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Fabrication and Raman study of twisted stacked few layer black phosphorus Fang, Tao 2018

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    Fabrication and Raman Study of Twisted Stacked Few Layer Black Phosphorus  by Tao Fang B. Sc, Nanjing University, Nanjing, China, 2016   A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in The Faculty of Graduate and Postdoctoral Studies  (Physics)  The University of British Columbia (Vancouver) August 2018 ⓒTao Fang, 2018   ii  The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled: Fabrication and Raman Study of Twisted Stacked Few Layer Black Phosphorus submitted by  Tao Fang   in partial fulfillment of the requirements for the degree of      Master of Science                                                         in   Physics    Examining Committee: Mona Berciu, Physics and Astronomy             Co-supervisor Guangrui Xia, Materials Engineering                               Co-supervisor ______________________________                                  Supervisory Committee Member _______________________________                                 Additional Examiner Additional Supervisory Committee Members: _______________________________                                Supervisory Committee Member _______________________________                                Supervisory Committee Member  iii   Abstract    Two-dimensional black phosphorus (BP) has attracted much interest as a promising semiconductor with a tunable direct bandgap of 0.3-2 eV, depending on its thickness. However, BP-based heterostructures, such as van der Waals junctions, and their interlayer couplings have not been well studied.    In this work, we first provided a new“film-based” transfer method, which can be used to transfer BP to specific positions. This is a very convenient transfer method for BP, since commonly used dry transfer and wet transfer methods do not work well for BP.    Based on this new method, we successfully fabricated twisted stacked few layer BP with different twist angles (7 to 90 degrees) and thicknesses (10 -30 nm). Raman measurements revealed an “abnormal blue shift” for the twisted few-layer BP. Density functional theory (DFT) calculations by Teren Liu provided an explanation for this phenomenon in terms of changes in charge distributions. Based on the calculated charge distributions, we propose that the interlayer coupling in BP is not just through van der Waals interactions. Other interactions, such as weak valence bond, may exist in this system.      iv   Lay Summary    Two-dimensional black phosphorus (BP) is a promising semiconductor that is atomically thin. For such thin layers, it is very hard to stack one layer on top of another layer. However, these stacked structures are quite useful for optical and electrical applications. Stacked BP had not been realized until we developed a new transfer method that allows us to stack one BP flake on another one. We also found that the lattice vibrations of the stacked structures are different from those of the unstacked ones. Computer simulations suggest that this difference may be a result of new bonding formed in these structures.            v   Preface    The author and Guangrui Xia initiated the project. Mona Berciu approved the project and helped the author apply for QMI fellowship. The author designed the experiments. The author and Rui Yang made BP samples. The author and Teren Liu carried Raman and AFM measurements. Teren Liu and the author did DFT calculations. The project was supervised by Guangrui Xia and Mona Berciu.   Two conference presentations were based on chapter 2 and 3.   1. Tao Fang, Teren Liu, Zenan Jiang, Rui Yang, Peyman Servati, Joshua Folk, Mona Berciu and Guangrui (Maggie) Xia, Observation of abnormal blue shift in Raman spectra for twisted few-layer black phosphorus, the 9th International SiGe Technology and Device Meeting (ISTDM), Potsdam Germany, May 2018.   2. Tao Fang, Rui Yang, Zenan Jiang, Teren Liu, Peyman Servati, Joshua Folk, Mona Berciu and Guangrui (Maggie) Xia, Fabrication of twisted stacked black phosphorus, accepted for oral presentation at American Physics Society March Meeting 2018, Session P36, Los Angeles, CA, USA.   One journal article manuscript was submitted to arxiv.org based on chapter 2 and 3.    Tao Fang, Teren Liu, Zenan Jiang, Rui Yang, Peyman Servati, Guangrui (Maggie)Xia Interlayer coupling effect in twisted stacked few layer black phosphorus revealed by abnormal blue shifts in Raman spectra arXiv link: https://arxiv.org/abs/1805.01135  vi   Table of Contents  Abstract…………………………………………………………………………………iii Lay Summary……………………………………………………………………………iv Preface…………………………………………………………………………………….v Table of Contents………………………………………………………………………..vi List of Tables…………………………………………………………………………...viii List of Figures……………………………………………………………………………ix Glossary………………………………………………………………………………….xi Acknowledgements……………………………………………………………………..xii 1. Introductions……………………………………………………………………........1 1.1 Background information…………………………………………............................1   1.2 Fabrication and processing of large scale few layer crystalline black phosphorus…………………………………………………………………….........6   1.3 Basic principles of Raman scattering……………………………………………...15 2. A modified transfer method for black phosphorus………………………………17   2.1 Wet transfer………………………………………………………………………..18   2.2 Dry transfer………………………………………………………………………..19   2.3 Film based transfer………………………………………………………………...20 3. The abnormal blue shift in twisted stacked few layer black phosphorus….........23   3.1 Analogy to other stacked 2D materials……………………………………………24   3.2 High frequency Raman modes in BP……………………………………………...26   3.3 The abnormal blue shift in twisted stacked BP……………………………………28   3.4 Superlattice in twisted bilayer BP…………………………………………………32   3.5 DFT calculation results (provided by Teren Liu).………………………………...33  vii    3.6 Discussions and explanations……………………………………………………..35 4. Conclusions and insights…………………………………………...........................38 Bibliography…………………………………………………………………………….39                    viii   List of Tables  Table 1.1 Lattice constants of BP………………………………………………………... 2 Table 1.2 Comparison of different fabrication methods of BP………………………….12 Table 3.1 DFT calculation results of untwisted bilayer BP and twisted bilayer BP.........33                  ix   List of Figures  Figure 1.1 Illustration of BP structure……………………………………………….........2 Figure 1.2 The first BP based transistor…………………………………………………..3 Figure 1.3 Band gap of BP and other materials…………………………………………..4 Figure 1.4 Phonon dispersion curves for bulk BP………………………………………5 Figure 1.5 Light absorption of BP with different thicknesses……………………….........6 Figure 1.6 Image of first BP based field transistor……………………………………….7 Figure 1.7 Image of a large flake of BP…………………………………………………..8 Figure 1.8 Numerical simulation and experimental work on liquid phase exfoliation of BP………………………………………………………………………………………….9 Figure 1.9 Size of BP made from liquid phase exfoliation……………………………...10 Figure 1.10 Size selection process of BP………………………………………………..11 Figure 1.11 Few-layer BP prepared by chemical vapor deposition (CVD) method.........12 Figure 1.12 Few-layer BP prepared by plasma thinning………………………………..13 Figure 1.13 The picture of the layer-by-layer nano-patterning and thinning……………14 Figure 1.14 Illustration of thermal sublimation of BP…………………………………..14 Figure 1.15 Energy level diagram in Raman scattering…………………………………15 Figure 2.1 Illustration of a typical wet transfer method…………………………………18 Figure 2.2 Experimental instrument and illustration of dry transfer….............................19 Figure 2.3 Optical image of twisted stacked few layer BP……………………………...21 Figure 2.4 Comparison of TEM diffraction pattern in Ref. [28] (left panel) and my results (right panel)………………………………………………………………………22 Figure 3.1 Raman spectra of twisted bilayer graphene on a Si/SiO2 substrate…….........24 Figure 3.2 Raman shifts of twisted bilayer MoSe2……………………………………...25 Figure 3.3 Illustration of three high frequency Raman active phonon modes in BP……27  x  Figure 3.4 Raman spectra of top flake, bottom flake and stacked flakes in sample shown in Figure 2.3……………………………………………………………………………...28 Figure 3.5 Twist angle characterization by angle-resolved polarized Raman spectroscopy (ARPRS)…………………………………………………………………………………29 Figure 3.6 Blue shift value versus twist angle in mode Ag1……………………………..30 Figure 3.7 Blue shift value versus twist angle in mode B2g…………………...………...30 Figure 3.8 Blue shift value versus twist angle in mode Ag2…………………...………...31 Figure 3.9 Crystal structure of 70.53°twisted bilayer black phosphorus and unit cell of 70.53°twisted bilayer black phosphorus…………………………………………………33 Figure 3.10 3D charge density map in unit cell of untwisted bilayer black phosphorus and 70.53° twisted bilayer black phosphorus……………………………………………34 Figure 3.11 2D charge density map in the cutting plane of untwisted bilayer black phosphorus and 70.53° twisted bilayer black phosphorus………………………….........34 Figure 3.12 Another 2D charge density map in the cutting plane (100) of twisted bilayer black phosphorus…….......................................................................................................35           xi   Glossary  2D  2-Dimensional 3D  3-Dimensional AFM  Atomic Force Microscopy ARPRS  Angle-resolved Polarized Raman Spectroscopy BP  Black Phosphorus CVD  Chemical Vapor Deposition DI  Deionized PC  Polycarbonate PDMS  Polydimethylsiloxane PMMA  Polymethyl Methacrylate PVA  Polyvinyl Alcohol SEM  Scanning Electron Microscope TEM  Transmission Electron Microscope TMDS  Transition Metal Dichalcogenides     xii   Acknowledgements  I would like to express my sincere gratitude to my supervisors Prof. Guangrui (Maggie) Xia and Prof. Mona Berciu. It is my honor to become their master student. Prof. Xia has a high standard toward her students, and I need to try my best to reach her demand of “high quality work”. Prof. Berciu is very virtuous and kind-hearted. Under their supervision, my master research has been productive and enjoyable.  Also, I would like to thank Prof. Joshua Folk, who provides the transfer stage for my experiment. I would like to thank Prof. Karen Kavanagh in at Simon Fraser University and Prof. Peyman Servati in Department of Electrical and Computer Engineering, University of British Columbia for their help in my BP research.   I would like to thank my groupmate Teren Liu who did DFT calculations to support my research. These results are compiled in Chapter 3.5. I would like to acknowledge my groupmates Yunlong Zhao, Guangnan Zhou and Jiaxin Ke. I would like to thank my friend Qian Song who helped me to initiate the project. I would like to acknowledge the Stewart Blusson Quantum Matter Institute (QMI) for funding me.   Last but not least, I would like to thank my family who supported my life and study. Your support encourages me to work hard and fulfill my dream. 1    Chapter 1 Introductions   This chapter provides basic knowledge and information about black phosphorus, including its emergence, crystal structure and fabrication. At the end of this chapter, we will discuss the principles of Raman spectra.  1.1 Background Information Two dimensional (2D) materials, starting from graphene [1], including black phosphorus (BP) [2], boron nitride (BN) [3] and transition metal dichalcogenides (TMDs) [4], have been widely studied recently because of their unique properties and potentially extensive applications. 2D black phosphorus is of particular interest because of its tunable direct bandgap, high carrier mobility and anisotropy along the two in-plane directions. Black phosphorus has a layer structure, which means phosphorus atoms are strongly bonded in-plane while the layers interact weakly through van der Waals forces. BP has an orthorhombic lattice, where each unit cell has four atoms and the space group is Cmca. Table 1.1 and Figure 1.1 below indicate some crystal structural parameters of BP in normal conditions [5].  2   Figure 1.1 (a) A part of one layer BP. (b) The projection of two adjacent layers on x-y plane. The parameters d1, d2 and α1, α2 are corresponding lattice constants in table 1.1. Figure is reprinted from Ref. [5] with permission. ⓒ (1986) The Physical Society of Japan.  Table 1.1 Corresponding lattice constants for Figure 1.1. Table is reprinted from Ref. [5] with permission. ⓒ (1986) The Physical Society of Japan.  The positions of phosphorus atoms in the unit cell are ± (uc, 0, vb) and (0.5c, 0, 0.5b) ± (uc, 0, -vb), where u and v are the structural parameters listed in Table 1.1. The structure has inversion symmetry about the middle points between atoms 1 and 2 and between 8  3  and 9.  Bulk BP was first synthesized in 1914 by applying a pressure of 1.2 GPa at an elevated temperature of 200 °C on white phosphorus (an allotrope of phosphorus) [6]. In 2013, Li et al [7] first reported the successful isolation of few-layer black phosphorus and the fabrication of a BP based field-effect transistor (Figure 1.2). After that, few layer black phosphorus attracted wide interest as a new promising 2D semiconductor material.   Figure 1.2 The first BP based transistor. Figure is reprinted from Ref. [7] with permission.  BP has a direct band gap at the Γ point of the Brillouin zone. This is different from graphene (which has no bandgap) and other semiconducting transition metal dichalcogenides (TMDs) such as MoS2, WS2 and WSe2 [8-9]. In Figure 1.3 [10], we compare the bandgap of BP with other major 2D materials and bulk semiconductors. The  4  2.05eV band gap of single layer BP has been measured by scanning tunneling spectroscopy (STS) [11], while the bandgap of 0.3 eV for bulk BP (thickness > 20 nm) has been established both theoretically and experimentally [5, 7]. Figure 1.4 shows the phonon dispersion curves for bulk BP.  Figure 1.3 Band gap of BP and other materials. BP bridges the gap between graphene and transition metal dichalcogenides (TMDs). Figure is reprinted from Ref. [6] with permission.  5   Figure 1.4 Phonon dispersion curves for bulk BP. Figure is reprinted from Ref. [5] with permission. ⓒ (1986) The Physical Society of Japan.  Because of its structure, BP has strong in-plane anisotropies in its transport and optical properties and Raman response. For example, as shown in Fig. 1.5, the light absorption edges vary from 1.55 eV (single layer BP) to 0.46 eV (bulk BP) in the armchair direction, while those for the zigzag direction vary from 3.14 eV (single layer BP) to 2.76 eV (bulk BP) [12].   6   Figure 1.5 Light absorption spectra of BP. Here x is armchair direction while y is zigzag direction. Figure is reprinted from Ref. [12] with permission.  1.2 Fabrication and Processing of Large Scale Few Layer Crystalline Black Phosphorus Currently, there are two major challenges in the study of BP. The first is the degradation of BP, which has been widely studied. For instance, Luo et al [13] discovered that with 5% oxygen/Ar or 2.3% H2O/Ar, the oxidation rate was < 5Å for 5h. In other words, it is safe to use bulk BP (thickness > 25 nm) within one day. Another challenge is the fabrication of large-scale few-layer crystalline BP. So far, three main methods were used to fabricate BP, but all of them have some disadvantages and only make raw products, which need to be further processed. These three methods are as follows.     7  (1) Mechanical Exfoliation Mechanical exfoliation is the most traditional way to make two dimensional materials, such as graphene. [14] Also, the first BP based field effect transistor was fabricated on a 6.5-nm-thick mechanically fabricated black phosphorus flake. (Figure 1.6) [7]  Figure 1.6 Image of first BP based field transistor. Figure is reprinted from Ref. [7] with permission.  We proposed a better way to fabricate large flakes of black phosphorus mechanically. This is by using PDMS as a sticker, sticking BP on Cleanroom tape and then transferring it onto a silicon substrate. The key is selecting a different kind of tape. In former work, Scotch tape and Nitto tape were used, which were not very successful in getting large flakes as the resulting flakes are less than 1000 μm2. In contrast, the size of BP flakes could reach up to 10000 μm2 by using Cleanroom tape. (Figure 1.7)  8   Figure 1.7 Image of a large flake of BP. The green area is the thinnest part of the BP flake. (Thickness around 20 nm from color-thickness relation)  However, the problem of mechanical exfoliation is the poor scalability and uniformity. As a result, samples made from mechanical fabrication need to be further processed, and we will discuss later on.  (2) Liquid Phase Exfoliation Liquid phase exfoliation is another common way to fabricate BP. This method has been studied thoroughly from many aspects, such as the influence of the solvent, the sonication time and even numerical simulations were performed [15-16]. Figure 1.8 below briefly summarizes the results of former research.  9   Figure 1.8 Numerical simulation and experimental work on liquid phase exfoliation of BP. Figure is reprinted from Ref. [15] and Ref. [16] with permission.  The liquid phase exfoliation process has the following steps: dissolving the BP in solvent, sonication, centrifugation, dropping it on substrate and removing the solvent residue. The major problem for liquid phase exfoliation of BP is that the final product is far from satisfactory in terms of flake size. In Ref. [16], the authors tried many organic solvents, including methanol, ethanol, acetone, 2-prapanol, dimethyl sulfoxide (DMSO), dimethyl formamide (DMF), 1,2-dichlorobenzene, N-vinylpyrrolidone and N-cyclohexyl-2-pyrrolidone. DMF and DMSO are the best solvents reported so far, but even with DMSO, the size of the resulting flakes is less than 2 μm, see Figure 1.9.   10   Figure 1.9 Size distribution of BP flakes made from liquid phase exfoliation. Figure is reprinted from Ref. [16] with permission.  Further research produced a size selection method. [17] With this method, we can control the time for sonication and centrifugation, and use sediment instead of supernatant to obtain a larger size. However, the size is still less than 5 μm, which makes it very difficult for applications. Figure 1.10 shows the size selection process and the final products.  11   Figure 1.10 Size selection process of BP. Figure is reprinted from Ref. [17] with permission.  In summary, liquid-phase exfoliation is an immature method that needs to be developed further. However, if one just needs to make small pieces of BP (such as for quantum dots), this is a good method.  (3) Chemical Vapor Deposition (CVD) Chemical vapor deposition has proved to be an effective method to make graphene and other two dimensional materials [18]. The research for CVD BP has started only very recently. In 2016, Smith et al successfully made few-layer BP by the chemical vapor deposition (CVD) method, [19] though the product had poor uniformity, and the resulting flakes were still rather small. (Figure 1.11)  12   Figure 1.11 Few-layer BP prepared by the chemical vapor deposition (CVD) method. (a): the SEM profile of the final product; (b): the comparison of the Raman spectra of the exfoliated BP, prepared amorphous BP and CVD BP. This shows that the product is not sufficiently crystalline. Figure is reprinted from Ref. [19] with permission.  A brief description of the CVD process is as follows: an amorphous red phosphorus film is first grown on a clean surface in a vacuum environment. Then, Sn/SnI4 mixture was used as a catalyst to transform amorphous red phosphorus into black phosphorus. However, Raman spectra of the final product indicate that it is not sufficiently crystalline nor uniform, see Figure 1.11. Table 1.2 below gives a comparison of the three different fabrication methods.  Size Thickness Size selection Uniformity Mechanical exfoliation Large (~100 μm) >10 nm (> 12 layers) By chance and depends on operation proficiency Liquid phase exfoliation Small (<5 μm) Small (few layer) Yes Yes Chemical vapor deposition Small (<10 μm) N/A (not uniform) Yes No Table 1.2 Comparison of different fabrication methods of BP  (a) (b)  13  In summary, so far none of the fabrication methods for BP is perfect and BP products made by these methods need to be processed. Another important item is controlling the thickness of BP, as the band gap is dependent on BP thickness. Currently, three different thinning methods are available for black phosphorus, namely plasma thinning, local anodic oxidation with water rinsing and thermal sublimation [20-22]. However, none of them could ensure a stable product (Figure 1.12-1.14). Also, BP transferring is another challenging problem, which we will discuss more in the next chapter.   Figure 1.12 Few-layer BP prepared by plasma thinning. The size of the plasma beam and defects introduced by Ar+ plasma bombardment may reduce the uniformity and crystallinity of products. Figure is reprinted from Ref. [20] with permission.    14   Figure 1.13 The AFM picture of the layer-by-layer nano-patterning and thinning. This method is very expensive, and the thinning rate is very time-consuming. Even its author did not make few layer products. Figure is reprinted from Ref. [21] with permission.   Figure 1.14 Illustration of the thermal sublimation of BP. The sublimation thinning depends on the quality of the pre-thinned BP flake. Figure is reprinted from Ref. [22] with permission.     15   1.3 Basic Principles of Raman Scattering Raman scattering is a widely used characterization method for materials.  It was first discovered by C. V. Raman [23]. It is based on second order light reflection. When a laser beam passes through a material, most of the photons are scattered without any energy changes (frequency stays the same, corresponding to Rayleigh scattering), but some will change their frequency because of the interactions between photons and phonons. This change allows one to measure the energy of phonon modes near the Γ point, and helps us identify chemical species and compositions.    Figure 1.15 Energy level diagram in Raman scattering. Figure is from Wikipedia. Link:https://en.wikipedia.org/wiki/Raman_spectroscopy#/media/File:Raman_energy_levels.svg (validated on July 29, 2018)   16  As Figure 1.15 shows, Raman scattering is composed of Stokes scattering (phonons are excited with the resulting photon frequency decreases) and anti-Stokes scattering (phonons are absorbed and the photon frequency is increased). The intensity of Stokes scattering is a normally larger than that of anti-Stokes scattering due to the phonon distribution to lower energy levels. In our experiments, we only recorded the intensity of Stokes line.  A crystal has sharp Raman peaks, while for an amorphous material, such as red phosphorus, the peaks are not well defined. Black phosphorus heterostructures fabricated in this work have very sharp peaks with small half band widths, giving further evidence of their high crystallinity after the mechanical exfoliation.              17    Chapter 2 A Modified Transfer Method for Black Phosphorus    Twisted stacked BP is composed of two BP flakes stacked with a rotation angle θ. Similar 2D materials with twisted bilayer structures, such as those made of graphene and MoSe2, have been studied by Raman Spectroscopy. A Raman spectrum of a twisted bilayer material is not a simple addition of those of the individual layers. Instead, additional new peaks will appear which correspond to new phonon modes. These peaks are strongly related to the rotation angle θ. To fabricate 2D heterostructures, wet transfer and dry transfer methods are commonly used. However, these methods are not suitable for making twisted few layer black phosphorus without careful considerations or modifications. In this chapter, I will briefly discuss the wet transfer and dry transfer methods previously studied, and then discuss a modified transfer method developed in this work, which could be called as “film based transfer”.      18   2.1  Wet Transfer Wet transfer is an old and complex way to fabricate 2D heterostructures. Before the emergence of dry transfer, Nathan et al [24] used this method to transfer BP for the fabrication of photodetectors. (Figure 2.1)  Figure 2.1 Illustration of a typical wet transfer method. Figure is reprinted from Ref. [24] with permission.  Here is the brief description for this method (Figure 2.1): a silicon substrate is spin-coated with PVA and then PMMA. After that, BP is mechanically exfoliated on the PMMA film. In the Ref. [19], the author used Nitto tape, however, from our practice, Cleanroom tape is better. Then, the whole sample is dipped in DI water to separate the Si substrate and the PMMA membrane. A 7 mm diameter TEM loop is used to catch the sample, and the sample is transferred to the target position. The disadvantages for wet transfer are obvious. Firstly, the transfer process is complex, and it is difficult to catch the PMMA membrane in DI water. Furthermore, water is used  19  in the transfer process, which will oxidize the BP. Since 2014, after dry transfer method became available, the wet transfer method has been rarely used in the fabrication of 2D heterostructure.  2.2  Dry Transfer Dry transfer is a new method proposed by Andres et al in 2014[25]. Figure 2.2 shows the detailed process.  Figure 2.2 Experimental instrument and illustration of dry transfer. Figure is reprinted from Ref. [25] with permission.  The stamp used here is a thin layer of commercially available viscoelastic material, such as Gelfilm (PDMS) from Gelpak. This is a good way to transfer BP on silicon substrate, but if we want to transfer BP on another two dimensional material, that is quite difficult. I have tried it many times during my research, but none of these trials succeed. PDMS is very sticky, so BP tends to stick to it if the BP and the other two dimensional material do not have strong van der Waals attraction. An exception is boron nitride, which has strong interaction with BP, so it can be used to pick BP up. [26]  20    A modified way of dry transfer is to use polycarbonate (PC) film as a sticker, and heat the sample to 190°C to crack the PC film. This is a good way to transfer graphene, and could ensure almost 100% success. However, it turns out to not be sufficiently sticky, so BP could not be picked up by this film. I tried this approach at many different temperatures, but none of them worked.   To make a stacked structure of BP, we need to find a new method different from the traditional dry transfer. In this work, a modified dry transfer method was developed (discussed below), which turned out to be a successful method to fabricate twisted stacked few layer black phosphorus. To the best of my knowledge, no other group used this method to fabricate a stacked structure of BP, though Wei Xin et al used wet transfer method to fabricate BP heterostructures and BP orientation-induced diodes. [27]   2.3  Film Based Transfer The modified dry transfer method was used after mechanical exfoliation to fabricate twisted stacked black phosphorus. 6% polycarbonate (PC) in chloroform solution was dropped on a glass slide to make a PC film. After that, BP flakes were transferred to this film by dry transfer. Optical microscopy was used to select proper BP flakes of sufficient size and uniformity on the PC film to be further transferred. Then, we positioned the PC film with the BP flakes on a BP flake bearing silicon substrate by a micro-feeding unit. In this step, the PC film/glass slide was in contact with the Si substrate face-to-face. The Si substrate was mounted on a heating stage. It was then heated to 190 °C for five minutes to make the PC film crack and peel off from the PC/glass slide. Finally, the PC film was removed by putting the sample in chloroform solution for one minute. This transfer  21  method may be called as “PC film based transfer”. The major modification is that PC film is functioned as a substrate, not a sticker here. It provides a convenient way to transfer BP on other 2D materials, and we have made BP/graphene heterostructures successfully by this method. Figure 2.3 shows the optical image of a twisted stacked few layer BP sample.  Figure 2.3 Optical image of twisted stacked few layer BP    With this new transfer method, BP could be transferred anywhere, and the position is completely controllable. Besides fabricating 2D heterostructures, this method is also suitable to transfer BP on copper network for TEM measurement. Figure 2.4 shows the comparison between my diffraction pattern and the pattern of a sample made with the wet  22  transfer method [28].    Figure 2.4 Comparison of TEM diffraction pattern in Ref. [28] (left panel) and my results (right panel). Figure is reprinted from Ref. [28] with permission.  Our result is better than that in Ref. [28] because it does not have a central principal maximum bright spot. That indicates our sample is in a crystalline form while the sample in Ref. [28] might be polycrystalline. Traditionally one uses wet transfer method for TEM, which is quite complex and might harm the delicate BP sample. In contrast, my new transfer method is simple and protects BP sample quite well. The TEM comparison proves the strengths of the film based transfer.     23    Chapter 3 The Abnormal Blue Shift in Twisted Stacked Few Layer Black Phosphorus     This chapter is the core chapter in the thesis. First, I will introduce the analogy to similar 2D materials, which is the motivation of this project. Then, I will discuss the discovery of the abnormal blue shift in twisted stacked few layer black phosphorus. The DFT calculations and explanations for this new phenomenon will be given at the end of this chapter. I would like to acknowledge Teren Liu for providing me with the DFT calculation results in chapter 3.5.       24   3.1  Analogy to Other Stacked 2D Materials   This abnormal blue shift in twisted stacked few layer BP is not a new phenomenon. Similar materials, such as graphene, also show some changes in their Raman spectra as a function of a twist angle. Figure 3.1 shows the details. [29]  Figure 3.1 Raman spectra of twisted bilayer graphene on a Si/SiO2 substrate. See text for details. Figure is reprinted from Ref. [29] with permission.     In the Figure 3.1 above, the asterisks point to the superlattice-induced Raman peaks originated from twisted bilayer graphene. Different colors correspond to different excitation lasers. For the same color, different curves correspond to different twist angles. The new peaks arise from interlayer coupling.   For another 2D material MoSe2, similar changes were observed as shown in Figure 3.2. [30]   25    Figure 3.2 Raman shifts of twisted bilayer MoSe2. Figure is reprinted from Ref. [30] with permission.   In Figure 3.2, Stokes and anti-Stokes Raman spectra were measured at different twist angles from 60° to 33.2° at room temperature. The corresponding optical images are in the middle. From these graphs, we see that for a twisted bilayer MoSe2 the peak position and intensity change if we change the twist angle.  So far, other 2D materials mainly focused on twisted bilayer structure, which is composed of two single atomic layers. However, it is difficult to fabricate two stacked monolayer BP experimentally. BP is well known to oxidize easily in air [31], and BP made from liquid phase exfoliation has a comparatively small size (less than 5μm) even with a size selection method [16-17]. Currently available thinning methods for black phosphorus,  26  as discussed previously, are still not sufficiently reliable. Therefore, in our experiment, we could only fabricate twisted few layer black phosphorus, or twisted stacked bulk black phosphorus. This is different from the analog studies of twisted bilayer graphene and molybdenum diselenide, which are composed of two single layers.   3.2  High Frequency Raman Modes in BP   As discussed in Chapter 1, BP has twelve phonon modes. Three of them are acoustic modes and the remaining nine are optical modes. By using harmonic approximation and diagonalizing the dynamic matrix, we identify the twelve phonon modes near Γ point, [32] 2𝐴𝑔 + 𝐵1𝑔 + 𝐵2𝑔 + 2𝐵3𝑔 + 𝐴𝑢 + 2𝐵1𝑢 + 2𝐵2𝑢 + 𝐵3𝑢 Among these twelve phonon modes, six are Raman active (2Ag, B1g, B2g and 2B3g), and the rest are infrared active or optically inactive. When bulk black phosphorus is thinned to few layer black phosphorus, translational symmetry along z-axis is lost, so the representation of phonon modes at the Γ point changes to [33] Γ𝑛 = n(2𝐴𝑔 + 𝐵1𝑔 + 𝐵2𝑔 + 2𝐵3𝑔 + 𝐴𝑢 + 2𝐵1𝑢 + 2𝐵2𝑢 + 𝐵3𝑢) where n is the number of layers. However, the point group of bulk black phosphorus and few layer black phosphorus stays the same (D2h), so they have the same character table. The Raman tensors are [32] 𝐴𝑔 = (𝑎 0 00 𝑏 00 0 𝑐) , 𝐵1𝑔 = (0 𝑑 0𝑑 0 00 0 0) , 𝐵2𝑔 = (0 0 𝑒0 0 0𝑒 0 0) , 𝐵3𝑔 = (0 0 00 0 𝑓0 𝑓 0)  27    The matrix elements are partial derivatives of the corresponding dielectric constant. The relative values for the numbers in the Raman tensors are a:b:c:d:e:f=1:1.34:1.14:0.01:0.6:0.005 Since d and f are comparatively small, it is very difficult to observe the B1g and B3g modes directly in the experiment. As a result, previous work mainly focused on the two Ag modes and the B2g mode. (Figure 3.3) These modes are all in the high-frequency region. In the low-frequency region, we have several other modes in few layer black phosphorus, such as Ag3, and they are strongly dependent to BP thickness. [33]  Figure 3.3 Illustration of three high frequency Raman active phonon modes in BP.       28   3.3  The Abnormal Blue Shift in Twisted Stacked BP  Figure 3.4 Raman spectra of top flake, bottom flake and stacked flakes of the sample shown in Figure 2.3.  Figure 3.4 shows the Raman spectra in different areas of sample in Figure 2.3. We see that the Ag1 and Ag2 Raman peaks of the overlapping area show blue shifts of 0.4 and 0.2 cm-1 respectively compared with those of the non-overlapping areas. The B2g peak is blue-shifted in this sample, but it may red-shift in other samples, depending on the twist angle. Previous studies have shown that Ag1, B2g and Ag2 modes should be red-shifted in untwisted BP on SiO2/Si substrates when thickness increases [10, 31], due to a laser heating and the sample heat absorption difference. In our experiment, the overlapping area is thicker than non-overlapping area, but the Raman peaks have a blue shift, rather than a red shift. Because of that, we call this phenomenon “abnormal blue shift”. Other  29  influence factors, such as equipment errors (+/-0.05 cm-1) and laser heating effect were excluded by careful examination.   Figure 3.5 Twist angle characterization by angle-resolved polarized Raman spectroscopy (ARPRS). Crystal orientations of top flake and bottom flake were measured simultaneously. The twist angle for this sample is 90±3 degrees.  ARPRS (Angle-resolved polarized Raman spectroscopy) was used to measure the twist angle. (Figure 3.5) The intensity ratio of the Ag1 and Ag2 peaks is strongly dependent on the angle between the polarization direction of the incident laser and the crystal orientation of the sample [34-36]. In the ARPRS work, crystal orientations of non-overlapping and overlapping areas were measured simultaneously. BP samples were rotated by 15° each step with a total of twenty four steps to cover 360°.    30   Figure 3.6 Blue shift value versus twist angle in mode Ag1  Figure 3.7 Blue shift value versus twist angle in mode B2g  31   Figure 3.8 Blue shift value versus twist angle in mode Ag2  The twist angle dependence of the blue shift for the three Raman peaks is shown in Figures 3.6-3.8. The Raman peaks of the sample with twist angle around 7°were found to show red shifts with increased thickness, which suggests that the phonon modes of a stacked BP with a small twist angle are close to those of an untwisted stacked BP. Excluding this sample, for the out-of-plane vibration mode Ag1, the peak shifts are all blue shifts of 0.2 to 0.5 cm-1; for in-plane vibration mode Ag2, a similar trend was observed with smaller blue shifts. For the in-plane vibration mode B2g, the peak shifts measured are more complicated showing one peak being red-shifted and others blue-shifted. The detailed explanation and discussion of this abnormal blue shift will be presented in sections 3.4-3.6. In these sections, we start from the moiré pattern and the construction of the unit cell of the twisted BP. Then we present the calculation results for the corresponding 72 phonon modes and charge distributions. The calculation suggests  32  that weak valence bond between layers may exist in BP.     3.4  Superlattice in Twisted Bilayer BP When two identical 2D structures are superposed with a twist angle θ, the resulting structure is called a Moiré pattern. The unit cell is larger than the regular one in this case. The new lattice base vectors can be constructed as follows:                                                  (𝑏1𝑏2) =𝑎2(−𝑝𝑠𝑖𝑛φ 𝑞𝑐𝑜𝑠φ𝑞𝑠𝑖𝑛φ 𝑝𝑐𝑜𝑠φ) (𝑖𝑗)                  (1)   Here, i, j are basis vectors for the untwisted black phosphorus. φ is the angle between two basis vectors of untwisted black phosphorus lattice, which is 35.27 °. b1, b2 are the new basis vectors for twisted bilayer black phosphorus superlattice. p and q are two integers starting from 1. For pure twisted stacking without slipping, the Moiré twist angle is given by [37-38]                                             cos𝜃 =(𝑞2+𝑝2)𝑐𝑜𝑠2φ+𝑞2−𝑝2𝑞2+𝑝2+(𝑞2−𝑝2)𝑐𝑜𝑠2φ  𝑝, 𝑞 ∈ 𝑁+                                      (2) Simple unit cells and thus superlattices only exist at discrete p and q values. The simplest superlattice corresponds to p = q = 1. In this case, the twist angle is 70.53° between layers. For this value, on each atomic layer the area occupied by a unit cell of the twisted bilayer black phosphorus is three times that of the untwisted bilayer black phosphorus. Since there are two atomic layers, altogether there are 4×3×2=24 phosphorus atoms in one unit cell (Figure 3.9). Therefore, there should be 24×3=72 phonon modes in this superlattice.   33   Figure 3.9 (a) Crystal structure of 70.53°twisted bilayer black phosphorus. (b) Unit cell of 70.53°twisted bilayer black phosphorus. The projection direction is along b-axis (perpendicular to 2D BP plane). This is the simplest case in twisted bilayer black phosphorus superlattice.  3.5  DFT Calculation Results (provided by Teren Liu)   The DFT calculations were performed by my groupmate Teren Liu. His study provided important insights to the experimental results discussed above. Therefore, it is necessary to quote some of his work in the discussion. His calculations were based on the simplest superlattice discussed above. A summary of the results for DFT calculation is shown in Table 3.1.  Mode Type of BP Symmetry Wavenumber Raman Intensity Blue shift value  Untwisted  Ag1 351.86 18768.502  Twisted  A 356.56 26606.2044  Untwisted  Ag2 455.57 28592.0377  Twisted  A 456.88 1655.471 Table 3.1 DFT calculation results of untwisted bilayer BP and twisted bilayer BP.  Ag1 Ag2 4.70 1.31 (cm-1) (cm-1)  34  Charge distributions in twisted and untwisted bilayer black phosphorus were also calculated by the DFT program. The results are compared in Figures 3.10-3.12.  Figure 3.10 (a) 3D charge density map in unit cell of untwisted bilayer black phosphorus. (b) 3D charge density map in unit cell of 70.53° twisted bilayer black phosphorus. Figure courtesy of Teren Liu.   Figure 3.11 (a) 2D charge density map in the cutting plane of untwisted bilayer black phosphorus. This cutting plane (020) is the middle-distance plane between the two 2D black phosphorus atomic planes. (b) 2D charge density map in the same cutting plane of 70.53° twisted bilayer black phosphorus. Figure courtesy of Teren Liu. (a) (b) (a) (b) Weak valence bond  35   Figure 3.12 Another cutting plane (100) of twisted bilayer black phosphorus, which is normal to the 2D atomic planes. Figure courtesy of Teren Liu.   3.6  Discussions and Explanations  The unit cell of the twisted bilayer black phosphorus is in the space group P222 (point group D2), while the unit cell of the untwisted bilayer black phosphorus is in space group Pbcm (point group D2h). Due to the lower symmetry, or “symmetry breaking”, the 72 calculated phonon modes of the twisted bilayer BP with 70.53° angle (24 atoms per unit cell) do not have special parity, and the symmetry notations reduce to A and B instead of Ag1, B2g and Ag2. Out of the 72 modes calculated, to identify the corresponding Raman peaks of twisted bilayer BP, we select two high intensity Raman active modes with same symmetry notation A, whose wavenumbers are close to the wavenumbers we measured in the experiment. To make the discussion easier to follow, in the following, the measured and calculated Raman peaks of twisted stacked BP are still called Ag1, B2g and Ag2 peaks. For example, the measured Ag1 and Ag2 peaks were at 362.06 and 466.44 cm-1 for twisted Weak valence bond  36  BP as in Figure 3.3 and the corresponding peaks selected from the DFT results of twisted bilayer BP are at 356.56 and 456.88 cm-1. The relative differences of the wavenumbers are less than 3%. The wavenumber calculation result of mode B2g is far away from that we observed in experiment, so it is not included in this Table 3.1. Next, we compared the calculated results of an untwisted bilayer BP and a twisted bilayer BP with a 70.53° twist angle. The DFT calculation results for the Ag1 and Ag2 peaks of twisted bilayer BP are 4.70 cm-1 and 1.31 cm-1 higher than those of the untwisted bilayer BP, consistent with the abnormal blue shift observed in Raman spectra. An interesting fact is that the shift values are larger in the DFT calculation than those observed in the experiment. This may be explained by the BP layer thickness differences between the experiments (few-layer) and the calculations (bilayer). Thicker flakes may reduce the phonon modulation effect and decrease the blue shift value. In the charge distribution comparison, we can see that the 3D charge distribution of the twisted bilayer BP in Figure 3.10 (b) has more overlap the between two layers, while that of the untwisted one in Figure 3.10 (a) is more localized. The cutting planes (020) in Figure 3.11 (a) and (b) are the middle-distance planes between the two layers. Significant distribution differences exist between two figures suggesting that a weak valence bond, as indicated in the graph, may exist in twisted bilayer BP. Another cutting plane (100) of twisted bilayer BP in Figure 3.12, which is normal to the 2D atomic planes, gives another perspective of this possible valence bond between phosphorus atoms in different layers. Based on the experiment and the DFT calculation results, this abnormal blue shift can be explained by a strong interlayer coupling effect and thus a strong phonon mode change near Γ point in this 2D heterostructure. This is consistent with the significant interlayer interaction reported before [39]. A phosphorus atom has five valence electrons, three of which form covalent intralayer bonds while the remaining two form an electron lone pair.  37  This electron lone pair may extend to the interlayer vacuum region and affect interlayer van der Waals interactions. When the twist angle is not equal to zero, there are different Coulomb interactions between layers because of electron distribution change. This change will cast a noticeable effect on phonon modes and may cause the abnormal blue shift observed in Raman spectra. Ag1 mode has a vibrating direction perpendicular to the 2D BP plane, so its larger shift compared to other modes is consistent with this scenario. This also indicates that BP interlayer interactions are not simply van der Waals interactions. Weak valence bond, as indicated in Figure 3.12, may exist between atoms in different layers of twisted bilayer black phosphorus. Other phenomena reported before, such as surface reactivity, support the hypothesis that additional interactions may exist as well [40-41].                38    Chapter 4 Conclusions and Insights   In conclusion, we have experimentally observed the unique optical response and the abnormal blue shift in twisted stacked black phosphorus. The phonon behavior could be qualitatively explained by our density functional theory calculation. This work suggests that interlayer coupling has a significant effect in twisted stacked black phosphorus, and interlayer interactions are not just van der Waals interactions. Additional interactions, such as weak valence bond between layers, may exist in this structure. We discuss some further applications and suggest that this discovery may be a platform for future research. More insights may arise from this work. 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