Properties of Charge Density Waves
in 1T-TaS
2
THESIS
submitted in partial fulfillment of the requirements for the degree of
MASTER OFSCIENCE
in PHYSICS
Author : Wouter Gelling
Student ID : 1250485
Supervisor : Johannes Jobst
Daily Supervisor : Tobias de Jong
1st corrector : Jan van Ruitenbeek
2ndcorrector : Jan Aarts
Properties of Charge Density Waves
in 1T-TaS
2
Wouter Gelling
Huygens-Kamerlingh Onnes Laboratory, Leiden University P.O. Box 9500, 2300 RA Leiden, The Netherlands
March 27, 2019
Abstract
In this project, magneto-transport measurements are performed on exfoliated trigonal tantalum disulfide (1T-TaS2) flakes with a top-contact Hall-bar
geome-try. Transport measurements reveal the presence of charge density waves and the related nearly-commensurate to commensurate phase transition. The phase transition is shown to depend on both the thickness of the crystal and the cool-ing rate. The observed critical thickness is approximately 80 nm, relatively large compared to literature. A clear deviation from literature is observed in the resistive behavior during the transition. The increase in resistivity due to the transition is considerably smaller and less abrupt. This deviation may be attributed to partial switching of the crystal, i.e. only some of the layers switching to the commensurate phase. Hall effect measurements in the super-cooled phase, i.e. below the suppressed phase transition, reveal large charge carrier density and extremely low mobility, both in agreement with literature. A down-turn is observed in the supercooled phase at low temperatures. This down-turn is also observed in literature, however its origin is not discussed. We propose that this down-turn is caused by weak anti-localization. The phase coherence length, extracted from fitting of the Hikami-Larkin-Nagaoka model (HLN) model to the weak anti-localization peaks, follows a power law with ex-ponent γ = −0.341±0.03. This exponent suggests that the electron transport is one-dimensional, substantiating the notion that in the nearly-commensurate phase, the electron transport is dominated by the domain boundaries.
1 Introduction 7
2 Charge Density Waves 9
2.1 Brief theoretical description . . . 9
2.2 Tantalum disulfide . . . 13
2.2.1 Transport in 1T-TaS2 . . . 15
2.3 Tunability of charge density waves in 1T-TaS2 . . . 17
2.3.1 Tuning by sample thickness . . . 17
2.3.2 Tuning by cooling rate . . . 19
2.3.3 Tuning by source current . . . 20
2.3.4 Tuning by pressure . . . 21
3 Nano-fabrication and Experimental Techniques 23 3.1 Electron-beam lithography . . . 23
3.2 Evaporation . . . 25
3.3 Atomic force microscopy . . . 26
4 Method 29 4.1 Sample fabrication . . . 29 4.1.1 Substrate preparation . . . 30 4.1.2 Stamping . . . 33 4.1.3 Overlay . . . 36 4.1.4 Height determination . . . 39 4.2 Measurement set-up . . . 40
5 Results and Discussion 43 5.1 Electrical properties of 1T-TaS2 . . . 43
5.1.1 Thickness dependence . . . 44 5.1.2 Cooling rate . . . 47 5.2 Magneto-transport . . . 50 5.2.1 Hall effect . . . 50 5.2.2 Down-turn . . . 52 6 Conclusion 57 7 Outlook 59 8 Acknowledgements 61
Appendices 67
A 69
Chapter
1
Introduction
Reducing the dimensionality of a system is often associated with exceptional electronic, optical and magnetic properties, as the reduction of available phase space and diminished screening lead to enhanced quantum effects and increased correlations. 2D materials, also known as Van der Waals materials, are layered materials characterized by extended crystalline planar structures held together by strong in-plane covalent bonds and weak out-of-plane Van der Waals forces. These forces allow for isolation of single layers by means of mechanical exfolia-tion (repeated peeling by adhesive tape), commonly known as the ”Scotch-tape method”. The first material to be included to the family of 2D materials was graphene [1] (a zero-overlap semimetal). The family of 2D crystals has grown to include metals (e.g., NbSe2), semiconductors (e.g., MoS2), and insulators (e.g.,
hBN). A plethora of opportunities appear when layers of different 2D materials are combined in one vertical stack [2], a so-called heterostructure (see Figure 1.1) allows researchers to explore novel and exciting physical phenomena such as collective quantum phenomena at the interfaces (e.g., superconductivity in the heterostructure of graphene and boron nitride [3]). A sub-group of the 2D fam-ily are the Transition Metal Dichalcogenides (TMDs). TMDs offer a broad range of electronic properties including collective phenomena such as superconduc-tivity (e.g., 2H-TaSe2) and charge density waves (e.g., 1T-TaS2). Charge density
waves in 2D crystals are known for a long time [4, 5], however nowadays still a most active research topic [6, 7]. The latest interest in TMDs arose from the coexistence of charge density waves and superconductivity in their phase dia-grams [8], their intricate interplay may possibly answer essential questions on high temperature superconductivity [9]. Although most of the electronic prop-erties of TMDs and their various charge density wave phases have been char-acterized, we are still far from understanding how and why the charge density waves in quasi-two-dimensional systems are formed [10].
In this work, the electronic properties of charge density waves in trigonal tanta-lum disulfide (1T-TaS2) have been investigated. The goal of this project was to
characterize the electronic properties of the crystal grown by HQ-Graphene R and to get a better understanding of charge density waves, including its asso-ciated transport mechanisms. This work could furthermore substantiate future
Low Electron Energy Microscopy (LEEM) measurements on 1T-TaS2performed
by my daily supervisor Tobias de Jong.
This thesis is structured as follows: Chapter 2 consists of a brief theoretical description of charge density waves and a description of 1T-TaS2 including its
electronic properties. Chapter 3 describes the nano-facbrication and experimen-tal techniques. The method, chapter 4, describes the nano-fabrication process, the measurement set-up and the measurement process are described. Results are discussed in Chapter 5, followed by a conclusion and outlook.
Figure 1.1:Building Van der Waals heterostructures. With the right technology, the con-struction of a huge variety of layered structures, analogous to LEGO, becomes possible. Taken from [2].
Chapter
2
Charge Density Waves
2.1
Brief theoretical description
A Charge Density Wave (CDW) is a modulation of the conduction electron den-sity, accompanied with a modulation of the lattice atom positions. Considering the 1D metal made of a linear chain of atoms with a inter-atomic spacing of a, including a cosinusoidally modulated electron density of the form:
ρ(r) = ρ0(r)[1+ρ1cos(q0r+φ)], (2.1)
where ρ0is the unperturbed electron density. The term within the square bracket
is what is known as a CDW, with amplitude ρ1, wavevector q0, and phase φ.
The phase describes the position of the charge density wave relative to the ions of the underlying lattice. The CDW causes each ion in the atomic lattice to ex-perience a modulated potential, forcing the ions to new equilibrium positions. The resulting periodic lattice distortion (PLD) has the form:
un =u0sin(n|q0|a+φ), (2.2)
where u0 is the amplitude of the modulation, typically small compared to a.
One may also consider the scenario in which a PLD of the form eq. (2.2) causes screening of the conducting electrons resulting in a CDW of the form eq. (2.1), demonstrating that a CDW and PLD are inseparably connected. Whether the PLD or CDW comes first, i.e. which is the driving force behind the formation, remains an open question. The CDW can either be commensurate with the crystal lattice, with a wavelength of an integer multiple of the lattice vectors, or more generally incommensurate in which case there is no preferred phase relation to the lattice.
A distortion of the atomic lattice will have a Coulomb and elastic energy cost ELattice, however, energy may be gained due to the opening of a band gap near
the Fermi energy, effectively lowering the conducting electron energies Eelectron.
In the case for which∆E = ∆Eelectron+∆Elattice <0, the system undergoes a
tran-sition to a new stable ground state with a spontaneously broken translational symmetry: Essentially a structural phase transition driven by strong electron-phonon coupling. The mechanism by which a CDW ground state might form was first proposed by Rudolph Peierls in 1930 [4]. The 1D equivalent of a CDW is known as the ”Peierls instability” and will be discussed in the following sec-tion.
Figure 2.1: The electron band of a 1D monovalent chain. (Left) Unperturbed atomic chain: The conduction band is exactly half-filled, following parabolic dispersion. (Right) Distorted atomic chain: Due to the periodic potential ρ(x), induced by the dou-bling of periodicity of the atomic lattice, a band gap (2∆CDW) opens up near the Fermi
Peierls instability In the case of a 1D monovalent chain of length L and inter-atomic spacing a (see Figure 2.1), the electrons are uniformly spaced in k-space with a spacing of 2π/L. As each atom contributes one electron, the conduction band will be exactly half-filled up to kF = π/2a. The 1D system will therefore
behave as a normal metal. However, when the lattice is distorted in such a way that every two atoms are slight moved towards one another (dimerization), a periodic a potential is introduced with periodicity 2a. The effect of this potential (close to kF) can be calculated by means of degenerate perturbation theory. The
Fourier components of the potential couple both points on the Fermi surface, resulting in the opening of a gap opening near the Fermi energy, as shown in Figure 2.1 (b). In general, a modulation of the lattice atoms of the in eq. 2.1 with
q0 = 2kF will produce gaps at±kF. The electrons residing in a state below the
gap are lowered in energy, the energy gain∆Eelectronis indicated in Figure 2.2 by
the hatched area. At high temperatures, the energy gain is reduced by thermal excitation of electrons across the gap such that the metallic state is maintained. However, at low enough temperatures, the energy gain of the electrons will eventually exceed the elastic energy loss, in which case the formation of a CDW becomes the preferred ground state. This is an example of a 1D Metal-Insulator-Transition (MIT).
Figure 2.2: When a band gap is opened up near the Fermi energy (kF = π/2a)), all
of the electron residing below the gap will be lowered in energy. The hatched area indicates the electron energy gain due to opening of the band gap. Adapted from [12].
Fermi nesting The occurrence of CDW in the majority of materials is not yet completely understood [10, 13]. Important to note is that the influence of Fermi surface nesting has in recent papers been questioned [14, 15]. Formation of CDW in more complex cases is typically described using linear response theory [16], which treats the response of an electron gas to a time independent poten-tial. Linear response theory shows that the CDW is only stable, i.e. energetically favorable, in 1D. Intuition on why the CDW is only stable in the 1D may arise from the shape of the Fermi surface, visualized in Figure 2.3. For an electron gas in 1D, the Fermi surface exists of two points, coupled by one vector q = 2kF.
All the electronic states will be lowered in energy when a gap opens up near the Fermi level, known as perfect nesting. In 2D, however, one vector may only couple an infinitesimal part (two points) on the Fermi surface (circle), see Fig-ure 2.3 (b). Therefore, the relative electronic energy gain due to gap opening is severely decreased. A similar story holds for 3D, where the Fermi surfaces (sphere) allows very little electron energy gain as there is no ideal vector (no nesting). While no material is strictly one-dimensional, a number of inorganic materials form very an-isotropic crystals, which lead to strongly an-isotropic electronic structures. An example of a ”quasi-2D” Fermi surface is depicted in Figure 2.3 (c). A substantial part of the Fermi surface is coupled by the same nesting vector, known as partial nesting. 1T-TaS2 is one of such materials and
will be thoroughly discussed in the next section. Further theoretical description lies outside the scope of this research project, for which I would like to refer to a recent overview paper on both the theoretical and experimental aspects of charge density waves [10].
Figure 2.3: Fermi surface nesting in 2D. (a) A parallel plate Fermi surface is perfectly nested by 2kF. (b) The Fermi surface of a 2D free-electron gas is cylindrical. Only two
points, an infinitesimal part in this case, are connected for a given nesting vector. (c) An elliptically shaped Fermi surface has large parallel components, allowing for partial nesting. Adapted from [11].
2.2
Tantalum disulfide
Tantalum disulfide (TaS2) belongs to the group of Transition Metal
Dichalco-genides (TMDs), layered semiconductors with chemical formula MX2. Where
M is a transition metal, i.e. an element with a partially filled d-orbital∗, and X a chalcogenide (X = S, Se, Te). TaS2 is a layered compound with three-coordinate
sulfide centers and trigonal prismatic metal centers, as depicted in Figure 2.4. TaS2has several crystalline phases, dependent on the relative orientation of the
sulfur atoms to the tantalum, such as trigonal (1T), hexagonal (2H) and rhom-bohedral (3R). More exotic polytypes have been reported in literature such as 6R and 4Hb [17]. The resistive behavior of each polytype is drastically different. The 1T phase exhibits a CDW and a Mott insulator state at low temperatures. In contrast, the 2H phase is a superconductor with a critical temperature Tc =
0.5 K [18].
Figure 2.4: Schematic representation of bulk TMDs, each layer consists out of a transi-tion metal sandwiched by two chalcogen atoms. The monolayers are bound together only by Van der Waals forces.
The CDW reconstruction of the 1T-TaS2 lattice forms a ”Star of David” pattern
as shown in Figure 2.5 (left). Every 12 Ta atoms move inward with respect to one central Ta atom, introducing a new periodicity of√13a. This new lattice vector is rotated by 13.9◦with respect to the original lattice vector, forming√13 x√13 diamond shaped supercells. Density-Functional Theory (DFT) band structure calculations of 1T-TaS2 reveal the opening of a gap near the Fermi energy in
the in-plane direction within the reconstructed supercell [10, 19]. In contrast, there is no formation of a gap in the out-of-plane direction. The presence of the ”Star of David” pattern has been demonstrated by means of Scanning Tunneling Microscopy (STM) imaging [20]. Similarly, Transmission Electron Microscopy (TEM) reveals new Bragg beaks in diffraction space after the CDW phase
sition, induced by the periodicity of the supercell [21]. DFT calculations and di-rect measurement of the Fermi surface by Angle-Resolved Photoemission Spec-troscopy (ARPES), have revealed its quasi-2D nature [11, 22]. The quasi-2D shaped Fermi surface allows for several nesting vectors, but no clear evidence has been found for Fermi surface nesting as a key scenario for CDW formation in 1T-TaS2. In addition to the different polytypes, the CDW may also reside in
Figure 2.5: (Left) Reconstruction of the 1T-TaS2lattice. 12 Ta atoms move inward with
respect to one central Ta atom, forming a ”Star of David pattern” including a√13 x√13 supercell (the dashed shape). Adapted from [23]. (Right) Schematic representation of the Ta atom network in the commensurate (left), hexagonal nearly-commensurate (middle), and incommensurate (right) phase. Adapted from [24].
several different phases. Dependent on temperature, the CDW is either in phase with the underlying lattice (Commensurate;CCDW), slightly out of phase (Nearly Commensurate;NCCDW) or completely out of phase (In-Commensurate;IC). The angle of the superlattice with respect to the undisturbed lattice rotates from 0 to
12◦ ± 1 to 13.9◦, for the ICCDW/NCCDW/CCDW phase, respectively. In the
NCCDW phase, commensurate domains are present, arranged in a hexagonal ’super-superlattice’ separated by incommensurate areas [25]. An impression of the lattice reconstruction for each phase is visualized in Figure 2.5 (right). Upon cooling, 1T-TaS2undergoes two successive first-order phase transitions: Firstly,
from ICCDW to NCCDW at 350 K, secondly from NCCDW to CCDW between 100–150 K. Each transition involves both conduction electron and lattice degrees of freedom: Large changes in electronic transport properties occur, concomitant with structural changes to the lattice. The electron transport properties of 1T-TaS2will discussed in the next section.
2.2.1
Transport in 1T-TaS
2The CDW phase transitions have drastic consequences on the resistive behavior of 1T-TaS2. As mentioned before, a gap is opened up within the reconstructed
supercell near the Fermi level in the in-plane direction. It is suggested that in the NCCDW phase, the free electrons in domain boundaries realize the con-ducting state [26, 27]. However, in the CCDW phase, only twelve out of thirteen electrons of the new unit cell occupy the electronic states below the gap energy created by the deformation. The ’thirteenth’ electron (donated by the central Ta atom of the ”Star of David” structure) resides above the deformation-induced gap [28]. The conductivity is further suppressed upon cooling below 2 K due to the formation of a Mott-insulator state of the electrons residing above the gap [29]. Within the intermediate regime, below the NCCDW–CCDW transition, bulk flakes decrease in resistivity upon cooling, in contrast to the decreasing resistivity of thin flakes. Recently, the resistive behavior was shown to be dom-inated by Arhenius hopping (ρ ∼e−T0/T), over a substantial temperature range in 75 nm and 90 nm thick flakes [30]. In the same paper, large anisotropy of the resistivity (ρ⊥/ ρk ∼1000) was demonstrated by in-plane and out-of-plane
transport measurements. Currently, the mechanism behind switching is still debated, in particular whether the pertinent physics is confined to the individ-ual 1T-TaS2layers, or 3D stacking plays an important role in the switching and
ordering [31].
Figure 2.6: Temperature dependence (T) of the resistivity (ρ) for bulk and nano-thick crystals of 1T-TaS2 including the incommensurate (ICCDW), nearly-commensurate
(NCCDW), commensurate (CCDW) and supercooled (SC) phase. The solid and dashed lines represent the cooling and warming cycle, respectively. Taken from [24].
Typical resistive behavior of 1T-TaS2 is shown in Figure 2.6. Well above room
temperature (T≈350 K), 1T-TaS2undergoes its first transition from the ICCDW
phase to the NCCDW phase. During this transition, the resistivity is increased by half an order of magnitude. Upon further cooling, the resistivity increases
monotonically until around T≈150 K, at which 1T-TaS2 undergoes its second
phase transition from the NCCDW phase to the CCDW phase. During this transition, the resistivity is increased by an order of magnitude. This phase transition exhibits clear hysteresis, as upon warming the NCCDW phase is only
retrieved at T≈220 K. The temperature at which the NCCDW-CCDW
transi-tion occurs seems thickness dependent, as the difference between the transitransi-tion temperature of bulk and thin flakes is almost 80 K.
The resistivity just after the NCCDW–CCDW transition remains finite due to the single electron residing above the band gap. The remaining conductivity is completely suppressed at low temperature due to electron-electron interac-tion, eventually forming a Mott-insulator ground state below 2 K. The red curve (24 nm) does not exhibit a NCCDW–CCDW transition and remains in the NC-CDW phase at low temperatures. This phase is known as the supercooled (SC)-NCCDW phase, once more adding a phase to the complicated phase diagram of 1T-TaS2. The nature of the meta-stable supercooled phase and the
2.3
Tunability of charge density waves in 1T-TaS
2Research has shown that the CDW in 1T-TaS2 may be tuned and even
com-pletely suppressed [21, 24, 27, 32, 33]. The NCCDW–CCDW transition, es-pecially in thin flakes, is very sensitive to the experimental conditions. The ICCDW–NCCDW transition, however, seems much more robust, only suppress-ible in extreme conditions. Once the ICCDW–NCCDW transition is suppressed, the general resistive behavior is completely altered, eventually resulting in a superconducting ground state [27, 33]. Several parameters of influence on the CDW in 1T-TaS2 are: Thickness, cooling rate, source current and pressure. In
this chapter the parameters and their influence on the CDW are discussed in greater detail.
2.3.1
Tuning by sample thickness
Figure 2.7: Temperature dependence of the sheet resistance for nano-thick crystals of 1T-TaS2. The solid and dashed lines represent the cooling and warming cycle,
respec-tively. Taken from [32].
Yoshida et al.’s results on the temperature dependence of the CDW phases
in 1T-TaS2 [32] are shown in Figure 2.7. They show full suppression of the
NCCDW–CCDW transition for flakes approximately below 40 nm in thickness. The ICCDW–NCCDW transition, however, remains robust down to 7 nm. In contrast, Tsen et al. [21] show the presence of the NCCDW–CCDW transi-tion in much thinner flakes, down to a few nm. The main difference may be
attributed to oxidation, in Tsen et al. flakes are exfoliated in an oxygen defi-cient environment (nitrogen inflated glove box) and directly capped by a layer of hBN. Whereas in Yoshida et al., flakes have been exfoliated under normal ambient conditions, in which oxidation is inevitable. High-resolution electron microscopy and energy dispersive spectroscopy reveal the strong presence of oxidation, i.e. the presence of an amorphous oxide layer of a few nm in thick-ness. It is suggested in Tsen et al., that oxidation leads to strong surface pinning which might possibly destroy charge ordering in ultra-thin samples.
A general feature seems to be the fact that the resistive behavior upon cooling and warming does not always reproduce. An example of this feature is shown in Figure 2.7 (31 nm), the flake undergoes what seems to be a NCCDW–CCDW transition during the warming cycle, but not during the cooling cycle†. It is not yet fully understood whether the suppression of the transition is due to intrin-sic effects related to thinning, or extrinintrin-sic consequences of oxidation. In another paper of M. Yoshida et al. [24], on the potential of memristive phase switching in 1T-TaS2, the following is mentioned: ”In terms of statistical mechanics, a
contin-uous change of a physical parameter such as thickness cannot result in such a sudden disappearance of long-range ordering. We therefore need to use another viewpoint-that of kinetics”. It is suggested that thinning reduces the growth kinetics, and that the growth kinetics are inseparably connected to the cooling rate, demonstrat-ing there exists a general trend in the phase diagram between a critical cooldemonstrat-ing rate and the critical thickness (Figure 2.8).
Figure 2.8:Critical cooling rate (Rc) versus thickness phase diagram. Taken from [24].
†”The transition on warming is not reproducible but certainly occurs in several occasions. This behavior suggest that the NCCDW–CCDW transition is hidden in the measured condition.”[32]
2.3.2
Tuning by cooling rate
Figure 2.9:Temperature dependence of the resistivity for different thicknesses at differ-ent temperature-sweeping rates. The solid and dashed lines represdiffer-ent the cooling and warming cycle, respectively. Taken from [32].
Yoshida et al. shows the dependence of the NCCDW–CCDW transition on the cooling rate in 1T-TaS2, see Figure 2.9. For bulk, the NCCDW–CCDW transition
remains robust up to high cooling rates (10 K/min). Thinner flakes, however, seem much more dependent on the cooling rates. At first only the transition temperature is altered, however, once the critical cooling rate is reached, the NCCDW–CCDW transition is completely suppressed. The ICCDW–NCCDW transition remains present, similar to the previous paragraph on thinning in-duced suppression of the NCCDW–CCDW transition. Once the NCCDW–CCDW transition is suppressed (i.e. the Mott-insulator ground state), the crystal re-mains in the supercooled phase. In this particular example, the NCCDW–CCDW transition in a 31 nm crystal was only achieved at cooling rates of 0.2 K/min, implying the importance of well-defined measurement conditions. During the warming cycle of the supercooled 21 nm thick crystal, a NCCDW-CCDW tran-sition is observed. Hall effect measurements, inlay of (b) in Figure 2.9, show the huge change in charge carrier density at 2 K for different cooling rates. Follow-ing up on the suggestion that the conduction is dominated by the free electrons within the domain boundaries, Yoshida et al. suggests that the cooling rate influences the growth kinetics of the CCDW domains. At lower cooling rates
CCDW domains have more time to grow, effectively decreasing the amount of free charge carriers. Higher cooling rates result in smaller CCDW domains, and therefore a larger charge carrier density. Interesting to note is the down-turn of the resistance for the 61 nm crystal. The resistance of the supercooled crys-tal monotonically increases down to ∼ 20 K, after which the resistance starts to decrease again. In Yoshida et al. it is mentioned that at low temperatures a metallic state is formed.
2.3.3
Tuning by source current
Figure 2.10: (a) AC resistance vs. temperature for a 4-nm thick device as a function of the DC-current. (b) Current vs. voltage sweep (3-6 V/min) at 150 K starting at the NCCDW phase (top) and CCDW phase (bottom). Adapted from [21].
The measurement conditions are of crucial importance on the CDW transitions in 1T-TaS2. One of such conditions is the in-plane current as shown by W. Tsen
et al [21], Figure 2.10 (a). The resistive behavior of a 4 nm thick crystal is mea-sured (AC) at several different in-plane DC source currents (2-wire), showing that the resistive behavior including the NCCDW–CCDW transition might be drastically altered. The NCCDW–CCDW seems to be fully suppressed at an in-plane current I = 27 µA, suggesting that constant current flow hinders the formation of the CCDW phase. However, as the actual dimensions of the con-ductive channel are unspecified, the current-density cannot be deduced. Fur-thermore, it is shown in 2.10 (b) that the NCCDW–CCDW transition might also be induced by in-plane currents, respectively below and above the transition temperatures. Close to the transition temperatures, 150 K (cooling) and 200 K
(warming), a voltage sweep is performed up to several Volts (3–6V/min). In the NCCDW phase (150 K), after reaching a in-plane current of approximately 30
µA, the current remains constant as the voltage is further increased. The large
in-plane current seems to induce NCCDW–CCDW transition, indicated by the green arrow in 2.10 (c).Similar behavior is observed for the CCCDW–NCCDW transition (orange arrow), again at a critical current of approximately 30 µA. The general idea is that the (meta)stable state may be pushed out of its local potential minimum, inducing a transition to another (meta)stable state. Inter-esting to note are the apparent steps within the resistance during a transition, possibly indicating partial transitions within the crystal.
2.3.4
Tuning by pressure
Figure 2.11: The temperature dependence of the resistivity for a large range of applied pressures, eventually a superconducting ground state is achieved at a critical tempera-ture Tc≈1.5 K. Taken from [27].
The previous three sections have demonstrated the tunability of the NCCDW– CCDW transition, effectively altering the insulating ground state. One might ask, however, if there exists the possibility of fully suppressing the CDW within a 1T-TaS2 crystal. The latter appears to be the case at very high pressures as
shown by B. Sipos et al. [27], see Figure 2.11. The temperature dependence of the resistivity of a 1T-TaS2nanocrystal at different pressures is shown. Initially,
the crystal undergoes a NCCDW–CCDW transition leading to an insulating ground state. Around 6.5 GPa the NCCDW–CCDW transition is suppressed,
at higher pressure (8 GPa), the resistivity at room temperature is decreased by several orders of magnitude, after which the low temperature resistive behav-ior is also completely altered. Eventually, a superconducting ground state is achieved at Tc ≈1.5 K. Similar behavior was observed in electrolyte gating
ex-periments, based on lithium intercalation, for which at some point a supercon-ducting ground state was formed at Tc ≈ 2 K [33]. Interesting to note is the
halfway suppression in the 0.8 GPa curve, including what looks like a step-wise transition (similar to the transitions in [21]).
This chapter has discussed the formation of the CDW in 1T-TaS2, its complicated
phase diagram and the tunability of the phase transitions. Several topics have been left untouched such as the influence of the substrate (strain) and crystal impurities. It might not come as a surprise that the CDW is still poorly under-stood as the number of factors that should be taken into account, including their intricate interplay, is enormous. Even distinguishing between the effects of di-mensionality and oxidation is challenging as is stated in Tsen et al. [21]:”Recent resistivity measurements on exfoliated 1T-TaS2 crystals have also reported the disap-pearance of CDWs in sufficiently thin flakes (5). It is not clear, however, whether these are intrinsic effects related to dimensionality or extrinsic consequences of oxidation.”. Scrutiny is necessary in order to distinguish between the myriad of possible effects and explanations. Selective procedures such as exfoliation in oxygen de-ficient environments, effectively excluding oxidation, may give insight in the intriguing mechanisms behind the formation of the CDW.
Chapter
3
Nano-fabrication and Experimental
Techniques
3.1
Electron-beam lithography
Lithography, originally a method of printing based on the immiscibility of oil and water, is in the field of experimental physics known as an umbrella term governing the patterning of nanoscale structures. There are several well-known lithographic methods such as e-beam, x-ray and photo-lithography. All of the lithographic methods generally rely on the same methodical principle: applying resist→exposure →development. Electron-beam lithography (EBL) is one of the key patterning techniques at the nanoscale that allows sub-10 nm resolution. A focused electron beam is scanned across a surface, only exposing selected areas, covered by an electron-sensitive material (resist) of which its solubility properties are changed according to the deposited charge.
Lithographic process As illustrated in Figure 3.1, a uniform layer of resist is deposited on a substrate (step 1). A thin uniform layer is acquired by means of spin coating, spinning the substrate at a certain rotation speed in order to equally distribute the resist on top. A typical spin coat recipe revolves at 2000–4000 rpm for 30–60 s. After spin coating, the sample is baked to evaporate excess resist solvent (i.e. to harden the resist), between 80 - 200◦C up to several minutes. The most common type of EBL-resist is polymethyl-methacrilate (PMMA), available in several different molecular weight forms (50–950 K), each requiring a slightly different exposure dose. Upon exposure, the long polymers are broken down into fragments that can be dissolved in methyl isobutyl ketone (MIBK), gener-ally known as a developer. A resist can either be positive or negative, for which the exposed part or the unexposed part is dissolvable by the developer, respec-tively. Exposed/unexposed resist is dissolvable in organic compounds such as aceton.
Figure 3.1:Illustration of a typical electron-beam lithographic process for positive and negative resist.
The exposure dose is defined as the amount of charge deposited per unit area, typically expressed in µC/cm2. However, depositing the theoretical exposure dose will not always result in the desired outcome. As the electrons pene-trate the resist, they begin a series of low-energy elastic collisions, eventually resulting in a cascade of secondary electrons effectively broadening the original incidental beam, known as forward scattering. Forward scattering is generally known to be more pronounced in thicker layers and at lower incident energies. At higher energies, most of the electrons penetrate the resist and enter the sub-strate, after which some will eventually re-emerge into the resist via large-angle scattering, this effect is known as backscattering. The backscattered electrons are the cause of the proximity effect, i.e. the dose that a pattern feature receives is influenced by the vicinity of other nearby features.
Development of a resist is usually not the final step in the nano-fabrication pro-cess. Often, nano-fabrication requires some kind of etching or lift-off to get rid of excess material generally covering the full surface of the substrate (e.g., evap-orated gold). To stimulate a lift-off, i.e. dissolving the resist underneath the excess material, it is useful to create an undercut (a sloped sidewall, broadening towards the substrate) structure within the resist. A undercut profile might be achieved in many ways, one of which is applying more than one layer of resist, increasing in molecular weight near the top.
3.2
Evaporation
Evaporation is a common method in thin-film deposition. The bulk of a depo-sition material undergoes a trandepo-sition from solid to vapor state by means of thermal heating (Figure 3.2) or electron bombardment. The material vapor con-denses in thin film form on the cold sample and a substantial part of the vacuum chamber. The vacuum allows the evaporated atoms to exhibit large mean free paths, typically on the order of the dimensions of the vacuum chamber, and therefore to travel in straight paths (ballistic) from the thermal source towards the substrate. Evaporation is an anisotropic (directional) growth process and much gentler in comparison to sputtering as the depositing atoms have a sub-stantially lower energy.
Figure 3.2:Schematic representation of a resistance evaporator.
The most common form of evaporation is resistance evaporation (thermal evapo-ration). A large current, up to several hundred amps, is passed through a restive wire or cup shaped filament containing the to be deposited material. The
evap-oration source is heated up to temperatures of over 1000 ◦C, vaporizing the
metal within the filament. Typical pressures within the vacuum chamber are 10−7 mbar, as contamination within the vacuum chamber might affect the uni-formity of the growth process. Evaporation typically has deposition rates of several ˚A/s.
3.3
Atomic force microscopy
Atomic Force Microscopy (AFM) is a form of microscopy belonging to the fam-ily of Scanning Probe Microscopes (SPM), which operate on a completely dif-ferent principles compared to conventional optical microscopes. AFM has a resolution on the order of a fraction of a nanometer, much smaller than the op-tical diffraction limit. AFM is most famously known for its imaging abilities but can also be used to measure or manipulate material properties or manipu-lation (i.e. purposely changing the surface structure). AFM can be performed in several different condition such as atmospheric pressure, vacuum and even in liquids.
Figure 3.3:Schematic representation of Atomic Force Microscopy (AFM). A laser beam is reflected, by the tip of the cantilever, onto a photo-diode. Any displacement of the cantilever, due to interaction with the surface, is measured via the subsequently dis-placed reflected laser beam.
Operating principle AFM operates by measuring the force between a probe and the sample, visualized in Figure 3.3. The probe is a sharp tip (pyramid shape) with a height of several microns and a radius of tens of nanometers. The vertical and lateral deflections of the cantilever are measured by monitoring the laser beam with a photo-diode. The positioning of the tip is controlled by piezo-electric position elements. Several forces may act upon the tip, while in close vicinity to a surface, such as repulsive forces due to the short-range Coulomb interaction, and attractive forces due to the Van der Waals interaction. AFM has
several operation modes that operate in different regions of the force-distance curve of the tip. Contact mode acts upon repulsive forces while non-contact mode acts upon attractive forces only. Different modes are used for different purposes and in different conditions. The intermittent mode, also known as tapping mode, is the most frequently used mode of AFM under ambient condi-tions.
Tapping mode In tapping mode AFM, the tip is driven near its resonance fre-quency (50–500 kHz). Subsequently, the oscillating tip is very carefully moved near the vicinity of the surface until it lightly taps the surface. By the intermit-tent contact, energy of the tip is decreased due to interaction of the tip with the surface, resulting in a change in frequency and amplitude. Typically, the reduc-tion in oscillareduc-tion amplitude is what is monitored and computed into surface features. In other words, the oscillation amplitude is what is kept constant by the feedback loop in Figure 3.3. Tapping mode has several practical advantages over contact mode such as minimization of damage to both the tip and the sam-ple surface.
Chapter
4
Method
4.1
Sample fabrication
For the purpose of (magneto)-transport measurements, a Hall-bar like contact structure is a necessity. Contacting of flakes, however, is more involved com-pared to grown thin films, as the latter allows patterning before growth. Writing bottom contacts on a substrate before stamping is a valid option, however, per-fect alignment of the flake with respect to the pre-written Hall-bar contact is very challenging. During this research project, a top contact recipe was devel-oped for stamped flakes (Appendix B). This sample production recipe has three separate processing steps: (1) Substrate preparation→(2) Stamping→(3) Overlay (i.e. contacting of the flake), illustrated in Figure 4.1. Electron-beam lithogra-phy was chosen over optical lithogralithogra-phy as features surrounding a flake are typically too small for optical lithographic resolution. Flakes furthermore vary in shape and size from sample to sample, making re-use of a standard mask im-practical. For contact deposition, evaporation was the most desirable technique as the low energetic atoms are virtually harmless to the fragile flakes. All of the essential experimental details will be discussed in order of the workflow within the following part of this chapter.
A thin layer of chromium (∼5 nm) is grown underneath the gold in order to increase the adhesion.
Figure 4.1: Schematic representation of the sample production process: (a) Si/SiO2
substrate including a stamped 1T-TaS2 flake (b) Spincoat a layer of resist (PMMA) (c)
E-beam exposure (d) Development (e) Evaporate gold top contacts∗(f) Lift-off.
4.1.1
Substrate preparation
Consideration The main challenge of contacting a flake is knowing where ex-actly the flake is on the Si/SiO2substrate. There are two ways to determine the
position and shape of the flake within the e-line design program. (1) Search for the flake by exposure within the e-beam tool in order to get an image which can be mapped to the relative position of the beam. (2) Pre-pattern the substrate such that an optical image of the flake and its nearby features can be aligned within the original e-line design. Although option (1) is less time consuming, for the purpose of this research project option (2) deemed more sound as most uncertainty such as overexposure of the flake is eliminated. Bottom contacts might be more practical for bulk flakes as the amount of gold necessary for con-tacts is almost an order of magnitude less. Evaporated top concon-tacts must be at least as thick as the flake itself due to the sharp edges of the exfoliated flakes and directionality of evaporated gold, see Figure 4.1. The 1T-TaS2 bulk crystal
is stored within a desiccator in order to minimize contact with air and subse-quent oxidation, as 1T-TaS2is prone to oxidation [21]. Occasionally, the crystal
is taken out of the desiccator for the purpose of exfoliation. Generally, bulk flakes are present on the first contact exfoliated tape. This so-called mother tape is therefore stored over longer periods of time, replaced every 2-3 weeks, as it may be sufficient for stamping of several different substrates.
Figure 4.2:4.5 mm x 4.5 mm e-line design: (a) Orientational L-shape (b) Global marker (c) 300 µm x 300 µm contact pad (d) Stamping field (e) Zoom-in of a single write field including numbering.
Design As visualized in Figure 4.2, the complete design is confined within a 4.5 mm x 4.5 mm area. Spun resist is not perfectly uniform on top of the substrate as it tends to heap up near the edges. Exposing these areas might in-troduce errors in patterning and are therefore avoided. The complete design is well confined within the typical size of the Si/SiO2substrate (5 mm x 5 mm). In
order to correctly determine the position of the stamped flake on top of the sub-strate, a 1.6 mm x 1.6 mm†stamping field (d), is designed. Within this area, each write field (100 µm x 100 µm) is labeled with write field markers, spaced 80 µm a part, and a numbering system (see Figure 4.2, (e)). A write field is the standard working area of the e-beam tool in which one can write without moving the motorized stage. Patterning errors typically occur due to improper alignment of the stage (stitching errors), therefore writing critical structures across several write fields is often avoided. The write field markers allow for alignment of the electron beam close to the critical structures. Each write field is numbered by its occurrence in each quadrant and binary labeled for its relative position within. The top three bits (dots) indicate the relative row, the bottom three bits label its relative column, with respect to the relevant quadrant. A typical image of a write field marker and numbering, the same write field as in the zoom-in of Figure 4.2, is presented in Figure 4.3.
Twelve contact pads are included‡, which allow for contacting of two complete Hall-bars per design (a Hall-bar consists out of a source, drain and four voltage probes). The contact pads are relatively big (300 µm x 300 µm) as they have to be connected to the chip carrier by wire bonding (aluminum wire). The L-shape (a) and global markers (b) are necessary in further overlay patterning procedures and will be elaborated on in the following paragraphs.
Figure 4.3:Optical image of a gold write field marker (10 µm x 10 µm) and numbering after deposition and subsequent lift-off on a Si/SiO2substrate.
4.1.2
Stamping
Figure 4.4: Schematic representation of the exfoliation and stamping process: (a) Me-chanical exfoliation from bulk 1T-TaS2 by Nitto tape (b),(c) Transfer exfoliated flakes
from tape to PDMS (d),(e) Transfer flake from PDMS to substrate.
Procedure The exfoliation and stamping process are visualized in Figure 4.4. Nitto-tape R
has been used for the purpose of mechanical exfoliation. From the crystal residue remaining on the mother tape, a new tape is exfoliated which will be used in the subsequent stamping procedures (stamping tape). In order to produce thinner flakes, the stamping tape is folded (while minimizing strain) and peeled back and forth several times, dependent on the desired thickness. Exfoliated flakes are transferred from the stamping tape onto Polydimethyl-siloxane (PDMS§), a commonly used silicon-based organic polymer, Figure 4.4 (c). A cotton swab is used to gently increase the contact of the stamping tape with the PDMS, effectively increasing the amount of transferred material. Be-fore the transfer, the PDMS is gently placed on a clean glass slide, any dirt or bubbles underneath the PDMS might complicate the stamping. The glass slide, PDMS facing towards the substrate¶, is mounted onto a mechanical pre-cision stage, allowing for precise movement in the x-y-z direction + tilt (Fig-ure 4.5).
§Gel-pak 4.
Figure 4.5: Stamping set-up with mechanical precision stage: (a), (a’) Control of the complete stage in the x, respectively y-direction (b),(b’) Control of the glass slide in the x, respectively y-direction (c) Control of the substrate in the z-direction (d), (d’) Control of the tilt of the glass slide by rotating around the y, respectively x-axis (e) Glass slide including PDMS stamp (f) Substrate (g) Optical microscope.
The glass slide and PDMS form the stamp that is used to transfer the flake. The transparency of the stamp allows for optical imaging of flakes, Figure 4.5 (f),(g). On each stamp several flakes are transferred onto the substrate, however, it is useful to find a flake of the right shape and dimensions beforehand such that it can be monitored while stamping. The latter furthermore allows for align-ment of the desired flake within a particular write field, easing e-beam overlay procedures. The stamp is brought into near contact with the substrate, while monitoring both the flake and the substrate. Once the alignment is sufficient, contact is made. At this point one can see a contrast difference between the part of the substrate that is in contact with the stamp, and the part that is not. If the stamp and substrate are properly aligned, the edge/front of contact moves as a straight line over the substrate. The glass slide is deliberately titled such that the stamp ”unrolls” on top of the substrate, with the front of contact moving from right to left (Figure 4.6). If the surface of the substrate contains dirt, air bubbles may form upon contact, complicating a controlled transfer.
Once the edge of contact is near to the flake (Figure 4.6), the substrate is heated to 60/90◦C (Figure 4.4 (d)). The PDMS expands due to the heating, increasing the surface area of contact between the PDMS and the substrate. The heating furthermore decreases the adhesion of the flake to the PDMS, after which the Van der Waals forces attracting the flake to the substrate start to dominate. Once the area around the flake is in complete contact, the glass plate is very gently moved upward while monitoring the flake. Any movement of the flake during this procedure indicates that the transfer was not successful. If this is the case, one can repeat the previous described stamping procedure several times. A rectangular flake, properly aligned within a write field, is shown in Figure 4.7 (a).
Figure 4.6: Optical image of the substrate while stamping: (a) The to-be transferred flake (∼30 µm x 8 µm) (b) The front of contact, moving from right to left.
4.1.3
Overlay
Figure 4.7:(a) Optical image of a rectangular flake (∼15 µm x 3 µm) stamped within a particular write field. The write field markers fulfill the purpose of a scale-bar (10 µm x 10 µm). (b) E-line overlay design on the flake from (a). Hall-bar design on flake (green) and large wires to the contact pads (brown).
Design A cropped optical image of a flake may be imported into the e-line design software, resulting in Figure 4.7. The original pre-patterned gold write field markers and numbering can be aligned with respect to the original de-sign. Once the alignment is sufficient, one may design a Hall-bar structure (green) and contact wires (brown) towards the pre-patterned electrodes. A stan-dard Hall-bar design was used for each flake, subsequently re-scaled and ro-tated. Typically, a rectangular flake is sought after allowing for a better-defined conduction channel and additionally neater transport measurements. The fine structure (Hall-bar) is always designed within one particular write field, cir-cumventing any potential stitching errors.
Procedure Before patterning the overlay design, one must perform a global alignment of the substrate with respect to the motorized stage of the e-beam (in particular structures written in any previous e-beam step). The global align-ment is performed by finding and aligning three global markers at the corners of the sample with respect to the beam position in the design. However, one first has to find the pre-written markers without exposing any crucial part of the substrate, this exactly is the purpose of the large L-shape in the design from Figure 4.2. First, an origin is defined, typically at the bottom left corner of the
substrate. From this origin, the beam is moved near the vicinity of the L-shape which position is well-defined within the e-line design. As the L-shape is far away from any potential crucial features, one may zoom out in order to identify the shape. Once the L-shape is in view, one may estimate the tilt of the sub-strate, and subsequently move the beam towards the bottom left global marker. From this point on one proceeds with the general three-point global marker alignment.
The overlay pattern is written in two separate steps with a different spot size. Firstly, the Hall-bar is written at a small spot size (PC 11) in order to get a suf-ficient resolution. Proper write field alignment is of importance as the over-lapping area of a voltage probe on the flake is typically small (< 1 µm2). The contacting wires are written at a large spot size (PC 1), as resolution is not im-portant and the writing time is drastically decreased.
However, one must be beware of a beam shift, i.e. an off-set in the beam align-ment at different spot sizes. It is typically useful to re-do the global alignalign-ment when switching spot sizes. The large rectangular overlapping shapes have been implemented to decrease the possibility of any disconnected wires due to beam shift. An optical image of a contacted flake after evaporation and subsequent lift-off, is shown in Figure 4.8. The experimental details on the overlay proce-dure are provided as a recipe in appendix B.
Figure 4.8: Overlay pattern after lift-off on the flake from Figure 4.7. The write field markers fulfill the purpose of a scale-bar (10 µm x 10 µm).
Lift-off Two layers of PMMA of different polymer length (600K and 950K) have been applied in order to achieve an undercut profile after and subse-quently enhance a lift-off. After development and deposition, the sample is put in aceton at 45◦C for one hour to several hours. One might also leave the sample overnight in aceton at room temperature. After some time, the gold on top of the substrate starts to wrinkle and comes off quite easily. The lift-off is stimulated by creating a flow of aceton within the beaker, close to the sample, by means of a pipette. It might occur that certain areas of gold do not come off, typically when two features are very narrowly spaced, enclosing the part of gold that should be lifted off. In such cases one could use ultrasonication. However, ultrasonication should only be used as a last resort, as it might po-tentially destroy one of the contacting wires or even lift off the flake completely. One should never take the sample out of the aceton before all of residue gold is lifted off, the remaining gold will redeposit on the surface of the substrate and will be very hard to remove.
The Au/Cr contacts are ohmic up to currents well above the probed source cur-rent in this research project (100 nA – 1 µA) within the full temperature range of the cryostat, see Figure 4.9. Contact resistances have been measured on several occasions, observing that the resistances roughly scales with the area of contact suggesting non-negligible transfer length. The source/drain contact resistance is typically 5Ω, whereas voltage probe contacts are on the order of 50–100 Ω (for comparison see Figure 4.8). The internal resistance of the insert wiring is 4 Ω per wire.
Figure 4.9:2-probe I(V) characteristics of 180 nm thick 1T-TaS2with top Au/Cr contacts
at 295 K and 1.6 K. Determined from the slope of the fit: R295K = 298.7 Ω and R1.6K =
4.1.4
Height determination
Figure 4.10:(a) AFM image of the edge of a flake, including the gold source/drain and voltage probe contacts. (b) Line-scan along (1) and (2), averaged over 10 pixels.
The thickness of a flake is determined by AFM imaging (Bruker Multimode, 70 KHz). In Figure 4.10, the edge of a flake is shown, including the source/drain electrode (bottom left) and a voltage probe (top right). One may determine the height from the trace/re-trace data of the AFM image, shown in (b). For the particular flake of Figure 4.8, the height is 25±2 nm. Typically, a flake is very flat (locally), however, certain domains of different thickness may occur (see optical contrast in Figure 4.7 (a)). The voltage probes are therefore deliberately designed within one optical domain of thickness. The thickness of a flake be-tween the voltage probes was used as the flake thickness standard. The thick-ness was determined after the transport measurements in order to avoid any risk of damaging the flake. However, some flakes have been damaged severely in the process of transport measurements such that the AFM data is not com-pletely trustworthy. The latter has been indicated accordingly.
4.2
Measurement set-up
Conventional transport measurements have been performed in 2 or 4-probe configuration. The majority of the measured samples initially consisted out of a Hall-bar such as in Figure 4.8, allowing for 4-probe and Hall effect mea-surements. However, most flakes (or contacts) have been destroyed after the fabrication process due to the consequences of ElectroStatic Discharge (ESD), see Figure 4.12. This chapter contains all experimental details on the cryostat, mea-surement instruments and meamea-surement settings, including measures taken to eliminate ESD.
Electrostatic Discharge ESD is the sudden flow electricity between two elec-trically charge objects caused by contact. ESD is particularly harmful to 2D ma-terials as several volts may lead to incredibly high current densities. One has to take extra precaution at procedures such as wire-bonding and mounting the sample, by correctly defining the ground of yourself and the involved machin-ery. However, in this research project, ESD has mostly been the consequence of mechanically connecting measurement equipment to the top of the insert (i.e. to the sample). Common practice is the involvement of a Breakout Box (see Fig-ure 4.11), placed in series between the measFig-urement equipment and the sample. The breakout box can define the potentials of the wiring to the sample, such that no voltage may drop over the sample when a connection to the measurement equipment is established.
The breakout box has two configurations: (1) Ground: Switch 1 is open and switch 2 is closed. The connections to the sample are connected to the ground through a high ohmic resistor, including a capacitor in parallel, effectively op-erating as a low-pass filter. Any voltage difference between connections to the sample and the measurement ground may discharge slowly over the re-sistor, whereas high frequency noise is discharged via the capacitor. (2) Mea-sure: Switch 2 is open and switch 1 is closed. While switching from Ground to Measure, switch 1 is closed before switch 2 is opened. This is a so-called Make-Before-Break switch (MBB). The MBB switch always makes sure that at all times, the voltage between the wiring to the sample is well defined.
Figure 4.11:Schematics of the measurement set-up. The breakout box is highlighted by the dashed rectangle. The breakout box includes two switches: (1) Direct connection to the ground (2) Connection to the ground through a high ohmic resistor (R = 500 MΩ), including a capacitor in parallel (C = 1 nF).
Preventing ESD: (1) Turn all the knobs on the breakout box to ”Ground” (2) Con-nect all of the involved SMB cables from the top of the insert to the back of the breakout box (3) Connect the measurement equipment to the front of the break-out box via BNC cables (4) Turn on the measurement equipment and make sure the output voltage is zero (5) Turn the involved knobs at the breakout box from ”Ground” to ”Measure”, after which one may carefully ramp the voltage.
Figure 4.12:The remnants of a flake after severe electrostatic discharge.
Measurement Instrument Transport measurements, on all but the last mea-sured flake (65 nm), have been performed with a Keithley 2450 sourcemeter, at a source current of 100 nA–1 µA. From this project on, the Keithley has been permanently replaced by two Lock-in Amplifiers (Stanford Research Systems; Model SR830), which allow for measurements of smaller signals including si-multaneous measurement of both longitudinal and transverse resistance. A
sine wave was set at ∼ 13.35 Hz, with a time-constant of several periods. A
high resistor of 10 MΩ, much larger than typical TaS2 flake resistances (0.1 - 10
kΩ), was placed in series such that a lock-in source amplitude of 1 V produces a source current of 100 nA.
Cryostat Cooling has been performed in an Oxford Instruments TeslatronPT cryostat, allowing accurate temperature control down to 1.6 K. The cryostat has a built-in superconducting magnet supporting magnetic fields up to 8 T in the z-direction with respect to the sample. The highest achievable constant cooling rate of the Variable Temperature Insert (VTI) is 1.5–2 K/min. Within this project, several adjustments have been made to the cryostat and its electronics, note-worthy information has been recorded in Appendix A.
Chapter
5
Results and Discussion
5.1
Electrical properties of 1T-TaS
2Within this research project, several flakes of different thicknesses have been measured either in 2 or 4-probe configuration with Au/Cr top contacts. In all of the presented data, contact resistances have either been estimated or measured and subsequently subtracted. The samples of thickness 25/40/55/80/180 nm have been fabricated by the top contact Hall-bar recipe described in the previ-ous chapter. The sample of 105 nm in thickness was measured in a 2-probe bot-tom contact configuration and showed distinctively different NCCDW–CCDW transition. Clear difference in the fabrication process was the highest reached temperature of the 1T-TaS2 crystal, 60◦C during stamping opposed to 180◦C
while baking the e-beam resist. To test this hypothesis, the last sample of this
research project (65 nm) was only baked at 60◦C. The NCCDW–CCDW
transi-tion and its dependence on the dimensionality and cooling rate have been ob-served. The general behavior agrees with literature. However, the quantitative behavior does differ significantly on several aspects, which will be discussed in the following.
5.1.1
Thickness dependence
The temperature dependence of the resistivity for flakes of different thickness is shown in Figure 5.1. The 80 nm (purple), 105 nm (brown) and 180 nm (pink) curves show a clear NCCDW–CCDW transition around 125 K (cooling) and 220 K (warming). Steps within the NCCDW–CCDW transition are visible in all curves, however most pronounced in the brown curve. In contrast, no transi-tion (i.e. the supercooled phase) is observed for 25 nm (blue), 40 nm (orange), 55 nm (green) and 65 nm (red). A clear down-turn is observed below 15 K for all curves in the supercooled phase. Most of the curves overlap relatively well. However, the observed resistivity at room temperature, approximately 5·10−3 Ω cm, is a factor 5 to 10 larger than in literature [24, 30, 32]. Inter-estingly, the 65 nm thick flake has a distinctly lower resistivity and thereby in much better agreement with literature, indicating that baking at 180◦C possibly alters the 1T-TaS2crystal. Important to note is the fact that the magnitude of the
NCCDW–CCDW transition for both the pink and purple curve has not shown any significant temperature dependence over the range of 0.1–1.5 K/min.
Figure 5.1: The resistivity of 1T-TaS2 as a function of temperature for different
thick-nesses at the lowest measured cooling rate (0.1–0.4 K/min). The solid and dashed lines represent the cooling and warming cycle, respectively. Flakes marked by† have been measured in a 2-probe configuration. The contact resistance and geometrical factor of the bottom-contacted 2-probe flake (105 nm) are unknown, its resistance curve has been arbitrarily re-scaled for comparison and therefore does not represent resistivity.
A clear thickness dependence of the NCCDW–CCDW transition is demonstrated, however, several differences with respect to literature are observed. The critical thickness is most likely just below 80 nm (purple), as the transition in the 80 nm thick crystal was only present at a very low cooling rate of 0.1 K/min (see Figure 5.3). The observed critical thickness is large compared to values found in literature,∼30 nm in [24] (Figure 2.7) and ∼40 nm in [32] (Figure 2.8). The transition temperature seems not to have a well-defined thickness dependence in contrast to [24], in which it is shown that the transition temperature clearly decreases for thicker flakes (see Figure 2.6). Another significant discrepancy is the fact that in literature the resistivity increases an order of magnitude due to the NCCDW–CCDW transition in a very pronounced manner (see Figure 2.6). For all curves, the magnitude of the increase in resistivity during the NCCDW– CCDW is relatively small compared to literature, the steepness of the slope dur-ing the transition as observed in literature is most closely resembled by the 105 nm thick, bottom-contacted-flake.
Oxidation The presence of an oxidized layer on top of the exfoliated 1T-TaS2
has been investigated. A thick oxidized layer might possibly explain the afore-mentioned discrepancy in resistivity at room temperature between our results and literature. As oxidation is a temperature dependent process, it might fur-thermore explain the difference in resistivity between the crystals baked at 180
◦C and 60◦C.
If one assumes that the conductivity of the oxidized layer is much smaller than the pristine layer (σTaS2 σoxide), the thicker the oxidized layer the higher the computed resistivity (as one takes the full thickness of the flake into account). The thickness dependence of the sheet conductivity (1/R ) might indicate the presence of an oxidized layer (doxide) in the following way:
σ =doxide·σoxide+ (dtotal−doxide) ·σTaS2. (5.1) The first term in eq. 5.1 is a constant positive offset, however negligible com-pared to the negative offset due to the last term (−doxide·σTaS2). The sheet con-ductivity is expected to scale linearly with the thickness, where the presence of an oxidized layer may be demonstrated by any negative offset. The point of intersection with the x-axis is an estimate for the thickness of the oxidized layer.
Figure 5.2: The thickness dependence of the sheet conductivity (σ ) at 50 K and 290 K, including a linear fit (ax+b). All of the data points in this plot have been fabricated by the exact same method. b290K = 2·10−4±5·10−4, b50K = 3.4·10−5±1.4·10−4.
The thickness dependence of the sheet conductivity at different temperatures is shown in Figure 2.6. Due to the error that might arise from the estimated dimensions of the conducting channel, i.e. geometrical factor and thickness, error bars have been included of±2 nm in thickness∗, and±20 % in resistivity†. The sheet conductance seems to fit the linear dependence relatively well, as is expected. However, due to the relatively large uncertainty it is impossible to exactly quantify the thickness of the potentially oxidized layer. As positive values for b have no direct physical explanation, it is clear that b is small and lies well within one standard deviation from 0. We expect at least some layers of the 1T-TaS2to be oxidized as is shown in [21], however, the aforementioned
difference in resistivity is most likely not due to layer-by-layer oxidation of the crystal. This model does not exclude degradation of the bulk crystal, in that case the sheet conductance is still linearly dependent on the total thickness, only
σTaS2is replaced by σDegraded. However, the fact that the 65 nm thick flake, baked at 60◦C from Figure 5.1, closely resembles the resistivity observed in literature opposes this argument.
∗55 nm has error bars of±5 nm as very few parts of the flake remained after severe ESD, complicating thickness determination.
†25 nm has slightly larger error bars of±30 % due to relatively unknown dimensions of the conductive channel.
5.1.2
Cooling rate
The cooling rate dependence of the NCCDW–CCDW transition in a 80 nm thick crystal is shown in Figure 5.3. At 1 K/min (green) and 0.5 K/min (blue), the transition is suppressed in the cooling cycle. Upon warming, however, some-thing that looks like a partial transition is observed. At 0.1 K/min (red), a pro-nounced transition is observed around 130 K. Note the fact that the resistive behavior after the transition is very similar to the behavior of the crystal in the supercooled phase, possibly indicating that the crystal does not fully switch to the commensurate phase. In the warming cycle of the red curve, the resistiv-ity clearly increases before transitioning back to the NCCDW phase around 220 K. This increase in resistivity during the warming cycle seems very similar to a partial NCCDW–CCDW transition. This behavior has only been observed under high pressure [27] or large in-plane current [21], none of which have been applied during the transport measurements of this research project. The mechanism that drives the transition in the warming cycle is not completely understood, however, it substantiates the notion of the meta-stable nature of the supercooled and commensurate phase. Most likely the CCDW state is still energetically favorable in the supercooled phase, however, unable to reach due to lack of thermal excitation. During the warming cycle, thermal energy is in-troduced by the heater which is mounted close by the sample. Perhaps the thermal energy induces local thermal excitation that drives the partial transi-tion between both meta-stable states.
Figure 5.3: Temperature dependence of the resistivity of a 80 nm thick 1T-TaS2crystal
Partial transition Several observations have led us to suspect that only parts of the crystal undergo a NCCDW–CCDW transition:
• The magnitude of the increase in resistivity due to the transition is much smaller than in literature.
• The resistive behavior after the transition is very similar to the resistive behavior in the supercooled phase.
• The Mott-like upturn of the resistivity has not been observed, traces of a down-turn in the CCDW phase even seem present in the 80 nm crystal of Figure 2.6.
One could in theory assume that after the transition, the CCDW domains do not cover the full area of each plane. However, the latter would only cause a constant shift due to the restriction of the conducting channel, or completely alter the resistive behavior due to the nature of resistances in series. Both have not been observed and therefore the most sensible model is to assume that only a fraction of the layers switch during the transition, such that the resistivity is still dominated by the layers in the NCCDW phase. Due to the parallel nature of the layered 1T-TaS2 crystal, the latter is most easily expressed in terms of
conductivity:
σ=r·σCCDW+ (1−r) ·σNCCDW, (5.2)
with r the ratio of layers in the CCDW phase. An estimate of r may be retrieved from Figure 5.3 in the following fashion:
1. The red curve with the transition (0.1 K/min) is assumed to be driven by NCCDW and CCDW planes in parallel, eq. 5.2 (σ).
2. The blue curve without the transition (0.5 K/min) is assumed to be σNCCDW.
3. Estimate from literature, just below the transition: σNCCDW/σCCDW ≈10.
4. Substitute for σ and σNCCDWjust below the transition (90 K) and solve for
Figure 5.4: (Left) Temperature dependence of the estimated CCDW resistivity on a normal temperature scale, (Right) on an Arhenius scale (1/K) including linear fit with T0= 17 K. The ratio is set to r = 0.28.
The fraction of layers switching to the CCDW phase r is determined at 0.28 (28 % of the total number of layers). For different ratios of σNCCDW/σCCDW (8–10),
r is found to only differ by ±0.01. The CCDW contribution to the resistivity may now be retrieved by subtraction of the red and blue curve (Figure 5.3) for r = 0.28, σCCDW = (σred−0.72·σblue)/0.28. The extracted contribution to the
resistivity of the ratio of layers (r = 0.28) in the CCDW phase is shown in Fig-ure 5.4. Interestingly, the behavior and magnitude of the resistivity are found to be very similar to literature. The resistivity exhibits a clear upturn and lies in the usual range of 10−2–10−1 Ω cm. Thermally activated behavior of the form
ρ =ρ0·e−T0/Tis observed between 50 K and 16 K, with a characteristic
temper-ature of T0= 17 K. The observed behavior seems similar to literature, however,
the characteristic temperature is much smaller (110 K in [30]). Although the par-tial switching hypothesis might be plausible, the mechanism that suppresses the transition within most of the layers is unknown.
