陰離子空缺對於層狀多晶與單晶1T-TiSe2-d的能帶與侷域結構之影響

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(1)The impact of anion vacancy defects on band picture and local structure of layered polycrystalline and single crystal 1T-TiSe2-. Presented by Song-Hsun Huang. Advisors: Hsiang-Lin Liu, Ph. D and Fang-Cheng Chou, Ph. D. A Thesis Submitted for the Degree of Doctor of Philosophy. Department of Physics. National Taiwan Normal University. July 2017.

(2) Acknowledgements I would like to thank my advisors Prof. Hsiang-Lin Liu and Prof. Fang-Cheng Chou for giving me support and opportunities to study the academic research work and develop the core technology of crystal growth. I would also like to thank Prof. Pai for providing an opportunity to study the crystals surface structure by using scanning tunneling microscopy. Further, I would also like to thank Prof. Chao-Hung Du and Prof. Ming-Che Chang for giving me suggestions on this thesis. In my present work, I would like to thank Dr. Guo-Jun Shu and Dr. We-Ting Chen for giving me great help through useful discussion in academic research work. And I would acknowledge for all of the lab members in HLL lab, Department of Physics, National Taiwan Normal University and FCC lab, Center for Condensed Matter Sciences (CCMS), National Taiwan University for nice working experiences and encouraging me to grow up. Finally, I would appreciate to my wife and my family for their long term patience, support, and encouragement. Thank you.. I.

(3) Abstract A systematic study of 1T-TiSe2 polycrystalline and single crystalline with controlled Se deficiency level indicates that a significant Se loss could be responsible for the controversial charge density wave (CDW) phase and on whether the nominal 1T-TiSe2 should be categorized as a semiconductor or a semimetal at room temperature. In the polycrystalline form, the second order CDW phase transition near ~200 K is found to be most pronounced in samples with δ ~0.12, corresponding to about one Se atom missing per eight formula units in average, which is incommensurate to the hexagonal symmetry and naturally leads to the charge ordering of 2a × 2a × 2c superlattice via exciton-phonon coupling. The anomalous resistivity (T) peak between 100 and 200 K indicates not only resistivity increase due to charge ordering, but also a concomitant pto n- carrier type change. An interpretation using band model for an extrinsic p-type semiconductor with an impurity band (IB) in proximity to the valence band (VB) is proposed to explain the evolution of Se vacancy level and electronic structure change for 1T-TiSe2-δ, from the low doping bound (δ ~0.08) of semiconducting behavior to the heavily doped (δ ~0.17) dirty semiconductor showing metallic-like n-type conduction. Supporting experimental evidences for the Se vacancy existence are provided by the integrated chemical and physical property analyses, including electron probe microanalysis (EPMA), Hall coefficient, and magnetic susceptibility. In single crystal form, the Se vacancy and Ti-intercalation are dominant near the crystal surface as explored by the scanning tunneling microscopy (STM). The Se vacancy level is found reduced on the crystal surface after prolonged annealing at high temperature, but the intercalated Ti level grows, which implies the occurrence of local re-structuring near the Se vacancy sites. Room temperature Raman scattering spectrum shows a red shift of A1g phonon mode and a blue shift of Eg phonon mode after the long time high II.

(4) temperature post-annealing. The high temperature post-annealing procedure has different impact on polycrystalline and single crystal samples, while samples of small grain size (~10-30 μm) have dominant Se deficiency in equilibrium, samples of large grain size (≳ 1 mm) shows significant amount of Ti-intercalation. This is most likely due to the different level of local re-structuring near the Se vacancy sites.. Keywords: Transition metal dichalcogenides (TMDCs), Charge density wave (CDW), Excitonic insulator, Semiconductor.. III.

(5) Contents Acknowledgements……………………………………………………....i Abstract………………………………………………………………….ii Contents………………………………………………………………....iv List of Figures…………………………………………………………...vi List of Tables…………………………………………………………….xi Chapter 1 Introduction………………………………………………….1 Chapter 2 Brief review of transition metal dichalcogenides………..…6 2.1 Transition metal dichalcogenides (TMDCs)…………………...…....6 2.2 Principles of the CDW: the Peierls transition………………………..9 2.3 CDW and other collective phenomena in the TMDC family……….11 2.4 CDW state in 1T-TiSe2…...……………………………………...…16 2.4.1 Crystal structure……………………………………………...16 2.4.2 Transport properties………………………………………….20 2.4.3 Excitonic condensate and Jahn-Teller effect………………....21 2.4.4 The intrinsic behavior of 1T-TiSe2 without Se vacancy defects22 Chapter 3 Sample preparation and experimental methods………....24 3.1 Polycrystalline sample synthesis and single crystal growth………..24 3.2 Powder X-ray diffraction………………………………………..….26 3.3 Rietveld refinement method………………………………………..30 3.4 Electron probe micro-analyzer (EPMA)……………………………32 3.5 Magnetic property measurement system (MPMS)…………………34 3.6 Physical Property Measurement system (PPMS)………………..…35 3.7 Scanning Tunneling Microscopy (STM)…………………………...38 3.8 Raman scattering spectroscopy…………………………………….41 IV.

(6) Chapter 4 Tunable Se vacancy defects and the unconventional charge density wave in 1T-TiSe2−δ……………………………………………..44 4.1 Experimental details………………………………………………..44 4.2 Synthesis and defects………………………………………………45 4.3 Crystal structure and defects……………………………………….48 4.4 Transport properties………………………………………………..51 4.5 Semiconductor or semimetal.............................................................54 4.6 Band picture description…………………………………………...55 4.7 Raman scattering study…………………………………………….58 4.8 Summary…………………………………………………………...60 Chapter 5 STM study of single crystal 1T-TiSe2 surface after the postannealing ...……………………………………………………………..61 5.1 Experimental details………………………………………………..62 5.2 Structure and transport property…………………………………....62 5.3 STM images on the crystal surface………………………………...67 5.4 Raman scattering study...……………………………………….…..74 Chapter 6 Summary and proposed further works…………………...79 References………………………………………………………………81. V.

(7) List of Figures Fig. 2.1:. The basic forms of layered compounds for TMDCs…..……………....7. Fig. 2.2:. The different stacking types of MX2 for M = group V and VI…..……..8. Fig. 2.3:. The polytypic transformation in TaSe2 system via different temperature heating process…..…………………………………………………….9. Fig. 2.4:. Peierls transition in a one-dimensional chain. The atomic arrangement and the corresponding electronic band structure (a) before and (b) after the transition……………………………………………………..…...11. Fig. 2.5:. Fermi surface nesting in 1D, 2D, and 3D electron gas…………….…11. Fig. 2.6:. The synchrotron X-ray transmission Laue pattern for 1T-TaSe2 crystal which exhibits a commensurate CDW √13 × √13 superlattice at room temperature…………………………………………….........…13. Fig. 2.7:. The temperature dependence of resistivity in 1T-TaS2. A metallic state is above 550 K; an incommensurate CDW (ICCDW) phase is above 350 K; an near commensurate CDW (NCCDW) phase is from 190 to 350 K; a commensurate CDW (CCDW) phase is below 190 K………………14. Fig. 2.8:. The temperature–pressure phase diagram of 1T-TaS2………………..14. Fig. 2.9:. The electronic phase diagram for CuxTaS2. Cu is proposed being intercalated into the vdW gap of the TaS2 planes……..……………...15. Fig. 2.10:. The crystal structure of 1T-TiSe2…………………………………......17. Fig. 2.11:. In-plane electrical resistivity perpendicular for crystals of 1T-TiSe2 grown by iodine vapor transport at different growth temperatures (Tg)…………………………………………..…………………….…18. Fig. 2.12:. (a) Lattice parameters of CuxTiSe2. (b) The CuxTiSe2 T–x electronic phase diagram…...……………………………………………….......19. Fig. 2.13:. The phase diagram of 1T-CuxTiSe2, where the horizontal axes stand for pressure and the content x of the intercalated Cu…………….............19. Fig. 2.14:. Pressure–temperature phase diagram of TiSe2……………………….20 VI.

(8) Fig. 2.15:. The densities of states for octahedral and trigonal prismatic layered materials that the ‘dz2 ’ band is slightly lower for trigonal prismatic than for octahedral coordination in TiSe6……...…………………………..23. Fig. 2.16:. There are two kinds of Ti environments for TiSe6 octahedron: (a) top and bottom face of Se atoms rotate around Ti, and (b) Ti moves closer to Se-Se edge of the octahedron………………………………...........23. Fig. 3.1:. The single crystal growth of 1T-TiSe2 by the CVT method using iodine as the transport agent. The temperature gradient is TH = 650 ℃ and TL = 550 ℃ in 35 cm…………………………………............................25. Fig. 3.2:. The as-grown 1T-TiSe2 single crystal deposited at the 550 ℃ cold zone by the CVT method………………………………..............................25. Fig. 3.3:. A sketch of X-ray diffractometer……………………….....................27. Fig. 3.4:. The Bruker D2 PHASER X-ray diffractometer………………….......28. Fig. 3.5. The Bruker D8 ADVANCE X-ray diffractometer…………………....28. Fig. 3.6:. A sketch of synchrotron radiation and the beamline distribution in NSRRC, Taiwan. The powder X-ray diffraction is operated at BL01C beamline. The photon energy of 20 keV (~0.61993 Å ) incident beam passing through the sample and scattered to a detector Mar345 to form a diffraction pattern……………………………………………...…...29. Fig. 3.7:. The XRD pattern for 1T-TiSe2 polycrystalline which obtained by synchrotron X-ray……………………………....................................30. Fig. 3.8:. (a) A 2D diffraction patterns forming a reciprocal lattice. (b) The random orientation powder scattering rays forming bright cycles…..32. Fig. 3.9:. Different types of interaction: (1) ionization and (2) generation of Bremsstrahlung…...………………………….....................................33. Fig. 3.10:. QD-SQUID VSM instrument with the helium cryo-cycle compressor in the Center for Condensed Matter Sciences (CCMS), National Taiwan University……………………………………….……………............35. VII.

(9) Fig. 3.11:. The QD-PPMS instrument with the helium cryo-cycle compressor in the Center for Condensed Matter Sciences (CCMS), National Taiwan University.…………………………………………………............…37. Fig. 3.12:. A sketch of four probe method for resistivity measurement………….38. Fig. 3.13:. A sketch of Hall effect measurement……………………....................38. Fig. 3.14:. A Schematic diagram of STM………..………………........................40. Fig. 3.15:. Schematic representation of operation of a scanning tunneling microscope in (a) constant current mode and (b) constant height mode………………………………………………………………….41. Fig. 3.16:. A sketch of the setup of the micro-Raman scattering………………....43. Fig. 4.1:. X-ray diffraction (XRD) patterns for 1T-TiSe2-δ which were obtained by using synchrotron radiation with wave length λ = 0.61993 Å and indexed with space group P3̅m1 (No.164)…………………………...47. Fig. 4.2:. The Se vapor condensed on the sealed quartz tube inner wall after postannealing…………………….……………………………………….47. Fig. 4.3:. An Arrhenius plot of Se deficiency level δ vs. inverse annealing temperature for 1T-TiSe2-δ powder samples………………………....48. Fig. 4.4:. The magnetic susceptibility for different Se deficiency level of 1TTiSe2-δ. The CDW transition temperature is shown in inset of figure and predicted by red dash arrow……………………………………….....49. Fig. 4.5:. The Se deficiency level δ dependence of the lattice constant a and c in 1T-TiSe2-δ…………………………………………………………….49. Fig. 4.6:. The Se deficiency level δ dependence of the bond length and bond angle in 1T-TiSe2-δ…………………………………………………….……50. Fig. 4.7:. The coordination number (CN) from TiSe6 of CN = 6 to TiSe5 of CN = 5 due to the Se vacancy……………………………….........………...50. Fig. 4.8:. The temperature dependence of resistivity for 1T-TiSe2-δ…………....52. Fig. 4.9:. The temperature dependence of Seebeck coefficient for 1T-TiSe2-δ…53 VIII.

(10) Fig. 4.10:. The temperature dependence of Hall coefficient for 1T-TiSe2-δ where δ = 0.14………………………………………………………………...53. Fig. 4.11:. Band pictures of 1T-TiSe2-δ…………………………………………..57. Fig. 4.12:. Temperature dependence of electrical resistivity which has a semiconducting background subtraction for 1T-TiSe2-δ, 𝛿 = 0.12….57. Fig. 4.13:. The room temperature Raman scattering spectra for 1T-TiSe2-δ polycrystalline (powder pellets with polished surface). The laser power is 2 mW………………………………………………………………59. Fig. 4.14:. The room temperature Raman scattering spectra for (a) no grinded and (b) grinded of 1T-TiSe2-δ polycrystalline. The laser power is 0.2 mW..59. Fig. 4.15:. The room temperature Raman spectra for 1T-TiSe2-δ polycrystalline (no grinding powder), δ = 0.17. The laser powers are 0.2 mW for black line and 2 mW for red line…………………………………………...……60. Fig. 5.1:. The synchrotron X-ray diffraction for different annealing temperature of 1T-TiSe2 crystals which are grinded to powders…………………..63. Fig. 5.2:. The lattice constants of 1T-TiSe2 crystals as function of annealing temperature…………………………………………………………..64. Fig. 5.3:. The Se deficiency level of 1T-TiSe2 polycrystalline and crystals with different annealing temperature which obtained by EPMA………....65. Fig. 5.4:. The temperature dependence of resistivity for the ab-plane of 1T-TiSe2 single crystals which annealing at different temperature……………66. Fig. 5.5:. The temperature dependence of magnetic susceptibility for the ab-plane and c-direction of 1T-TiSe2 single crystals which annealing at different temperature……………………………………………………..........67. Fig. 5.6:. STM image of 1T-TiSe2 by 550 ℃ post-annealing. 20 × 20 nm2, V = 0.15 V, I = 0.8 nA at 77 K……………………………………………..68. Fig. 5.7:. STM image of 1T-TiSe2 by 750 ℃ post-annealing. 20 × 20 nm2, V = 0.15 V, I = 0.8 nA at 77 K……………………………………………..69. IX.

(11) Fig. 5.8:. STM image of 1T-TiSe2 by 950 ℃ post-annealing. 15 × 15 nm2, V = 0.6 V, I = 0.8 nA at 77 K………...…………………………….............69. Fig. 5.9:. Bias dependence of STM images for 1T-TiSe2 after 950 ℃ postannealing. Sample bias V = (a) -0.1, (b) -0.2, (c) -0,3, (d) -0.4, (e) -0,5, (f) -0.6, (g) -0.7, (h) -0.8, and (i) -0.9 V (filled State), I = 0.8 nA, 15 x 15 nm2 at 77 K.…………………………………………………….…70. Fig. 5.10:. Bias dependence of STM images for 1T-TiSe2 after 950 ℃ postannealing. Sample bias V = (a) 0.1, (b) 0.2, (c) 0,3, (d) 0.4, (e) 0,5, (f) 0.6, (g) 0.7, (h) 0.8, and (i)-0.9 V (empty State), I = 0.8 nA, 15 x 15 nm2 at 77 K………………………………………………………………..71. Fig. 5.11:. Number density of Se vacancy in 1T-TiSe2 crystals for different annealing temperature………………………………………..……....72. Fig. 5.12:. Number density of Ti-intercalation in 1T-TiSe2 crystals for different post-annealing temperature……………………..................................73. Fig. 5.13:. The defect distributions (Ti-intercalation) on 750 ℃ post-annealing 1T-TiSe2 surface. 30 × 30 nm2, V = -0.5 V, I = 0.8 nA at 77 K………..73. Fig. 5.14:. Displacement vectors for the infrared- and Raman-active modes in the 2H and 1T polytypes...........………………..…………...............….....76. Fig. 5.15:. Room temperature Raman scattering spectra of 1T-TiSe2 crystals for different post-annealing temperature excited by 532 nm laser line.......77. Fig. 5.16:. (a) The red shit of A1g and (b) the blue shift of Eg Raman phonon modes………………………………………………………………...77. Fig. 5.17:. The Ti atom was introduced into the van der Waals gap and bonded with top and bottom layer of TiSe2...............................................................78. X.

(12) List of Tables Table 1.1:. Single crystal growth of 1T-TiSe2 in the literature, including growth temperature, transport agent used in CVT, and physical property measurements…………………………………………………...……….4. Table 2.1:. The common groups of transition metals for TMDCs, MX2, X = S, or Se, or Te……………………………………..………………………………7. Table 2.2:. The CDW and superconductivity transition temperature of TMDCs….16. Table 4.1:. The lattice parameters, selected bond length and angle, and goodness of fit for 1T-TiSe2-δ polycrystalline varied with different Se deficiency level δ.……………………………………………………………………….50. Table 4.2:. Carrier concentrations and mobilities derived from resistivity and Hall effect measurement results for δ ∼0.14…………………………….…..53. Table 4.3:. The activation energy Ea and CDW onset of 1T-TiSe2−δ………………..53. Table 5.1:. The lattice parameters, selected bond length and angle, and goodness of fit for 1T-TiSe2 single crystals varied with different annealing temperature…………………………………………………………….64. Table 5.2:. The atomic ratio for different annealing temperature of 1T-TiSe2 polycrystalline and crystals by EPMA…………………..……………...66. Table 5.3:. Symmetries and selection rules for the long-wavelength acoustic and optic phonons in the 1T and 2H polytype geometries……..…………...76. XI.

(13) Chapter 1 Introduction The layered transition metal dichalcogenides (TMDCs) MX2 have been studied for more than four decades [1]. They exhibit several interesting phenomena including charge density wave (CDW), superconductivity (SC), and ferromagnetism. The quasi two-dimensional atomic structure of X-M-X sheets is composed by the transition metal (M) from group IVA to VIIA with chalcogene elements (X = S, Se, and Te) having crystal electric field (CEF) in octahedral (e.g., 1T-TaSe2, 1T-TaS2) or trigonal prismatic (e.g., 2H-TaSe2, 3R-TaSe2, and 4Ha-TaSe2) coordination, also of mixed coordination in 4Hb-TaSe2 and 6R-TaSe2. The layered sheets of MX2 are separated by a van der Waals (vdW) gap, which causes such materials to possess highly anisotropic mechanical and electrical properties. The electrical properties of TMDC family covered a wide range from metal to insulator, including anomalous behaviors like a charge density wave phase (CDW) accompanied with a periodic lattice distortion (PLD) below the transition temperature. 1T-TiSe2 is a well-known material in the TMDCs family showing a second order CDW transition with contomitanted commensurate (2 x 2 x 2) PLD below ~202 K [2, 3, 4]. The origin of the CDW state has been under debate by several different proposed explanations. The driving force of CDW state in 1T-TiSe2 was first proposed by Di Salvo et al. [2] in 1976 to be driven by electron-hole coupling, and Wilson called it as an “excitonic insulator” [3, 5]. Many explanations to the origin of CDW state have been proposed, from Jahn-Teller effect [6], electron correlation [7], to the exciton-phonon coupling [8, 9]. The common explanation to the CDW formation due to Fermi surface nesting must be excluded for 1T-TiSe2 because the Fermi surface does not show evidence of large parallel components in the BZ, i.e., Fermi surface nesting. Jahn-Teller 1.

(14) effect and excitonic condensate became the mainstream explanations on the formation of CDW in recent year. An excitonic scenario is favored as a result of experimental and theoretical predictions. The band-type Jahn-Teller effect was suggested to be responsible for the mechanism of periodic lattice distortion under the CDW state in TiSe2, which lowers the energy by structural distortion from 1T-octahedral to 2H-trigonal prismatic coordination and the energy of Ti 3d band will be lower [10]. Whangbo and Canadell suggested that the structural modulation originates from the p band energy lowering is associated with the Ti–Se bond shortening, and Rossnagel et al., also observed the p band energy lowering in ARPES [11, 12]. Further, Kidd et al. considered electron-hole coupling together with a novel indirect Jahn-Teller effect to drive the CDW transition [13]. The excitonic insulator was first predicted from the theoretical consideration that occurs in semiconductors or semimetals with a small band gap or band overlap at sufficiently low temperature.[14] The description of excitonic condensate was proposed to be similar to the Cooper pairs in BCS theory for superconductor without Meissner effect, but being formed as a bound state to reduce the conductivity. The experimental results of angle-resolved photoemission spectroscopy (ARPES) study [15] and theoretical calculations [16] suggested that backfolded bands with periodic lattice distortion form the valence band at Γ point has a large transfer of spectral weight into L point due to excitonic condensate. This has been the preferred explanation in the formation of CDW state transition so far. Whether the normal state of 1T-TiSe2 is a semiconductor [13, 17-21] or a semimetal [2, 5, 15, 22-26] (as shown in Table 1.1) has been under extensive debate also. Recently, the finding of chiral CDW phase has provided a new viewpoint about the CDW state in 2.

(15) 1T-TiSe2 [26]. Superconductivity (SC) has been introduced via cation-intercalation [27, 28] and pressure [29], which leads to the suppression of the CDW state approaching the quantum-critical-point (QCP) at Tc ~ 0 K [30]. A summary of the 1T-TiSe2 single crystal study reported in the literature is summarized in Table 1.1. In this thesis, we present experimental results of electronic transport and magnetic properties of a series of 1T-TiSe2 polycrystalline samples of different Se vacancy levels in Chapter 4. The CDW state and transition temperature (Tc) was found affected by the Se deficiency level significantly. The normal state of stoichiometric 1T-TiSe2 is confirmed to be a semiconductor based on electrical conductivity. In addition, the nature of electrical transport properties is transformed from a semiconducting to metallic behavior with increasing Se vacancy level. The excitonic condensate played the key role in the CDW transition. A series of 1T-TiSe2 single crystal samples after post-annealing at different temperatures are reported. Two defect types of Se-vacancy and Ti-intercalation on the crystal surface have been observed with STM. The Se vacancy is found dominant for low temperature post-annealed samples, but Ti-intercalation sites become more populated in samples after higher temperature annealing. We propose that the Se vacancy defects are first created by thermal energy, which induces relative excess Ti atoms near the Se vacancy sites. After re-structuring of Se vacancies at high temperature, especially after a prolonged annealing period, the intercalated Ti becomes the dominant defect type for crystal samples. This leads to the softening of the out-ofplane vibration A1g phonon mode, and hardening of the in-plane vibration Eg phonon mode. The details will be discussed in Chapter 5.. 3.

(16) Table 1.1: A summary of single crystal growth of 1T-TiSe2 in the literature, including growth temperature, transport agent used in CVT, and physical property measurements. Types: 1T-TiSe2. Growth. Transport agent. Experiments and normal state. Ti1+xSe2. 1. 575~900 2. 590. Iodine with excess Se (1.5 mg/cm3). Resistivity, Hall effect, neutron scattering (second-order phase transition) Semimetal. TiSe2. unknown. Iodine. Electronic structure Semimetal. [5]. TiSe2. 570-640. Iodine. ARPES, Semiconductor. [13]. TiSe2. Unknown. unknown. ARPES and theoretical calculations Semimetal. [15]. TiSe2. 800-900. Iodine. Optical properties (reflectance). [17]. o. temp. ( C). Reference [2, 22]. Semiconductor TiSe2. 540-640. Iodine with excess Se. ARPES, Eg ~150 meV. [18]. Semiconductor TiSe2. 1. 630 2. 740. TiSe2. Theoretical calclation. TiSe2. 640-540. TiSe2. ARPES, (Eg ~150 meV, Ref:. Iodine. [19-21]. [18] ) Semiconductor LDF (local density fnction) Semimetal. [23]. Iodine with excess Se. ARPES Semimetal. [24]. 500. ICl3 with excess Se. ARPES Semimetal. [25]. TiSe2. 650-550. Iodine. Optical spectroscopy Semimetal. [26]. TiSe2. Sample A: 700. self-vapor transportation method. STM (chiral charge-densitywaves). [27]. Sample B: 800. Ref: [32]. 4.

(17) TiSe2. 650~700. Self-vapor transportation method Se2 (~4mg/cm3). Resistivity, Hall effect. [32]. TiSe2. 1. 450-850 2. 500. A: I2, Br2 B: ICl2 All with excess Se. Resistivity, Hall effect. [33]. TiSe2. 600. Iodine with excess Se. Resistivity, Hall effect under high pressure. [34]. TiSe2. TH = 780 TL = 740. Iodine. Crystal growth. [35]. TiSe2. 590. Iodine with excess Se Ref: [22]. Specific heat. [36]. TiSe2. 660. Iodine with excess Se. Two-photon photoemission. [37]. 3. (3 mg/cm ). (2PPE) spectroscopy. 5.

(18) Chapter 2 Brief review of transition metal dichalcogenides 2.1 Transition metal dichalcogenides (TMDCs) The layered transition metal dichalcogenides consists of layers of three atomic sheets of transition metal elements (M = transition metal of IVA-VIIA elements) sandwiched between chalcogenide atoms (X = chalcogen elements: S, Se, Te) (as shown in Table 2.1), and these layers are bounded by the van der Waals force. The crystal field formed with X-M-X can be arranged in octahedral (AbC) or trigonal prismatic (AbA) coordination as shown in Fig. 2.1. The stacking slabs have various polytypes: including a pure octahedral (e.g., 1T-TaSe2, 1T-TaS2), a pure trigonal prismatic (e.g., 2H-TaSe2, 3R-TaSe2, and 4Ha-TaSe2), or a mixture of both (e.g., 4Hb-TaSe2, 6R-TaSe2) (see Fig. 2.2). The different notations of 1T, 2H, 3R, 4Ha, 4Hb or 6R denote the number and type of layers per unit cell. T, H and R refer to the symmetry of the unit cell, namely trigonal, hexagonal or rhombohedral, respectively, as shown in Fig. 2.2. The polytypic transformation especially for TaSe2 system depends strongly on the heating process, such as quenching from high temperature, slow cooling, or annealing at low temperature. Some of the processes are reversible and some are not, as shown in Fig. 2.3. The electronic properties cover wide range of characters from metals like VSe2 and NbSe2, semiconductors like MoS2, to insulators like HfS2 [1].. 6.

(19) Table. 2.1: The common groups of transition metals for TMDCs of MX2 with X = S, or Se, or Te.. Transition Metal (M). Group. IV. Ti. Zr. Hf. V. V. Nb. Ta. VI. Cr. Mo. W. VII. Mn. Tc. Re. Fig. 2.1: The basic forms of layered TMDCs [1].. 7.

(20) Fig. 2.2: The different stacking types of MX2 for M = group V and VI [1].. 8.

(21) Fig. 2.3: The polytypic transformation in TaSe2 system via different temperature heating process [1].. 2.2 Principles of the CDW: the Peierls transition TMDCs layered compounds show interesting charge density wave (CDW) state of periodic modulations on the charge with concomitant periodic lattice distortion (PLD), which has been discussed widely in the condensed matters physics. This collective phenomenon of intrinsic instabilities often appears in low-dimensional electronic system. Most CDW states are generally related to the Fermi surface nesting with Peierls instability [38]. This Peierls instability transition scenario is a good starting point to understand the origin of CDW transition. For a one-dimensional metal with the lattice of spacing a, its electronic structure consists of a half-filled conduction band with a homogeneous charge density (freeelectron-like) (Fig. 2.4 (a)). The Fermi wave vector is kF = ± π/2a and the interaction of electrons with the underlying lattice is weak. When the periodicity of the charge density modulation is doubled, the Brillouin zone will be cut into half and the energy near the 9.

(22) vector kF will be lowered to open a gap of 2Δ (see Fig. 2.4 (b)), similar to a free electron gas sitting in a periodical potential. Near the kF, the occupied lower electronic branch allows the total electronic energy reduction. Because the lattice distortion doubles the lattice periodicity to display as dimerized ions, the generated lattice elastic energy cost is used to balance the electronic energy gain at the new ground state. This Peierls transition opens a gap at EF and transforms a metal into an insulator. The rearrangement of the ion cores in a Peierls transition would produce periodic fluctuations in the electron density. These are commonly called charge density waves (CDW). The corresponding atomic and electronic structure after this transition is shown in Fig. 2.4 (b). In a one-dimensional metal, there are two parallel planes of Fermi surface separated by the vector 2kF. There are large numbers of electrons under Umklapp scattering with the nesting vector 𝑞⃑ = 2kF (Fig. 2.4 (b)). In a two-dimensional metal, the parallel portions become lines (Fig. 2.5). Therefore, Femi surface nesting is expected to appear more in low-dimensional materials. In the case of 1T-TiSe2, the Fermi surface nesting has been ruled out due to the topology of its Fermi surface without showing large parallel components, the details will be described fully in Section 2.4.. 10.

(23) Fig. 2.4: Peierls transition in a one-dimensional chain. The atomic arrangement and the corresponding electronic band structure (a) before and (b) after the transition [39].. Fig. 2.5: Fermi surface nesting in 1D, 2D, and 3D electron gas [40].. 2.3 CDW and other collective phenomena in the TMDC family In generally, the origin of CDW in TMDCs has been explained due to an emerging electronic periodicity that induces gap opening at the zone boundary, and often being reflected as the Fermi surface nesting in the band picture. The nesting probability will be increased in the reduced dimensionality. Superconductivity is also a different type 11.

(24) of collective electronic condensation in the form of Cooper pair as a CDW, and the coexistence and competition of superconductivity and conventional CDW has been explored intensively. Many high pressure and intercalation studies on the CDW and superconductivity of TMDCs compounds have also been reported, including: 1T-TaSe2: 1T-TaSe2 exhibits an incommensurate (√13 × √13) CDW above Td = 473 K, while a first-order transition CDW locks into a commensurate (√13 × √13)R13.9o modulation below Td = 473 K (as shown in Fig. 2.6) [41]. The actual mechanism is not clear, both the electron-electron and the electron-phonon interactions are taken into account to the possible driving force of CDW [42]. 1T-TaS2: 1T-TaS2 is similar to 1T-TaSe2, it displays an incommensurate (√13 × √13) CDW above Td1 = 352 K and a first-order transition and commensurate (√13 × √13)-R13.9o below Td2 = 200-230 K, being an irreversible behavior with structural hysteresis (as shown in Fig. 2.7) [41]. However, the situation is slightly more complicated to show additional near-commensurate phase between 230 and 352 K. The origin of this CDW is not clear yet and a Mott transition has been proposed to explain the low temperature commensurate phase which is accompanied by an increase in the resistivity [43]. The observation of broad dispersive features below EF and the absence of clear quasi-particles at EF in the commensurate phase has been suggested to be a polaron-based phase at low temperature, instead of nesting [44, 45]. Sipos et al. carried out a pressure effect study to the electronic structure for 1T-TaS2, it was found that the CDW and superconductivity coexist in the pressure range of 1–7 GPa (Fig. 2.8) [46]. 2H-TaSe2: 2H-TaSe2 shows a second-order incommensurate CDW phase transition at 122K and a commensurate (3 × 3) CDW transition at 90K. The mechanism of the CDW was proposed to be in agreement with a significant nesting of the Fermi surface [47]. 12.

(25) 2H-TaS2: 2H-TaS2 undergoes a second-order CDW transition below 70 K, and it also exhibits superconductivity below 1 K [48, 49] (as shown in Fig. 2.9 (a) and (c)). The competition between CDW and superconductivity has attracted great interest to both experimental and theoretical physicists. TMDCs are in general favorable to intercalation of foreign atoms into the van der Waals gap, which opens new opportunities for studying the CDW phase. Wagner et al. have studied TaS2 intercalated with Cu up to 12%, it was found that intercalation of Cu kills the CDW phase progressively, but enhances superconductivity of Tc up to 4K at x ~ 4% (Fig. 2.9) [50]. The CDW and the superconductivity transition temperature for TMDCs are also summarized in Table 2.2.. Fig. 2.6: The synchrotron X-ray transmission Laue pattern for 1T-TaSe2 crystal which exhibits a commensurate CDW √13 × √13 superlattice at room temperature.. 13.

(26) Fig. 2.7: The temperature dependence of resistivity in 1T-TaS2. A metallic state is above 550 K; an incommensurate CDW (ICCDW) phase is above 350 K; an near commensurate CDW (NCCDW) phase is from 190 to 350 K; a commensurate CDW (CCDW) phase is below 190 K [46].. Fig. 2.8: The temperature–pressure phase diagram of 1T-TaS2 [46].. 14.

(27) Fig. 2.9: The electronic phase diagram for CuxTaS2. Cu is proposed being intercalated into the vdW gap of the TaS2 planes [50].. 15.

(28) Table 2.2: The CDW and superconductivity transition temperature of TMDCs.. TMDCs. CDW transition temp. (K). Superconducting transition temp. (K). Reference. 1T-TaS2. Td = 200 K and 352 K. Tc = 1.5-5 K, (2.5-25 GPa). [41, 46]. 2H-TaS2. T0 = 80 K. Tc = 0.8 K Tc = 2.5-4.5 K, CuxTaS2 (x = 0.1-0.12). 4Hb-TaS2. Td = 20 K and 315 K. [41]. 1T-TaSe2. Td = 473 K. [41]. 2H-TaSe2. T0 ~ 120 K. Tc = 0.15 K. [48, 49, 50]. [47]. 2H-NbS2. Tc = 6.3 K. 3R-NbS2. Tc = 5.5 K. [52]. Tc = 7.2 K. [52, 53]. 2H-NbSe2. T0 = 33.5 K. [41, 51, 52]. 2.4 CDW state in 1T-TiSe2 In this thesis, 1T-TiSe2 is focused because the physical properties and the driving force of CDW have been studied extensively over the past 40 years, however, many issues are still under debate as of 2017. Although many previous works were aware of the defect existence in 1T-TiSe2, a systematic and quantitative study is lacking. The influence of defect and its impact on CDW is explored in this thesis. Below we review the basic physical properties and the CDW mechanisms first.. 2.4.1 Crystal structure Unlike other TMDC compounds having many types of structure variation, e.g. 1T-, 16.

(29) 2H-, 3R, 4H-TaSe2, or 2H, 3R-NbSe2, etc., we choose to study TiSe2 which has only on type of 1T-TiSe2. The 1T-type TiSe2 has TiSe6 octahedral coordination packed in 2D layer to show 3D crystal point symmetry in space group P3̅ m1, and the unit cell lattice constants are a = b = 3.534 Å and c = 6.008 Å , as shown in Fig. 2.10.. Fig. 2.10: The crystal structure of 1T-TiSe2. 1T-TiSe2 has attracted great interest because of the puzzling observation of both a CDW transition at Tc ≈ 200K with an accompanied periodic lattice distortion in (2 × 2 × 2) superlattice. However, the observed CDW does not fit into the conventional model of Fermi surface nesting, which led to the debate on the origin the CDW transition until today. In 1976, Di Salvo et al. first studied the 1T-TiSe2 single crystal in detail with neutron-diffraction and electrical transport studies (Fig. 2.11) [2]. Holt et al. showed evidence of phonon-softening behavior near the CDW transition temperature by using x-ray thermal diffuse scattering [54]. Because of the layered structure having van der Waals gap between layers, 1T-TiSe2 is a good candidate for cation intercalation. Many studies of intercalation with different doping elements have been reported, such as Ag [55], Ni [56], Fe [57], Mn [58], Cr [58-60], Co [61], Rb [62], Cu [28], and Pd [29]. Among which, the most interesting one is the report on superconductivity onset at 4 % Cu-intercalated and with Max Tc ~ 4.15 17.

(30) K at 8 %, as well as the Cu doping level forms a dome shape of x-dependence for the superconducting phase [28], as shown in the phase diagram of Fig. 2.12 (b). The lattice parameters evolution upon Cu doping is shown in Fig. 2.12 (a). The lattice parameters show systematic expansion up to x = 0.11 and reach the limit of solubility for CuxTiSe2. High pressure has also been shown to induce superconductivity at 2-4 GPa, and the 𝑀𝑎𝑥 superconducting transition reaches the maximum of T𝑆𝐶 ≈ 1.8 K at about 3 GPa [30]. (Fig. 2.13). The CDW is suppressed by pressure near the quantum critical point (QCP) at 5.1 ± 0.2 GPa to hit the commensurate-incommensurate phase domain wall above the superconducting dome [31] (Fig. 2.14).. Fig. 2.11: In-plane electrical resistivity for crystals of 1T-TiSe2 grown by iodine vapor transport at different growth temperatures (Tg) [2].. 18.

(31) (a). (b). Fig. 2.12: (a) Lattice parameters of CuxTiSe2. (b) The CuxTiSe2 T–x electronic phase diagram [28].. Fig. 2.13: The phase diagram of 1T-CuxTiSe2, where the horizontal axes stand for pressure and the content x of the intercalated Cu [30].. 19.

(32) Fig. 2.14: Pressure–temperature phase diagram of TiSe2 [31].. 2.4.2 Transport properties The CDW transition of 1T-TiSe2 is signified by an abrupt electrical resistivity increase below Tc and reaches a maximum near ~150 K. Whether the normal state of 1T-TiSe2 is a semiconductor or a semimetal has been under debate since the 70s. A positive Hall coefficient RH above Tc indicates the transport charge carriers are dominated by the holes. However, the dominant charge carriers become electrons again at low temperature, as shown by the negative RH [2]. Di Salvo et al. have grown 1T-TiSe2 single crystal at different growth temperature between 575 to 900 ℃ (Fig. 2.11 (a)) and found changes of CDW transition temperature and resistivity ratio 𝜌(max)/ ρ(300K) according to the growth temperature. It was proposed that excess Ti-intercalated into the van der Waals gap between layers as Ti1+xSe2. The physical properties of 1T-TiSe2 have been shown sensitive to small deviations from the stoichiometry, impurities were found to suppress 20.

(33) the CDW state [2].. 2.4.3 Excitonic condensate and Jahn-Teller effect 1T-TiSe2 undergoes a second-order phase transition at Tc ~200 K into a commensurate CDW phase with accompanying (2 x 2 x 2) superlattice. [2, 4]. The the electronic structure has been studied extensively both experimentally [6, 25, 63, 64] and theoretically [23, 65, 66], which exhibits a maximum of Se 4p valence band and a minimum of Ti 3d conduction band. In view of a semimetal, the overlap between the uppermost 4p band at Г and the lowest 3d band at L has been carefully estimated to be smaller than 120 meV [6]. However, the mechanism of CDW formation in 1T-TiSe2 is still controversial, several possible mechanisms have been proposed. Nesting effect: In the case of 1T-TiSe2, the Г point hole pockets and the L point electron pockets should be nesting to induce electron-lattice interaction and produce periodic distortion. However, the Fermi surface nesting was ruled out from the calculated band structure, and the experimental results of ARPES indicates low possibility of nesting near the Fermi level, mostly due to the different shapes of electron and hole pockets [25, 16]. The Fermi surface does not show clear evidence of large parallel components in the BZ of 1T-TiSe2 when CDW emerges. Jahn-Teller effect: Band-type Jahn-Teller effect has been proposed to explain the periodic lattice distortion under the CDW state in 1T-TiSe2 [10]. The overall density of states of the ‘dz2 ’ band is slightly lower for trigonal prismatic than for octahedral coordination in TiSe6 (Fig. 2.15). The periodic lattice distortion (PLD) appears that the upper and lower faces of the trigonal prismatic coordination (Fig. 2.16 (a)). Whangbo and Canadell suggested that the structural modulation originates from the p band energy lowering is associated with the Ti–Se bond shortening in the neighboring octahedron 21.

(34) (Fig. 2.16 (b)) [12]. Rossnagel et al. observed energy lowering is much stronger for the p band (from Se) than for the d band (from Ti) in ARPES, which favors the proposal of Whangbo and Canadell [11]. Furthermore, Kidd et al. proposed that the 1T-TiSe2 is a very small indirect gap semiconductor and the unconventional CDW phase is driven by an indirect Jahn-Teller effect combined with electron-hole coupling [13]. Excitonic insulator phase: In a semimetal with very small number of electrons and holes near the Fermi level, the Coulomb interaction between different carriers is only weakly screened, a bound states between electron and hole is possible and called exciton [3, 5]. This semimetal-semiconductor transition is necessarily accompanied with the periodic lattice distortion, a small band gap or band overlap corresponds to the exciton binding energy [67, 68]. The experimental results of angle-resolved photoemission spectroscopy (ARPES) study [15] and theoretical calculations [16] support the scenario of excitonic condensate. Recent studies preferred the excitonic scenario as the origin of CDW state.. 2.4.4 The intrinsic character of 1T-TiSe2 without Se vacancy defects Except for the debate on the origin of the CDW state, whether the normal state of 1T-TiSe2 is a semiconductor or a semimetal remains to be controversial. The temperature dependence of resistivity usually shows a metallic behavior, except below the CDW transition. In the ARPES investigation, Rasch et al. showed that 1T-TiSe2 has a narrow band gap by adsorbing H2O on TiSe2 crystal surface to bend the conduction and valence band below the Fermi level [18]. However, why is the transport behavior of 1T-TiSe2 exhibiting a metallic behavior experimentally always? We believe doping from the defect formations could affect the intrinsic behavior, i.e., 1T-TiSe2 should not be assumed to be stoichiometric. There are two types of defects in 1T-TiSe2, either due 22.

(35) to Ti excess to form Ti1+xSe2 or Se vacancy to form TiSe2-δ. How much Se is lost in 1TTiSe2 depends on the temperature and time used on post-annealing. The influence of defect type and level on 1T-TiSe2 will be discussed in the following chapters.. Fig. 2.15: The densities of states for octahedral and trigonal prismatic layered materials that the ‘ dz2 ’ band is slightly lower for trigonal prismatic than for octahedral coordination in TiSe6 [10].. Fig. 2.16: There are two kinds of Ti environments for TiSe6 octahedron: (a) top and bottom face of Se atoms rotate around Ti, and (b) Ti moves closer to Se-Se edge of the octahedron [10, 12].. 23.

(36) Chapter 3 Sample preparation and experimental methods 3.1 Polycrystalline sample synthesis and single crystal growth 1T-TiSe2 polycrystalline sample was synthesized using row materials of Ti and Se powders. The precursors with the stoichiometric molar ratio were thoroughly mixed and sealed in an evacuated quartz tube. To avoid Se vapor loss, the heating process used low reaction temperature of 350 ℃ for a prolonged period, with repeated grinding and re-sealing after each 24 hours heating cycle. After the single phase of 1T-TiSe2 was confirmed with X-ray diffraction, the polycrystalline sample was used as the precursor for post-annealing treatments at different temperature, ranging from 350 to 950 ℃ for one day each. Light Se vapor with red brown color was found to deposit on the inner wall of the tube. Some Se vapor was found condensed into droplet-like deposit in shinning black color after the higher temperature annealing. Using single phase TiSe2 polycrystalline sample as the precursor, single crystals of 1T-TiSe2 were grown with the chemical vapor transport (CVT) method, where iodine as the transport agent and sealed together with the precursor in an evacuated. A twozone tube furnace was set at 650 ℃ and 550 ℃ for a gradient in 30 cm. Polycrystalline precursor with transport agent iodine was located at the high temperature zone (Fig. 3.1) initially. Single crystals are grown into 3 x 3 mm2 size and 0.1 mm thick (as shown in Fig. 3.2) at low temperature zone in two weeks. The iodine also condensed at the low temperature zone and mixed with TiSe2 crystals. In order to remove the iodine from crystal mixtures, we re-heated up the low temperature zone to about 300 ℃ to allow iodine condenses to the room temperature end. The as-grown single crystals at 550 ℃ were then separated and vacuum-sealed into 24.

(37) batched to do additional post annealing, from 550 to 950 ℃ for one day each. Light Se vapor deposit was found in the inner wall of the sealed tube after annealing, the higher annealing temperature the thicker Se deposit.. Fig. 3.1: The single crystal growth of 1T-TiSe2 by the CVT method using iodine as the transport agent. The temperature gradient is TH = 650 ℃ and TL = 550 ℃ in 35 cm.. Fig. 3.2: The as-grown 1T-TiSe2 single crystal deposited at the 550 ℃ cold zone by the CVT method.. 25.

(38) 3.2 Powder X-ray diffraction The X-ray powder diffraction (XRD) is an analytical technique primarily used for phase identification of a crystalline material and unit cell dimensions. The purity of a sample can be determined from its diffraction pattern due to symmetry difference, especially used on identifying the presence of impurities phase. The powder diffraction equipment used in this study is shown in Fig. 3.3. There are three movable parts for the XRD measurement, the X-ray source tube, the detector, and the sample holder. Usually only two of the three parts are designed as movable/rotatable in practice. For example, for the Bruker D8 X-ray diffractometer, all three parts are rotatable, but for the D2 PHASER X-ray diffractometer, only two rotatable parts, i.e., the 2θ/θ is locked. The D2 PHASER (Fig. 3.4) is a desktop X-ray diffractometer enabling the analysis of polycrystalline material with all-in-one crystalline phase analysis database. The D8 ADVANCE is a fully extensible modular system and addressing the analytical needs of powder, bulk and thin film samples, at ambient and non-ambient conditions. The D8 diffractometer (Fig. 3.5) can collect with high angular resolution (< 0.008°, 2𝜃) powder XRD patterns of polycrystalline samples. This diffractometer can also be used for routine measurement when samples are large quantity and with automatic sample loader for a series of samples measuring. Our synchrotron X-ray diffraction measurements were performed in the BL01C beamline in National Synchrotron Radiation Research Center (NSRRC), Hsinchu, Taiwan. Comparied with the in-house X-ray equipment, the synchrotron radiation provides much brighter X-ray source and has the advantage of tunable wavelength. The sketch of the synchrotron X-ray setup is shown in Fig. 3.6. The incident photon flux is 1.4 × 1010 photons/sec and to photon energy is 12 ~ 33 keV (1.03 ~ 0.37 Å ). Our 26.

(39) measurements used photons energy of 20 keV (~0.61993 Å in wavelength). The sample was packed in a glass capillary tube of 0.1 mm inner diameter. The incident beam passing through the sample is scattered to arrive an image plate. The diffraction patterns form many concentric lines collected to the image plate and any cross section of the diffraction rings is equal to the in-house XRD pattern as shown in Fig. 3.7.. Fig 3.3: A sketch of X-ray diffractometer. 27.

(40) Fig. 3.4: The Bruker D2 PHASER X-ray diffractometer. Fig. 3.5: The Bruker D8 ADVANCE X-ray diffractometer. 28.

(41) Fig. 3.6: A sketch of synchrotron radiation and the beamline distribution in NSRRC, Taiwan. The powder X-ray diffraction is operated at BL01C beamline. The photon energy of 20 keV (~0.61993 Å ) incident beam passing through the sample and scattered to a detector Mar345 to form a diffraction pattern [69, 70]. 29.

(42) x-ray wave length: 0.6199 Å. Intensity (arb. units). (0 1 1). (0 1 2) (0 0 1). (1 1 0). (2 0 1) (1 0 3) (0 0 4) (1 1 1) (1 1 2). (0 0 2) (1 0 0) (0 0 3). 4. 6. 8. (2 0 0). (2 0 2) (0 1 4) (0 2 3) (1 1 3). 10 12 14 16 18 20 22 24 26 28 30 2 (degree). Fig. 3.7: The XRD pattern for 1T-TiSe2 polycrystalline obtained using synchrotron Xray.. 3.3 Rietveld refinement method A fundamental assumption of the X-ray powder diffraction is the random orientation which means the orientation of each microcrystal is random distribution. In such a condition, each microcrystal scatters rays forming spherical surface in 3-dimensional space (a 2D simplified sketch map is shown in Fig. 3.8). However, the geometry of Xray diffraction (XRD) allows us to collect only one dimensional patterns; resulting in information losses of the reciprocal lattice vectors. For example, in Fig. 3.8 (b), we get ⃑⃑ | , but cannot distinguish two different the absolute value of reciprocal vector |𝐾 reciprocal vectors ⃑⃑⃑⃑⃑ 𝐾1 and ⃑⃑⃑⃑⃑ 𝐾2 . Usually, using Rietveld refinement method can improve the analyzing results of the powder diffraction patterns. The basic concept of the Rietveld refinement method is that all reflecting intensities at each 2θ step should be taken into account in the refinement process, so called full profile refinement. It is different from the old method, which only uses the positions of the constructive interference peaks. The advantage of the Rietveld refinement is that 30.

(43) the modeling pattern would be fully consistent with experiment pattern. There are some requirements of the Rietveld refinement method: (i) a good guess of crystal structure, including space group, lattice constants, and atomic position etc. It provides the refractive peak positions in the 2θ plot; (ii) a suitable profile of the refractive peaks, which gives the intensity distribution away from the constructive peaks, and (iii) a mathematical algorithm to fit the modeling result with experimental data and lead to a more reliable set of parameters. The Rietveld refinement method can be applied on not only X-ray powder diffraction but also neutron diffraction by changing the peaks profile and the equipment parameters. It also has an advantage to analyze thermal vibration of irons or deal with mixed phase powder diffraction. However, it should be noted that the refinement method only models the experimental data and generates a set of well self-consistent parameters (lattice constants and atomic positions, etc.). It cannot be exactly used to solve the crystal structure with only powder diffraction profile. Many softwares have been developed to systematically analyze the XRD data base on the Rietveld refinement method. One of the popular software is General Structure Analysis System (GSAS) which was developed by A. C. Larson and R. B. Von Dreele [71]. The complete guide, software download, manual, and training course can be found in web site [72]. There is also a Graphical user interface to use GASA named EXPGUI which was developed by B. H. Toby [73]. Most of our powder refraction data are refined by GSAS and EXPGUI combined package.. 31.

(44) Fig. 3.8: (a) A 2D diffraction patterns forming a reciprocal lattice. (b) The random orientation powder scattering rays forming bright cycles.. 3.4 Electron probe micro-analyzer (EPMA) EPMA has been used as an analytical tool on non-destructively determination of the chemical composition of solid materials. EPMA is basically identical to a Scanning electron microscope (SEM) with added function of chemical analysis. Electron beam excites the sample to emit X-ray of characteristic frequency corresponding to atoms with intensities proportional to their relative quantity. The characteristic wavelengths and energies (frequency) of these X-rays are analyzed to provide information about the chemical elements in a qualitative analysis. The measured X-ray intensities can be compared with the reference materials of known stoichiometric ratios to determine the actual material element. The principle of incident electron beam and scattered characteristic X-ray of each element is shown in Fig. 3.9. There are two major interaction mechanisms under the influence of electrons bombard on the sample: (1) the inelastic interacting with an inner orbital electron to form “electron hole” and the outer orbital electron filling in to generate discrete wavelengths of X-rays, which is characteristic for different element. (2) When the incident electron beam does not collide with the orbital electrons but being 32.

(45) decelerated by the Coulombic field associated with sample atoms, the inelastic scattering produces a continuous X-ray spectrum, called Bremsstrahlung. This continuous energy radiation forms the background for the characteristic X-ray lines. Other interaction processes include the release of secondary electron, backscattered electrons, and the occurrence of cathodoluminescence. Overall, the effects of electronselements interaction allow an integrated imaging, qualitative, and quantitative chemical analysis for the samples. Our EPMA measurements were performed in the Instrumentation Center, National Taiwan University. The sample thickness should be larger than 100 μm to avoid the electron beam penetrate and scattered the holder signal, especially for layered single crystals. If the material is a semiconductor or an insulator, the sample surface needs to be coated with carbon to assist the scattered electrons to conduct with holder. The total molecular weight percent of quantitative data should be larger than 95% to make sure the signals mostly come from the sample. In 1T-TiSe2 single crystals and polycrystalline, the EPMA quantitative measurements are obtained and calculated more than 10 dots for each sample.. Fig. 3.9: Different types of interaction: (1) ionization and (2) generation of Bremsstrahlung [74]. 33.

(46) 3.5 Magnetic property measurement system (MPMS) The Quantum Design vibrating sample magnetometer (VSM) for the magnetic property measurement system (MPMS) is a fast and sensitive DC magnetometer. The instrument can be used to study the magnetic properties of small experimental samples over a broad range of temperature and magnetic fields. Extremely sensitive magnetic measurements are performed with superconducting pickup coil and superconducting quantum interference device (SQUID). So the MPMS family of instruments are called SQUID magnetometers. The VSM is vibrated at a known frequency and phase-sensitive detection is employed for rapid data collection and spurious signal rejection. The size of the signal produced by a sample is independent on the frequency of vibration, but depends on the magnetic moment of the sample. The MPMS SQUID-VSM utilizes a superconducting magnet with a solenoid of superconducting wire to subject samples to magnetic fields up to 7 Tesla (70000 Oe). The SQUID and superconducting magnet must be cooled with liquid helium. Liquid helium is also used to cool the sample chamber, providing temperature control of samples from 400 to 1.8 K. The instrument of SQUID-VSM is shown in Fig. 3.10.. 34.

(47) Fig. 3.10: QD-SQUID VSM instrument with the helium cryo-cycle compressor in the Center for Condensed Matter Sciences (CCMS), National Taiwan University.. 3.6 Physical Property Measurement system (PPMS) The PPMS provides a flexible, automated workstation that can perform a variety of experiments requiring precise thermal control to execute magnetic, electric-transport, or thermoelectric measurements (the instrument as shown in Fig. 3.11). The principle and technique of transport measurements are introduced below using a Quantum Design (QD) PPMS. 35.

(48) Resistivity: In a four-wire resistance measurement, current is passed through a sample via two current leads, and two separate voltage leads measure the potential difference across the sample (Fig. 3.12). In theory, a perfect voltmeter draws no current whatsoever. Therefore, by using the four-wire method, it is possible to know, to a high degree of certainty, both the current and the voltage drop across the sample and thus calculate the resistance with Ohm’s law. The resistivity 𝜌 is calculated by 𝜌 =. 𝑉𝐴. (3.6.1). 𝐼ℓ. where V is the measured potential drop across the sample and I is the current through the sample, the voltage lead separation ℓ and the cross-sectional area through which the current passes A. Hall coefficient: When charge carriers move perpendicular to magnetic field, a force is exerted on them perpendicular to both the field and the direction of carrier motion ⃑⃑. F = q𝑣⃑ × 𝐵. (3.6.2). Therefore, a transverse current is passed through a sample in a longitudinal magnetic field, charge carriers often build up on one edge of the sample and disappear from the other edge, leading to a potential difference across the sample to be named as the Hall potential (see Fig. 3.13). The signal of the Hall potential generally indicates a conductor/semiconductor is n-type or p-type, and the magnitude of the Hall potential is related to the density of charge carriers in the sample. The Hall coefficient Rh describes these two properties is defined by RH =. 𝐸𝐻 𝑗𝐵. =. 𝑉𝐻 𝐴 𝐼ℓ𝐵. =. 1 𝑛𝑞. ,. (3.6.3). where 𝐸𝐻 is the Hall field, VH is the Hall potential, j is the current density given by I/A (which is the current divided by the sample cross section), and ℓ is the separation of the transverse voltage leads. It can be shown that RH = (nq)-1 (in units of Ω-cm/Oe = 108 cm3/coulomb) with n representing the number of charge carriers per unit volume in 36.

(49) the sample, and q representing the charge of the carriers. Thermal transport: Thermal conductivity is a measure of the ability of a material to conduct heat, so measuring this quantity provides information about scattering of heat-carrying phonons and electrons. The Seebeck coefficient describes the thermal diffusion of free charge carriers (electrons or holes), which creates an electric field inside a material when a temperature gradient is sustained. Much like the electrical resistivity, this property is very sensitive to subtle changes in the electronic scattering processes and can be a powerful probe in that regard.. Fig. 3.11: The QD-PPMS instrument with the helium cryo-cycle compressor in the Center for Condensed Matter Sciences (CCMS), National Taiwan University.. 37.

(50) Fig. 3.12: A sketch of the four probe method for resistivity measurement [75].. Fig. 3.13: A sketch of Hall effect measurement [76].. 3.7 Scanning Tunneling Microscopy (STM) STM is a Surface imaging instrument to resolve the atomic scale of surface structure which was invented by G. Binnig and H. Rohrer in 1981 [77]. The resolution can be < 1 Å lateral resolution and < 0.1 Å depth resolution under the ultra-high vacuum Pressure (P ~3 × 10-11 torr). It provides highly accuracy microscopy technique and convenient to use, but it is limited to observe the surface structure of the materials. In-depth investigate the bulk structure of the materials still need X-ray or neutron diffraction, or transmission electron microscopy techniques. STM still has a potential to figure out the 38.

(51) characteristics of materials, and the surface/interface structure on two-dimensional materials where become more interesting and important in future. STM basic components (also shown in Fig 3.14): 1. A sharp tip as a probe (The tip is often made of tungsten or platinum-iridium) 2. A piezoelectric scanning unit, which can control the lateral and vertical motion of the tip. 3. A coarse positioning unit, which moves the tip to approach the sample and tipsample separation (~ few Å ) to be the tunneling range. 4. A vibration isolation stage to avoid acoustic and mechanical vibration to interfere the scanning system. 5. A set of electronics, which can detect the small tunneling current (∼10 pA-1 nA), controls the piezo-tube scanner with feedback, and drives the coarse positioning. In STM principle, a bias voltage is applied between the tip and the sample. When the tip is approached within about 10 Å of the sample, tunneling electrons from the sample through the 10 Å gap to the tip is a filled state. On the other hand, an empty state means electrons tunnel from tip to sample at positive sample bias. The result of tunneling current varies with tip-to-sample spacing, and the sample must be conductors or semiconductors. Thus, STM cannot image insulating materials. The tunneling current is an exponential function of distance. Based on quantum mechanics, the tunneling current (It) is 𝐼𝑡 = 𝑒 −𝑘𝑑. (3.7.1). where d is the distance between tip and sample. If the tip-sample separation changes by the order of 1 Å , the tunneling current will change by an order of magnitude. There are three basic operation modes in STM imaging: 39.

(52) Constant current mode: By using a feedback loop to set the tunneling current always constant and the tip is vertically adjusted with different atomic height of sample surface. When the current is proportional to the local density of states, the tip follows a contour of a constant density of states during scanning. The vertical position of the tip reflects on a topographic image of the surface (as shown in Fig. 3.15 (a)). Constant height: This mode also known as current imaging mode. In this mode the vertical position of the tip is fixed, the current as a function of lateral position represents the surface image. This mode is only appropriate for atomically flat surfaces or otherwise a tip would be crashed unpredictable. One of its advantages is that it can be used at high scanning frequencies as fast as to 10 kHz (about 1 image per 0.1 second). In comparison, the scanning frequency in the constant current mode is about 1 image per several minutes (as shown in Fig. 3.15 (b)). Scanning tunneling spectroscopy (STS): STS is a set of methods of STM which the voltage between the tip and the sample is varied to obtain the information on the local electronic structure of the surface.. Fig. 3.14: A Schematic diagram of STM [78, 79].. 40.

(53) Fig. 3.15: Schematic representation of operation of a scanning tunneling microscope in (a) constant current mode and (b) constant height mode [80, 81].. 3.8 Raman scattering spectroscopy The Raman effect was first observed by Raman and Krishnan in 1928 [82], although the Raman effect had been predicted by Smekal in 1923 [83]. Raman and Krishnan reported the phenomenon obtained by many liquids, some gases, crystals, and amorphous substances like glass. They reported the appearance of modified lines on either side of the exciting line, the lines appearing on the longer wavelength (Stokes) side being more numerous and intense than the ones appearing on the shorter wavelength (anti-Stokes) side. They showed that the difference between the frequencies of the emitted radiations and the frequencies of the exciting radiation, closely agreed in many cases with the frequencies of infrared absorption bands of the same substances. The frequency shifts observed in scattering are the frequencies of oscillation of the chemically bonded atoms of a molecule which is dependent on the geometry of the molecule and the forces of chemical affinity. Pringsheim recognized Raman’s discovery and named the new scattering phenomenon as Raman effect, as well as the spectrum of the new lines is Raman spectrum [84, 85]. The Raman effect can be described as the inelastic scattering of light by matter. When a photon of the visible light, too low in energy to excite an electronic transition, interacts 41.

(54) with a molecule, it can be scattered in one of three ways. It can be elastically scattered and thus retain its incident energy or it can be inelastically scattered by either giving energy up, or by removing energy from the molecule. Photons undergoing inelastic loss of energy give rise to Stokes scattering while photons undergoing inelastic gain of energy give rise to anti-Stokes scattering. The energy gained by the molecule in Stokes scattering appears as vibrational energy and where a molecule has excess vibrational energy above the ground state, it is the energy which is lost to the anti-Stokes scattered photons. The Raman scattering spectroscopy provides an extraordinary easy and convenient way to realize the lattice vibration of the materials and develops a wholly new field in the study of molecular structure. The Raman scattering spectroscopy instrument in our lab is SENTERRA R200L (No. 127) which has a frequency resolution with 0.5 cm -1. The optical setup of Raman scattering spectroscopy also shown in Fig. 3.16. The instrumental components will be described in below. Laser source system: There are three kind of laser source, one is the 532 nm wavelength laser line that is excited by diode-pumped solid-state laser (DPSS) with 20 mW maximum power. Another one is the 488 nm wavelength laser line that is also excited by DPSS laser with 40 mW maximum power. And the other one is 785 nm wavelength laser line that is excited by diode-laser with 100 mW maximum power. The excitation laser light passes through a microscope objective lens which is the Olympus BX51 microscope model for focusing with the x100 (NA = 0.9) magnification for 1 ~ 2 μm spatial resolution. The focused laser light incidents perpendicular to the sample surface, and then the scattering light signal is detected by charge coupled device (CCD). Spectrometer system: The spectrometer type of Raman scattering spectroscopy instrument is dual grating which has three kinds of raster density. The raster density is 42.

(55) based on the replacement of two different wavelengths of laser. When 532, or 488, or 785 nm wavelength light source is applied, the 400, or 1200 grooves/mm raster density of grating will be used in the spectrometer. The 1200 grooves/mm raster density of grating is usually used for obtaining the high resolution spectra. Detector system: The number of the equipment is Infinit 1 which is a CCD. The detector has a silicon chip with the two-dimensional photonic array of the 1024 × 256 pixel resolution. The best working temperature of the equipment is about -60 ℃.. Fig. 3.16: A sketch of the setup of the micro-Raman scattering.. 43.