What happens when transition metal trichalcogenides are interfaced with gold?

Transition metal trichalcogenides (TMTs) are two-dimensional (2D) systems with quasi-one-dimensional (quasi-1D) chains. These 2D materials are less susceptible to undesirable edge defects, which enhances their promise for low-dimensional optical and electronic device applications. However, so far, the performance of 2D devices based on TMTs has been hampered by contact-related issues. Therefore, in this review, a diligent effort has been made to both elucidate and summarize the interfacial interactions between gold and various TMTs, namely, In4Se3, TiS3, ZrS3, HfS3, and HfSe3. X-ray photoemission spectroscopy data, supported by the results of electrical transport measurements, provide insights into the nature of interactions at the Au/In4Se3, Au/TiS3, Au/ZrS3, Au/HfS3, and Au/HfSe3 interfaces. This may help identify and pave a path toward resolving the contemporary contact-related problems that have plagued the performance of TMT-based nanodevices. I–V characteristics of (a) TiS3, (b) ZrS3, and (c) HfS3


Introduction
Shrinkage of the lengths and widths of transistor channels down to a few nanometers does not favor the use of three-dimensional semiconductor materials as transistor channels for field-effect transistors (FET). So is the case because, in the nano regime, the gate oxide cannot offer reliable control of the channel bias owing What happens when transition metal trichalcogenides are interfaced with gold?
Invited Feature Paper-Review , where t s is the thickness of the semiconductor channel, t b is the thickness of the gate oxide, and E s and E d are the dielectric constants of the semiconductor and gate oxide, respectively [6][7][8]. This natural length scale ( µ ) indicates how efficiently the gate and gate dielectric control the channel. As a rough metric, for highly efficient control, the semiconductor conduction channel should be at least five times smaller than the length of the channel [5]. Thus, for efficient device performances, the shorter the semiconductor channel, the thinner it must be. Consequently, to circumvent the deleterious short-channel effects, two-dimensional (2D) semiconducting materials are thought to be favored as the transistor channels. This solution to combat the short-channel effects will, however, only work if these 2D semiconducting materials are not plagued by the catastrophic edge scattering or edge states that make the semiconductor channel metallic.
The purpose of this concise yet comprehensive review is to encapsulate recent research efforts that are all targeted toward deciphering the metal-TMT interface and provide an outlook for further technological development in the field of TMT-based devices. This work focuses on the interface resulting from the interactions between TMTs and Au, since it is one of the most commonly used materials for making connections and contacts to commercial semiconductors [61,62]. Au, a metal with a very high work function [63][64][65], is frequently regarded as a chemically inert metal in comparison with most metals but chemical reactions with Au are still possible. Since this review is focused on the surface and metal contact interfaces of the semiconducting TMTs, the emphasis here is on the TMTs studied thoroughly enough such that their reported device characteristics are backed by systematic X-ray photoemission spectroscopy (XPS) measurements. Prior review articles (see refs. [39,40]) have not addressed the very important metal-TMT interface, but given the increasing attention given to TMT devices, discussion of the interfacial interactions between Au and each of the following TMTs, In 4 Se 3 , TiS 3 , ZrS 3 , HfS 3 , and HfSe 3 , is both timely and of importance.

Experimental details
The In 4 Se 3 single crystals were synthesized via the Czochralski method in a graphite-based crucible, in the presence of hydrogen, at 540°C [50,53,66]. The studied TiS 3 crystals were synthesized through a direct reaction between sulfur vapors and metallic titanium in vacuum-sealed quartz ampules, which were heated at 550°C, as has been reported in prior works [13,[67][68][69]. Likewise, the ZrS 3 crystals were obtained as the product of a chemical reaction between vapors of sulfur and metallic zirconium, in vacuum-sealed quartz ampules at 800°C [69][70][71]. For the synthesis of HfS 3 crystals, just like its titanium and zirconium counterparts, metallic hafnium was made to react with sulfur vapors in a vacuum-sealed quartz ampule at 600°C [72,73]. Eventually, after annealing the HfS 3 ampules at 600°C for 2 weeks [72, 73], a few-millimeter long crystals of HfS 3 were gathered. The HfSe 3 crystals were synthesized from elemental hafnium and selenium as described in the following text. About 0.2 g of hafnium foil (Alfa Aesar, 99.9% metal basis excluding Zr, Zr nominal 2%) and 0.3 g of selenium powder (~ 13% excess to stoichiometry; Alfa Aesar, 325 mesh, 99.999%) were sealed in a quartz ampule under a vacuum of about 200 mTorr. The ampule was placed in a tube furnace with one side of the ampule located near the edge of the furnace to create a temperature gradient. The furnace was heated to 750°C and the ampule was annealed for the duration of 7 days, after which the furnace was slowly cooled down. The excess of selenium accumulated at the colder end of the ampule, while 2-mm-long black HfSe 3 crystals were found on hafnium foil and on the inside of the quartz tube.
The XPS spectra of TiS 3 , ZrS 3 , and HfS 3 were collected using an Al K α SPECS X-ray anode, with the X-ray photon energy of 1486.6 eV, and a PHI hemispherical electron analyzer (Model: 10-360). All the XPS measurements were carried out in an ultrahigh vacuum chamber as the base pressure was always better than 1.9 × 10 -10 Torr, as described elsewhere [73][74][75]. To extract the information about the individual S 2p core-level components, the fits to all the XPS spectra were performed using the XPST curve fitting package available in Igor Pro.
The Au coverage-dependent XPS spectra of HfSe 3 crystals were recorded using the same equipment and under similar parameters as mentioned above. Deposition of Au adlayers onto the surface of HfSe 3 crystals was achieved by thermal evaporation using a tungsten wire basket, and the thickness of the

Surfaces of the TMTs
Knowledge of the correct crystal structure and surface termination of a material is indispensable if its device properties are to be properly investigated and understood. This is because the surface of a material and the interactions occurring at the interface, between the material and the metal contact, have strong influence on device characteristics of a material [76][77][78]. The TMTs that are subject of this work, especially the MS 3 -type, have been much investigated recently. It is not just the sheer variety of their promising applications [12,33,34,[39][40][41][42] that makes them exciting, but also the abundance of exotic physics they possess [16,37]. However, as is the case for any material, both the fundamental understanding of these TMTs and a reliable realization of their device applications rely heavily on the correct interpretation of the information conveyed by standard characterization techniques. This problem has often been addressed by combining device characterization with photoemission spectroscopy studies, which is now a decades-long tradition.
Surface termination of materials can easily be determined through angle-resolved X-ray photoemission spectroscopy (angle-resolved XPS). This is a technique that is known to offer nondestructive depth-profiling of materials [79]. As angleresolved XPS is an enhancement of the usual XPS technique, its results provide information that can be even more surface sensitive [80] in nature than the information collected by the standard normal-emission XPS [81]. The basic mathematical equation describing the working principle of this technique, i.e., angle-resolved XPS, is the well-known Beer-Lambert law equation [79,82]. The Beer-Lambert law equation can be derived from the scratch with a trivial assumption. The assumption is that upon traveling an infinitesimal distance ds through a continuum the photoelectron flux intensity I is attenuated by dI, which is proportional to both the distance traveled through the continuum and the flux intensity (i.e., dI = -IAds) [79]. However, without diving deep into the mathematical treatment of the Beer-Lambert law, the equation applicable to the angle-resolved XPS data collected for real samples (as opposed to a theoretically assumed continuum) is given as [79,82]: In this equation, I is the attenuated photoelectron flux intensity that is received at the photoelectron detector from a layer of atoms located at a vertical probing depth z beneath the surface of the material. Here, I 0 is the photoelectron flux intensity that is received at the detector from a layer of atoms at the surface of the material, and θ is the photoemission take-off angle with respect to the normal to the surface of the sample. The remaining parameter in the above equation, , is the inelastic mean free path of the detected photoelectron [83][84][85]. As the name suggests, the inelastic mean free path of a photoelectron signifies how far it can travel on average before losing its energy as a consequence of inelastic collisions. Therefore, the inelastic mean free path of a photoelectron quantifies its attenuation length as it travels within the sample [79,[83][84][85]. Moreover, since plasmonic excitations are responsible for most of the energy losses that occur in photoemission spectroscopy, the inelastic electron mean free path tends to be shorter for metals than it is for either semiconductors or dielectrics. Just the same, the mean free path of the typical photoelectron generated with an Al K α or Mg K α X-ray source is typically 1 to 2 nm or less, which is to say that the XPS probing depth will be very short and limited to the surface region of the studied TMTs.
An extensive derivation of the Beer-Lambert law equation and a detailed description of the all the parameters, which appear in this equation, are presented in ref. [79]. A schematic representation of the geometry of an angle-resolved XPS measurement is shown in Fig. 1. In Fig. 1, the X-rays incident on the TMT samples (in green) are shown in black, while the emitted photoelectron is depicted by the arrow in blue. The vertical probing depth z beneath the surface of the TMT is illustrated by the double-sided arrow (in yellow), and the photoemission take-off angle θ , with respect to the normal to the surface of the studied TMT, is signified by the red arc. While a little cumbersome, angle-resolved XPS may also be used to calculate the thickness of the samples of interest [79,80,82], if the layers are thin enough (i.e., on the nanometer scale).
Single-phase In 4 Se 3 tends to crystallize in the orthorhombic Pnnm space group [48,86] with four formula units per cell (Z = 4) with the lattice constants a, b, and c equal to 1.2355 nm, 1.5350 nm, and 0.4097 nm, respectively [48,53]. The representative crystal structure of In 4 Se 3 , with quasi-2D clusters of [(In 3 ) 5+ (Se 2− ) 3 ] − and 1D chains [53,75,87], is shown in Fig. 2(a). Despite its layered structure, In 4 Se 3 is not a van der Waals (vdW) material due to the highly ionic nature of the interlayer interactions [53]. Based on the angle-resolved XPS measurements [shown in Fig. 2(b)], the surface of In 4 Se 3 , contrary to the theoretical predictions, is found to terminate in indium [75]. It is also worth mentioning that indium from the bulk of In 4 Se 3 tends to segregate to the selvedge (or subsurface region) as the sample temperature is increased [88], suggesting that region near the surface of In 4 Se 3 is likely to become rich in indium. The indiumrich surface region could be an important factor to consider from the standpoint of device fabrication as the indium-rich surface may affect the contact potential.
Unlike In 4 Se 3 , all the other TMTs that are discussed here, i.e., TiS 3 , ZrS 3 , HfS 3 , and HfSe 3 , are more akin to vdW materials [13] and bear the MX 3 (M = transition metal; X = chalcogen) form. While the lattice constants of all these MX 3 -type TMTs differ, they do belong to the same space group and are isostructural [52,69,89]. Figure 3(a) shows the crystal structure of an MX 3 -type TMT where X 2− and X 2 2− indicate two distinct chalcogen species; since all the MX 3 -type TMTs are isostructural, determining the surface termination of just one of them would suffice as it would be the same for all other TMTs of the MX 3 kind. Figure 3(b) shows results of the angle-resolved XPS of ZrS 3 , which implies that the surface of ZrS 3 terminates in disulfide (S 2 2− ) and not sulfide (S 2− ) [90]. Because the MX 3 -type TMTs are isostructural, the insights into the surface termination of ZrS 3 can be extended to all other MX 3 -type TMTs. In other words, TiS 3 and HfS 3 should also terminate in disulfide and HfSe 3 should terminate in diselenide (Se 2 2− ).
While isostructural with TiS 3 and ZrS 3 , unlike TiS 3 and ZrS 3 , the photoemission spectroscopy data of HfS 3 show signature of oxidation of hafnium that appears to occur upon exposure of HfS 3 to ambient air [73], implying that the surface of HfS 3 is nontrivial. Figure 4 shows the XPS data of the Hf 4f core-level of HfS 3 . The red triangles in Fig. 4 represent the raw photoemission spectrum of the Hf 4f core-level and the fits are indicated by the solid lines. The overall fit to the raw data (solid black  line) requires two Hf 4f doublets (shown by solid red and solid blue lines). The higher intensity doublet (solid red lines) consists of an Hf 4f 7/2 peak at 16.0 ± 0.1 eV and an Hf 4f 5/2 peak at 17.7 ± 0.1 eV, implying a spin-orbit splitting of ~ 1.7 eV between the two peaks. The lower intensity doublet, shown by solid blue lines, has the two Hf 4f peaks separated by ~ 1.7 eV as well, with the Hf 4f 7/2 peak occurring at 16.7 ± 0.1 eV and the Hf 4f 5/2 peak appearing at 18.4 ± 0.1 eV. The higher binding energy of the Hf 4f doublet in blue, in comparison with the binding energy value of the doublet in red, implies more charge donation in the former case compared to the latter. Therefore, in accordance with the existing literature [91][92][93][94][95], the lower intensity Hf 4f core-level doublet at the higher binding energy value is attributed to the Hf-O bonding environment; whereas the Hf 4f core-level doublet at the lower binding energy is characteristic of the Hf-S bonding environment [73]. These results imply facile dissociative chemisorption of oxygen on HfS 3 . Now, this is crucial because the oxygen chemisorption at the surface of HfS 3 helps reconcile two prior experimental studies on HfS 3 with contradictory claims, as the study conducted by Xiong et al. [96] showed that HfS 3 is a p-type semiconducting material, whereas the study conducted by Flores et al. [97] claimed that HfS 3 is an n-type material instead. Chemisorption of oxygen at the HfS 3 is also consistent with the electrical transport data shown in refs. [73,96], and explains how the exposure of HfS 3 to ambient air makes it transition from being an n-type semiconductor, in its as-synthesized form, to a p-type semiconductor.
While there exist several photoemission spectroscopy studies on these three TMTs (i.e., TiS 3 [36,52,68,69,74,89], ZrS 3 [52,69,89,90], and HfS 3 [73]), a comparison of the corelevel photoemission data for the sulfur core-levels of each of these trichalcogenides can provide indications of predominant location of the sulfur vacancies [98,99]. In the case of HfS 3 , such a comparison can help identify the location of sulfur sites that are filled in by oxygen instead. Figure 5 shows the photoemission spectra of the S 2p core-levels of TiS 3 , ZrS 3 , and HfS 3 . The fits to the S 2p core-level spectra of both  Reproduced from ref. [73] with permission from the Royal Society of Chemistry.

Figure 5:
The XPS spectra of the S 2p core-levels of (a) TiS 3 , (b) ZrS 3 , and (c) HfS 3 . The solid circles represent the raw data while the overall fits to the raw data are shown by the solid red lines. Each of these spectra contains four photoemission components: S 2− 2p 3/2 , S 2− 2p 1/2 , S 2 2− 2p 3/2 , and S 2 2− 2p 1/2 . All the individual S 2p core-level components are indicated by green arrows.
(S 2− 2p 1/2 and S 2 2− 2p 3/2 ), and 163.4 ± 0.1 eV (S 2 2− 2p 1/2 ). Overall, it is fair to say that the binding energy values of the four S 2p core-level features of HfS 3 are in great agreement with the binding energy values of the four S 2p core-level components of its zirconium and titanium counterparts. This is, therefore, both expected and reassuring since all these three TMTs are isostructural [69,73]. Nonetheless, a closer look into the XPS spectra of their respective S 2p core-levels discloses that HfS 3 differs from both TiS 3 and ZrS 3 . The variation in the ratio of the photoemission peak areas of the S 2 2− 2p core-level to the S 2− 2p core-level as a function of the Z of the transition metal, which both the sulfur species are bonded to, is summarized in Fig. 6. All the photoemission peak areas, used to plot Fig. 6, were calculated from the S 2p core-level XPS spectra shown in Fig. 5. From the trend shown in Fig. 6, it can be inferred that the XPS intensities of the S 2 2− 2p and S 2− 2p core-level photoelectrons depend on the transition metal they are bonded to. While this could partly be a direct consequence of a variation in the inelastic mean free path of the S 2p core-level photoelectrons, the oxidation HfS 3 is in fact the likely origin of why there is a significant increase in the I(S 2 2− 2p)/I(S 2− 2p) ratio for HfS 3 . The high ratio of the photoemission peak areas of the S 2 2− 2p core-level to the S 2− 2p core-level of HfS 3 is in agreement with the existing theory [11,100] that found the S 2− vacancy formation to be the most energetically likely scenario among all the possible vacancy formation scenarios. The highly likely S 2− vacancy formation in HfS 3 along with a I(S 2 2− 2p)/I(S 2− 2p) ratio of ~ 3.2 is also consistent with the chemisorption of oxygen at the HfS 3 surface and indicates that oxygen preferentially binds itself to Hf by occupying the S 2− vacancies.
Our analyses of the XPS spectra of the S 2p core-levels of TiS 3 , ZrS 3 , and HfS 3 , therefore, imply that oxygen occupies the sulfur sites in HfS 3 that are the most highly coordinated with the Hf ions, i.e., the S 2− sites. The displacement of sulfur atoms in HfS 3 by oxygen atoms thus implies that the nature of this displacement is such that the oxygen atoms show affinity toward binding with the Hf ions via the sulfur sites that participate in stronger Hf-S bonds. Such an oxygen chemisorption mechanism ensures that once oxygen binds itself to Hf ions, more electron charge is donated by the Hf ions to the oxygen atoms. Greater electron charge donation to oxygen means more facile hole doping of the HfS 3 as a consequence of oxygen chemisorption. Further weak chemisorption would occur on top of the surface at the S 2 2− sulfur sites, and this appears to be reversible as the bulk of HfS 3 is n-type in vacuum and p-type in ambient atmosphere (as revealed by the electrical transport studies [73]).

The complex interfacial interactions of the TMTs with Au
When a metal is interfaced with a semiconductor, depending on the difference between their respective work functions, there is a possibility for the formation of a potential barrier at the metal-semiconductor interface [101]. The Schottky-Mott rule [102,103] suggests that a Schottky barrier will form when an n-type semiconductor is brought in contact with a relatively high work function metal [101] (like Au [63][64][65]). Similarly, a Schottky-barrier formation can be expected at the metal/ptype semiconductor interface if a low work function metal is deposited on the surface of a p-type semiconductor with a relatively high work function. Now, one may rightly argue that the Schottky-Mott rule does not always tell the full story. This is because the chemical interactions at the metal-semiconductor interface also contribute to the resulting barrier as opposed to the difference between their work functions alone: for example, Fermi level pinning as a consequence of metal-induced gap states [104][105][106][107][108][109]. As a starting point, photoelectron spectroscopy is a good tool to ascertain the Schottky-barrier formation by measuring band bending at the semiconductor interfaces [101,110,111]. Such band bending manifests itself in apparent shifts in the binding energies of the photoemission core-level components, of the elements of the underlying semiconductor, as the coverage of the deposited metal increases.
Upon exposing the surface of In 4 Se 3 to Au [75], a clear shift in the binding energy of the surface In 3d 5/2 core-level component is observed as the Au adlayer thickness is increased (Fig. 7). To be precise, the binding energy of the surface In 3d core-level doublet is found to be lowered by ~ 0.6 eV (illustrated by solid circles in Fig. 8). However, no real dependence of the binding energy of the bulk component of the In 3d core-level doublet on the Au coverage is revealed (depicted by solid triangles in Fig. 8). Since In 4 Se 3 is an n-type semiconductor [53,75,112] with the surface work function less than that of Au, the evident shift in the binding energy of the In 3d core-level doublet to lower values indicates upward band bending and implies the formation of an expected Schottky barrier at the Au/In 4 Se 3 interface [113][114][115][116][117][118].
Since both TiS 3 and ZrS 3 , like In 4 Se 3 , are n-type semiconducting materials [89] with relatively low work functions in comparison with that of Au [60], depositing Au on both the TMTs should also lead to the formation of a Schottky barrier at the Au/TiS 3 and Au/ZrS 3 interfaces. Contrary to the expectations based on the Schottky-Mott rule, this is not what is observed. The Au coverage-dependent XPS spectra of the S 2p and Ti 2p core-levels of TiS 3 , shown in Fig. 9(a) and (b), respectively, do not show any evidence of band bending at the Au/TiS 3 interface, which implies that the Au/TiS 3 interface is actually Ohmic [74]. Likewise, deposition of Pt contacts on TiS 3 also results in an Ohmic Pt/TiS 3 interface [74], despite an extremely high work function of Pt [119]. This is likely due to an interfacial metal-sulfide formation, i.e., Au-S (or Pt-S) [72], at the Au/TiS 3 (or Pt/TiS 3 ) interface.
The interaction between Au and ZrS 3 does not, however, lead to an obvious Ohmic Au/ZrS 3 interface as the Au/ZrS 3 interface is somewhat more complicated [90] than the Au/TiS 3 interface. The shifts in the binding energies of the S 2p and Zr 3d core-levels of ZrS 3 as a function of Au coverage are shown in Fig. 10(a) and (10), respectively. The vertical dashed lines in Fig. 10 denote the peak XPS binding energies of S 2p and Zr 3d core-levels, whereas the horizontal dashed lines denote the shifts in binding energies. In this figure, the XPS spectra collected for the bare ZrS 3 (i.e., the XPS spectra corresponding to 0 Å of Au adlayer thickness) are at the top (in red), the XPS spectra corresponding to 4 Å of Au adlayer thickness are shown in blue, the XPS spectra corresponding to 8 Å of Au adlayer thickness are shown in green, the XPS spectra shown in purple correspond to 12 Å of Au adlayer thickness, and the spectra shown in black correspond to 16 Å of Au, respectively [90]. As the Au coverage is increased from 0 Å (spectra shown in red in Fig. 10) to 4 Å (spectra shown in blue in Fig. 10), an upward band bending, implied by the shifts in the binding energies of both the core-levels, is observed. But this band bending is found to be suppressed as a consequence of strong Au-S and Au-Zr interactions, which only get stronger as the thickness of the Au adlayer is increased further. Although the implications of such a complicated Au/ZrS 3 on the performance characteristics of ZrS 3 -based nanodevices are discussed in the following section, a detailed explanation for the same is provided in ref. [90].
As discussed above, HfS 3 , in spite of being isostructural with TiS 3 and ZrS 3 , is more controversial in that HfS 3 has been reported to show both p-type [96] and n-type [97] semiconducting characteristics. This peculiarity of HfS 3 was addressed in an elaborate detail through a combination of XPS and electrical transport measurements [73]. Now, since chemisorption of adsorbates, like O 2 , at the surface of HfS 3 renders its surface p-type and its work function is more than that of Au [60], formation of a p-type Schottky barrier may be expected at the Au/ HfS 3 interface. In Fig. 11, the XPS spectra shown in red were collected for bare HfS 3 (i.e., for 0 Å of Au adlayer thickness), the XPS spectra corresponding to 6 Å of Au adlayer thickness are shown in blue, the ones shown in green correspond to 12 Å of Au adlayer thickness, and the XPS spectra shown in purple  were taken for 18 Å of Au adlayer thickness, respectively. In this figure, the peak XPS binding energies of the S 2p and Hf 4f core-levels are denoted by the vertical dashed lines, and the shift (of ~ 0.8 eV) in their respective binding energies is illustrated by the horizontal dashed line [73]. From this figure (Fig. 11), there is an unambiguous downward band bending implied by   The photoemission spectra of (a) the S 2p and (b) Hf 4f core-levels of HfS 3 as a function of Au adlayer thickness. Reproduced from Ref. [73] with permission from the Royal Society of Chemistry. an increment in the binding energies of the S 2p and Hf 4f corelevels of HfS 3 by ~ 0.8 eV, upon interfacing with Au, confirming the formation of a p-type Schottky barrier [120][121][122][123][124] at the Au/ HfS 3 interface.
Not only do the TMTs with different transition metal interact differently with Au, as can be inferred from the preceding discussions, but even the TMTs with the same transition metal but different chalcogens behave distinctively when interfaced with Au. One viable way to elucidate such an oddity among the TMT systems could be to compare the Au thickness-dependent XPS spectra of the core-levels of the TMTs composed of the same transition metal but different chalcogens. Therefore, capitalizing on the discussions in the preceding paragraph, let us now compare the XPS spectra shown in Fig. 11 with the Au coverage-dependent photoemission spectra of the Se 3d and Hf 4f core-levels of HfSe 3 (shown in Fig. 12). Upon the first deposition of Au contact (i.e., 5 Å of Au), the binding energies of both Se 3d and Hf 4f core-levels are increased by ~ 0.6 eV (spectra shown in blue in Fig. 12); thereafter, as the Au coverage is increased to 15 Å, no further change in the binding energy of the Se 3d core-level is observed. This incremental increase in the core-level binding energies of the constituent elements of HfSe 3 implies a p-type Schottky-barrier formation [120][121][122][123][124] at the Au/HfSe 3 interface, which is somewhat reminiscent of what was observed at the Au/HfS 3 interface. Also, here it should be noted that the shape of the spectra shown in Fig. 12(a) changes drastically as the thickness of the Au adlayer is increased. This happens because, expectedly, the XPS signal from the Au 5p 3/2 core-level overpowers the XPS signal from the Se 3d core-level [125][126][127] as the Au coverage is increased.
Qualitatively speaking, a direct comparison of Fig. 12(a) with Fig. 11(a) indicates that the trend of the Au coveragedependent shift in the binding energy of Se 3d core-level of HfSe 3 is similar to that of the S 2p core-level of HfS 3 ; however, this is not the case when the trends of the shifts in the binding energies of their respective Hf 4f core-levels (Figs. 12(b) and 11(b)) are compared. A closer examination reveals that the binding energy of the Hf 4f core-level of HfSe 3 now decreases by ~ 0.2 eV as the Au coverage increases from 5 Å (spectrum in blue in Fig. 12(b)) to 10 Å (spectrum in green in Fig. 12(b)). And this does not stop there because the binding energy of the Hf 4f core-level decreases by ~ 0.2 eV, yet again, as the Au coverage increases from 10 Å to 15 Å (spectrum in purple in Fig. 12(b)). The difference between the trends of the Au thickness-dependent binding energy shifts of the Se and Hf core-levels ( Fig. 12) can be easily explained on the basis of the electronegativity argument. On the Pauling electronegativity scale, Au and Se have similar electronegativities [128][129][130][131][132], whereas there is a considerable difference between the electronegativities of Au and Hf [128][129][130][131][132][133]. Now since Au is more electronegative than Hf, and the downward bending of the HfSe 3 energy bands at the Au/HfSe 3 interface will lead to an accumulation of electrons at the surface of HfSe 3 , the electrons will tend to move from Hf to Au. This motion of electrons, from Hf to Au, counteracts the downward band bending that initially happens as a result of Fermi level matching at the Au/HfSe 3 interface [ Fig. 12(b)]; but since there is no real difference between the electronegativities of Au and Se, no such phenomenon is observed in Fig. 12(a).

Implications on characteristics of TMT-based devices
The implications of the XPS studies at the Au/TMT interfaces are reflected in the transport measurements. In consistency with the results of the photoemission measurements shown in Figs. 7 and 8, the non-Ohmic Au/In 4 Se 3 interface is manifested in the I-V characteristics of a two-terminal In 4 Se 3 -based device shown in Fig. 13. Interestingly, this nonlinear I-V behavior is hard to avoid even when the lower work function Cr/Au contacts are used (as opposed to higher work function pure Au contacts) and the In 4 Se 3 phototransistors are exposed to radiation with energy higher than its band gap (see inset of Fig. 13) [43,75]. The Cr/ Au contacts may change the electrical properties of nanoelectronic devices only slightly but the Cr-Au alloy formation leads to a sturdier physical contact in comparison with the pure Au contact [134], which is what is needed to take reliable electrical transport data for the In 4 Se 3 -based nanoelectronic devices.
The differences in the band bending at the Au/TiS 3 , Au/ ZrS 3 , and Au/HfS 3 interfaces, indicated in the XPS measurements (see Figs. 9, 10, and 11) discussed above, are exhibited in the I-V characteristics of the FETs based on TiS 3 [ Fig. 14(a)], ZrS 3 [ Fig. 14(b)], and HfS 3 [ Fig. 14(c)], respectively. Among these three TMTs, only the devices based on TiS 3 show linear I-V curves and, thus, an Ohmic behavior. The I-V characteristics of the ZrS 3 FET show some non-linearity at lower sourceto-drain voltage (V DS ) and a close-to-linear behavior at higher V DS . The devices with HfS 3 have a plateau of low conductance at V DS between − 0.3 V and + 0.3 V, and again a close-to-linear behavior at higher V DS .
These differences can be qualitatively interpreted using the model that is elaborately discussed in Ref. [135]. Based on the model given by Penumatcha et al. [135], the Au/TiS 3 interface likely has a low Schottky-barrier height. However, one cannot simply identify the range of lower conductance for ZrS 3 and HfS 3 FETs as the source-to-drain voltage overcomes the energy height of the Schottky barrier even though the height of the Schottky barrier, in each case, remains unchanged. The mechanism instead is that increasing the V DS leads to the increase of the free carrier density; this decreases the geometrical width of the Schottky barrier, and the tunneling current through the barrier becomes dominant. In this case, the behavior of the contact becomes close to Ohmic, i.e., a linear dependence on V DS . The influence of the gate voltage (V G ) in the case of the HfS 3 FET is such that at positive V G it moves the Fermi level closer to the band edge and ensures higher carrier concentration and higher conductance; and at negative V G , it moves the Fermi level away from the band edge and inhibits the thinning of the Schottky barrier.
While the electrical transport of a HfSe 3 -based device [38] does not exactly mimic that of a HfS 3 -based device [73,96], the non-linearity in the I-V curves of an HfSe 3 -based device, in agreement with the Au coverage-dependent XPS measurements on HfSe 3 (Fig. 12), still persists (Fig. 15). Figure 15 shows the electrical transport of an HfSe 3 -based device [38]. It is worth noting that while the I-V characteristics   [74]. Copyright (2019) by the American Institute of Physics. Reproduced with permission. All rights reserved. (b) Is taken from Ref. [90]. © IOP Publishing. Reproduced with permission. All rights reserved. (c) Is reproduced from Ref. [73] with permission from the Royal Society of Chemistry. of an HfSe 3 -based device do not exactly mimic that of an HfS 3 -based device [73,96], the non-linearity in the I-V curves of an HfSe 3 -based device (Fig. 15), in agreement with the Au coverage-dependent XPS measurements on HfSe 3 (Fig. 12), still persists.

Conclusions and future work
In conclusion, the Schottky-Mott rule alone is inadequate when explaining the Au/TMT interfaces, as the effects of the chemical interactions at these interfaces appear to play a significant role. The strength of gold-chalcogen interaction is a factor too important to disregard when explaining the nature of Au/TMT interfaces. Since the gold-chalcogen interaction can sometimes suppress the Schottky-barrier formation, this explains why the surface termination of In 4 Se 3 in indium results in a Schottky barrier at the Au/ In 4 Se 3 interface along with the varying trends observed when Au is interfaced with TiS 3 , ZrS 3 , and HfS 3 . In other words, the stronger the interaction between sulfur and the transition metal, the weaker the Au-S interaction. And since the electronegativity of Hf is lower than that of both Zr and Ti, the Au-S interaction at the Au/HfS 3 interface is weaker than it is at either the Au/ZrS 3 or Au/TiS 3 interface. Thus, the absence of a strong Au-S interfacial interaction (the presence of which suppresses Schottky-barrier formation at the Au/ZrS 3 [90] and Au/TiS 3 [74] interfaces) results in the formation of a Schottky barrier at the Au/HfS 3 interface. The simple electronegativity argument also sheds some light on the oddities observed in the trends of the Au thicknessdependent binding energy shifts of the Se and Hf core-levels of HfSe 3 (Fig. 12).
The results of photoemission spectroscopy-aided investigations [73][74][75]90] of the Au/TMT interfaces are reflected in the electrical transport measurements of the devices based on these TMTs [52, 73-75, 90, 96, 136]. Among all the TMTs reviewed herein, only the devices based on TiS 3 show Ohmic behavior, while the devices derived from the rest of the TMTs do not. Nevertheless, there are a few ways that can help circumvent this issue in the foreseeable future: (i) dope the contact regions degenerately to manipulate the Schottky-barrier height [137,138]; (ii) select the contact metals with the right work function with respect to the semiconducting type of the TMT of interest [139] (i.e., selecting high work function metals for p-type TMTs [140][141][142][143][144] and low work function metals for the n-type ones [53,75,89,112]); (iii) use ionic-liquid gates to reduce the Schottky-barrier height [145]; and (iv) pick contact materials whose work function can be tuned as needed [146].

Acknowledgments
This work was supported by National Science Foundation through EPSCoR RII Track-1: Emergent Quantum Materials and Technologies (EQUATE), Award OIA-2044049.

Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declarations
Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.

Open Access
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