Raman Spectroscopy of Few-Quintuple Layer Topological

Transcription

1 SUPPORTING INFORMATION FOR Raman Spectroscopy of Few-Quintuple Layer Topological Insulator Bi Se 3 Nanoplatelets Jun Zhang,, Zeping Peng, Ajay Soni, Yanyuan Zhao, Yi Xiong, Bo Peng, Jianbo Wang, Mildred S. Dresselhaus,,ξ and Qihua Xiong,, * Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore School of Physical Science and Technology, MOE Key Laboratory on Luminescence and Real-Time Analysis, Southwest University, Chongqing 40075, China School of Physics and Technology, Center for Electron Microscopy and MOE Key Laboratory of Artificial Micro- and Nano-Structures, Wuhan University, Wuhan 43007, China Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 039 ξ Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 039 Division of Microelectronics, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore *To whom correspondence should be addressed. Qihua@ntu.edu.sg. These authors contribute equally to this work.

2 BiSe3 Nanoplatelets (NPs) Synthesis The BiSe3 NPs were synthesized via a polyol method.- Bismuth (III) nitrate pentahydrate (Bi (NO3)3 5HO), sodium selenite (NaSeO3), polyvinyl pyrrolidone (PVP), and ethylene glycol (EG) were purchased from Alfa Aesar. All reagents are of analytic purity and were used without further purification. A typical reaction of BiSe3 NPs synthesis was conducted as follow: 0.0 g of bismuth (III) nitrate pentahydrate (Bi(NO3)3 5HO), 0.05 g of sodium selenite (NaSeO3), 0. g of polyvinyl pyrrolidone (PVP), and 0 ml of ethylene glycol (EG) were added into a 5.0 ml two-neck flask containing a Teflon-coated magnetic stirring bar. The flask was connected with a reflux condenser and placed on a heating mantle. The temperature of the solution was increased to 90 oc under constant stirring. After h, the flask was then removed from the heating mantle. The product was cooled, centrifuged, washed with isopropyl alcohol (IPA) several times, and then dried at 60 C. (a) (b) θ θ (º) Intensity (A.U.) (d) 08 (c) 70 Figure S- SEM images and XRD diffraction pattern. SEM images of the product for different reaction times of min (a), 0 min (b) and 00 min (c). (d) XRD spectrum of as-grown nanoplatelets. All the peaks can be indexed for a rhombohedral phase (JCPDS card No ). Figure S- (a)-(c) shows representative SEM images of chemically grown NPs as a dependence on reaction time for min (a), 0 min (b) and 00 min (c). As can be seen from the evolution with reaction time, it took a certain incubation time to finally achieve uniform thin NPs. If the reaction time is short (a), the product was still mainly composed of the precursors. After a medium reaction time (e.g., 0 min shown in (b)), an intermediate product with a flow-like morphology was observed. We found that uniform thin NPs were achieved after a 00 min reaction time. Most good NPs exhibit hexagonal morphologies with planar dimensions extending up to several micrometers, while some of them show a truncated trigonal morphology. The XRD pattern as shown in Figure S- (d) indicates that the product shown in (c) has the rhombohedral phase (JCPDS card No ) with good crystallinity. The Refractive Index of BiSe3 by Kramers-Kronig Analysis3 To evaluate the contrast quantitatively, we need to know the refractive index of each layer material. The refractive indices of BiTe3,4 SiO and Si5 are available, but that of BiSe3 has not been reported in

3 the literature to the best of our knowledge. Here we obtained the refractive index of Bi Se 3 from the reflectance spectra reported by D. L. Greenaway and G. Harbeke in the 970s. 4 The real and imaginary parts of the refractive index n and k can be obtained from the normal incidence reflectivity spectrum R(ω) where ω is the photon frequency. By calculating the phase angle at a frequency ω: d ln R( ') ' + 0 d ' ' n and k can then be deduced from the equation: ω ω ω θ ( ω) = ln dω ' π, (S-) ω ω ω n ik = iθ R e. (S-) n ik + For the evaluation of θ, in principle, one must know R(ω) over the entire spectral region from zero to infinity. In optical spectra, the reflectivity is often still varying at the highest frequencies used in the measurement. One therefore has to extrapolate the measured reflectance to higher energies in a proper way. A general approach is to extrapolate R by 6-7 R R ω = ω, (S-3) where the exponent p is fitted in order to give the best agreement with experiment at high energies. Here we obtained p=4 from the reflectance spectra. 4 p (a) Bi Se 3 300K (b) Bi Se 3 300K Figure S-, (a) The refractive index of Bi Se 3 calculated by the Kramers-Kronig method from (b) giving the indicated reflectivity spectra [4]. We used the Dat-Lab software to solve eq (S-) and (S-3), and we obtained the refractive index of Bi Se 3 as shown in Figure S-. The n and k correspond to the real and imaginary part of the complex refractive index n% = n ik. 3

4 Laser Power Dependence of Raman Scattering It is well known that Bi Se 3 has a low thermal conductivity. 8 To exclude the possibility of phonon softening due to lattice expansion induced by laser heating, we conducted power-dependent Raman scattering measurements as shown in Figure S-3 for a NP with a thickness of 8 QL. Similar results were obtained for a thicker NP (>0 nm), and therefore the data are not shown here. As can be seen from Figure S-3, the position and lineshape (i.e., FWHM) of all four peaks didn t show pronounced changes as the excitation power was increased from 5 µw to mw. A higher laser excitation power level is not suggested since devastating damage was observed after a short time (a few minutes) illumination at a higher power level. The largest redshift observed at the maximum power of mw was less than cm -, which is within the resolution of our spectrometer. At the same time, the FWHM of all peaks also do not show any broadening with increasing of laser power as shown in the figure S-3. Therefore, the redshift and FWHM discussed for A g and E g are not due to the outcome of a laserinduced heating effect, since the laser excitation power was only ~ 65 µw and ~ 5 µw for the 63.8 nm and 53 nm lasers, respectively. 8 mw Intensity (a.u.) 0.5 mw 0.37 mw 0.6 mw 0.6 mw 0.06 mw 0.05 mw Raman Shift (cm - ) Figure S-3 Power dependence of an 8 QL sample excited by 63.8 nm. No pronounced redshift and broadening of all Raman modes were observed as the power was increased. Solid curves are multiple Lorentzian lineshape fittings, while the vertical dashed line is a guide to the eye. Ag Line shape Analysis For a perfect bulk crystal with long range order at ambient temperature, phonons are quasiparticles that can be described by the model of a damped harmonic oscillator with a finite lifetime. This oscillation corresponds to a Lorentzian dispersion lineshape in the energy domain, in which the FWHM corresponds to the natural broadening of a phonon. In practical Raman measurements, the FWHM is the convolution of the natural linewidth and the equipment broadening. 4

5 Figure S-4 shows the Lorentzian fittings of the Stokes Raman spectra for 7 and 6 QL thick Bi Se 3 NPs. A perfect fitting for the other three modes was observed, except for the Ag mode at ~7 cm -. As shown in Figure S-4 (c) and (d), the A g mode showed a slight high-frequency asymmetry which deviated from a Lorentzian lineshape. Generally speaking, the phonon confinement effect 9 and laser heating effect 0- would lead to an asymmetric broadening and downshifting of the Raman band in nanostructures. The Fano effect also introduces an asymmetric line shape in the Raman spectrum attributed to Fano interference between the scattering from the discrete optical phonon and an electronic continuum. -5 (a) (b) Intensity (a.u.) (c) (d) Raman Shift (cm - ) Figure S-4 The Lorentzian fitting of the Raman spectrum of (a) 7QL and (b) 6 QL Bi Se 3 NPs. (c) and (d) correspond to the zoom-in figure of the Ag mode in (a) and (b), respectively. Based on the phonon confinement phenomenological theory proposed by Richter et al. 9 for spherical nanocrystals (i.e., quantum dots) and extended by Fauchet and Campbell to include nanowires and thin films, 6 the bulk Raman wave vector selection rule q=0 is relaxed, such that a range of phonons from the expanded Brillouin zone will be activated in Raman scattering (the RFC model). Since the optical phonon dispersion curves of most semiconductor materials have a negative slope away from the Brillouin zone center, the sampling of a continuum of phonon wave vectors should cause a redshifting and an asymmetric broadening towards the low energy side for a one-phonon line. The model was based on the assumption that the size of the crystal is still much larger than the lattice constants (at least in one direction) such that the translational symmetry and the Bloch theorem are still applicable. If the 9, 6 wavefunction which describes a phonon state q 0 in an infinite crystal is as follows where ( ) i 0 (, ) (, ) Φ = u e q r q r q r, (S-4) 0 0 u q r is the Bloch function with the periodicity of the lattice, then the modified wavefunction 0, due to confinement is 5

6 where w(, d ) (, ) w(, d ) (, ) (, ) u (, ) Ψ q r = r Φ q r = Ψ q r q r, (S-5) r is the confinement function, and d is the characteristic dimension of the confinement, e.g., the diameter of quantum dots or nanowires. In many cases a Gaussian function is used in the literature to describe the confinement. According to this model, the intensity of the first order Raman spectrum I ( ) 0 ω of a single nanostructure is given by: where (0, ) ' C(0, q) 3 I0( ω) A d q, (S-6) Γ [ ω ω( q) ] + C q is the Fourier coefficient of the spatial confinement function w(, d ) r, ω( q) is the phonon dispersion, and Γ is the measured FWHM of the bulk Raman peak. This model has been successfully used to interpret the confined phonon states in various nanostructures. 7-8 integration of For the D platelet geometry the platelet size in-plane is much larger than its thickness, and the 3 d q in eq (S-6) can be written as dqxdqydq, where q, x y and q are the wavevectors inplane and along the confinement direction ( i.e. the [] direction along the trigonal axis), respectively. Thus, the eq S-6 can be written as an integral only for dq : qmax C(0, q ) I0( ω) A0 dq 0. (S-7) Γ [ ω ω( q )] + Considering that the x-y plane of the film is infinite, the Raman scattering selection rule of q x, y = 0 is valid. The integration of dqxdqy along the in-plane direction of the film is a constant and can be included into setting the value for the amplitude coefficient A 0 qmax. In this context, the value of = π / ( c / 3) corresponds to the Z symmetry point 9 along the trigonal axial of the Brillouin Zone of Bi Se 3, and c is the lattice constant of Bi Se 3. Therefore eq (S-7) was used to evaluate the lineshape change versus thickness assuming the RFC model is still valid down to atomically thin layers. The results are plotted in Figure 6c in the main text. 6

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