Raman spectroscopy regulation in van der Waals crystals

Wei Zheng; Yanming Zhu; Fadi Li; Feng Huang

doi:10.1364/PRJ.6.000991

Abstract

Raman spectroscopy is a versatile tool widely used for comprehensive probing of crystal information. However, generally when applied in narrow-band-gap van der Waals crystals, it is liable to form a “bug,” especially in transition-metal-dichalcogenides (TMDs). That is, several resonant Raman-scattering (RS) modes will inevitably appear in the Raman spectra with strong intensity, interfering with the desired signal of optical-phonon modes. Here, we propose cross-sectional polarized Raman scattering capable of regulating the intensity of RS modes in accordance with quasi-sinusoidal rules. Typically, for

{MoS}_{2}

and

{WS}_{2}

, when the polarization vector of excited light is along the

c

axis of the crystal, all RS modes are nearly completely “expunged” from the Raman spectra. The mechanism is that the absorption of most TMDs with a space group of

R_{3 m}

for the light polarized along the

c

axis is infinitesimal, thus forming a small coupling intensity of electronic states excited optically and acoustic-phonon modes at point

M

, which in turn restrain the appearance of RS modes. The regulating strategy proposed can be applied to other van der Waals crystals so as to obtain a high signal-to-noise ratio Raman spectrum.

1. INTRODUCTION

Van der Waals crystals, such as layered semiconductor transition-metal-dichalcogenides (TMDs), are expected to integrate with silicon or other heterogeneous wafers as logic units to realize logical operations ^[1–3]. In order to fabricate an integrated logic device, the layered TMDs are inevitably bonded to other functional materials such as metal, organics, dielectrics, and semiconductors ^[4–6]. However, the bonding process may incite a potential problem: due to their small crystal lattice energy, van der Waals TMDs are liable to trigger crystal lattice distortion in the environment of a heterogeneous interface, thus resulting in some unpredictable optoelectronic properties and reducing the reliability of the TMD-based logic device ^[5,7]. Therefore, a non-destructive and in situ tool is needed to probe into the TMDs in the micro-zone and to provide accurate information about the changes in their lattice structure and optoelectronic properties.

Micro-Raman spectroscopy, meeting the above requirements, is an ideal tool for probing van der Waals crystals ^[8–10]. It has already been widely used to measure the crystallinity, number, and orientation of layers ^[11,12] and the types and quality of edges ^[13], as well as to analyze the perturbation effect under strain, doping, or electromagnetic conditions ^[8]. In spite of such extensive applications, Raman spectroscopy still has a “bug” for probing narrow-band-gap TMDs. Generally, a large number of resonant Raman-scattering (RS) modes, coming from the coupling of acoustic-phonon modes at point $M$ and optically excited electronic states, occur in Raman spectra, which interfere optical-phonon (OP) modes under conventional excitation conditions ( $λ_{exc} =$ 532,633 nm). This bug significantly decreases the signal-to-noise ratio (SNR) of Raman spectra in typical TMDs such as ${MoS}_{2}$ and ${WS}_{2}$ ^[9,14–16].

As mentioned before, resonant Raman scattering in semiconductors mainly comes from the coupling of acoustic phonon modes and electronic states excited by photons. Thus, to eliminate the RS mode, it is necessary to inhibit the absorption of excited light in the measured crystals as much as possible. Here, typically for ${MoS}_{2}$ and ${WS}_{2}$ , we first figure out the anisotropic absorption characteristics comprehensively within the visible light range via first-principles calculations. The results indicate that both ${MoS}_{2}$ and ${WS}_{2}$ have infinitesimal absorption for out-of-plane polarized light ( $e_{i} ∥ c$ axis), even if the excited photon energy exceeds the band gap. Based on theoretical understanding, we achieve a quasi-sinusoidal control of the scattering intensity in RS modes under the cross-sectional scattering geometry configuration, realize an almost complete suppression of the RS modes, and obtain Raman spectra with ultra-high SNR. The strategy used in this research of combining theory and experimental research can be also extended to the regulation and suppression of RS modes in other van der Waals crystals.

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2. EXPERIMENTAL RESULTS AND DISCUSSION

The two typical van der Waals crystals for Raman regulation in this work, ${MoS}_{2}$ and ${WS}_{2}$ , have an indirect bandgap of 1.5 eV and 1.4 eV, respectively ^[17,18]. In normal Raman-scattering measurements, usually, the excited laser wavelength is 532 nm and/or 633 nm, and with the wave vector $k_{i}$ along the $c$ axis of crystals (i.e., $k_{i} ∥ c$ axis, $e_{i} ⊥ c$ axis), any excited light polarized in-plane produces strong RS modes ^[8,14,15], as shown in Fig. 1. Obviously, the obtained typical Raman spectra contain a large number of RS modes, causing difficulties in identifying the lattice-distortion-sensitive OP modes ^[19,20], such as $A_{1 g}$ .

Figure 1.Typical Raman spectra of ${MoS}_{2}$ and ${WS}_{2}$ scattering from in-plane ( $e_{i} ⊥ c$ axis). (a) Typical Raman-scattering spectrum of ${MoS}_{2}$ excited by a 633 nm laser, and a large number of LA(M)-related RS modes are excited. All recoded modes in ${MoS}_{2}$ Raman spectroscopy are identified as 179 $[A_{1 g} (M) + LA (M)]$ , 383 $[E_{2 g}^{1} (Γ)]$ , 409 $[A_{1 g} (Γ)]$ , 421 $[B_{2 g}^{2} + E_{1 u}^{2} (Γ - A)]$ , 454 [2LA(M)], 465 $[A_{2 u} (Γ)]$ , 529 $[E_{1 g} (M) + LA (M)]$ , 572 $[2 E_{1 g} (Γ)]$ , 600 $[E_{2 g}^{1} (M) + LA (M)]$ , 644 $[A_{1 g} (M) + LA (M)]$ , 767 (unknown), 785 (unknown), and 824 (unknown) ${cm}^{- 1}$ [14,16]. (b) Typical Raman-scattering spectrum of ${WS}_{2}$ excited by a 532 nm laser, and the recoded modes are identified as LA(M) at $175 {cm}^{- 1}$ , $E_{2 g}^{1} (M) - LA (M)$ at $195 {cm}^{- 1}$ , $A_{1 g} (M) - LA (M)$ at $233 {cm}^{- 1}$ , $2 LA (M) - 2 E_{2 g}^{2} (M)$ at $298 {cm}^{- 1}$ , $E_{1 g} (M)$ at $323 {cm}^{- 1}$ , 2LA(M) at $351 {cm}^{- 1}$ , $A_{1 g} (Γ)$ at $421 {cm}^{- 1}, E_{2 g}^{1} (M) + LA (M)$ at $523 {cm}^{- 1}$ , $A_{1 g} (M) + LA (M)$ at $585 {cm}^{- 1}$ , and 4LA(M) at $701 {cm}^{- 1}$ [9].

As mentioned earlier, the resonant Raman-scattering intensity is strongly dependent on the absorption of excited lights (absorption mainly comes from the electronic transitions). To understand the scattering behavior of RS modes in van der Waals crystals, it is necessary to probe into the anisotropic optical absorption characteristics systematically. Therefore, first we apply the first-principles method to calculate the absorption characteristics of ${MoS}_{2}$ and ${WS}_{2}$ to visible lights with different polarizations via the Perdew–Burke–Ernzerhof functional ^[21], and the results are shown in Fig. 2.

Figure 2.Normalized optical absorption coefficients of the cross section ( $k_{i} ∥ a$ axis) in (a) ${MoS}_{2}$ and (b) ${WS}_{2}$ calculated via first principles, where ordinate $θ$ is the angle between the incident light polarized vector $e_{i}$ and the $c$ axis of the crystals. The absorption coefficients of the in-plane area ( $k_{i} ∥ c$ axis) in (c) ${MoS}_{2}$ and (d) ${WS}_{2}$ , where the ordinate $φ$ represents the angle between the incident light $e_{i}$ and the $c$ axis.

The results in Fig. 2 indicate that ${MoS}_{2}$ and ${WS}_{2}$ show no optical absorption anisotropy in-plane [Figs. 2(c) and 2(d)] yet boast strong anisotropy in the cross section [Figs. 2(a) and 2(b)]. Importantly, when the electric vector is along the $c$ axis ( $e_{i} ∥ c$ axis, i.e., $θ = 0$ or $π$ ), the absorption coefficient is close to zero, and it is also weakly related to photon energy, even for those whose energy is greater than the band gap.

The calculation results can be further clarified by a physical description as follows ^[22]. The electrons in the plane of layered ${MoS}_{2}$ and ${WS}_{2}$ can move freely and interaction with the photons’ polarization lies in-plane. For example, the conduction-band minimum (CBM) of layered ${WS}_{2}$ is predominately constructed by W ${d z}^{2}$ orbitals, whereas the valence-band maximum (VBM) constructed by W $d x y$ and $d x^{2} - y^{2}$ orbitals, leaves only a small amount of room for S $p x$ and $p y$ orbitals to contribute ^[23]. On the one hand, once the incident photon polarization lies in-plane along the $a$ axis (corresponding to the $x$ axis in mathematics), the absorption coefficient can be calculated by $α_{a} = {| ⟨ CBM | x | VBM ⟩ |}^{2} = {| \int d x d y d z z^{2} x^{2} |}^{2}$ . The even integrand and the finite integral indicate that an oscillation between the W $d z^{2}$ orbital and the S $p x$ orbital of electron density is induced by the photon polarized in-plane. Thereafter, it brings about a bright transition, absorbing the incident photons. On the other hand, if incident photon polarization is placed along the $c$ axis (corresponding to the $z$ axis in mathematics), the integrand will be odd, written as $α_{c} = | ⟨ CBM | x | VBM ⟩ |^{2} = 0$ , and the absorption coefficient will reach zero. From the above explanation, it is clear that optical absorption cannot be brought by photons polarized out-of-plane. ${MoS}_{2}$ , too, follows similar procedures.

These theoretical results give guidelines for designing a Raman-scattering geometric configuration to suppress RS modes. Based on the understanding of optical absorption in Fig. 2, we conduct Raman measurements on ${MoS}_{2}$ and ${WS}_{2}$ again under an $x (z -) x$ geometric configuration. The expected Raman spectra with a high SNR is obtained, and RS modes are nearly inhibited, as shown in Fig. 3. It is noteworthy that under such an out-of-plane polarization geometric configuration, unlike the increased intensity of $A_{1 g} (Γ)$ , the scattering intensity of $E_{2 g}^{1} (Γ)$ is weakened, regulated by the Raman selection rules.

Figure 3.Improved Raman spectra of (a) ${MoS}_{2}$ and (b) ${WS}_{2}$ scattering from out-of-plane polarization ( $e_{i} ∥ c$ axis). Compared to Fig. 1, the RS modes here are fully suppressed and the high SNR of the OP mode is highlighted.

To provide a clear explanation for the above satisfactory experimental results, it is necessary to conduct a systematic study of the evolution of RS modes when van der Waals ${MoS}_{2}$ and ${WS}_{2}$ are under different polarization conditions. In response, we carry out the following polarized Raman-scattering measurements comprehensively. Figures 4(a) and 4(b) show the cross-sectional angle-dependent polarized (CAP) Raman spectra, boasting strong anisotropy, while Figs. 4(c) and 4(d) show the in-plane angle-dependent polarized (IAP) Raman spectra, bearing almost no anisotropy.

Figure 4.The cross-sectional angle-dependent polarized (CAP) Raman spectra of (a) ${MoS}_{2}$ and (b) ${WS}_{2}$ , where the ordinate $θ$ is defined as the angle between the incident light polarization $e_{i}$ and the $c$ axis, and the in-plane angle-dependent polarized (IAP) Raman spectra of (c) ${MoS}_{2}$ and (d) ${WS}_{2}$ , where the ordinate $φ$ is defined as the angle between the incident light polarization $e_{i}$ and the $a$ axis.

It can be found through careful observation that OP and RS modes in Figs. 4(a) and 4(b) display distinct anisotropic behaviors. The relationship between the scattering intensity of the $A_{1 g}$ OP mode and $θ$ is close to the quasi-sine wave [details are shown in Figs. 5(a) and 5(b)], while the RS modes the quasi-cosine wave [Figs. 5(c) and 5(d)].

Figure 5.Raman intensities of OP and RS modes extracted from Figs. 4(a) and 4(b) via Lorentzian fitting. (a) and (b) display angle-dependent intensities of $A_{1 g}$ OP modes in ${MoS}_{2}$ and ${WS}_{2}$ , respectively, and reveal a similar changing rule in ${MoS}_{2}$ and ${WS}_{2}$ . The red line gives the corresponding fitting results based on the Raman selection rule, i.e., Eq. (1). (c) and (d) show the angle-dependent intensities of resonant scattering modes in layered ${MoS}_{2}$ and ${WS}_{2}$ , respectively. All modes appear with the same $θ$ angle dependence: when $θ = (n + 1 / 2) π$ , the scattering intensity reaches the highest value; while $θ = n π$ , the value approximates to zero.

The anisotropic scattering behavior of the OP mode $A_{1 g}$ accords with the Raman selection rule tightly, i.e., $I \sim {| e_{s} \cdot R \cdot e_{i} |}^{2}$ ^[22,24–27], where $I$ is Raman-scattering intensity, $e_{i}$ is the polarization of incident light, $e_{s}$ is the polarization of scattering light, and $R$ is the Raman tensor. For the current measured crystals and geometric configuration, the Raman tensor is $R [A_{1 g}] = [\begin{matrix} a \\ a \\ b e^{i ϕ} \end{matrix}],$ (1) $e_{i} = e_{s} = (\begin{matrix} \sin θ \\ 0 \\ \cos θ \end{matrix}) .$ (2)Thus, the Raman-scattering intensity of the $A_{1 g}$ mode is derived as follows: $I_{A_{1 g}} (θ) \sim {| a |}^{2} \sin^{4} θ + {| c |}^{2} \cos^{4} θ + \frac{1}{2} | a | | c | \sin^{2} (2 θ) \cos ϕ,$ where $ϕ$ is defined as the apparent phase ^[28]. The matched fitting results in Figs. 5(a) and 5(b) show that the formula can elaborate the anisotropic behaviors of $A_{1 g}$ modes well.

However, Raman selection rules cannot describe the anisotropic behaviors of RS modes because they do not originate from the Raman-activated optical phonon. The RS modes are derived from the coupling intensity of optical excited electronic states and acoustic phonon modes at point $M$ , so the light absorption coefficient can reasonably be used to explain the anisotropic behaviors of RS modes.

The scattering intensities of the RS modes in Figs. 5(c) and 5(d) completely reproduce anisotropic distribution of the optical absorption coefficients in Figs. 1(a) and 1(b). When the excited light polarization is perpendicular to the $c$ axis of the crystals (i.e., $θ = π / 2$ or $3 π / 2$ ), the corresponding light absorption reaches the maximum value, which in turn makes the intensities of all the RS modes attain the maximum value. When the polarization is parallel to the $c$ axis of the crystals (i.e., $θ = 0$ or $π$ ), the light absorption attains the minimum value, resulting in the minimum RS mode intensities. Thus, the RS modes could be almost submerged in the background of Raman spectra, ensuring that the obtained Raman spectra have an ultra-high SNR. This strategy of Raman spectroscopy regulation can also be extended to other van der Waals crystals as an ideal tool for exploring and analyzing crystals’ quality and orientation, number of layers, types of edges, and effects of perturbations.

3. CONCLUSION

We propose a Raman regulation method or strategy to inhibit the occurrence of RS modes in the Raman spectra of van der Waals crystals and to obtain the desired Raman spectra with a high SNR. More specifically, when the polarization of excited light is along the $c$ axis of crystals, the long-awaited improved Raman spectra containing only OP modes without any RS modes are achieved. The mechanism is that, under out-of-plane polarization, most TMDs with a space group of $R_{3 m}$ will produce an extremely weak light absorption and, anomalously, an extremely strong Raman scattering of $A_{1 g}$ OP modes.

4. METHODS

A. First-Principles Calculation

All density functional calculations are performed via the Vienna Ab-initio Simulation Package (VASP), using the Perdew–Burke–Ernzerhof functional ^[21]. The plane-wave energy cutoff for all the calculations is 680 eV. The lattice constants with a Monkhorst–Pack k-grid of $7 \times 7 \times 1$ are not fully relaxed until the energy difference between two successive iterations is lower than $10^{- 5} eV$ and the forces on every atom are lower than $10^{- 3} eV / Å (1 Å = 0.1 nm)$ ^[29]. GW calculations of optimized bulk structures are used to obtain electronic absorption spectra of linearly polarized light. The polarization absorption coefficient formula is written as $α (θ) = α_{c} + (α_{c} - α_{a}) \sin^{2} θ$ ^[30], where $α_{c}$ is the absorption coefficient of the polarization vector parallel to the layers, while $α_{a}$ is that of the polarization vector perpendicular to the layers.

B. Raman-Scattering Measurements

${MoS}_{2}$ and ${WS}_{2}$ samples are the ideal crystals for commercial use. CAP Raman measurements on ${MoS}_{2}$ and ${WS}_{2}$ are carried out via a Renishaw micro-Raman spectrometer (inVia Reflex) in backscattering geometry, using 633 nm and 532 nm lasers with a power of 0.25 mW and 0.3 mW, respectively. For CAP Raman-scattering measurement, the incident excitation laser focuses on the cross section of ${MoS}_{2}$ ( ${WS}_{2}$ ), which is laid on a rotating stage by a $50 \times$ objective lens; the rotating angle $θ$ is noted as the angle between the polarization vector $e_{i}$ of incident light and the $c$ axis of the crystals. For IAP Raman-scattering measurement, the incident excitation laser focuses on the in-plane area of ${MoS}_{2}$ ( ${WS}_{2}$ ); the rotating angle $φ$ is noted as the angle between the polarization vector $e_{i}$ of the incident light and the $a$ axis of the crystals. For the cross-sectional angle-dependent polarized Raman scattering, a polarizer was inserted into the scattering light path to enable the scattered light with polarization parallel to that of the incident laser, namely, $e_{i} ∥ e_{s}$ .