*Article* **Interlayer Di**ff**erence of Bilayer-Stacked MoS2 Structure: Probing by Photoluminescence and Raman Spectroscopy**

**Xiangzhe Zhang <sup>1</sup> , Renyan Zhang 1,\* , Xiaoming Zheng 2, Yi Zhang 2, Xueao Zhang 3,\*, Chuyun Deng 2,\* , Shiqiao Qin 1,\* and Hang Yang <sup>2</sup>**


Received: 16 April 2019; Accepted: 17 May 2019; Published: 24 May 2019

**Abstract:** This work reports the interlayer difference of exciton and phonon performance between the top and bottom layer of a bilayer-stacked two-dimensional materials structure (BSS). Through photoluminescence (PL) and Raman spectroscopy, we find that, compared to that of the bottom layer, the top layer of BSS demonstrates PL redshift, Raman E1 2g mode redshift, and lower PL intensity. Spatial inhomogeneity of PL and Raman are also observed in the BSS. Based on theoretical analysis, these exotic effects can be attributed to substrate-coupling-induced strain and doping. Our findings provide pertinent insight into film–substrate interaction, and are of great significance to researches on bilayer-stacked structures including twisted bilayer structure, Van der Waals heteroand homo-structure.

**Keywords:** film–substrate interaction; photoluminescence; Raman spectroscopy; molybdenum disulfide; bilayer-stacked structure

#### **1. Introduction**

By stacking up two single-layer two-dimensional (2D) materials, bilayer Van der Waals (VdW) homo- and hetero-structures can be fabricated [1]. Owing to the existence of interlayer coupling, these bilayer-stacked structures usually exhibit distinct properties from their monolayer counterparts. For example, energy band gap evolution is found in bilayer VdW homo-structures compared to the corresponding monolayer, as previously reported in graphene and MoS2 [2,3]. Additionally, interlayer-coupling-induced p–n junction in VdW hetero-structure can lead to novel optoelectric effects [4,5]. Further, if stacking up two films with a misorientation angle, a brand-new tunable dimension is introduced to the bilayer-stacked two-dimensional materials structure (BSS), such BSS is referred to as twisted bilayer structure (tBLS). As a result, numerous exotic effects, induced by the twisted dimension and distinct from those in monolayer or bilayer without twisted angle, are expected. tBLS are tunable in their properties with variation in the twisted angle, thus have attracted intensive researches. For one thing, phonon in tBLS can be affected by interlayer coupling varying with angle, providing a simple but effective way to tune diverse properties such as, crystalline asymmetry [6], nonlinear optical effects [6,7], Raman scattering [8,9], and thermal conductivity [10–15]. For another, periodical interlayer Van der Waals potential can impact carrier performance of tBLS, which is first confirmed by the observation of Moiré pattern of twisted bilayer graphene (tBLG) under scanning

tunneling microscope in 2005 [16]. Van Hove Singularity (VHS) [17] and angle-dependent electrical conductivity [18] are another two examples for this effect. Moreover, cutting-edge advances on twisted bilayer structure (tBLS) like, unconventional superconductivity in magic-angle tBLG [19] and mirror Dirac cone in incommensurate-angle tBLG [20], imply that there remains a lot that is yet to be explored.

However, all these findings about BSS focus only on the interlayer-coupling-induced effects, while ignoring the difference between the top and bottom layer of BSS. The BSS sample fabricated by transfer method can be divided into three different regions: stacked region where top and bottom layer overlap each other, bottom region (bottom layer excluding stacked region), and top region (top layer excluding stacked region). Although bottom and top regions are both supposed to be in direct contact with the substrate, there exists great difference between the top-substrate and the bottom-substrate coupling. Substrate coupling can affect 2D materials in many aspects. For example, on the one hand, substrate contact can employ strain on 2D materials, leading to phonon variations measured by Raman spectroscopy [21–23]. On the other hand, substrate can provide or deplete carriers depending on its doping type [24–26], thus tuning electrical and optical properties of materials deposited on it [27]. Furthermore, substrates with different permittivities and surface polar phonon modes demonstrate different scattering mechanisms limiting the electron mean free paths and mobility in 2D materials [28–30]. Band gap of semiconductors can also be tuned by dielectric environment permittivities [31]. Consequently, bottom and top region may demonstrate different phonon and exciton performance.

As one sort of transitional metal dichalcogenide (TMD) materials, MoS2 monolayer with a two-dimensional structure demonstrates intriguing effects in various aspects, including optical [32–34], electrical [35–37], and thermal properties [38–40]. Especially, due to its unique direct band gap [41], monolayer MoS2 is expected to have strong photoluminescence (PL) emission, which has been confirmed both experimentally and theoretically. Excited by 532 nm laser at ambient conditions, monolayer MoS2 is reported to have two prominent PL peaks at 625 nm (B peak) and 670 nm (A peak) [42–44]. These two peaks correspond to two direct excitonic transitions at the Brillouin zone K point, while the difference between them comes from the spin-orbital coupling caused by valence band energy splitting [42]. Also, two easily identified Raman peaks are observed in MoS2 monolayer [32,45], located near 390 cm−<sup>1</sup> (E1 2g, in-plane vibration mode) and 409 cm−<sup>1</sup> (A1g, out-of-plane vibration mode), respectively.

Through photoluminescence and Raman spectroscopy, we found that, in bilayer-stacked MoS2 (BSM) samples fabricated by transfer, exciton and phonon performance in the top and bottom regions are remarkably different. Despite the fact that both top and bottom layers of BSM are transferred, compared to the bottom region, the top region demonstrates PL intensity reduction and peak redshift, implying less p-doping to top region from substrate. Meanwhile, redshift of in-plane Raman mode E<sup>1</sup> 2g is observed in top region, suggesting that vibration softens in top region. To exclude the film–substrate interaction, freestanding monolayer MoS2 samples are fabricated. It is found that, compared to the supported region, the suspended region of monolayer MoS2 demonstrates redshift in PL and Raman peaks, which are consistent with those in the top region of BSM, thus providing evidence for coupling difference between top-substrate and bottom-substrate.

Since the interlayer difference in BSS can complicate the experimental results, and is also affected by interlayer coupling, our findings are of great significance to distinguish between contributions from interlayer coupling and film–substrate interaction, which is of great significance to researches on interlayer-coupling-induced effects like optoelectric effects in VdW hetero-structure and twisted angle dependence in tBLS. Furthermore, our findings are universal and, apart from MoS2 bilayer-stacked structure on SiO2 substrate, we are sure this work can be informative to film–substrate interaction study on other 2D materials and substrates.

#### **2. Materials and Methods**

#### *2.1. Sample Preparation*

For this study, a convenient fabrication process is employed to obtain BSM samples. First, all single-layer flakes are deposited on a SiO2/(001)Si substrate (SiO2 layer is 300 nm thick), with a size of approximately 50 μm by chemical vapor deposition (CVD). Then, we transferred two sheets of monolayer MoS2 to one substrate, by which method we can obtain tens of BSM samples with various angles in a single step. It should be noted that, in this work, both top and bottom layer of the BSM undergo transfer process to avoid preparation method induced difference. During the transfer process, any solvent that may cause doping in MoS2 was avoided. Universally used transfer methods like, PMMA-way (poly-methyl-methacrylate) [46] and PVA-way (poly-vinyl-alcohol) [47] introduce contamination or wrinkles to the surface of materials. Herein, a previously reported PLLA-way (poly-L-lactic-acid) [48] is chosen to ensure the transfer is residual-free and of high-uniformity. After transfer, the as-fabricated samples undergo ultraviolet treatment [49] and annealing [50] (in a tube furnace in Ar/H2 flow at 300 ◦C for 2 h) to remove residues and enhance interlayer coupling.

As for free-standing monolayer MoS2 samples, they are fabricated by PLLA transfer onto SiO2/(001)Si substrate (SiO2 layer is 300 nm thick) with 300 nm-depth holes. These holes are of a radius 5 μm each, fabricated by reactive ion etching (RIE) method in SF6/CHF3 mixed gas flow (30 sccm).

#### *2.2. Sample Characterization and Measurement*

In this work, all bright field optical micrographs are taken by Nikon LV150 microscope, using 50× objective lens (Nikon, Tokyo, Japan). Dark-field optical micrographs are taken by ZEISS Axio Scope A1 microscope, using a 50× objective lens (Zeiss, Oberkochen, Germany). Atomic force microscopy (AFM) images are taken by NT-MDT Prima AFM system, using semi-contact scanning mode (NT-MDT, MoscowRussia). PL and Raman spectroscopy are measured by WITec Alpha300R confocal Raman system, using a 50× objective lens (WITec, Ulm, Germany). A 532 nm laser is used as the excitation source. For Raman measurements, the laser power is 1 mW, while for PL measurements laser power is 0.5 mW, sufficiently low to avoid heating effects. Optical gratings used for Raman and PL measurements are 1800 L/mm and 600 L/mm, respectively, providing respective spectral resolution smaller than 1 cm−<sup>1</sup> and 1 nm.

#### **3. Results**

#### *3.1. PL and Raman Di*ff*erence between Layers of BSS*

One as-fabricated BSM sample is shown in Figure 1. From the bright-field and dark-field optical micrographs in Figure 1a, we can see its surface is free of large-sized residual spots and wrinkles (of several micrometers size). To investigate its surface-height fluctuation in details, atomic force micrograph (AFM) is taken (Figure 1d). In Figure 1d, the sample's surface seems bubble-free, uniform, and plane within each region (no sharp morphology fluctuations of several micrometers size). At the edge between the stacked and top region, where top layer falls from bottom layer to substrate, there seems no ramp but a vertical cliff.

As is plotted in Figure 1b, bottom, stacked, and top region of this BSM sample demonstrate easily distinguishable PL intensity. Bottom region demonstrates the strongest PL intensity, then followed by the top region and stacked region in turn. Meanwhile, Figure 1c shows spatial inhomogeneity within the top region. The area in the vicinity of the stacked region (V-area), outlined by magenta dashed line, exhibits lower intensity than rest of the top region. Moreover, there appears a general correlation between PL and Raman over the mapped area, i.e., this V-area can also be easily identified in Raman intensity map and Raman shift map, as is shown in Figure 1e,f respectively. In this V-area, compared to the rest of the top region, Raman mode E1 2g demonstrates redshift and intensity enhancement.

**Figure 1.** Interlayer difference of one twisted bilayer structure (tBLS) sample. Photoluminescence (PL) and Raman are all excited by 532 nm laser. (**a**) Optical micrograph. Inset corresponds to dark-field optical micrograph. The green and white dash lines outline the bottom and top layer respectively, while the red box outlines the scanning area in (**b**). (**b**,**c**) PL intensity map in high and low contrast respectively. (**d**) Atomic force microscopy (AFM) micrograph. (**e**) Raman intensity map of mode E1 2g. (**f**) Raman shift map of mode E<sup>1</sup> 2g. Green, black, and magenta circles in (**b**–**f**) point out bottom, stacked, and top region respectively.

This difference in PL and Raman spectra between the top and bottom regions is also observed in other as-fabricated BSM samples, as is shown in Figure 2. For all samples in Figure 2b, the maximum E1 2g-to-A1g Raman shift difference among the top region and bottom region is below 19 cm<sup>−</sup>1, which is the signature of monolayer MoS2, indicating these samples are stacked by two individual monolayer MoS2. For each sample, compared to the bottom region, the top region exhibits PL intensity reduction and redshift (Figure 2a), and E1 2g Raman mode redshift (Figure 2b), indicating this interlayer difference in all samples shares a common origin.

**Figure 2.** Photoluminescence and Raman spectra comparison between bottom (green) and top (magenta) layers. Bot and Top refer to bottom and top region, respectively. (**a**) PL spectra comparison. For clarity, spectra of one same tBLS sample are shifted vertically in small gap while spectra of different tBLS samples in large gap. Peak A and B are labeled. (**b**) Raman spectra comparison. Mode E1 2g and A1g are labeled.

#### *3.2. Spatial Inhomogeneity in BSS*

In addition, apart from the difference between the top and bottom layer, spatial inhomogeneity of PL emission and Raman scattering in the top region is prevalent among various BSM samples. Most importantly, it is found that, in many samples, area with lower PL intensity compared to the rest of the top region tends to emerge in the V-area. Another tBLS sample is shown in Figure 3, its PL intensity distribution on each region is consistent with the sample in Figure 1. It is noteworthy that an area (P2) outlined by pink dashed line in Figure 3c,e demonstrates identical PL intensity and E1 2g Raman shift with the V-area (P1) in this BSM sample. For more details, PL and Raman spectra on various regions are presented in Figure 3d,f respectively. Compared to the rest of the area of top region, PL emission of P1 and P2 demonstrates lower intensity and redshift, while Raman mode E<sup>1</sup> 2g also demonstrates redshift. Obviously, P1 and P2 are nearly same in PL and Raman spectra, implying identical exciton and phonon performance in these two regions. Moreover, though PL and Raman spectra in the V-area are remarkably different from rest of the top region (in Figures 1b–f and 3c,e), their corresponding AFM micrographs (Figures 1d and 3b) are spatially homogeneous. In contrast, the inhomogeneous area, with lower PL intensity, of bottom region (Figure 3c) matches exactly with the wrinkle and crack shown in the corresponding dark-field micrograph (Figure 3a inset). This implies that, the spatial inhomogeneity of PL and Raman spectra in top region is not due to abrupt variations in film morphology, like wrinkle, crack, and bubble.

**Figure 3.** Photoluminescence and Raman inhomogeneity of tBLS. (**a**) Optical micrograph of one tBLS sample. Corresponding dark-field optical micrograph is shown in inset. Bottom and top layers are outlined by green and white dashed lines, respectively. Red box defines the scanning area of (**c**,**e**). (**b**) AFM micrograph of the same sample in (**a**). (**c**) PL intensity map. (**e**) Raman shift map of mode E<sup>1</sup> 2g. (**d**,**f**) PL and Raman spectra of different regions. These regions are labeled by circles in corresponding colors in (**c**,**e**).

#### *3.3. PL and Raman of Freestanding MoS2*

Interlayer difference and spatial inhomogeneity of PL and Raman spectroscopy in BSS possibly come from substrate-coupling difference between the layers, and among the top layer, respectively. To confirm this, we fabricated a freestanding sample (in Figure 4a) by transferring monolayer MoS2 to SiO2/Si substrate with holes of diameter 300 nm. The suspended (SUS) area of this sample totally excluded the film–substrate interaction. In Figure 4b–f, we can see that the suspended region demonstrates great intensity enhancement in PL and Raman spectroscopy, compared to that of the supported (SUP) region. This can be attributed to constructive interference effect in the top region [51]. Moreover, compared to the supported region, the suspended region demonstrates redshift in PL

(Figure 4c,d) and Raman peaks (Figure 4g–i). This implies less p-doping and vibration mode softens in suspended region, which is consistent with the top region, P1 (V-area), and P2 in BSM. Therefore, similar to suspended region, we can assume that top region, V-area, and P2 might be less affected by substrate contact.

**Figure 4.** Free-standing monolayer MoS2. (**a**) Bright-field optical micrograph. Red box outlines the scanning area of the middle and right column. (**b**) PL intensity map. (**c**) PL shift map. PL and Raman spectra in (**d**,**g**) are normalized for clarity. (**d**) PL spectra of suspended and supported region. SUP and SUS refer to supported and suspended region, respectively. (**e**,**f**) Raman intensity map of E1 2g and A1g, respectively. (**g**) Raman spectra of suspended and supported region. (**h**,**i**) Raman shift map of E<sup>1</sup> 2g and A1g, respectively.

#### **4. Discussion**

A schematic illustration is shown in Figure 5a. According to our findings in Figure 4, less p-doping and vibration mode softening are observed in suspended region compared to its substrate-supported counterpart, which are also observed in top region, V-area, and P2 in BSM. Therefore, we speculate that, while bottom region and supported region are in strong coupling with the substrate, top region just like the suspended region is in intermediate or weak coupling with the substrate, thus leading to less carrier transfer and strain from substrate. In transferred-fabricated samples, this coupling mainly comes from Van der Waals bonding instead of chemical bonding [26,52]. In addition, as shown in Figure 5, there might be film morphology fluctuations in the top region, including ripple formed by strain and stair at the edge of the bottom region. Stair and ripple correspond to P1 (V-area) and P2 region in Figure 3 respectively. Though these film morphology fluctuations might be less than one nanometer (the order of monolayer MoS2 thickness), not sufficiently macroscopic to be detected by bright-field/dark-field optical microscope and atomic force microscopy, they can remarkably reduce film–substrate coupling.

**Figure 5.** Schematic illustration. (**a**) Film–substrate coupling difference among bilayer-stacked two-dimensional materials structure (BSS) films. (**b**) Three-level energy diagram including exciton, trion, and ground. G represents the generation rate of exciton. Γex, Γf, and Γtr represent exciton decay rate without trion formation rate, trion formation rate, and trion decay rate, respectively. (**c**) Schematic of in-plane Raman mode E1 2g for monolayer MoS2.

For one thing, PL emission of MoS2 is resulted from exciton (radiative wavelength: ~660 nm) and trion recombination (radiative wavelength: ~680 nm) [53]. According to related studies [24–26], the contribution ratio of exciton against trion determines the intensity and position of peak A. Since monolayer MoS2 is an n-type semiconductor, the silicon oxide depletes equilibrium electrons in regions of strong coupling with substrate [25], which stabilize the radiative recombination process of exciton (Γex) while suppressing the trion formation rate (Γf) at the same time, as is shown in Figure 5b. PL emission, in regions of strong coupling with substrate (e.g., bottom region), is exciton-dominant, thus demonstrating intensity enhancement and blueshift. In contrast, areas of less coupling with substrate, such as top region, ripple, and stair, where exciton contribution is reduced, are supposed to demonstrate lower intensity and redshift of PL.

For another, the in-plane Raman mode E1 2g corresponds to Mo and S atoms oscillating in the anti-phase parallel to the crystal plane, as shown in Figure 5c. As previously reported, E1 2g mode demonstrates redshift with uniform tensile uniaxial strain [21,22]. At the same time, it has been reported that film morphology fluctuations that lead to less coupling with substrate, like wrinkle and bubble, yield uniaxial tensile strain [54,55]. As a result, compared to the bottom region of strong substrate coupling, the top region of less substrate coupling is supposed to demonstrate E1 2g mode redshift caused by tensile uniaxial strain. Especially in ripple and stair regions, E1 2g is expected to demonstrate the strongest redshift.

The discussions above provide a reliable explanation for our findings. Admittedly, interference effects can induce intensity change of PL and Raman. However, on the one hand, the minor height fluctuations in BSS film cannot result in remarkable interference variations. On the other hand, interference-induced intensity change would be broad band, which is not consistent with our experimental results. Therefore, we conclude that substrate-coupling-induced strain and doping to BSS play the dominant part in interlayer difference and spatial inhomogeneity of phonon and exciton performance.

#### **5. Conclusions**

In summary, we conducted a systematic investigation on PL and Raman spectroscopy of bilayer-stacked MoS2 fabricated by the transfer method. PL and Raman spectroscopy of freestanding monolayer MoS2 are also measured for comparison. Interlayer difference and spatial inhomogeneity of exciton and phonon performance are experimentally observed in as-fabricated BSS samples, which we attribute to film–substrate coupling-induced strain and doping. Additionally, our findings prove that, even surface fluctuations less than one-atom-layer thickness can be easily identified by Raman and PL spectroscopy. This work will be of great use to inform future researches on BSS including tBLS, VdW homostructure and heterostructure, and improve our understanding of substrate effects on optical and transport properties of 2D materials.

**Author Contributions:** X.Z. (Xiangzhe Zhang) and R.Z. conceived and designed the experiments; X.Z. (Xiangzhe Zhang), X.Z. (Xiaoming Zheng), Y.Z. performed the experiments; S.Q., C.D., R.Z., H.Y. and X.Z. (Xueao Zhang) provided valuable suggestions; X.Z. (Xiangzhe Zhang) wrote the paper.

**Funding:** This work was supported by National Natural Science Foundation (NSF) of China (Grant No. 11802339, 11805276, 61805282, 61801498, 11804387, 11404399, 11874423, 51701237); Scientific Researches Foundation of National University of Defense Technology (Grant No. ZK16-03-59, ZK18-01-03, ZK18-03-36, ZK18-03-22); NSF of Hunan province (Grants No.2016JJ1021); Open Director Fund of State Key Laboratory of Pulsed Power Laser Technology (SKL2018ZR05); Open Research Fund of Hunan Provincial Key Laboratory of High Energy Technology (Grant No. GNJGJS03); Opening Foundation of State Key Laboratory of Laser Interaction with Matter (Grant No. SKLLIM1702); Youth talent lifting project (Grant No. 17-JCJQ-QT-004).

**Acknowledgments:** The authors would like to acknowledge professor Gang Peng for constructive suggestions. We also acknowledge Yuehua Wei for providing materials.

**Conflicts of Interest:** The authors declare no conflicts of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Direct Observation of Raman Spectra in Black Phosphorus under Uniaxial Strain Conditions**

#### **Stacy Liang, Md Nazmul Hasan and Jung-Hun Seo \***

Department of Materials Design and Innovation, University of Buffalo, Buffalo, NY 14260, USA; stacyli@buffalo.edu (S.L.); mhasan9@buffalo.edu (M.N.H.)

**\*** Correspondence: junghuns@buffalo.edu; Tel.: +1-716-645-1881

Received: 22 February 2019; Accepted: 25 March 2019; Published: 8 April 2019

**Abstract:** In this paper, we systematically studied the Raman vibration of black phosphorus (BP) transferred onto a germanium (Ge)-coated polydimethylsiloxane (PDMS) substrate, which generates a much higher contrast in BP. This engineered flexible substrate allowed us to directly observe a much thinner BP layer on the flexible substrate at the desired location. Therefore, it enabled us to perform Raman spectroscopy immediately after exfoliation. The Raman spectra obtained from several BP layers with different thicknesses revealed that the clear peak shifting rates for the Ag 1, B2g, and Ag 2 modes were 0.15, 0.11, and 0.11 cm<sup>−</sup>1/nm, respectively. Using this value to identify a 2–3-layered BP, a study on the strain–Raman spectrum relationship was conducted, with a maximum uniaxial strain of 0.89%. The peak shifting of Ag 1, B2g, and Ag <sup>2</sup> caused by this uniaxial strain were measured to be 0.86, 0.63, and 0.21 cm<sup>−</sup>1/Δε, respectively.

**Keywords:** black phosphorus; uniaxial strain; flexible substrate

#### **1. Introduction**

Strain engineering has been known as an effective way to modulate the electronic, transport, and optical properties of semiconductors [1–4]. This method is particularly powerful when engineering low-dimensional semiconductors, such as one- and two-dimensional semiconductors (1D and 2D, respectively), since these low-dimensional semiconductors can tolerate much higher strain levels than three-dimensional (3D) semiconductors, such as bulk or thin-films [5,6]. For example, graphene is known to sustain strains of up to 15% without any noticeable damage to its crystalline structure [6,7]. As a result, strain engineering is a viable way to tune low-dimensional semiconductors' electrical, optical, chemical, and mechanical performances [8–12].

Recently, black phosphorus (BP, also known as phosphorene) was mechanically exfoliated from its bulk format [13–15]. Unlike the widely studied graphene, BP exhibits a finite and direct band gap varying from 0.5 eV in bulk to ~1.2 eV for a single layer, and its free-carrier mobility (approximately 1000 cm2/v·s) is better than that of other typical 2D semiconductors, such as molybdenum sulfate (MoS2; approximately 200 cm2/v·s) [16–19]. As a result, various optoelectronic applications such as photodetectors and field-effect transistors, have been recently demonstrated [20–23]. Another attractive property of BP is its wide range of band gap tunability by mechanical strain. It is predicted that the band gap of BP can be modulated from as low as 0.55 eV up to 1.1 eV, while still maintaining a direct band gap by the application of ±8% of mechanical strain [24–26]. Such a wide tunability in the band gap of BP from 0.55 eV to 1.1 eV corresponds to the 1000 nm to 2200 nm wavelength range, suggesting that BP can be used as an active material for the near-infrared tunable light source. For this reason, there have been several theoretical and empirical attempts to demonstrate the characteristics of BP under strain conditions [27,28]. However, most of the experiments on the strain properties of BP have used thick BP (>10 nm thickness), because the visibility of BP decreases dramatically as it

becomes thinner (similar to other 2D materials). For example, 13 nm- and 15 nm-thick BP (>20 layers) were used in the studies by Zhu et al. to examine the mechanical robustness of flexible BP devices under bending conditions. Material characterization studies of few-layered BP directly on a flexible substrate under strain conditions have not been performed so far.

In this paper, we investigated the strain dependence of the Raman characteristics of BP, taken directly from a flexible polymer substrate, enabled by a thin layer of germanium (Ge) coated on the backside of the polymer. This thin Ge contrast booster reflector on the backside of the polymer substrate provided a much higher contrast in BP and allowed us to investigate BP at the desired location with specific thicknesses. Also, our structure allowed us to perform Raman spectroscopy immediately after exfoliation and to perform Raman characterization faster avoiding the structural degradation caused by environmental factors, such as oxidation, which can potentially cause unintended Raman shifts.

#### **2. Materials and Methods**

Figure 1 shows a schematic illustration of the preparation of the BP sample. The BP sample (purity of 99.9999%) was purchased from 2D Semiconductors USA Inc (Scottsdale, AZ, USA). The process started with mechanical exfoliation from the bulk BP using a well-known micromechanical cleavage technique (also known as the "Scotch-tape" method), which is commonly used to create other 2D semiconductors from their bulk formats (Figure 1(i)) [29]. In this step, thin layers of BP that were a few nanometers thick were obtained. The thin BP layers were then carefully placed onto an ultrathin (>30 um) polydimethylsiloxane (PDMS) substrate prepared by spin-coating on a Petri dish (Figure 1(ii,iii)). Prior to the BP transfer step, a thin Ge layer (200nm) was deposited on the backside of the PDMS substrate using an e-beam evaporation method, which significantly enhanced the reflection of BP on the PDMS substrate. As shown in Figure 1(iv), once the transfer process was completed, the samples were immediately characterized under different strain conditions within 10 min to avoid unwanted BP degradation. Also, we prepared new samples each time we performed Raman spectroscopy under different strain conditions to maintain a high BP quality.

**Figure 1.** A schematic illustration of the sample preparation process on a Ge-coated polydimethylsiloxane (PDMS) substrate. (**i**) Mechanical exfoliation of black phosphorus (BP) flakes from bulk BP using blue tape, (**ii**) pick-up process of exfoliated BP flakes from the blue tape, (**iii**,**iv**) a transfer process of BP flakes onto the Ge-coated PDMS substrate, (**v**) cross-sectional view of the final structure under bending conditions.

#### **3. Results and Discussion**

#### *3.1. Structure Analysis by Optical Simulation*

In most of the 2D materials, it is well known that mono- or few-layered 2D materials are visible only when they are transferred onto a specific substrate that has particular refractive index and dielectric constant. Figure 2a,b show the relationship between the simulated reflectance versus wavelength of BP on a thin PDMS substrate (with and without Ge-coating on the PDMS substrate) as a function of BP thickness. To simulate the contrast enhancement of the BP layer obtained by employing the Ge-coated PDMS substrate and compare it with that of the reference bare PDMS substrate, we calculated the reflection of the multi-layered structure (BP/PDMS/Ge) using the Fresnel equation and Snell's equation [30]. The light reflected by an interface is determined by the discontinuity components of the two materials. For multiple interfaces, the total amount of reflected light is the sum of individual reflections. Depending upon their phase relationships, the reflections from the interfaces can be calculated using Equation (1) [30]:

$$R = \frac{(n-2)^2 + k^2}{(n+2)^2 + k^2} \tag{1}$$

where *n* is the refractive index, and *k* is the absorptance of the film. The optical contrast (*Cλ*) is the fractional change of reflection because of the presence of the Ge layer on the substrate and is defined by Equation (2) [31]:

$$C\_{\lambda} = \frac{R\_{BPonPDMS} - R\_{Ge+BPonPDMS}}{R\_{Ge+BPonPDMS}} \tag{2}$$

where *RGe + BPonPDMS* and *RBPonPDMS* are the reflected intensities collected from the Ge-coated PDMS substrate and the reference PDMS substrate, respectively. Therefore, when we designed the substrate structure, we carefully checked the reflective index of each layer, since the visibility (i.e., the contrast of BP) can be enhanced or reduced depending on the reflective index (*n*). In our case, the refractive indices of 3.1 and 1.4 for BP and PDMS, respectively, were used in the calculation. However, any materials that have a high-reflective index, such as Si (*nSi* = 4.1), can also enhance the contrast of BP, although Ge has better optical and process advantages (higher reflective index and easier to deposit at a lower temperature) compared to Si. The simulated reflectance clearly indicated that the reflectance of BP was nearly invisible (<5%) when the thickness of the BP was less than 3.5 nm (i.e., five layers), which agrees well with experimental observations [19]. On the other hand, as shown in Figure 2b, the simulated reflectance of BP on a thin Ge-coated PDMS substrate showed a significantly enhanced reflectance, namely, 37%, 20%, 9%, and 4.5% for 7, 3.5, 2.1, and 0.7 nm-thick BP, respectively. Interestingly, the peak wavelength shifted to a shorter wavelength as the thickness of BP was reduced. For example, the peak wavelength that appeared at 480 nm for the 7 nm-thick BP appeared at 410 nm for the 0.7 nm-thick BP. This simulated color shift was also observed in our experiment, as shown in Figure 2c. As shown in Figure 2d, an atomic force microscopy (AFM) analysis was carried out using a Bruker AFM system with non-contact mode from the 20 mm × 20 mm area to prevent any possible damage to the sample during surface profiling. The layer thickness profile also matched well with the simulated thickness–color relationship. In other words, the wavelength changed depending on the refractive index and thickness of the thin film: 2·*t* = *m*·λ/*n*film, where λ is the wavelength of the reflected light, and m is an integer. When the refractive index is fixed, as in our case, this equation can be rewritten as 2·*t* = *m*·λ/*n*film, which shows a proportional relationship between the thickness of a thin film (*t*) and the wavelength (λ). As simulated and experimentally verified, we observed the wavelength shift to a lower wavelength as the thickness of the BP layer decreased. This thickness–wavelength shifting relationship was stronger when the refractive index was higher.

**Figure 2.** Simulated reflectance of BP on (**a**) a typical PDMS substrate (~30 um) and (**b**) a Ge-coated PDMS substrate (30 um + 200 nm). The inset of Figure 2a is the log-scale reflectance of BP to show the details of reflectance. (**c**) Microscopic image showing typical BP flakes on a Ge-coated PDMS substrate. (**d**) (lower) AFM surface profile between point A and B. (upper) The scanned area is shown.

Therefore, it is clear that the thin Ge-coated PDMS substrate improved the reflectance of BP enough to directly observe its crystal shapes under the microscope. Such high contrast also allowed us to find the same location in Raman spectroscopy during strain characterization, as described below.

#### *3.2. Characterization of the Relationship between Raman Spectraand Thickness in BP*

In order to investigate the crystalline quality of BP, Raman spectroscopy was performed using Renishaw Raman spectroscopy. The excitation was provided by a linearly polarized 514 nm excitation laser along a zigzag direction with a 50× objective lens. The diameter of the laser spot was 1 μm. In order to avoid BP ablation caused by laser-induced heating, all Raman spectra were recorded at a low laser power (200 uW) with an exposure time of 10 s and accumulations of 10 times. Figure 3a shows the Raman spectra of transfer-printed BP ranging from 150 nm to 3 nm on a Ge-coated PDMS substrate. Figure 3a represents the Raman spectra of BP layers with different thicknesses ranging from 360 cm−<sup>1</sup> to 480 cm<sup>−</sup>1. In each spectrum, three Raman modes were present at 360 cm−1, 436 cm−1, and 464 cm−1, each of which was assigned a unique phonon mode of BP: (1) Ag 1, (2) B2g, (3) and Ag <sup>2</sup> [19,32,33]. Since the observed BP phonon modes matched the phonon modes seen in their bulk form (centered at 361 cm−1, 438 cm−1, and 466 cm−1), the Raman spectra confirmed that the lattice of BP was retained during the exfoliation step. Also, when we performed Raman spectroscopy, we investigated the edge of the BP flake and confirmed the armchair direction by comparing the relative peak intensity of the Ag 1, B2g, and Ag <sup>2</sup> phonon modes. Once we confirmed the direction of the BP edge, the sample was rotated 90 degrees and attached to the metal mold to perform a Raman spectroscopy under bending conditions. Figure 3b–d shows each phonon mode of BP as its thickness was reduced from 150 nm to 3 nm. All of the Raman phonon modes (Ag 1, B2g, and Ag 2) demonstrated blue-shifting as the thickness increased. Figure 3b–d presents the overlay peak positions of the Ag 1, B2g, and Ag <sup>2</sup> phonon modes as a function of the wavenumber, which showed a noticeable peak shifting. Figure 4a–c represents

the trend in Ag 1, B2g, and Ag <sup>2</sup> Raman peaks as a function of their thickness. The blue dotted lines in Figure 4 show the polynomial extrapolation of the measured data points. The peak wavenumbers of the Ag 1, B2g, and Ag <sup>2</sup> modes reached 364 cm−1, 442 cm−1, and 469 cm−1, as BP became a monolayer. The peak positions of the Ag 1, B2g, and Ag <sup>2</sup> modes gradually decreased until the thickness of BP reached about 40–50 nm. As shown in Figure 4, all the Ag 1, B2g, and Ag <sup>2</sup> phonon modes were saturated when thicker than 40–50 nm; therefore, the BP thickness of 40–50 nm was a transition point at which the bulk property became dominant. We also noticed that the three Raman modes (Ag 1, B2g, and Ag 2) had different sensitivities to their thicknesses; in other words, the peak shifting rates for the Ag 1, B2g, and Ag <sup>2</sup> modes were 0.15 cm−1/nm, 0.11cm−1/nm, and 0.11cm−1/nm, respectively. The slightly higher shifting rate in the Ag <sup>1</sup> mode could be explained by the stiffer Ag1 vibration with increasing BP thickness. Therefore, the peak distance between the Ag <sup>1</sup> modes and B2g or Ag <sup>2</sup> modes, namely, the difference in their frequencies (Δω), could be used as an effective thickness indicator in order to examine the thickness of BP layers.

**Figure 3.** (**a**) Raman spectra of BP taken at different thicknesses from 150 nm to 3 nm. (**b**–**d**) Magnified Raman spectra of the Ag 1, B2g, and Ag <sup>2</sup> Raman modes as a function of their thickness.

**Figure 4.** Peaks of (**a**) Ag 1, (**b**) B2g, and (**c**) A2 g Raman modes as a function of their thickness.

*3.3. Characterization of the Raman vs Strain Relationship of BP*

After we confirmed the crystalline quality and thickness of BP layers, we performed a strain–Raman relationship spectral study to investigate the Raman shifts under different uniaxial strain conditions. On the basis of the results shown in Figures 2 and 3, the thickness of BP for the strain-Raman relationship spectrum study was found to correspond to 2–3 layers. In order to accurately measure the changes in the Raman spectrum under uniaxial strain conditions, we employed convex

and concave molds that have different curve radii ranging from 110 mm to 20 mm, which corresponded to uniaxial strains of up to 0.89% of the tensile strain (for the convex mold) and up to 0.24% of the compressive strain (for the concave mold). The strain-dependent characteristics of the Ag 1, B2g, and Ag 2 modes are shown in Figure 5. While the three different modes showed the same qualitative behavior with respect to the applied strains and exhibited a linear increase (blue shift), the rate of increase was different for each phonon mode. In order to examine the degree of peak shifting, the peak shift as a function of strain was plotted, as shown in Figure 6. The peak shifting values of Ag 1, B2g, and Ag 2 were measured to be 0.86 cm−<sup>1</sup> /Δε, 0.63 cm<sup>−</sup>1/Δε, and 0.21 cm<sup>−</sup>1/Δε, respectively. The out-of-plane Ag <sup>1</sup> mode resulted from the opposing vibrations of the top and bottom P atoms with respect to each other within the same layer. The B2g, and Ag <sup>2</sup> modes were associated with the in-plane vibration of the P atoms in different directions [34,35]. Therefore, it is reasonable to assume that the Ag <sup>1</sup> mode was slightly more sensitive under bending conditions, because the crystal distortion in the vertical direction was more than in the horizontal direction under uniaxial strain. However, these measured slopes were smaller than in the other BP strain studies. It is speculated that the difference derives from the vibrational interaction and light diffraction between BP and the substrate, which was also observed in the other two-dimensional materials [36].

**Figure 5.** (**a**) Raman spectra of BP measured under uniaxial strains of up to 0.89% of the tensile strain (for the convex mold) and up to 0.24% of the compressive strain. (**b**–**d**) Magnified Raman spectra of the Ag 1, B2g, and Ag2 Raman modes as a function of the applied strain.

**Figure 6.** P peaks of (**a**) Ag 1, (**b**) B2g, and (**c**) Ag <sup>2</sup> Raman modes as a function of the applied strain.

#### **4. Conclusions**

In summary, we have systematically studied the Raman vibration of BP transferred onto a Ge-coated PDMS substrate, which provided a much higher BP contrast in BP compared to the uncoated substrate and allowed us to investigate much thinner layers of BP directly on a flexible substrate. The Raman spectra taken from several BP layers with different thickness revealed that the clear peak shifting rates for the Ag 1, B2g, and Ag <sup>2</sup> modes were 0.15 cm−1/nm, 0.11 cm−1/nm, and 0.11 cm−1/nm, respectively. Also, the full width at half maximum (FWHM) of all three Raman phonon modes increased as the thickness of the BP layer decreased. Particularly, the peak of the Ag 2 mode increased faster than those of the Ag <sup>1</sup> and B2g phonon modes, indicating that Raman spectra provide a simple way to identify the number of layers of BP. Using this parameter to identify the 2–3-layered BP, a stain–Raman relationship spectrum study was conducted with a maximum uniaxial strain of 0.89%. The peak shifting values of the Ag 1, B2g, and Ag <sup>2</sup> modes by uniaxial strain were measured to be 0.86 cm<sup>−</sup>1/Δε, 0.63 cm<sup>−</sup>1/Δε, and 0.21 cm<sup>−</sup>1/Δε, respectively. Therefore, the phonon mode peak shifting is a good indicator to gauge strain information.

**Author Contributions:** All authors performed the research. J.-H.S. conceived the idea and designed and managed the research. S.L. and M.N.H. conducted the experiments. S.L. and J.-H.S. wrote the paper.

**Funding:** This work was supported by the University at Buffalo Innovative Micro-Programs Accelerating Collaboration in Themes (IMPACT) program and the New York State Center of Excellence in Materials Informatics (CMI) program.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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