Angle-resolved Raman scattering study of anisotropic two-dimensional tellurium nanoflakes

Anisotropic two-dimensional (2D) tellurium (Te) flakes are formed by the stacking of helical atomic chains into a hexagonal close-packed lattice structure.¹ As an important elemental semiconductor, Te has garnered significant interest for the fabrication of high-performance transistors,^1,2 sensors,³ photodetectors,⁴ electronic memory devices,⁵ memristors,^6,7 and infrared detectors,^8,9 owing to its exceptional physical properties, including low thermal conductivity,^10,11 high carrier mobility,¹² strong chemical stability, and a layer-number-dependent bandgap.^13,14 The evolution of the bandgap, ranging from 1.00 eV for monolayer Te to 0.35 eV for bulk Te, highlights its potential as a highly promising candidate for the fabrication of mid-infrared photodetectors.^1,8

In addition, as an in-plane anisotropic material, two-dimensional Te has been found to exhibit remarkable anisotropic properties, including extinction,^3,15 photocurrent,^16,17 light-matter interaction,^18,19 thermal conductivity,^20,21 and electrical magnetochiral anisotropy.^22,23 For example, Te nanoflakes exhibit ∼12% absorption when the incident light is polarized along the [0001] direction and ∼19% absorption when the incident light is polarized along the $[ 1 2 ¯ 10]$ direction for light with a wavelength of 1.25 μm.⁸ The anisotropic absorption over a broad wavelength range makes it feasible to fabricate polarized infrared photodetectors, which show high photo-responsivity and specific detectivity. A detection rate of 2 × 10⁹ cm Hz^1/2 W⁻¹ at a wavelength of 1.7 μm based on Te photodetectors has been achieved at room temperature.²⁴ Additionally, anisotropic thermal conductivity has been observed in Te nanoflakes (<20 nm) with along-chain and cross-chain in-plane thermal conductivities of 1.60 and 0.64 W m⁻¹ K⁻¹, respectively. This anisotropic thermal conductivity is attributed to anisotropic phonon dispersions.²⁵ Furthermore, the helical crystal structure of Te enables the observation of strong electrical magnetochiral anisotropy in trigonal tellurium (t-Te), as demonstrated by current-induced shifts in the ¹²⁵Te Nuclear Magnetic Resonance (NMR) frequency measurements. This finding paves the way for further studies of chiral magnetic order and spin fluctuations by using Te.²² 

To investigate the rich physics and novel device applications enabled by the in-plane anisotropy of Te, it is essential to identify the crystal orientation and accurately determine the crystal axis in Te. Transmission electron microscopy (TEM) is a conventional method of identifying the crystal axis in various materials. However, this method often requires complex sample preparation, expensive equipment, and is time-consuming, destructive, and costly.²⁶ Therefore, a rapid and effective method of identifying the crystal axis in Te nanoflakes will facilitate its anisotropic study. Raman spectroscopy has been employed to study Te nanoflakes, with anisotropic Raman scattering being observed. However, the relationship between polarized Raman behaviors and the crystal axis in Te remains unclearly established.^27–31 Additionally, studying the anisotropic scattering behavior in Te nanoflakes will advance their use in the fabrication of photonic elements such as polarizers, polarization detectors, and wave plates.

Here, high-quality two-dimensional Te nanoflakes of different thicknesses are synthesized using a hydrothermal method. The morphology and atomic structure of the synthesized Te nanoflakes are characterized by scanning electron microscopy (SEM) and TEM. Raman tensors for two-dimensional Te nanoflakes are introduced, and an analysis of polarization-dependent Raman scattering is presented. The interference effect in the Te nanoflake-based multilayer stacking system is theoretically studied, with a consideration of anisotropic absorption. Electron–phonon coupling ratio for the A₁ Raman mode along different crystal axes is quantitatively determined. It has been verified that the angle-resolved Raman spectroscopy, as a non-destructive optical technique, provides a rapid and effective way for determining the crystal orientation in Te nanoflakes. In addition, theoretical simulations of Raman scattering from two-dimensional Te nanoflakes under different light polarizations have been conducted. The simulated Raman scattering electric field intensity ratio closely aligns with experimental observations, revealing that the interference effect in the multilayer stacking system, combined with anisotropic absorption and anisotropic electron–phonon coupling, contributes to crystal-orientation-dependent Raman field scattering in two-dimensional Te nanoflakes.

The hydrothermal method is employed to synthesize two-dimensional Te nanoflakes. Figure 1(a) shows a schematic illustration of this hydrothermal process. Specifically, 48.5 mg of Na₂ TeO₃ and 126 mg of PVP are mixed in ultra-pure water at room temperature to form a homogeneous solution through magnetic stirring. The resulting uniform solution is subsequently transferred into a Teflon-lined stainless steel autoclave, which is filled with ammonia solution (25%, wt./wt. %) and hydrazine hydrate (80%, wt./wt. %). The autoclave is sealed and heated at 180 °C for 22 h. After the reaction, the autoclave is allowed to cool naturally to room temperature, and a solid silver-gray product is obtained through centrifugation at 8000 rpm for 7 min, followed by washing three times with distilled water. The solid silver-gray products are stored in a vacuum chamber at a low temperature of 5 °C. During the measurement process, the solid silver-gray products are transferred to a SiO₂/Si substrate for immediate Raman analysis.^32–34 

The thickness of the synthesized two-dimensional Te nanoflakes is measured by AFM, as shown in Fig. 1(b), with a thickness of 26.8 nm. Figure 1(c) gives a low-magnification optical image of the synthesized two-dimensional Te nanoflakes. Most of the synthesized two-dimensional Te nanoflakes exhibit elongated-strip morphologies (highlighted by a red ellipse), with lengths ranging from 20 to 200 μm. The top left corner shows an optical image of two-dimensional Te nanoflakes at higher magnification. Figure 1(d) gives the atomic structure of the two-dimensional Te nanoflakes. As seen in the figure, neighboring Te atoms are covalently bonded together, forming quasi-one-dimensional atomic chains, which are further stacked into a hexagonal close-packed lattice structure by weak van der Waals force. The different bonding including the strong covalent bonding and the weak van der Waals bonding leads to the anisotropic properties of two-dimensional Te nanoflakes. The crystal directions with high symmetries, including $[0001]$⁠, $[ 1 2 ¯ 10]$⁠, $[ 11 2 ¯ 0]$⁠, and $[ 2 ¯ 110]$⁠, are highlighted by solid and dashed blue lines in the figure.

Polarized Raman spectroscopy is a powerful tool to determine the crystal axis and the molecular orientation for anisotropic materials, including black phosphor, GeSe₂, and α-MoO₃.^35–37 Here, polarized Raman spectroscopy is employed to study the anisotropic scattering in Te nanoflakes. Figure 2(a) shows a schematic illustration of the angle-resolved polarized Raman scattering measurement. The Raman spectra were obtained using an XploRA PLUS Raman system with a 532 nm excitation laser, and the laser power at the sample was kept below 1 mW to avoid laser-induced heating. The integration time, laser power, and focus were kept consistent for all Raman spectra of the Te flakes. A 50× objective lens with a numerical aperture of 0.50 was used during the Raman experiments. The polarization of the incident laser was controlled by a polarizer and focused onto the sample through an objective lens. The scattered Raman signal from the sample was collected in a backscattering configuration. The Te nanoflake was mounted on a rotation stage, allowing the angle between the incident light polarization and the crystal axis of the two-dimensional Te nanoflake to be adjusted in a clockwise direction. The 0° angle corresponds to the incident light polarization being parallel to the long strip of the two-dimensional Te nanoflake, which, as measured by TEM, aligns with the [0001] direction of the Te nanoflake. Figure 2(b) gives the angle-resolved polarized Raman spectroscopy of a two-dimensional Te nanoflake with a thickness of 26.8 nm at room temperature, obtained by rotating the nanoflake in 30° increments. Three Raman modes, including E₁-TO (89 cm⁻¹), A₁ (119 cm⁻¹), and E₂ (138 cm⁻¹), are observed, consistent with previously reported results.¹ It can be seen that the intensities of these Raman-active modes vary periodically with the rotation angle, showing a 180° period, with their maximum values occurring at a rotation angle of ∼90°.

Figures 2(c)–2(e) show the Raman intensities of the E₁-TO mode (89 cm⁻¹), A₁ mode (119 cm⁻¹), and E₂ mode (138 cm⁻¹) at different rotation angles. Schematic illustrations of the corresponding Raman modes are also included in this figure. The intensities of these Raman modes are extracted using Lorentz function fitting (pink dots), while the blue solid lines are the theoretical results calculated based on the analysis of the Raman tensor (Note S1 in the supplementary material). For crystals with reduced symmetry, such as orthogonal black phosphorus or monoclinic molybdenum telluride, the Raman tensor can be expressed as $[ u v v w ]$⁠. There are non-diagonal elements in the Raman tensor for in-plane anisotropic materials. The Raman intensity of each Raman mode can be calculated using the equation $I=| e i ⋅ R ⋅ e s | 2$⁠, where $e i$ and $e s$ are the incident and scattering polarization vectors, respectively. R is the Raman tensor for each mode (Note S1 in the supplementary material). The strong anisotropy in the Raman scattering is further found as an effective way of identifying the crystal axis in two-dimensional Te nanoflakes, as shown below.

It is further demonstrated that the polarized Raman intensity of the A₁ mode can be used to identify the crystal axis in two-dimensional Te nanoflakes. Figure 3(a) shows the TEM results of a Te nanoflake, obtained by transferring the nanoflake onto a carbon grid. The optical image of the nanoflake prior to transfer is given in the left inset. A plane spacing of 0.606 nm was observed, corresponding to the Te (0001) plane. The right inset of Fig. 3(a) shows the diffraction pattern of the Te nanoflake associated with different crystal planes, demonstrating the high crystal quality of the synthesized Te nanoflake. Based on the TEM results, it is found that for the synthesized Te nanoflake, the long strip morphology is parallel to the [0001] axis in Te, corresponding to a rotation angle of 0° in the polarized Raman measurement. Figure 3(b) shows the schematic image of the polar map of Raman peak intensity, where the crystal directions of [0001] and $[ 1 2 ¯ 10]$ in the Te nanoflake are highlighted. The polar Raman intensity pattern provides a rapid and non-destructive method for identifying the crystal axis in Te nanoflakes. Figure 3(c) shows the normalized angle-resolved polarized Raman intensity of the A₁ mode for Te nanoflake with thicknesses of 26.8, 51.1, and 81.4 nm corresponds to 69, 132, and 211 layers, respectively, based on a layer spacing of 0.386 nm. The colored lines represent the theoretical fitting results obtained by performing Raman tensor analysis (Note S1 in the supplementary material). It can be seen that the intensity of the A₁ Raman mode varies periodically with the rotation angle, showing a period of 180°, with maximum intensities occurring at a rotation angle of 90°, corresponding to incident light polarized along the $[ 1 2 ¯ 10]$ direction. This suggests that the polarized A₁ mode intensity provides a reliable method for identifying the crystal axis in Te nanoflakes. Figure 3(d) depicts the polar coordinate diagrams of the Raman A₁ mode for a Te nanoflake with a thickness of 26.8 nm. The green line is the theoretical results obtained through Raman tensor analysis (Note S1 in the supplementary material). It is found that the A₁ Raman mode shows maximum scattering intensity at a rotation angle of 90°. Additionally, the normalized angle-resolved polarized Raman intensity of the A₁ mode for Te nanoflakes with thicknesses of 51.1 and 81.4 nm are provided in Note S2 in the supplementary material, showing a consistent polarized Raman pattern. The strong Raman intensity, along with its intrinsic vibrational properties of the A₁ mode, specifically, neighboring Te atoms vibrating oppositely along the $[ 1 2 ¯ 10]$ direction, while the [0001] axis is perpendicular to the vibration direction, make the A₁ mode a promising candidate for determining the crystal axis in Te nanoflakes.

The Raman intensity of anisotropic two-dimensional nanoflakes under specific excitation energy is primarily influenced by effects of interference enhancement and electron–phonon coupling, as systematically studied in black phosphorus and α-MoO₃.^38–40 The former effect is related to both the intensity of the excitation energy within the flake and the Raman signal that can be transmitted into the detector. The latter effect is associated with the symmetry matching between the vibration direction of phonons and the spatial extension direction of excited-state electrons. For Te nanoflakes supported on a SiO₂(300 nm)/Si substrate, a multilayer stacking configuration is formed, and the Raman intensity is influenced by the interference effects. We further calculate the Raman intensity for the A₁ mode (with a scattering wavelength of 535.6 nm) in Te flakes under 532 nm excitation, considering light polarized along the [0001] direction and perpendicular to the [0001] direction (e.g., $[ 1 2 ¯ 10]$⁠), respectively. Both the incident light intensity within the flake and the generated Raman scattering intensity are accounted for in the interference effect, as schematically shown in the insets of Figs. 4(d) and 4(e). The calculations are performed using equations from our previously reported works.⁴¹ Anisotropic absorption is incorporated into the calculation by considering different refractive indices along various crystal directions in Te nanoflakes.⁴² 

As shown in Figs. 4(a) and 4(b), the Raman intensity (enhancement factor) along different crystal directions initially increases with the number of layers, reaching maximum values at nine layers and 14 layers for the respective crystal directions and then decays to a constant value for much thicker Te nanoflakes. It is understandable that due to the absorption within the Te nanoflakes, the incident laser can only penetrate a limited thickness, contributing to the Raman scattering signal. Further increases in thickness do not enhance the Raman signal due to the limited penetration depth of the laser. Figure 4(c) further gives the anisotropic interference enhancement factor ratio, defined as the ratio of Raman intensity along the [0001] direction and perpendicular to the [0001] direction. Enhancement factor ratios (EF_‖[0001]/EF_⊥[0001]) of 0.48, 0.56, and 0.58 are obtained for the Te nanoflake with 69, 132, and 211 layers, respectively, as shown in Fig. 4(c). Additionally, the polarization-dependent Raman spectra of the Te nanoflakes are fitted using Eq. (S2) in the supplementary material, and the Raman tensor elements (u, v, and w) are obtained. The experimental anisotropic ratio of the A₁ Raman mode for Te nanoflakes with 69, 132, and 211 layers along and perpendicular to the [0001] direction, is obtained as 0.33, 0.35, and 0.33, respectively (Note S3 in the supplementary material). Furthermore, the anisotropic electron–phonon coupling ratios along and perpendicular to the [0001] direction for Te nanoflakes with different thicknesses are determined to be 0.83, 0.79, and 0.75, respectively (Table S1 in the supplementary material). These values are determined as the square root of the anisotropic Raman intensity ratio divided by the square root of the interference enhancement ratio, indicating that the resulting electron–phonon coupling ratio is approximately independent of the number of layers. This observation is consistent with the in-plane vibration nature of the A₁ Raman mode, which exhibits weak coupling along the [0001] direction and strong electron–phonon coupling perpendicular to the [0001] direction.

Figure 5 systematically studies the intensity distributions for incident light and Raman scattering light for a two-dimensional Te nanoflake-based multi-layer structure using the finite element method (FEM). The detailed simulation process is described in Note S4 in the supplementary material. The intensity ratio of the polarized dipole along the [0001] direction and perpendicular to the [0001] direction is set as 0.83, based on the previously obtained intensity ratio of anisotropic electron–phonon coupling. The supported substrate for the Te nanoflake is SiO₂(300 nm)/Si, consistent with the configuration used in the Raman measurements. Figures 5(a) and 5(e) show the schematic configurations studied. A 26.8 nm Te nanoflake is positioned on the xoy plane with its [0001] direction aligned along the x-axis and its $[ 1 2 ¯ 10]$ direction aligned along the y-axis. The incident light propagates along the −z direction, with polarizations along the x-axis and y-axis, respectively. For the simulation, the incident electric field is modeled a Gaussian beam with a peak value of 1 V/m for both polarizations. The position of the SiO₂ surface is set at z = 0. Figures 5(b) and 5(f) present the simulation results of the incident electric field intensity distribution in the xoz plane for two different configurations. In the simulation, the dielectric constant along the x-axis is set as n = 1.57–2.94i, while along the y-axis is set as n = 1.12–3.96i at 532 nm.⁴² As shown in Figs. 5(b) and 5(f), light with a peak electric field of 1 V/m propagates through air and is incident on the surface of the Te nanoflake, polarized along the x-axis and y-axis, individually. The electric field of the incident light within the Te nanoflake varies, reaching values of 1.08 and 1.16 V/m, as given in Figs. 5(b) and 5(f), individually. This variation arises from the anisotropic absorption properties of the Te nanoflake, where the strong absorption along the y-axis results in a higher incident electric field intensity.

Figures 5(c) and 5(d) display the simulated electric intensities of A₁ mode Raman scattering light (535.6 nm) with different polarizations in the xoz plane for the configuration given in Fig. 5(a), where the incident light is polarized along the x-axis. It is found that for the intensities of Raman scattering light polarized along the x-axis and y-axis are different, with maximum intensities of 7.1 × 10⁷ and 7.9 × 10⁷ V/m, respectively. Figures 5(g) and 5(h) show the electric intensities of A₁ mode Raman scattering light with different polarizations in the xoz plane for the configuration given in Fig. 5(e), where the incident light polarized along the y-axis. For light incidence polarized along the y-axis, the intensities of Raman scattering light polarized along the x-axis and y-axis are different, with maximum intensities of 9.0 × 10⁷ and 9.8 × 10⁷ V/m, individually.

We further compare the Raman scattering fields with x-polarization when excited by light of different polarizations, as shown in Figs. 5(c) and 5(g), and obtain a scattering electric field intensity ratio of 0.789. Similarly, by comparing the Raman scattering fields with y-polarization when excited by light of different polarizations, as shown in Figs. 5(d) and 5(h), and a scattering electric field intensity ratio of 0.806 is obtained. These values are close to the experimentally obtained square root of the anisotropic Raman intensity ratio for 26.8 nm Te, which is 0.57. Therefore, the numerical simulations clearly demonstrate that the anisotropic Raman scattering in two-dimensional Te nanoflakes can be attributed to the combined effects of interference, anisotropic absorption, and anisotropic electron–phonon coupling. This approach provides valuable insights into understanding the anisotropic Raman scattering in Te and can also assist in the study of other anisotropic materials.

In this study, two-dimensional Te nanoflakes are successfully synthesized using a hydrothermal method. Angular-resolved Raman spectroscopy is demonstrated to be a fast and non-destructive way to identify crystal orientation of two-dimensional Te nanoflakes. The polarized Raman scattering intensity of the two-dimensional Te nanoflakes is systematically simulated, and its behaviors are explained in terms of the anisotropic interference effect, anisotropic absorption, and electron–phonon coupling. This work contributes to a better understanding of the anisotropic Raman scattering in two-dimensional Te nanoflakes.

See the supplementary material for the theoretical analysis of angle-resolved Raman scattering, polar coordinate diagrams of the Raman A1 mode for Te of different thicknesses, fitted Raman tensors and parameters obtained for Te nanoflakes of different thicknesses, and the detailed simulation process for the spatial distributions of polarization-dependent incident and scattered electric fields.

The authors have no conflict of interest.

Yuhao Duan: Data curation (equal); Formal analysis (lead); Methodology (equal); Writing – original draft (equal). Deming Zhao: Data curation (equal); Methodology (equal); Writing – original draft (equal). Zhonglin Li: Data curation (equal); Formal analysis (equal); Writing – original draft (equal). Jing Yu: Data curation (equal); Formal analysis (equal); Validation (equal). Yao Liang: Data curation (equal); Formal analysis (equal); Validation (equal). Yingying Wang: Conceptualization (lead); Data curation (equal); Methodology (equal); Supervision (lead); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.