaks in the spectra of Bi 4 Te 3 and assign P1, P2, P4 and P6 to the Raman eigenpeaks of Bi 4 Te 3 films.Interestingly, these four peaks all develop a few wavenumber redshift when compared with the corresponding modes in Bi 2 Te 3 films. Th redshift in the spectra of Bi 4 Te 3 films could be caused by the changed bonding at the boundaries between the Bi 2 and the QL slabs but the exact details need to be further studied.

B. Raman spectra analysis
The frequencies of P1-P6 are assigned to the E 1 g (TO), A 1 1g (LO), E 2 g (TO), E 3 g (TO), A 2 1g (LO), and A 3 1g (LO) modes, respectively.To the best of our knowledge, all six of the Raman modes predicted by group theory have been observed and resolved entirely for the first time in the Raman spectra of Bi 4 Te 3 .The band-structure calculation suggests that Bi 4 Te 3 can be easily exfoliated and terminated with an intact Bi 2 slab or QL slab. 8Owing to the weak bonding at the slab boundaries, P1, P2, P4 and P6 are involved with QL slabs while P3 and P5 primarily arise from Bi 2 slabs.Therefore, Raman-active phonon oscillations in Bi 4 Te 3 films exhibit the vibrational properties of those in both Bi and Bi 2 Te 3 films.
In Fig. 3, in addition to the six expected peaks, there are three additional peaks (A1 to A3), and their frequencies are listed in Table I.It is worth noting that A1 was also observed in the Raman FIG. 3. Raman spectrum of a 50 nm Bi 4 Te 3 /Si thin film obtained under 4 mW irradiation power of 532 nm excitation laser (corresponding to the blue curve in Fig. 2(a)).The blue dotted curve is the measured spectrum, the green curves are the fitted peaks with a Gaussian line-shape, and the red curve is the sum of these fitted peaks.spectra of the 20-50 nm Bi 2 Te 3 films, where A1 has been ascribed to surface oxidation for the reason that Bi 2 Te 3 films are easily oxidized on the surface when exposed in the air. 27Similarly, A1 in the spectra of Bi 4 Te 3 films is most likely to arise from the same origin.When the laser power was increased to 4 mW, A2 (182 cm −1 ) and A3 (204 cm −1 ) began to appear (see Fig. 2(a)) and the eigenpeak of Si substrate at 520.5 cm −1 began to be observed, indicating that A2 and A3 most possibly result from the LHE-induced oxidation, and the laser penetration depth is larger than the thickness of Bi 4 Te 3 films when the laser power is 4 mW.Comparing the frequencies of A2 and A3 with those of bismuth oxide and tellurium oxide, [28][29][30] A2 and A3 are tentatively assigned to the vibrational modes from α-Bi 2 O 3 (185 −1 ) and Bi 12 SiO 20 (205 cm −1 ), respectively.

IV. CONCLUSIONS
A Raman spectroscopy study was carried out for 50 nm Bi 4 Te 3 films on Si substrates grown by MBE.The directly observed and fitted peaks in the Raman spectra are all assigned to the corresponding phonon modes.The structural properties of Bi 4 Te 3 are introduced and the Raman tensors are investigated based on group theory and Raman selection rules.No Raman spectra of Bi 4 Te 3 films with the six complete expected peaks have been previously published.Based on the frequencies and assignments of the six eigenpeaks, Raman-active phonon oscillations in Bi 4 Te 3 films are found to exhibit the vibrational properties of those in both Bi and Bi 2 Te 3 films.

FIG. 1 .
FIG. 1. Crystal structures of Bi 4 Te 3 and Bi films with the same symmetry properties and similar lattice constants.The orange spheres denote tellurium atoms while the purple spheres denote bismuth atoms.(a) Crystal structure stacking along the c axis of Bi 4 Te 3 films.(b) The layered structure of Bi films.

Figure 2 (
Figure2(a) shows the measured Raman spectra of a 50 nm Bi 4 Te 3 film with changing intensity of the excitation laser power and exposure time (the obtained spectra from the other three 50 nm samples remain the same).The frequencies of the observed peaks almost remain the same with

Figure 2 (
Figure 2(b) shows the obtained Raman spectrum of a 50 nm Bi 2 Te 3 film, in which the four eigenpeaks are highlighted by the black solid lines.The frequencies and assignments of these four peaks are listed in TableIand are comparable with the previously reported data.24It is particularly noticeable that the three eigenpeaks at lower frequencies of the Bi 2 Te 3 film can also be directly observed in the spectra of Bi 4 Te 3 films.In Figure2(a), the E 1 g and the A 1 1g modes are distinct, albeit with a few wavenumber redshift, while the E 2 g mode is obscured when the irradiation power was below 2 mW.When the irradiation power and exposure time was increased to 4 mW and 40 s, respectively, the E 2 g mode can also be pronouncedly observed.The A 2 1g mode of Bi 2 Te 3 films can be distinguished from the spectra of Bi 4 Te 3 films by multiple peak fitting.Figure3displays the Raman spectrum of a Bi 4 Te 3 film under 4 mW excitation (the blue curve in Fig.2(a)), which is analyzed by Gaussian fitting to decompose the overlapped peaks.According to the fitting results, the spectrum consists of nine separate peaks, which are labelled as shown in Fig.3, whose frequencies are listed in TableI.P1, P2 and P4 correspond to the three Raman-active peaks at lower frequencies of Bi 2 Te 3 films, and P3 and P5 have been analyzed above.As can be seen, the frequency of P6 is very close to that of the A 2 1g mode of Bi 2 Te 3 films.The four Raman peaks of Bi 2 Te 3 films correspond to the Raman-active oscillation modes (E1