Broadband Optical Properties of Bi2Se3

Abstract

Materials with high optical constants are of paramount importance for efficient light manipulation in nanophotonics applications. Recent advances in materials science have revealed that van der Waals (vdW) materials have large optical responses owing to strong in-plane covalent bonding and weak out-of-plane vdW interactions. However, the optical constants of vdW materials depend on numerous factors, e.g., synthesis and transfer method. Here, we demonstrate that in a broad spectral range (290-3300 nm) the refractive index n and the extinction coefficient k of Bi₂Se₃ are almost independent of synthesis technology, with only a ~10% difference in n and k between synthesis approaches, unlike other vdW materials, such as MoS₂, which has a ~60% difference between synthesis approaches. As a practical demonstration, we showed, using the examples of biosensors and therapeutic nanoparticles, that this slight difference in optical constants results in reproducible efficiency in Bi₂Se₃-based photonic devices.

Keywords: nanophotonics; optical constants; refractive index; spectroscopic ellipsometry; topological insulators; transition metal dichalcogenides.

Figure A1

Comparison of dielectric functions of chemical vapor deposition-grown [27] and exfoliated [12] MoS₂.

Figure A2

Additional structural and morphological study of Bi₂Se₃. (a) Scanning electron microscopy image of Bi₂Se₃ surface. (b) X-ray diffraction pattern of Bi₂Se₃ with pronounced peaks which correspond to the (006), (009), (0012), (0015), (0018), and (0024) crystallographic planes of Bi₂Se₃.

Figure A3

Angular optical sensitivity of the SPR biosensor as a function of the thickness of the auxiliary Bi₂Se₃ layer. Calculations were performed neglecting the optical conductivity contribution from the topological surface states (red line) and accounting for this by adding a monolayer of graphene (gray line).

Figure 1

Bi₂Se₃ sample characterization. (a) Crystal structure of Bi₂Se₃. (b) Optical image of Bi₂Se₃ sample. (c) AFM color map of Bi₂Se₃ sample. (d,e) XPS spectra of Bi₂Se₃ with several Bi and Se peaks: Se3p_1/2 (165.0 eV); Bi4f (BiO_x) (164.2 eV); Bi4f_5/2 (163.2 eV); Bi4f (BiO_x) (158.9 eV); Bi4f_7/2 (157.9 eV); Se3p_3/2 (159.6 eV); Se-O (58.9 eV); Se⁰ (54.7 eV); Se3d_3/2 (54.2 eV); Se3d_5/2 (53.4 eV). Black, red, green, purple, blue, orange, violet, and cyan colors label experimental, total, Se3p_1/2 or Se3p_3/2, Bi4f (BiO_x), Bi4f_5/2 or Bi4f_7/2, Se3d_3/2, Se3d_5/2, and Se⁰ XPS signals, respectively. Raman spectra of Bi₂Se₃ for (f) $\lambda =$ 532 nm and (g) $\lambda =$ 632.8 nm.

Figure 2

Variable-angle spectroscopic ellipsometry of Bi₂Se₃. Ellipsometry spectra of Bi₂Se₃ (a) $\Psi$ and (b) $\mathsf{\Delta }$. Solid and dashed lines denote the experimental and calculated optical model data. (c) Refractive index and (d) extinction coefficient of Bi₂Se₃ for differently synthesized samples: chemical vapor deposition (CVD); density functional theory (DFT) calculations attributed to exfoliation; and molecular beam epitaxy (MBE), adopted from [40]. The inset in panel (c) is the calculated band structure of Bi₂Se₃. The inset in panel (d) shows a comparison between the experimental reflectance spectra of Bi₂Se₃ and the simulated one. Tabulated optical constants of Bi₂Se₃ are collected in Table A1.

Figure 3

Photonic applications of Bi₂Se₃. (a) The reflectance of the surface plasmon resonance (SPR) sensor based on a SiO₂/Au (40 nm) chip with CVD and MBE-grown Bi₂Se₃. (b) The dependence of SPR sensor angular sensitivity on the thickness of Bi₂Se₃ layers. The inset is a schematic representation of an SPR sensor. For comparison, we also added the Gr and MoS₂ performance. (c) The multipole decomposition of the extinction spectrum of a single Bi₂Se₃ nanosphere with a diameter d of 100 nm. (d) Extinction and (e) absorption cross-section of nanoparticles with diameters $d$ of 100 nm for CVD and MBE-grown Bi₂Se₃. (f) Spectral dependence of the heating of nanoparticles with diameters $d$ of 100 nm for CVD and MBE-grown Bi₂Se₃. The gray regions in panels c–f show spectral therapeutic region NIR-I (700–980 nm). For comparison, we included the performance of Au, Si, and MoS₂ NPs.