Two-dimensional (2D) transition metal dichalcogenides (TMDs) hold immense promise as ultrathin-body semiconductors for cutting-edge electronics and optoelectronics. In particular, their sustained charge mobility even at atomic-level thickness as well as their absence of surface dangling bonds, versatile band structures, and silicon-compatibility integration make them a prime candidate for device applications in both academic and industrial domains. Despite such high expectations, group-VI TMDs reportedly exhibit a range of enigmatic properties, such as substantial contact resistance, Fermi level pinning, and limited unipolar charge transport, which are all rooted in their inherent defects. In other words, intrinsic physical properties resulting from their native defects extend their influence beyond the material level. Bridging point-defect-induced material properties and their behavior at the device level, this Perspective sheds light on the significance of crystalline defects beyond a rather simple defect–property relationship. As a distinctive approach, we briefly review the well-established defect model of conventional III–V semiconductors and further apply it to the emergent defect behaviors of 2D TMDs such as their defect-induced gap states. Within the main discussion, we survey a range of behaviors caused by the most prevalent intrinsic defect, namely, vacancies, within 2D TMDs, and their implications for electronic and optoelectronic properties when employed at the device level. This review presents an in-depth summary of complexities in material properties as well as device characteristics arising from intrinsic point defects and provides a solid foundation for the cross-links among native defects and material/device properties.

Since the successful mechanical isolation of graphene from graphite, there has been an explosive interest in the properties and applications of two-dimensional (2D) materials within both academia and industry domains. Among them, layered transition metal dichalcogenides (TMDs) emerge as promising candidates for next-generation semiconductors.1–3 Currently, ongoing research is concentrated on the practical application of such semiconducting materials with atomic-layer thickness in real-world industrial settings.4,5 These materials are typically represented as MX2, with M denoting a central transition metal from group VI and X representing a chalcogen atom (S, Se, or Te).6 In transition metal complexes, bonding typically entails the interaction between the vacant orbitals of the metal and the lone pairs (LPs) of ligands. The metal atom contributes four electrons to occupy the bonding states, leading to formal charges of +4 for the transition metal and −2 for the chalcogens.6 The LP electrons of the chalcogen atoms, residing in sp3-hybridized orbitals, occupy the surfaces of TMDs. Consequently, the coordination around the chalcogenides is unbalanced, leading to distinct cleavage properties perpendicular to the hexagonal/trigonal symmetry axis.7 The absence of dangling bonds results in highly stable and chemically inert surfaces.

Furthermore, TMDs can serve as the transition from a direct bandgap in the monolayer to an indirect bandgap in a bilayer or multilayers resulting from interlayer hopping, as the band extrema Kv, Γv, and Qc (located between M and Γ) valleys, in the Brillouin zone all split as the number of layers increases. The extent of this splitting reflects the strength of interlayer hopping. Significantly, the greater splitting observed at Γv and Qc compared to Kv can be attributed to the fact that the Bloch states at Kv are predominantly based on the d orbitals of the metal, whereas the Bloch states at Γv and Qc have substantial contributions from the chalcogen pz-orbital.8,9

Weak van der Waals (vdW) interactions between layers within TMD crystals facilitate mechanical exfoliation into single- or few-layer nanosheets, leading to distinctive semiconducting physical and electronic properties that distinguish them from their bulk counterparts.10,11 In addition, TMDs structure generally exists in two polymorphs: trigonal prismatic and octahedral phases; the former belongs to the D3d point group with a honeycomb motif, whereas the latter is associated with the D3d point group featuring a centered honeycomb motif.12 Additionally, few-layer TMDs can exhibit the 3R polymorph13 (i.e., rhombohedral symmetry, three layers per unit cell, and trigonal prismatic coordination). Group-VI TMD monolayers are commonly found as three polymorphs, with each imparting distinct optical and electronic characteristics in different crystal phases. These phases include the semiconducting 2H (hexagonal),14 the metallic 1 T (trigonal),15 and the semimetallic 1T′ (monoclinic)16 phases. Therefore, TMDs exhibit a diverse range of electronic characteristics influenced by their interlayer property and chemical composition and crystal structural configurations.6,17 Examples of prominent semiconducting TMDs include monolayer MoS2 and WS2, which play pivotal roles in electronic and optoelectronic applications.18,19

Furthermore, recent studies have thoroughly investigated various defect categories, including vacancies, interstitial atoms, and impurities, along with their impacts on the properties of TMDs.20–22 Additionally, numerous review articles have offered comprehensive insights into several areas, such as electronics, photonics, and energy conversion and storage.23–25 Within crystalline TMDs, point defects involve vacancies, substitutional impurities, and interstitials, and the studies indicate that these defects are crucial in modifying the electronic and optical characteristics of TMDs.26,27 Therefore, the type, quantity, distribution, and electrical variations of the defects play a crucial role, either compromising the functionality of the devices or, conversely, creating new functionalities in emerging devices. In contrast, research examining the functionalities within the relevant devices and the connections between these functions and the point defects inducing them is relatively limited.

The defects in 2D layered materials, such as TMDs, primarily arise due to their high surface-to-volume ratio, which results in substantial impact on material property. Typically, the trend of bond-breaking at the surface is encountered due to a lower energy barrier compared to the bulk material. Consequently, in the case of an exfoliated TMD sample, a single vacancy density on the order of 1013 cm−2 is observed, indicating an average defect distance of approximately a few nanometers.28 Furthermore, vacancy-induced gap states exhibit relatively consistent positions relative to the conduction band minimum (CBM) regardless of the choice of metal (M = W and Mo) across different systems (0.1–0.3 eV below the CBM).29,30 Also, partial phase transitions are commonly observed around the vacancy cluster. Therefore, the presence of native point defects within TMD nanosheets has ushered in exciting opportunities for harnessing the unique optical and electronic attributes of the latter.

For example, sulfur vacancies can be tuned to control the interactions between many particles (e.g., trions and excitons) in MoS2.26 In addition, the presence of a substantial density of native chalcogen vacancies leads to a unique tendency to carry negative charges and induce localized shifts in chemical potential with surrounding materials. This characteristic plays a pivotal role in effectively stabilizing the Fermi level closer to the conduction band edge. Consequently, this observation not only clarifies the frequently encountered n-type doping effect31,32 found in materials such as MoS2 but also offers valuable insights into the phenomenon of Fermi level pinning (FLP).27,33 Furthermore, crystal phases readily interact with chalcogen monovacancies through the migration of sulfur atoms, giving rise to localized crystal phases. Also, chalcogen monovacancies can induce lattice distortion and stabilize charged states.34,35 This gives rise to the phenomenon of persistent photoconductivity.36 These discoveries have uncovered intriguing possibilities involving charge transfer, crystal distortion, and phase transitions. Consequently, they offer an avenue for tailoring the functionality of TMDs in electronic and optoelectronic applications.37–40 

From this Perspective, our review provides the cross-links among native defects, material properties, and device performances, thereby shedding light on the significance of crystalline defects. In short, with a comprehensive analysis of structural elements and defect functionalities, it offers insights into the physical origins of device characteristics (Fig. 1). Initially, we briefly summarize the widely accepted defect model41 of III–V semiconductors and its correlation to the defect-induced properties of TMDs. Within the main discussion, we survey the distinct behaviors of the most prevalent intrinsic defects (atomic vacancies) within 2D TMDs and their impacts on electronic and optoelectronic properties. This comprehensive review offers a profound summary of intrinsic point defects and their versatile applications in the domain of 2D semiconducting TMDs.

FIG. 1.

A schematic summary of connecting intrinsic native defect behavior to material properties as well as the device performances based on TMDs.

FIG. 1.

A schematic summary of connecting intrinsic native defect behavior to material properties as well as the device performances based on TMDs.

Close modal

The real crystal structure inevitably departs from a perfect arrangement due to the thermodynamics of materials and the kinetics of their synthesis processing. A considerable density of structural imperfections, which are referred to “defects,” affects the physical and chemical properties of the material. Hence, we commence with a systematic and comprehensive analysis of point defect characteristics in 2D semiconducting TMDs. The structure of a typical layered TMD can extend within its basal planes but remains atomically thin perpendicular to the planes.42 Therefore, native defects in 2D TMDs could be classified according to dimension as zero-dimensional (0D) (point defects: vacancies, interstitial, and anti-sites), one-dimensional (1D) (line defects: grain boundaries and edges), and 2D (wrinkling, folding, and scrolling). Among these defects, the formation of point defects is inevitable in any crystalline material, as suggested by the second law of thermodynamics. At temperatures above 0 K, there is always a thermodynamically equilibrium concentration of 0D defects such as vacancies. 1D and 2D defects, despite being energetically less favorite than 0D defects, can be generated through various processes, including mechanical deformation (e.g., strain43), post-synthetic procedures (e.g., transfer44), and specific operating conditions during synthesis.45 Nevertheless, due to the generation mechanisms of 1D and 2D defects, their density is much lower compared to 0D defects. Therefore, herein, we exclusively focus here on point defects, which are the simplest intrinsic defects, when the crystal structure is perturbed without the presence of foreign atoms.

Most three-dimensional (3D) semiconductors retain many of their original properties when small amounts of defects are introduced, but certain semiconductor properties, such as conductivity, free carrier mobility, and carrier lifetime, undergo significant changes when defects and impurities are introduced even at the parts per million (ppm) or parts per billion (ppb) level, particularly at surfaces or interfaces.46 

Electrically active defects in semiconductor crystals possess varying characteristics, which are contingent upon the placement of their energy states concerning the conduction or valence band edges. Shallow defects exhibit energy levels located within a few tens of meV from the corresponding band edges, whereas deep defects tend to occupy the middle-third of the semiconductor energy bandgap. However, it is important to note that this straightforward definition is no longer universally valid. Deep levels have highly localized wave functions, whereas shallow-level wave functions can extend extensively, influenced by the far-reaching Coulomb potential.46 Shallow defects can be described using hydrogen-like models because they exist in a homogeneous medium with a relative dielectric constant (ɛ) and an effective electron/hole mass (m*) corresponding to the particular band extremum. Applying Coulomb's force, Newton's law, and the Bohr model, the binding energy ( E b) of a shallow defect is defined as the energy needed to move an electron from the ground state ( n = 1) to the conduction-band minimum, which can be expressed as follows:47,
E b = 1 2 m e 4 ( 4 π ε ε 0 ) 2 = ( 13.6 e V ) ( m m ) ( 1 ε 2 ) ,
(1)
where m is the fundamental electron mass, is the reduced Planck constant, ε 0 is the vacuum permittivity, and e is the elementary charge. It is also important to note that the electrons or holes associated with shallow defects exhibit strong delocalization, meaning their wave functions extend over a significant volume resembling a continuous medium with an average dielectric constant. However, as deep-level defects have localized wave functions, the potential energy of an electron or a hole of the deep-level defect should be considered as follows:48,
V ( r ) = 1 4 π ε ε 0 e 2 r + δ V ( r ) ,
(2)
where δ V ( r ) represents the central cell potential, encompassing short-range components attributed to the chemical individuality of the defect. Due to the addition of δ V ( r ), the hydrogen-like model is no longer valid. The properties of deep states follow the trend of the localized potential and it leads to outcomes that deviate from the characteristics of intrinsic semiconductors.46 In addition, it is necessary to consider various factors such as the distorting defect, defect hybridization, and interaction with surrounding materials, as the defect extends over several lattice constants.34 The results of these factors lead to a significant change in minority carrier lifetimes as well as their role as traps for charge carriers. Some deep-level traps can be utilized to position the Fermi level in the middle of the energy gap, creating highly resistive materials.49 Furthermore, certain deep-level traps have the ability to alter their geometric configuration,50 displaying metastable or bistable states,51 leading to the phenomenon of persistent photoconductivity (PPC). PPC is characterized by the extended conductivity of a material even after the external light source has been removed accomplished by sustaining the altered geometric configuration.52 

The primary and most prevalent imperfections found in TMDs are vacancies and anti-sites. In TMD nanosheets, six distinct categories of intrinsic point defects can be identified: mono-chalcogen (X) vacancies (VX), di-chalcogen vacancies (VX2), vacancy complexes of a transition metal (M) nearby three chalcogen atoms (VMX3), vacancy complexes with a transition metal nearby three di-chalcogen pairs (VMX6), and anti-site defects with a transition metal atom substituting a X2 (chalcogen) column (MX2) or a X2 column substituting a transition metal atom (X2M) [Fig. 2(a)]. To demonstrate the structural stability of the various point defect types, we present the formation energies of each point defect in molybdenum disulfide (MoS2) as a representative material. These energies are shown in Fig. 2(b) as a function of the chemical potential of sulfur (S).20 In the whole range of the chemical potential of S, VS is found to have the lowest formation energy, whereas MoS2 and S2Mo anti-site defects are among the second highest formation energies under S-rich and Mo-rich environments, respectively.21,22 These phenomena have also been verified by experimental results showing that VS was observed in all chemical vapor deposition (CVD)-grown samples in one study, with anti-site defects discovered infrequently.20 Besides the vacancies and anti-site defects, adatoms (interstitial) of M and X were generated scarcely in synthetic TMDs. As shown in Fig. 2(c), there are four different types of adatoms in TMDs: a transition metal absorbed on a mono-chalcogen site (Ma−X), a transition metal absorbed on top of a transition metal site (Ma−M), a single chalcogen atom absorbed on a transition metal site (Xa−M), and a di-chalcogen interstitial in the center of a hexagonal ring (X2a−hex).

FIG. 2.

(a) Fully relaxed structural models of the six types of point defects observed in MoS2. Blue and yellow balls represent Mo and S atoms, respectively, and green and red dot circles represent each Mo vacancy and S vacancy. (b) Formation energy of each point defects as a function of sulfur chemical potential at the range of –1.4 eV (the formation of bulk Mo) < μS < 0 eV (the formation of bulk alpha-S). (c) Mo and S adatoms on monolayer MoS2. Low-pass filtered STEM-ADF images (left images for each adatoms) and deconvolved images (right images for each adatoms) of various Mo and S adatoms on monolayer MoS2. From left to right: Mo adsorbed on a mono-S site (or at mono-S vacancy); Mo adsorbed on top of the Mo site; single S atoms adsorbed on Mo sites; and di-sulfur interstitial in the center of the hexagonal ring. (b) and (c) Reproduced with permission from Zhou et al., Nano Lett. 13(6), 2615–2622 (2013). Copyright 2013 American Chemical Society.20 

FIG. 2.

(a) Fully relaxed structural models of the six types of point defects observed in MoS2. Blue and yellow balls represent Mo and S atoms, respectively, and green and red dot circles represent each Mo vacancy and S vacancy. (b) Formation energy of each point defects as a function of sulfur chemical potential at the range of –1.4 eV (the formation of bulk Mo) < μS < 0 eV (the formation of bulk alpha-S). (c) Mo and S adatoms on monolayer MoS2. Low-pass filtered STEM-ADF images (left images for each adatoms) and deconvolved images (right images for each adatoms) of various Mo and S adatoms on monolayer MoS2. From left to right: Mo adsorbed on a mono-S site (or at mono-S vacancy); Mo adsorbed on top of the Mo site; single S atoms adsorbed on Mo sites; and di-sulfur interstitial in the center of the hexagonal ring. (b) and (c) Reproduced with permission from Zhou et al., Nano Lett. 13(6), 2615–2622 (2013). Copyright 2013 American Chemical Society.20 

Close modal

Point defects generate a defect state between the valence bands and conduction bands of TMDs. Notably, VS, which has the lowest formation energy as in the case of MoS2, reveals an unoccupied deep state below the CBM. Density functional theory (DFT) calculations of the vacancy defects in MX2 compounds containing S and Se show that the formation energy of S/Se vacancies is the lowest. Additionally, DFT calculations indicate that the positions of the 0/−1 transition relative to the CBM remain relatively consistent irrespective of the choice of metal (M = W and Mo) across different systems: MS2 (0.34–0.36 eV below the CBM), MSe2 (0.12–0.13 eV below the CBM), and MTe2 (0.22 eV below the CBM), as shown in Fig. 3(a).20,53–55

FIG. 3.

(a) DFT calculations indicate that the positions of the 0/−1 transition relative to the CBM remain relatively consistent irrespective of the choice of metal (M = W and Mo) across different systems: MS2 (0.34–0.36 eV below the CBM), MSe2 (0.12–0.13 eV below the CBM), and MTe2 (0.22 eV below the CBM). (a) Reproduced with permission from Kim et al., npj 2D Mater. Appl. 6, 75 (2022). Copyright 2022 Springer Nature Ltd.55 (b) The nature of the band structures for the defect-tolerant and defect-sensitive cases, respectively. The chalcogen p states are shown in blue and the metal d states in red. The regions with mixed color have mixed p and d character. The terms “defect-sensitive” and “defect-tolerant” generally align with the orbital character. (c) Sketch showing the filling of the electronic levels of the different groups of TMDs. The TMDs of group-IV are defect-tolerant, whereas the TMDs of group-VI and X are defect-sensitive. (b) and (c) Reproduced with permission from Pandey et al., Nano Lett. 16(4), 2234–2239 (2016). Copyright 2016 American Chemical Society.56 

FIG. 3.

(a) DFT calculations indicate that the positions of the 0/−1 transition relative to the CBM remain relatively consistent irrespective of the choice of metal (M = W and Mo) across different systems: MS2 (0.34–0.36 eV below the CBM), MSe2 (0.12–0.13 eV below the CBM), and MTe2 (0.22 eV below the CBM). (a) Reproduced with permission from Kim et al., npj 2D Mater. Appl. 6, 75 (2022). Copyright 2022 Springer Nature Ltd.55 (b) The nature of the band structures for the defect-tolerant and defect-sensitive cases, respectively. The chalcogen p states are shown in blue and the metal d states in red. The regions with mixed color have mixed p and d character. The terms “defect-sensitive” and “defect-tolerant” generally align with the orbital character. (c) Sketch showing the filling of the electronic levels of the different groups of TMDs. The TMDs of group-IV are defect-tolerant, whereas the TMDs of group-VI and X are defect-sensitive. (b) and (c) Reproduced with permission from Pandey et al., Nano Lett. 16(4), 2234–2239 (2016). Copyright 2016 American Chemical Society.56 

Close modal

These defects cause changes in the way the electronic structure near the energy levels of a material works.47 This leads to effects like scattering charge carriers, capturing excitons, and accelerating the recombination of electrons and holes. A key factor determining the role of a defect is whether it creates localized states within the bandgap.46 If defect states are located near the conduction or valence band edges, they have the potential to increase charge carrier density and enhance conductivity. Therefore, it can be summarized that the extent of a defect state's localization exerts a significant influence on electronic systems.57 Materials that have deep gap states due to defects are termed “defect-sensitive,” as these defects can substantially compromise performance. In contrast, materials that have either shallow or no defect states are termed “defect tolerant” and exhibit a tendency to maintain electronic performance even when defects are present.

The terms “defect sensitive” and “defect tolerant” generally align with the orbital character. Defect-sensitive materials exhibit conduction and valence bands composed of bonding and antibonding combinations of similar orbitals, while the defect-tolerant material features valence and conduction bands composed of orbitals with distinctly different characters, as depicted in Fig. 3(b).56 

Based on the above description, Pandey et al. conducted first-principles investigations on defect tolerance in 29 monolayer TMDs. Their findings reveal that TMDs based on group VI develop deep gap states when a chalcogen vacancy is created. These states are formed by dangling metal d bonds localized around the chalcogen vacancy. Also, their study demonstrates that group-VI and X TMDs exhibit a “defect-sensitive” nature, while the group-IV TMDs are “defect tolerant,” as summarized in Fig. 3(c).56 Additionally, by deactivating deep states through the chemical passivation of vacancies and subsequently maximizing quantum efficiency, it has been experimentally confirmed that vacancies are capable of creating localized states.58,59

Typically, defect-sensitive materials are prone to FLP. To understand the FLP effect of deep states, extensive studies have been conducted on III–V semiconductors.47,60 In the 20th century, III–V semiconductors such as GaAs, InP, and GaSb presented convincing evidence of FLP, even in the absence of intrinsic surface states, as illustrated in Fig. 4(a).61 The absence of intrinsic surface states is analogous to TMD materials, whose surfaces have an absence of dangling bonds.7 

FIG. 4.

(a) A schematic diagram of surface electronic and lattice structure GaAs (110) that does not exhibit intrinsic surface states in the bandgap. (a) Reproduced with permission from Spicer et al., Thin Solid Films 56(1–2), 1–18. Copyright 1979 Elsevier.61 (b) Schottky barrier height as function of alloy composition x for Au contacts to n-type Al1−xGaxAs, GaAs1−xPx, Ga1−xInxP, InP1−xAsx, and In1−xGaxAs. The theoretical barrier heights correspond to the antisite defect cation-on-anion-site (e.g., GaAs). (b) Reproduced with permission from Sankey et al., J. Vac. Sci. Technol. B 3, 1162–1166. Copyright 1985 American Vacuum Society.62 (c) The diagrams illustrating the defect reaction energy of GaAs for As (dashed line) and Ga defects (solid line). (c) Reproduced with permission from Walukiewicz, Phys. Rev. B 37, 4760. Copyright 1988 American Physical Society.63 (d) Calculated monolayer MoS2 energy level diagram vs concentration of S-vacancies (2.77%, 6.25%, and 25%). (e) Experimental band structures of the pristine [≤3%)] and sputtered monolayer MoS2 [7% and 25%] obtained by plotting the second derivative of the ARPES experimental data as a function of the momentum and binding energy. Dashed dotted line indicates the EF position. (d) and (e) From Bussolotti et al., ACS Nano 15(2), 2686–2697 (2021). Copyright 2021 American Chemical Society.64 (f) Possible defect structures that can be introduced by sputtering and the local electronic structure changes caused by these defects (Vs, V2s, and VMo). (g) Illustration of energy band alignment for the MoS2/Au sample. (f) and (g) Reproduced with permission from Chen et al., ACS Nano 12(3), 2569–2579 (2018). Copyright 2018 American Chemical Society.65 

FIG. 4.

(a) A schematic diagram of surface electronic and lattice structure GaAs (110) that does not exhibit intrinsic surface states in the bandgap. (a) Reproduced with permission from Spicer et al., Thin Solid Films 56(1–2), 1–18. Copyright 1979 Elsevier.61 (b) Schottky barrier height as function of alloy composition x for Au contacts to n-type Al1−xGaxAs, GaAs1−xPx, Ga1−xInxP, InP1−xAsx, and In1−xGaxAs. The theoretical barrier heights correspond to the antisite defect cation-on-anion-site (e.g., GaAs). (b) Reproduced with permission from Sankey et al., J. Vac. Sci. Technol. B 3, 1162–1166. Copyright 1985 American Vacuum Society.62 (c) The diagrams illustrating the defect reaction energy of GaAs for As (dashed line) and Ga defects (solid line). (c) Reproduced with permission from Walukiewicz, Phys. Rev. B 37, 4760. Copyright 1988 American Physical Society.63 (d) Calculated monolayer MoS2 energy level diagram vs concentration of S-vacancies (2.77%, 6.25%, and 25%). (e) Experimental band structures of the pristine [≤3%)] and sputtered monolayer MoS2 [7% and 25%] obtained by plotting the second derivative of the ARPES experimental data as a function of the momentum and binding energy. Dashed dotted line indicates the EF position. (d) and (e) From Bussolotti et al., ACS Nano 15(2), 2686–2697 (2021). Copyright 2021 American Chemical Society.64 (f) Possible defect structures that can be introduced by sputtering and the local electronic structure changes caused by these defects (Vs, V2s, and VMo). (g) Illustration of energy band alignment for the MoS2/Au sample. (f) and (g) Reproduced with permission from Chen et al., ACS Nano 12(3), 2569–2579 (2018). Copyright 2018 American Chemical Society.65 

Close modal

When comparing experimental and theoretical Schottky barrier heights (SBHs), Sankey et al. made the significant discovery that the barriers (for Au contacts) could be attributed to surface antistites, particularly cations occupying anion sites. Interestingly, this observation holds a high degree of quantitative agreement in most III–V semiconductors, as shown in Fig. 4(b).62 To elucidate this phenomenon, Spicer et al. initially suggested a defect model.66 However, this model faces a challenge: the absence of experimental evidence definitively linking specific acceptor and donor levels to types of defects around 0.6 eV for n-GaAs and 0.5 eV for p-GaAs. To address this challenge, Walukiewicz proposed the amphoteric defect model, which is rooted in the existence of native defects with amphoteric properties; he determined that, depending on the Fermi-level position, gallium vacancy ( V Ga) and arsenic vacancy ( V As) retain their character or undergo transformation to arsenic antisite ( A s Ga ) + V As and gallium antisite ( G a As ) + V Ga, respectively.67,68

The creation of deep trap states occurs due to the charge state of a defect significantly impacting the formation enthalpy. If the defect carries a charge of +1, it signifies that an electron has been donated to the semiconductor. The energy of this electron is equivalent to the Fermi energy (EF), which must be included in the defect's formation enthalpy. Conversely, if the defect carries a charge of −1, it implies that it has extracted an electron from the Fermi level; in this case, EF should be subtracted from the formation enthalpy. Generally, we incorporate the term qEF, where “q” represents the charge state (e.g., −1, 0, 1). The influence of charge state is significant because it can lead to self-compensation. For example, for heavily doped n-type GaAs, the gallium vacancy V Ga is a triple acceptor, with a charge state of q = −3. When EF is high, the formation enthalpy for V Ga is low. As the concentration of compensating V Ga acceptors increase, though, EF is lowered. When the Fermi level is ∼0.6 eV above the valence band, V Ga becomes unstable. One of the neighboring arsenic atoms moves into V Ga, forming an A s Ga. This defect reaction is given by V Ga V As + A s Ga. The vacancy-antisite pair is a triple donor. The transformation of the native acceptor into a donor prevents the Fermi level from decreasing any further.46 

A similar mechanism explains in irradiated GaAs. For n-type GaAs, irradiation-induced defect reactions on Ga and As sublattices are G a Ga + A s As G a As + V Ga + A s i or V Ga + G a i + A s As, where A s i is arsenic interstitial and G a i is gallium interstitial. Similarly, for p-type GaAs, G a Ga + A s As A s Ga + V As + G a i or V As + A s i + G a Ga.63 The process of compensation results in a shift of the Fermi level away from the band edge. As defect concentrations increase significantly, the Fermi energy reaches a stable position, which is determined by the absence of net charge transfer between the Fermi sea and the defects, as illustrated in Fig. 4(c).63 This energy is called the Fermi stabilization energy (EFS).

In a similar context, when intrinsic TMDs undergo processes such as sputtering with Ar gas, two scenarios can be considered: (i) the formation of S-vacancy clusters64,69 and (ii) the generation of various types of vacancies, including single and double S vacancies, as well as single Mo vacancies.65 As an illustrative example, Fig. 4(d) presents experimental data depicting the band dispersion of pristine monolayer MoS2 (3%) and sputtered MoS2 (7% and 25%) on highly oriented pyrolytic graphite (HOPG). Following the sputtering process and the subsequent increase in S-vacancy concentration (7% and 25%), a noticeable decrease in binding energy (approximately 1 eV) is evident. This observation aligns with the outcomes derived from core-level analysis and computational calculations, as demonstrated in Fig. 4(e).

In one study, lattice defects were introduced into monolayer MoS2 through low-energy Ar+ sputtering, and an investigation was carried out to assess changes in photoemission binding energy, peak shape, and optical properties when MoS2 was placed on an Au substrate. Possible defect structures that can be introduced by sputtering and the local electronic structure changes caused by these defects (VS, V2S, and VMo) as shown in Fig. 4(f). Notably, the defects introduced by ion irradiation significantly modified the band alignment between MoS2 and Au. Specifically, the Mo 3d5/2 binding energy decreased by 0.8 eV, whereas the Au 4f7/2 peak remained unchanged even after sputtering with a 0.5 keV Ar+ ion beam for 1 min. It is worth noting the presence of conspicuous states within the bandgap of MoS2, facilitating the charge-transfer process between MoS2 and Au, as depicted in Fig. 4(g). Both scenarios can lead to a shift in the Fermi level, stabilizing it at a certain energy until there is no net charge transfer between the Fermi sea and the defects. Therefore, the shift in the Fermi level away from the conduction/valence band edge might be a result of deposition-induced gap states (DIGSs),70 which is relevant with the high contact resistance of the field-effect transistor.27 However, it remains uncertain whether group-VI TMDs also conform to the Fermi stabilization rule, which suggests a tendency for the Fermi energy to universally shift toward 4.9 eV below the vacuum level due to defect formation, a phenomenon that is commonly observed in various materials and most III–V semiconductors.

Next, we aim to compile existing research on vacancies, which are the most prevalent type of point defects within TMDs, as well as their impact on electronic structure. Vacancies can not only lead to performance issues (e.g., increased contact resistance and unintended unipolar operation) but also worsen the device's stability due to lattice distortion.33,71 Experimental analysis revealed a single sulfur vacancy density of MoS2 on the order of 1013 cm−2, indicating an average inter-defect distance of approximately 1.7 nm, even in the case of an exfoliated sample.28 Such defect levels can undoubtedly have a significant impact on the electronic structure of group-VI TMDs.72,73

We shall commence by discussing the effects of vacancies, specifically their impact on FLP. In a typical scenario, the SBHs exhibited by different metals on a semiconductor tend to fluctuate in accordance with the work function of the metal. This relationship is governed by a pinning factor denoted as “S,” which ranges from the tightly pinned condition of S = 0 to the loosely pinned condition of S = 1. A lower pinning factor indicates that the SBH is less constrained, limiting the control that is achievable by adjusting the work function of the contacting metal. This reduced adjustability allows the SBH to be firmly pinned at the charge neutrality level of deep states,47 
S = 1 1 + N δ e 2 ε ,
(3)
where N is the density of gap states, δ is the decay length of the states, e is the electronic charge, and ɛ is the local dielectric constant. Generally, these gap states can arise from either intrinsic metal-induced gap states (MIGS) or vacancy-induced gap states (VIGS) in TMDs. Some have speculated that the presence of a vdW gap between TMD layers might lead to excellent contact properties. This, in turn, could decrease the density of gap states “N,” leading to an increase in the pinning factor “S.” Consequently, the SBH could be more conveniently controlled.

In contrast to the prediction, Das et al. experimentally observed a pronounced pinning effect, with a pinning factor of S. This effect could be due to the presence of additional gap states at the interfaces due to defects, which intensify the pinning phenomenon.74 Bampoulis et al. comprehensively investigated FLP in TMDs, employing spatially resolved SBH maps obtained using a conductive atomic force microscope (c-AFM) to unveil significant disparities between pristine and metal-like defective surfaces within TMDs.75,76 Although they emphasized that the overall FLP trend in TMDs aligns with the MIGS model, they noted a substantial increase of approximately 40% in FLP factors near metal-like defects (∼0.1), as shown in Fig. 5(a). The measured pinning factors were determined to be 0.3 and 0.28 on pristine surfaces for MoS2 and WSe2, respectively. Upon comparing these values with that (approximately S = 0.3) previously reported by Kang et al.,79 Gong et al.,80 and Guo et al.,81 it should not be overlooked that this value is comparable with the pinning factor derived from the MIGS model.

FIG. 5.

(a) The mapping data on the Schottky barrier height (SBH) near a defect in MoS2, measured using conductive atomic force microscopy (C-AFM). The pinning factor for both pristine MoS2 and the defect. (a) Reproduced with permission from Bampoulis et al., ACS Appl. Mater. Interfaces 9(22), 19278–19286 (2017). Copyright 2022 American Chemical Society.75 (b) The schematic representation of the MoS2 band structure. The presence of a vacancy defect, denoted as VS, results in the emergence of midgap states (a1, e). Based on experimental observations, electron capture and detrapping events lead to transitions between discrete states, specifically VS (0) ↔ VS (−1) and VS (−1) ↔ VS (−2). The energy barriers Eβ and Eα are instrumental in determining the degree of meta-stability for VS(0) and VS (−2), respectively. (b) Reproduced with permission from Song et al., Nat. Commun. 8, 2121 (2017). Copyright 2017 Springer Nature Ltd.77 (c) Energy levels of ML-MoS2 as a function of substrate work function. Plot of ionization energy (IE, blue) and electron affinity (EA, red) of ML-MoS2 as a function of the bare substrate work function, for the substrates: polycrystalline Au, Ag(111), HOPG, sapphire, PCBM)/ITO, poly(3-hexylthiophene-2,5-diyl) (P3HT)/ITO, SiO2 (native oxide)/n-Si, and SiO2 (thermal oxide). Schematic energy diagrams before and after contact between ML-MoS2 and a substrate, for the cases that before contact gap state energy levels lie above the substrate Fermi level and below the substrate Fermi level. (c) Reproduced with permission from Park et al., ACS Nano 15(9), 14794–14803 (2021), Copyright 2022 American Chemical Society.78 

FIG. 5.

(a) The mapping data on the Schottky barrier height (SBH) near a defect in MoS2, measured using conductive atomic force microscopy (C-AFM). The pinning factor for both pristine MoS2 and the defect. (a) Reproduced with permission from Bampoulis et al., ACS Appl. Mater. Interfaces 9(22), 19278–19286 (2017). Copyright 2022 American Chemical Society.75 (b) The schematic representation of the MoS2 band structure. The presence of a vacancy defect, denoted as VS, results in the emergence of midgap states (a1, e). Based on experimental observations, electron capture and detrapping events lead to transitions between discrete states, specifically VS (0) ↔ VS (−1) and VS (−1) ↔ VS (−2). The energy barriers Eβ and Eα are instrumental in determining the degree of meta-stability for VS(0) and VS (−2), respectively. (b) Reproduced with permission from Song et al., Nat. Commun. 8, 2121 (2017). Copyright 2017 Springer Nature Ltd.77 (c) Energy levels of ML-MoS2 as a function of substrate work function. Plot of ionization energy (IE, blue) and electron affinity (EA, red) of ML-MoS2 as a function of the bare substrate work function, for the substrates: polycrystalline Au, Ag(111), HOPG, sapphire, PCBM)/ITO, poly(3-hexylthiophene-2,5-diyl) (P3HT)/ITO, SiO2 (native oxide)/n-Si, and SiO2 (thermal oxide). Schematic energy diagrams before and after contact between ML-MoS2 and a substrate, for the cases that before contact gap state energy levels lie above the substrate Fermi level and below the substrate Fermi level. (c) Reproduced with permission from Park et al., ACS Nano 15(9), 14794–14803 (2021), Copyright 2022 American Chemical Society.78 

Close modal

However, it can also be inferred that the values obtained from the above-mentioned experiment (S = 0.3) may represent the combined impact of VIGS and MIGS82 for the following reasons. First, the amount of vacancy-type defects in the materials used in this experiment was reported to be approximately 1013 cm−2, which is significantly higher than the number of metal-like defects (1011 cm−2) claimed to be the stronger pinning factor.75,76 Second, the presence of a sufficiently high density of sulfur monovacancies exhibiting a tendency toward VS−1 formation and a locally raised chemical potential would stabilize the overall Fermi level (EF) at a position closer to EC, which would explain the almost universally observed n-type behavior of MoS2 as well as the FLP that underlies the high contact resistance of MoS2.32,77

In general, the 0/−1 transition level of VIGS corresponds to the acceptor ionization energy in theory. Under this condition, as shown in Fig. 5(b), the singlet a1 state is occupied by two electrons, and a doubly degenerate e state remains unoccupied. Consequently, these vacancies have the ability to trap two electrons, making them act as acceptor-like states.53 However, chalcogen vacancies of TMDs can also function as donor states by filling acceptor-like states with electrons through charge transfer from other nearby materials, such as substrates (e.g., SiO283 and AlOX84,85), molecules (e.g., H86 and H2O87), and electrodes (e.g., Au88,89). For example, Park et al. conducted an extensive investigation into electronic energy levels at interfaces involving monolayer MoS2 (ML-MoS2) transferred onto a diverse range of substrates, including metals, semimetals, organic and inorganic semiconductors, and insulators, as shown in Fig. 5(c).78 Their study yielded valuable insights into how the charge injection barrier is influenced by the work function of the substrate (Φsub). Their findings also uncovered two distinct regimes of level alignment: (i) When Φsub < 4.5 eV, strong FLP was observed, with an approximate value of S ≈ 0. (ii) Conversely, for Φsub > 4.5 eV, a near-vacuum level alignment was observed, but the S values exhibited variations for electrons and holes. In regime (i), with FLP, a significant reduction in the ionization energy (IE) and electron affinity (EA) of ML-MoS2 was noted. In regime (ii), characterized by the absence of interfacial ground state charge transfer, the SBH depended on Φsub and the extent of dielectric screening provided by the supporting substrate.

Liu et al. conducted another remarkable experiment enhancing this pinning factor by avoiding the damage of the channel, utilizing a transfer method for electrode fabrication to create well-defined vdW gaps between metals and TMDs.90 Their work demonstrated that DIGS, which emerge during the metallization process, are the root cause of deep level pinning, as we deduced in Sec. II D. Of note, the use of metals with elevated work functions (e.g., Au and Pt) enables a significant degree of polarity control (n-type to p-type) when interacting with a MoS2 channel and polymethyl methacrylate (substrate charge blocking layer).90 This phenomenon had not been previously identified in metal-deposited devices and is effectively explained by the following experiment conducted by Jing et al. They theoretically showed that under low sulfur vacancy (VS) concentrations (0.36 × 1014 and 0.82 × 1014 cm−2), VS only acts as an electron acceptor, resulting in a p-type Schottky contact when using an Au contact. However, at higher VS concentrations (1.64 × 1014, 2.46 × 1014, and 3.28 × 1014 cm−2), the polarity switches to an n-type Schottky behavior due to the generation of VS−1 acting as an electron donor.88 Therefore, MoS2 with lower VS concentrations can be used in Schottky-barrier field effect transistors (SBFETs). Also, a high pinning factor of almost 1.0 was observed from the transferred contacts, as extracted using the modified Arrhenius method. This observation indicated an enhancement not only in DIGS but also in MIGS and VIGS. However, these values are in stark contrast to the MIGS-induced pinning values calculated using the vdW contact configuration. We attribute this difference to the limitations of the modified Arrhenius method.

In general, this method assumes that thermionic emission dominates carrier transport. Therefore, the reverse current in the Schottky diode is most commonly the best data for extracting the SBH. The modified Arrhenius method is the most widely employed extraction technique for SBH in 2D devices. It was initially employed for carbon nanotube field effect transistors (CNTFETs), which are less vulnerable to defects than group-VI TMDs.91,92 However, the modified Arrhenius method can potentially introduce a considerable error when extracting SBH parameters in TMDs, where deep states, modulated by electrostatic gating, are inherent due to defects.93 According to the modified Arrhenius method, the thermionic emission current can be expressed as follows:47,
I D = W A T 3 / 2 exp ( q ψ B ( V G ) k B T ) ( 1 exp ( q V D k B T ) ,
(4)
where W is the channel width, A is the modified Richardson constant, T is the temperature, q is the elementary charge, ψ B ( V G ) is the gate-voltage-dependent effective SBH, k B is the Boltzmann constant, and V D is the applied drain voltage. Arrhenius plots can be obtained by varying temperatures and gate biases as follows:47 
I n ( I D T 3 / 2 ) ( q ψ B ( V G ) k B ) ( 1 T ) .
(5)

The effective SBH ( ψ B ) can be determined from the slope of the Arrhenius plot, I n ( I D / T 3 / 2 ) vs 1 / T, under the flatband condition ( V G = V F B ). V F B is typically obtained from the transition point from linearity to nonlinearity in the ψ B curve as a function of V G, as tunneling becomes non-negligible beyond V F B, as shown in Fig. 6(a). If a flatband shift ( Δ V F B) occurs, indicating ionization effects from donor states (VS−1) that are associated with inherent vacancy defects within TMD semiconductors, this method could lead to significant inaccuracies.69 This implies that an increase in carrier concentration within the semiconductor due to temperature variations becomes unreliable in this method when it leads to the change in flatband voltage at the metal–semiconductor barrier, as shown in Fig. 6(b).

FIG. 6.

(a) Energy band diagrams corresponding to the applied gate biases in three distinct regions: Below the flat band, at the flat band, and above the flat band. The contribution from tunneling current becomes negligible when VGS is at or below VFB. The IDS–VGS curve shows the current variation from thermionic to tunneling dominance. (b) The IDS–VGS curve demonstrates that the thermionic current varies in response to the ionization energy when the semiconductor contains such localized states within the bandgap. This phenomenon changes the position of the VFB. (c) The illustration shows that the knee-point in a semiconductor device does not always correspond to the flatband condition. At low SBH, the knee-point may manifest even before reaching the flatband condition. In cases of a high SBH, the tunneling component in the total current can be minimal, and yet, the extracted value of the barrier height remain well within the exponential region, extending beyond the flatband condition. (c) Reproduced with permission from Murali et al., Adv. Funct. Mater. 31, 2010513 (2021). Copyright 2021 Wiley-VCH.94 

FIG. 6.

(a) Energy band diagrams corresponding to the applied gate biases in three distinct regions: Below the flat band, at the flat band, and above the flat band. The contribution from tunneling current becomes negligible when VGS is at or below VFB. The IDS–VGS curve shows the current variation from thermionic to tunneling dominance. (b) The IDS–VGS curve demonstrates that the thermionic current varies in response to the ionization energy when the semiconductor contains such localized states within the bandgap. This phenomenon changes the position of the VFB. (c) The illustration shows that the knee-point in a semiconductor device does not always correspond to the flatband condition. At low SBH, the knee-point may manifest even before reaching the flatband condition. In cases of a high SBH, the tunneling component in the total current can be minimal, and yet, the extracted value of the barrier height remain well within the exponential region, extending beyond the flatband condition. (c) Reproduced with permission from Murali et al., Adv. Funct. Mater. 31, 2010513 (2021). Copyright 2021 Wiley-VCH.94 

Close modal

Another concern suggested recently by Murali et al. is that the knee-point in a semiconductor device does not always correspond to the flatband condition for source injection and can be influenced by gate electrostatics, as illustrated in Fig. 6(c).94 For example, at a low SBH, the knee-point may manifest even before reaching the flatband condition. Conversely, in cases of a high SBH, the tunneling component in the total current can be minimal, and yet the extracted value ψ B of (the barrier height) may remain well within the exponential region, extending beyond the flatband condition. Therefore, this caveat is particularly important when extracting the SBH within the flatband voltage region; it may be advisable to evaluate them using the traditional Schottky diode method in the reverse bias region.

The other effects caused by vacancies are structural change of point defects, such as distortion, migration, and phase transition. Hennig et al. utilized DFT calculations to demonstrate the relaxed lattice configurations of VS0, VS−1, and VS−2 vacancies in MoS2. According to their calculations, when in the −1 charged state, the Mo atoms can adopt an isosceles triangular arrangement around the S vacancy. Therefore, two Mo–Mo pairs are situated approximately 3.05 Å apart, while the third Mo–Mo pair spans 3.18 Å. This combined breaking of electronic and geometric symmetries exemplifies a Jahn–Teller distortion. Notably, Hennig et al propose that this dislocation plays a crucial role in stabilizing the −1 charged S vacancy in both monolayer and layered bulk MoS2 systems, as shown in Fig. 7(a).35,95 For this reason, it may be that acceptor-like states associated with S vacancies could act as donor states stabilized by the −1 charge and distortion. Indeed, in scanning tunning spectroscopy measurements, the electronic structure between the symmetric and distorted vacancy species is distinct, as shown in Fig. 7(a).35 

FIG. 7.

(a) The projected DOS shows the degeneracy between these two orbitals is broken, with the additional electron occupying a state with dominant dx2−y2 character in the −1 charge state. The insets illustrate the electronic orbitals corresponding to the defect states of interest. STM topography of annealing-induced VS−1 (colored circles) in monolayer MoS2/QFEG/SiC and white dashed box in containing a distorted (top right) and a symmetric (bottom left) VS−1. (a) Reproduced with permission from Xiang et al., arXiv:2308.02201 (2023).35 Time-lapse series of ADF images of a S (b) and Mo (c) vacancy show atomic-scale migration. (b) Reproduced with permission from Precner et al., Sci. Rep. 8(1), 6724 (2018). Copyright 2018 Springer Nature Ltd.96 (c) Reproduced with permission from Hong et al., Nano Lett. 17(6), 3383–3390 (2017). Copyright 2022 American Chemical Society.97 (d) The energy differences between the 2H and 1T′ phases as a function of the Te vacancy concentration from the DFT calculation. (e) Conductance of a MoS2 device as a function of temperature before, during, and after exposure to light illumination. PPC transient of the device at 200 K. Inset: optical image of a four-probe device for PPC measurement (scale bar: 20 μm). Configurational coordinate diagram showing the three energies to characterize the DX center and describe the five PPC processes. Reproduced with permission from S. Cho et al. Science. 349(6248), 625–628 (2015). Copyright 2015 American Association for the Advancement of Science. (e) Reproduced with permission from Ci et al., Nat. Commun. 11, 5373 (2020). Copyright 2020 Springer Nature Ltd.36 

FIG. 7.

(a) The projected DOS shows the degeneracy between these two orbitals is broken, with the additional electron occupying a state with dominant dx2−y2 character in the −1 charge state. The insets illustrate the electronic orbitals corresponding to the defect states of interest. STM topography of annealing-induced VS−1 (colored circles) in monolayer MoS2/QFEG/SiC and white dashed box in containing a distorted (top right) and a symmetric (bottom left) VS−1. (a) Reproduced with permission from Xiang et al., arXiv:2308.02201 (2023).35 Time-lapse series of ADF images of a S (b) and Mo (c) vacancy show atomic-scale migration. (b) Reproduced with permission from Precner et al., Sci. Rep. 8(1), 6724 (2018). Copyright 2018 Springer Nature Ltd.96 (c) Reproduced with permission from Hong et al., Nano Lett. 17(6), 3383–3390 (2017). Copyright 2022 American Chemical Society.97 (d) The energy differences between the 2H and 1T′ phases as a function of the Te vacancy concentration from the DFT calculation. (e) Conductance of a MoS2 device as a function of temperature before, during, and after exposure to light illumination. PPC transient of the device at 200 K. Inset: optical image of a four-probe device for PPC measurement (scale bar: 20 μm). Configurational coordinate diagram showing the three energies to characterize the DX center and describe the five PPC processes. Reproduced with permission from S. Cho et al. Science. 349(6248), 625–628 (2015). Copyright 2015 American Association for the Advancement of Science. (e) Reproduced with permission from Ci et al., Nat. Commun. 11, 5373 (2020). Copyright 2020 Springer Nature Ltd.36 

Close modal

In addition, the migration of vacancies is a commonly observed phenomenon in TMDs. For example, Precner et al. observed the migration of sulfur vacancies in MoS2.96 Their images highlight two sulfur vacancies denoted by green dashed circles, spaced a few unit cells apart, as shown in Fig. 7(b). In the image, a lower-right S vacancy site becomes re-occupied by an adatom (green square) acquired after 225 s. Subsequently, after 300 s, an impurity atom suddenly emerges (blue arrow) and travels to the upper-left sulfur vacancy site due to the influence of the scanning electron beam irradiation. Finally, after 750 s, both vacancy sites are once again re-occupied by adatoms. Sulfur vacancy sites during this time demonstrate mobility and are easily eliminated. Similarly, Hong et al. also conducted observations of the movement of Mo vacancies within a monolayer of MoS2 at room temperature using time-lapsed annular dark-field imaging. The progression of vacancy migration, as depicted in Fig. 7(c), involved an interim phase denoted as VMo, offering insights into the mechanism governing the hopping of Mo vacancies between adjacent sites in the Mo sublattice.97 

Vacancies also exhibit the capability to induce phase transitions. Traditionally, this phenomenon was attributed to the transversal sliding of an entire chalcogen atomic layer. The conventional explanation for chalcogen vacancy-induced phase transitions in 2D TMDs involves the lateral movement of a complete chalcogen atomic layer to occupy hollow sites. Experimental findings also observed the local distortion in MoTe2. Cho et al. conducted in situ scanning transmission electron microscopy observations, revealing a structural distortion in a monolayer of MoTe2 caused by Te defects. They obtained a filtered high-resolution image near a Te vacancy, which shows the splitting of the Te atom. The Te atoms start splitting but do not yet completely reach the 1T′ phase over the entire area.98 The energy differences between the 2H and 1T′ phases, as a function of the Te vacancy concentration from the DFT calculation, clearly show a Te monovacancy concentration exceeding 3%, which causes the 1T′ phase to be more stable than the 2H phase, as shown in Fig 7(d).

In TMDs, vacancies can function as DX centers, showcasing several unique physical characteristics; these include persistent photoconductivity and a notable difference between their thermal and optical ionization energies. The underlying phenomenon can be summarized as follows: the initial transition of these defects occurs through the optical ionization process. Notably, these optical transitions occur within a timeframe too short for lattice modifications. Following ionization, lattice relaxation takes place through phonon emission. Consequently, when exposed to illumination, the DX center undergoes a transformation into a metastable donor state, which results in the creation of a potential barrier due to the differing lattice relaxation between these two states. This phenomenon was discovered by Ci et al. in MoS2, as shown in Fig. 7(e).36 

During the initial stage of thermal equilibrium (stage 1), a significant portion of electrons becomes trapped within DX centers. Upon energizing electrons within the DX center energy EDX (stage 2) beyond a specific threshold through the absorption of incident light, a transition to the extended conduction band (ECB) occurs. Notably, these electrons persist in the ECB even after the light source is deactivated due to the barrier EC, which prevents their return to the EDX state. This occurrence leads to the manifestation of PPC (stage 3). As the temperature increases (stage 4), more electrons are thermally excited, subsequently transitioning back to the EDX state. This thermal activation process effectively restores the conductivity to its original dark-state configuration (stage 5). These findings might support the assertion that acceptor-like states associated with S vacancies could act as donor states stabilized by the −1 charge and distortion.

To harness these intriguing phenomena, it is beneficial to know how to control defect density. Therefore, we will offer a concise overview of methods for inducing defect formation. The simplest method is to manipulate the synthesis parameter. According to the second law of thermodynamics, spontaneous reactions require an increase in entropy equal to or greater than zero. This principle drives the minimization of Gibbs free energy (ΔG = ΔH − TΔS) within a system at a specified temperature and pressure, resulting in defect formation in crystals. Therefore, in deposition processes, such as CVD, the growth temperature or pressure can exert a significant influence on defect formation in monolayers. Growth situations might be close enough to equilibrium to warrant the use of the equilibrium approach. Consequently, defect concentration can roughly be modulated by growth parameters. However, achieving accurate and consistent defect control during synthesis is challenging. Therefore, defect engineering through post-growth treatments is recognized as a more effective and controllable approach, particularly for 2D TMDs given their atomically thin nature.

Post-thermal annealing is a simple method to create chalcogen vacancies in 2D TMDs. For example, Zhu et al. observed that annealing the few-layer MoS2 in the temperature range of 300–600 °C led to a progressive increase in sulfur vacancy density, revealing a temperature-dependent pattern.99 Specifically, for MoS2 annealed at 600 °C, a sulfur vacancy density of approximately 1.8 × 1014 cm–2 was attained as shown in Fig 8(a).

FIG. 8.

(a) Schematic of sulfur vacancy generation of ML MoS2 through Ar/H2 thermal annealing. (a) Reproduced with permission from Zhu et al., ACS Nano 17(14), 13545–13553 (2023). Copyright 2023 American Chemical Society.99 (b) Schematic of pattering periodic defect arrays on semiconducting TMDs via focused laser irradiation. (b) Reproduced with permission from Kim et al. Adv. Mater. 28(2), 341–346 (2016). Copyright 2015 Wiley-VCH.100 (c) Schematic of defect-gradient formation on PtSe2 by plasma treatment. (c) Reproduced with permission from Jo et al., Nat. Commun. 13(1), 2759 (2022). Copyright 2022 Springer Nature Ltd.101 (d) Schematic of electron beam irradiation treatment on MoS2 and MoTe2 for chalcogen vacancies generation. (d) Reproduced with permission from Lin et al., ACS Appl. Electron. Mater. 1(5), 684–691 (2019). Copyright 2019 American Chemical Society.102 (e) Schematic of gallium ion beam irradiation on suspended ML TMDs for producing single-atom defect. (e) Reproduced with permission from Thiruraman et al., Adv. Funct. Mater. 29(52), 1904668 (2019). Copyright 2019 Wiley-VCH.103 (f) Schematic of defect healing process of ML WSe2 through thiol treated annealing. Reproduced with permission from (f) Schwarz et al., npj 2D Mater. Appl. 7(1), 59 (2023). Copyright 2023 Springer Nature Ltd.104 

FIG. 8.

(a) Schematic of sulfur vacancy generation of ML MoS2 through Ar/H2 thermal annealing. (a) Reproduced with permission from Zhu et al., ACS Nano 17(14), 13545–13553 (2023). Copyright 2023 American Chemical Society.99 (b) Schematic of pattering periodic defect arrays on semiconducting TMDs via focused laser irradiation. (b) Reproduced with permission from Kim et al. Adv. Mater. 28(2), 341–346 (2016). Copyright 2015 Wiley-VCH.100 (c) Schematic of defect-gradient formation on PtSe2 by plasma treatment. (c) Reproduced with permission from Jo et al., Nat. Commun. 13(1), 2759 (2022). Copyright 2022 Springer Nature Ltd.101 (d) Schematic of electron beam irradiation treatment on MoS2 and MoTe2 for chalcogen vacancies generation. (d) Reproduced with permission from Lin et al., ACS Appl. Electron. Mater. 1(5), 684–691 (2019). Copyright 2019 American Chemical Society.102 (e) Schematic of gallium ion beam irradiation on suspended ML TMDs for producing single-atom defect. (e) Reproduced with permission from Thiruraman et al., Adv. Funct. Mater. 29(52), 1904668 (2019). Copyright 2019 Wiley-VCH.103 (f) Schematic of defect healing process of ML WSe2 through thiol treated annealing. Reproduced with permission from (f) Schwarz et al., npj 2D Mater. Appl. 7(1), 59 (2023). Copyright 2023 Springer Nature Ltd.104 

Close modal

To perform micropatterning treatment, laser irradiation is a useful method [Fig. 8(b)]. Typically, when a focused laser beam irradiates a specific area, it results in a significant increase in temperature, followed by rapid cooling once the irradiation is complete. This swift alternation between heating and cooling establishes a distinctive reaction environment that promotes the direct preservation of defects in the final products. For example, Cho et al. showed that laser irradiation could elevate the local temperature to approximately 400 °C in 2H-phase MoTe2, leading to the creation of atomic Te defects in specific regions.98 

Another convenient and efficient method to create chalcogen vacancies is plasma treatment [Fig. 8(c)], which does not rely on thermal energy. Oxygen and argon plasmas are commonly used to generate various types of defects through ion sputtering. Nonetheless, oxygen or argon plasma has the potential to unintentionally introduce charges that get trapped within TMDs or neighboring materials, leading to challenges in achieving precise control. Otherwise, electron beam irradiation has proved to be a good method for creating chalcogen vacancies within a selective area in 2D TMDs, as depicted in Fig. 8(d).105 Indeed, a precise number of chalcogen defects was created via electron beam irradiation in both 2H-MoS2 and 2H-MoTe2 by controlling electron beam irradiation dosages.99 Similarly, ion beam irradiation is particularly well-suited for 2D materials owing to its sub-nanometer beam size and adjustable energy [Fig. 8(e)]. Low-energy (100 eV) He+ ion irradiation can provide precise control over the concentration of only the top sulfur defects in monolayer MoS2.106 

Another approach to modulating the vacancies involves reducing the number of vacancies rather than creating them. Healing chalcogen vacancies has proven to be an effective method for controlling vacancy density, as shown in Fig 8(f). For example, Mahjouri-Samani showed that post-selenization via pulsed laser vaporization can eliminate vacancies in MoSe2 by repairing them.107 During the selenization process, the selenium vacancy concentration decreased from approximately 20% to around 3%, allowing for the tuning of the optical and electrical properties of crystals through the healing of selenium vacancies.

In this section, we provide recent examples where vacancies in TMDs play a pivotal role to serve as active sites or defects that can significantly impact in functionality, enabling inventive and captivating applications in the field of electronic and optoelectronic devices.

Shen et al. utilized oxygen during the CVD process, enhancing the stability of oxygen bonding to VS.108 In their study, they examined three types of monolayer MoS2 FETs: O-MoS2 (oxygen growth), SM MoS2 (sulfur-mild growth), and SE MoS2 (sulfur-excess growth). This passivation technique resulted in an enhancement of the contact resistance (RC), as determined by the transfer length method. The SM-MoS2 and SE-MoS2 FETs exhibited elevated RC values of approximately 3.9 and 7.8 kΩ μm, respectively. In comparison to conventional CVD-grown MoS2 without oxygen exposure, the O-MoS2 transistor exhibited a lower RC value of approximately 1 kΩ μm. This finding—vacancies can be efficiently passivated solely using oxygen, resulting in a decreased RC of 1 kΩ μm via gate voltage modulation (@ n2D of 4 × 1012 cm−2)—holds great significance in understanding the role of vacancy, as shown in Fig. 9(a). This effect is attributed to the alleviation of defect state pinning and the enhancement of gate control in the contact region.

FIG. 9.

(a) Band diagrams are shown for the OFF states of 2D FETs fabricated on O-MoS2 and MoS2 with donor defect states, where VS-MoS2 represents both SE-MoS2 and SM-MoS2. O-MoS2 monolayers exhibit a larger work function, resulting in a positive shift of VT. Band diagrams also qualitatively illustrate the MIGS at the Ni/MoS2 interfaces for the ON states of 2D FETs fabricated on O-MoS2 and defective MoS2, indicating a lower SBH and high gate controllability in O-MoS2 FETs. (b) Fabrication and electrical characteristics of monolayer MoS2 FETs with sulfur-vacancy-engineering (SVE) contacts. Construction process of MoS2 FETs with SVE and output curves op on different plasma exposure times of 0, 10, 20, and 35 s at room temperature. (b) Reproduced with permission from Xiao et al., Small Methods 7, 2300611 (2023). Copyright 2023 Wiley-VCH.109 

FIG. 9.

(a) Band diagrams are shown for the OFF states of 2D FETs fabricated on O-MoS2 and MoS2 with donor defect states, where VS-MoS2 represents both SE-MoS2 and SM-MoS2. O-MoS2 monolayers exhibit a larger work function, resulting in a positive shift of VT. Band diagrams also qualitatively illustrate the MIGS at the Ni/MoS2 interfaces for the ON states of 2D FETs fabricated on O-MoS2 and defective MoS2, indicating a lower SBH and high gate controllability in O-MoS2 FETs. (b) Fabrication and electrical characteristics of monolayer MoS2 FETs with sulfur-vacancy-engineering (SVE) contacts. Construction process of MoS2 FETs with SVE and output curves op on different plasma exposure times of 0, 10, 20, and 35 s at room temperature. (b) Reproduced with permission from Xiao et al., Small Methods 7, 2300611 (2023). Copyright 2023 Wiley-VCH.109 

Close modal

In another study, Xiao et al. used Ar bombardment to form sulfur vacancies, thus achieving ohmic contact between the metal and monolayer MoS2 with high-density sulfur vacancies.109 After successful n-doping, the contact regions by introducing VS, the contact resistance of the monolayer MoS2 FET reached as low as 1.7 kΩ μm (Cr/Au: RC of 1.7 kΩ μm @ n2D of 7.8 × 1012 cm−2), as shown in Fig. 9(b).

Based on a comprehensive review of previous research, the strategies for improving device performance using native point defects can be summarized into two main directions: minimizing the acceptor-like states through “passivation” to achieve effective gate control (Ni: RC of 1 kΩ μm @ n2D of 4 × 1012 cm−2) and utilizing vacancies as “donor states” to maximize the doping effect in the contact region (Cr/Au: RC of 1.7 kΩ μm @ n2D of 7.8 × 1012 cm−2). Both of these approaches can be effectively combined with reducing MIGS and maximizing the doping effect in the contact region using semimetals (e.g., Bi110 with an RC of 123 Ω μm @ n2D of 1.5 × 1013 cm−2; Sb111 with an RC of 42 Ω μm @ n2D of 3 × 1013 cm−2).

A memristor is a representative example of a device application utilizing the defects in an electronic device. Memristive devices play a crucial role as representative non-volatile storage devices derived from controlling the number and distribution of defects. Memristors have an electrically changeable resistance state (SET and RESET process) and can be switched by controlling defects, which can create conductive pathways in memristive devices. In conventional 3D-based memristors, when the thickness of the dielectric layer decreases under scaling down, switching reliability decreases as a result of lowering the forming threshold of the conductive pathway, causing non-uniform switching behavior. However, 2D vdW materials inherently have atomically thin layer structures. Therefore, defects in vdW layers can be discretely and precisely controlled by various methods (e.g., thermal, optical, or electrical).112,113 Therefore, 2D vdW materials can exhibit consistent switching behavior and minimize variability when compared to traditional 3D memristive devices. Single-defect 2D TMD-based memristors exhibit current densities in the range of 107 A cm−2, which are comparable to those seen in mesoscopic-scale devices while further minimizing the scale.114 Given the substantial abundance of sulfur vacancies, ranging from 1012 to 1013 per cm2, in TMD-based nanosheets, the dominant change in resistivity can be attributed to the presence of sulfur vacancies in 2D memristors. The resistivity can be controlled through both the quantity and distribution of vacancies by applying an external electric field, as depicted in Fig. 10(a). Vacancies also facilitate the movement of electric charges and can be replaced by metal or oxygen atoms on sulfur vacancies, allowing for a precise adjustment of the resistive properties of the memristive device.117 

FIG. 10.

(a) Schematic of 2D vdW-based memristor switching by vacancy migration. Blue sphere is the vacancies in TMDs representing the reversible switching process. (b) The device undergoes ON switching with a 13 ns voltage pulse and (c) OFF switching with a 14 ns voltage pulse, requiring 299.8 fJ for SET and 125.6 fJ for RESET operations, respectively. (b) and (c) Reproduced with permission from Yan et al., Small 15, 1901423 (2019). Copyright 2019 Wiley-VCH.115 (d) Diagrams depicting MoS2-based atomristors are shown, illustrating two configurations: one without a filament (top) and another with a semi-filament (bottom). (e) Formation of a 1T phase triangular shape within the natural 2H phase, mainly due to sulfur displacement, facilitated by sulfur vacancy boundaries. (e) Reproduced with permission from Chaste et al., ACS Nano 14(10), 13611–13618 (2020). Copyright 2020 American Chemical Society.39 (f) Transfer characteristics of monolayer MoS2 FET in a MoS2-FET device showing the GPPC. The black curve depicts the transfer characteristics of the MoS2 device before UV irradiation, while the red curve represents the transfer characteristics immediately after UV irradiation (λ = 365 nm) for 5 min with an intensity of approximately 30 mW cm−2. The colored curves illustrate the time-dependent changes in transfer characteristics following UV irradiation. The inset provides an optical microscopy image of the MoS2-FET device, with a scale bar indicating a length of 10 μm. (f) Reproduced with permission from George et al., npj 2D Mater. Appl. 5, 15 (2021). Copyright 2021 Springer Nature Ltd.116 

FIG. 10.

(a) Schematic of 2D vdW-based memristor switching by vacancy migration. Blue sphere is the vacancies in TMDs representing the reversible switching process. (b) The device undergoes ON switching with a 13 ns voltage pulse and (c) OFF switching with a 14 ns voltage pulse, requiring 299.8 fJ for SET and 125.6 fJ for RESET operations, respectively. (b) and (c) Reproduced with permission from Yan et al., Small 15, 1901423 (2019). Copyright 2019 Wiley-VCH.115 (d) Diagrams depicting MoS2-based atomristors are shown, illustrating two configurations: one without a filament (top) and another with a semi-filament (bottom). (e) Formation of a 1T phase triangular shape within the natural 2H phase, mainly due to sulfur displacement, facilitated by sulfur vacancy boundaries. (e) Reproduced with permission from Chaste et al., ACS Nano 14(10), 13611–13618 (2020). Copyright 2020 American Chemical Society.39 (f) Transfer characteristics of monolayer MoS2 FET in a MoS2-FET device showing the GPPC. The black curve depicts the transfer characteristics of the MoS2 device before UV irradiation, while the red curve represents the transfer characteristics immediately after UV irradiation (λ = 365 nm) for 5 min with an intensity of approximately 30 mW cm−2. The colored curves illustrate the time-dependent changes in transfer characteristics following UV irradiation. The inset provides an optical microscopy image of the MoS2-FET device, with a scale bar indicating a length of 10 μm. (f) Reproduced with permission from George et al., npj 2D Mater. Appl. 5, 15 (2021). Copyright 2021 Springer Nature Ltd.116 

Close modal

For example, Yan et al. studied a vacancy-induced 2D WS2 nanosheet-based memristor with a fast switching time (ON and OFF switching using a 13 and 14 ns voltage pulse, respectively) and low power consumption (SET and RESET energies of 299.8 and 125.6 fJ, respectively), as seen in Figs. 10(b) and 10(c).115 They suggest that the generation of sulfur and tungsten vacancies, along with electron hopping between these vacancies, is the primary mechanism driving the resistance switching performance in these devices. Their DFT calculations showed that the defect states created by sulfur and tungsten vacancies are located at deep energy levels. This positioning effectively prevents leakage current and enables low power consumption, making these devices suitable for neuromorphic computing applications. As the ability to precisely control sulfur vacancies in nanosheet-based materials can produce a stronger effect than in 3D-based devices, the ability to control defects easily and precisely via external factors is crucial for studying 2D material-based devices.

A recent study has investigated non-volatile resistance-changing devices based on 2D monolayer TMDs, also referred to as “atomristors.” Figure 10(d) shows the structure of a typical MoS2 atomristor without a filament (top, high-resistance state) and with a semi-filament, where a metal atom is present in the vacancy (bottom, low-resistance state).114 Due to their atomic-level thinness, these atomic sheets offer a solution to the size-scaling issue faced by conventional memristors. Hus et al. provided valuable insights into the fundamental mechanism governing the observed switching behavior in atomic sheets, employing monolayer MoS2 metal–insulator–metal (MIM) device. Through precise atomistic imaging and spectroscopy, they determined that introducing metal atoms into sulfur vacancies led to a non-volatile alteration in resistance. This introduction of metal elements was induced by the applied voltage between the top and bottom electrodes, effectively substituting them into the sulfur vacancy sites. The resistance indicates transition between a high resistance value of 2.5 GΩ and a low resistance value of 110 MΩ. Such resistive switching events have never been witnessed in defect-free MoS2 regions, establishing a direct link between the presence of sulfur vacancy defects and the occurrence of these switching events. Importantly, changes in electrode polarity can restore sulfur vacancies to their original state, enabling reversible switching between two states.

Monolayer TMD-based atomristors offer precise control of metal ions and defects at the atomic level, setting them apart from conventional memristors. In a monolayer TMD, even a single atom can change the resistance, enabling atomic-level defect control. This capability results in exceptional reliability, rapid switching, low power consumption, and high integration density. Achieving an atomic-scale understanding and regulation of resistive switching represents a groundbreaking development in materials science and opens doors to advanced memory applications.

In the field of optoelectronics, PPC has emerged as an innovative resource for exploring a wide range of novel devices. Owing to the capacity of PPC to manipulate the gradual dissipation of charge carriers once the light source is deactivated, this photo-response capability opens exciting possibilities for groundbreaking applications. The technology of controlling PPC through vacancies offers versatile device-shaping via two key techniques: regulating S-vacancy diffusion through external factors (e.g., voltage and optical modulation), enabling precise phase transitions in specific regions and effectively managing the vacancy state to influence PPC and manipulating recombination time with mechanical strain, enabling innovative applications across electronics, optics, and quantum technology. Notably, TMDs exhibit unique optical properties that are closely intertwined with chalcogen vacancies; however, the full potential of these optical attributes has yet to receive the attention it truly deserves.

Due to their inherent properties, S vacancies can induce unique phenomena within TMDs. It is well-established that the diffusion ability of S vacancies can trigger local phase transitions in TMDs. Chaste et al. were able to control the drift of sulfur vacancies at the nanometer scale using easily adjustable external factors, such as voltage and optical elements. They showed that S vacancies have a high in-plane diffusivity, and they can promote the transition from the 2H to 1T′ phase, as seen in Fig. 10(e).39 This work introduced a groundbreaking concept that by controlling phase transitions through S-vacancy manipulation, it is possible to regulate persistent photocurrent in devices.

Furthermore, by controlling the recombination time of electrons trapped in S vacancies through strain relaxation, a very long PPC retention time can be maintained. George et al. demonstrated that the extremely long-living giant PPC (GPPC) in monolayer MoS2 arises mainly from the intrinsic properties of monolayer MoS2, such as lattice defects, which induce many localized states in the forbidden gap.116 They also showed that ultraviolet light (λ = 365 nm) exposure induced GPPC in monolayer MoS2 FETs [Fig. 10(f)] with a time constant of ∼30 days. This effect led to a large enhancement of the conductivity, up to a factor of 107. Figure 10(f) shows the transfer characteristics of the monolayer MoS2 FETs before and after UV irradiation, with a very strong enhancement of Ids after UV irradiation. They also found that the GPPC persisted even days later at room temperature. Aberration-corrected high-resolution TEM clearly demonstrated the presence of sulfur vacancies in the monolayer MoS2, and they attributed the fluctuations in the band structure to the concentration and spatial distribution of point defects within MoS2. Furthermore, lattice mismatch between the CVD-grown MoS2 and SiO2 substrate caused a difference in the thermal expansion coefficient during the cooling process, leading to lattice strain, which caused band structure fluctuations and contributed to the observed photoconductivity in the MoS2 FETs. Therefore, the atomic vacancies caused deep-lying states, resulting in the slower relaxation time. This work highlights the significant influence of inherent atomic defects that can introduce unique electronic states and alter the band structure in 2D TMDs on their optoelectronic properties. The technologies of manipulation of vacancies in 2D TMDs hold immense promise for the future of optoelectronic technologies.

In summary, the formation of point defects is an inevitable occurrence in any material, even in 2D materials, as suggested by the second law of thermodynamics. Therefore, our primary focus has been on point defects, which create defect states between the valence and conduction bands in TMDs. VX exhibits the lowest formation energy and displays deep states below the CBM. Chalcogen vacancies are the most common defects in TMDs and have a significant impact on (opto-)electronic structure. Group-VI TMDs possess ideal acceptor states associated with chalcogen vacancies, which are among the most common native point defects. These defects exhibit relatively deep energy levels, typically around 0.3 eV, and may function as donor-like states with charge transfer, lattice distortion, and charge stabilization. In addition, the functionalities of memristors and PPC can be controlled within a single vacancy and are anticipated to provide insights across various applications due to their extremely low energy consumption and non-volatile characteristics.

There is a crucial need for an in-depth exploration of native defects and the correlations between device functionalities and point defects within different surrounding environments in future research. Energetic modulation of vacancies might provide a solution for doping through the dielectric screening effect of substrates, as illustrated in Fig. 11(a).118–124 Moreover, the migration, phase transition, and lattice distortion induced by point defects might exhibit different characteristics within different surrounding environments. Therefore, for fine-tuning and novel functionality, additional research is required to explore the potential of an encapsulation layer made from carefully selected vdW insulators. Examples include h-BN, oxyhalides, transition-metal nitride halides, and alkaline metal hydroxides, which exhibit a clean surface (or periodic interface states with the channel material) and a high dielectric constant (k > 15), as illustrated in Fig. 11(b).125,126

FIG. 11.

(a) Illustration of enhanced Coulomb interaction screening in 2D semiconductors. (Right) Schematic representation depicting the influence of augmented Coulomb interaction screening on the electronic bandgap (Eg), exciton binding energy (Eb), and optical bandgap (Eopt) of 2D semiconductors. Reproduced with permission from (a) Wang et al., Light Sci. Appl. 9, 192 (2020). Copyright 2020 Springer Nature Ltd.124 (b) Schematic depiction of monolayer Group-VI TMDs encapsulated with oxyhalides, transition-metal nitride halides, and alkaline metal hydroxides, featuring a vdW structure and high-k.

FIG. 11.

(a) Illustration of enhanced Coulomb interaction screening in 2D semiconductors. (Right) Schematic representation depicting the influence of augmented Coulomb interaction screening on the electronic bandgap (Eg), exciton binding energy (Eb), and optical bandgap (Eopt) of 2D semiconductors. Reproduced with permission from (a) Wang et al., Light Sci. Appl. 9, 192 (2020). Copyright 2020 Springer Nature Ltd.124 (b) Schematic depiction of monolayer Group-VI TMDs encapsulated with oxyhalides, transition-metal nitride halides, and alkaline metal hydroxides, featuring a vdW structure and high-k.

Close modal

This work was supported by the National Research Foundation of Korea (NRF) grants funded by the Korea government (MIST) (Nos. 2020R1C1C1011219, 2022M3H4A1A01013228, 2022M3I7A2079098, and RS-2023–00258309) and by the Air Force Office of Scientific Research under Award No. FA2386–23–1–4102. This work was also partially supported by the research project fund (No. 1.240007.01) of UNIST (Ulsan National Institute of Science and Technology).

The authors have no conflicts to disclose.

Kyungmin Ko: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Writing – original draft (equal). Mingyu Jang: Conceptualization (supporting); Investigation (supporting); Writing – original draft (supporting). Jaeeun Kwon: Formal analysis (supporting); Investigation (supporting); Writing – original draft (supporting). Joonki Suh: Conceptualization (lead); Funding acquisition (lead); Supervision (lead); Writing – review & editing (lead).

The data that support the findings of this study are available within the article.

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