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Article

Intrinsic Defect-Induced Local Semiconducting-to-Metallic Regions Within Monolayer 1T-TiS2 Displayed by First-Principles Calculations and Scanning Tunneling Microscopy

by
P. J. Keeney
,
P. M. Coelho
and
J. T. Haraldsen
*
Department of Physics, University of North Florida, Jacksonville, FL 32224, USA
*
Author to whom correspondence should be addressed.
Crystals 2025, 15(3), 243; https://doi.org/10.3390/cryst15030243
Submission received: 18 February 2025 / Revised: 25 February 2025 / Accepted: 26 February 2025 / Published: 3 March 2025
(This article belongs to the Section Materials for Energy Applications)
Browse Figures
Versions Notes

Abstract

Using density functional theory (DFT) and scanning tunneling microscopy (STM), the intrinsic point defects, formation energy, and electronic structure of 1T-TiS2 were investigated. Defect systems include single-atom vacancies, interstitial and adatom additions, and direct atomic substitution. Using a collective approach for analyzing realistic systems for point defect investigation, we provide a more straightforward comparison to the experimental measurements, reproducing more realistic environmental conditions related to thin film growth. STM images are compared to computationally simulated electron density images to identify specific geometries that result from favorable point defects. DFT suggests that titanium interstitials are the most energetically favorable intrinsic defect, and sulfur vacancies are more likely to form than titanium vacancies within this realistic analysis, which is in agreement with STM data. A pristine, stoichiometric monolayer system is calculated to have a direct band gap of 0.422 eV, which varies based on local point defects. Local semiconducting-to-metallic electronic transitions are predicted to occur based on the presence of Ti interstitials.

1. Introduction

With graphene rising to notoriety in 2004 [1], so-called 2D materials, categorized as thin films reducible to one unit cell in thickness, have followed suit. Two-dimensional materials present numerous advantages, the most obvious of which is that they are smaller, which allows for smaller devices. In addition, the properties of 2D materials can often be finely tuned, even more so than their bulk counterparts. Given that thin films inherently have fewer interatomic interactions and exchanges, the impact that local defects, doping, and interfaces between heterostructures have upon the properties of the material is greater in proportion than within a bulk sample. Understanding these local modifications will be key in idealistically applying 2D materials within their respective applications. Therefore, many research groups have focused their efforts on understanding how electronic, magnetic, mechanical, and optical properties can be tuned through defect engineering [2,3,4,5], doping [6,7,8,9], and heterostructure formation [10,11].
Although graphene often takes the most popular notoriety of all 2D materials, it does have certain limitations. For one, graphene does not exhibit a band gap [12,13,14,15,16] and consequently has a limited role within the realm of 2D semiconductors. As such, other semiconducting materials must be investigated to fill this void. An intriguing family of 2D materials is known as transition metal dichalcogenides (TMDs), which follow a chemical formula of MX2 (M = Ti, W, Mo, etc.; X = S, Se, Te). TMDs typically exhibit metallic or semiconducting properties (band gaps range from 0.1 to 2.5 eV [17]), allowing them to make significant contributions within the scope of 2D semiconductors. In addition, TMDs have been shown to have tunable properties, such as electronic properties dependent on the thickness of the material, including electronic band structure and density of states [18,19]. As another example, molybdenum disulfide (MoS2), one of the most researched TMDs, has been shown to exhibit a direct band gap as a monolayer and an indirect band gap as a bulk [20]. There is also a thickness-dependent band gap, with bulk MoS2 exhibiting a band gap of 1.29 eV [21] compared to 2.15 eV for monolayer [22].
Various applications for TMDs have been proposed, mainly focused on electronic and magnetic devices [23,24,25,26], as well as general nano-sensors [27]. The ability for TMDs to be reduced to the monolayer limit is intriguing, not only for the apparent aspect of creating smaller devices but also due to the possibilities of tuning properties through doping and the application of external fields. Doping can be performed during synthesis and post-synthesis, influencing the properties, changing its electronic configuration, and even introducing magnetism into an otherwise non-magnetic material [28,29].
TMDs typically exhibit either an octahedral (1T or CdI2-type) or trigonal prismatic structure [30] (2H or MoS2-type) with the transition metal located within the polyhedra, highlighted in Figure 1. The 1T and 2H structures correspond with space groups 164 ( P 3 ¯ m 1 ) and 194 ( P 6 3 / m m c ), respectively. These polyhedra are extended throughout a material, with hexagonal sheets of transition-metal atoms sandwiched between two hexagonal layers of chalcogenide atoms.
We will be focused on TiS2, a TMD that has gained attention for possible applications toward ion batteries [8,11,31], photovoltaic devices [32,33,34], spintronics, and various biomedical devices [35,36]. It was the first electrode used in Li-ion batteries [37], establishing its importance. Specifically, TiS2 is proposed to be valuable as an electrode for ion batteries, given the material’s high metal ion adsorption energies and low diffusion barriers [38]. TiS2 generally exists in the 1T polytype under ambient conditions [39,40,41] and has experimentally determined lattice parameters of a = b = 3.38 Å and c = 5.77 Å [42,43]. These lattice parameters and crystal symmetry will thus be implemented within our computational methodology.
This paper sets out to extend what is currently known regarding intrinsic point defects within a monolayer TiS2 lattice and how point defects influence the electronic properties and topography of the lattice. As such, it is vital to understand the current state of the literature on monolayer and thin film TiS2. Wang et al. state that the stoichiometry of Ti:S often ranges from 1:1.93 to 1:1.96 [44], resulting in the system favoring an increased ratio of titanium to sulfur atoms. Additional titanium atoms at interstitial sites and sulfur vacancies have been shown to be energetically favorable within a bulk [44,45,46] and/or monolayer sample of TiS2 [47]. Whether TiS2 exhibits a band gap within TiS2 has sparked much controversy.
Here, we present a new discussion of monolayer TiS2 by analyzing the formation energies of interstitial and adatom sites compared to the pristine lattice and how energetically favorable defects impact electronic properties such as band structure and density of states. This is performed by using scanning tunneling microscopy to analyze the surface of a bulk 1T-TiS2 sample and density functional theory to analyze monolayer 1T-TiS2, which is approximated as the surface of a bulk sample. This paper also presents a collective approach for first-principles-based analysis of point defects within quantum systems, further explained within the computational methodology. Of note, this collective analysis simulates the experimental environment of a vacuum chamber during thin film growth, where the vacuum chamber contains titanium and sulfur gases readily available for adsorption.

2. Methodology

All calculations are performed using the Kohn–Sham-based QuantumATK software, and we analyze a geometry-optimized, pristine 3 × 3 × 1 1T-TiS2 cell with various modifications. These are carried out using a meta-generalized gradient approximation (MGGA) with a SCAN functional and a linear combination of atomic orbitals (LCAO) basis set [48,49,50]. A PseudoDojo pseudopotential with a medium basis set is implemented along with a k-mesh sampling of 6 × 6 × 1 applied to the initial self-consistency calculation and the projected density of states [51,52]. The iteration control parameter is set to 10 − 7 eV, and the maximum force for geometry optimization is 0.05 eV/Å. Through a systematic benchmarking method, we find that applying these parameters predicts a semiconducting mother compound with a band gap of 0.422 eV, in agreement with the recent literature [53,54,55].
Previous publications involving formation energy analysis often correct for the difference in atoms between defect systems through chemical potential-based adjustments, summarized in Freysoldt et al., 2014 [56]. Here, we employ a collective approach for formation energy analysis with the formation energy correction for differences in atoms between systems. This is based on displacing atoms from within the lattice to the vacuum space within the cell of analysis so that interaction energies are negligible. Rather than having interstitial and adatom calculations with an additional atom within the analysis cell and vacancy calculations with one atom removed from the analysis cell, the pristine comparison cell is calculated with available titanium and sulfur atoms. This allows any changes in atoms within the monolayer to be corrected by placing them within the vacuum space versus removing them entirely from the calculation, as with the chemical potential correction. While this new analysis method can be more computationally intensive, as any changes in parameters and/or systems can require new calculations for each respective system under analysis, it also provides a more straightforward analysis of the formation energies by removing any arbitrary chemical potential corrections and leaving a simplified formation energy equation given by
E t o t = E a t o m + E i n t ,
where E t o t represents the total energy of each respective quantum system, E a t o m represents the sum of intrinsic atomic energy of each atom within the system (held constant within the methodology), and E i n t represents the interaction energies, which is essentially the only difference between systems within this computational analysis. Each cell of analysis simulates a 3 × 3 × 1 TiS2 lattice with one additional Ti- or S-atom within the vacuum spacing of the cell, allowing us to simulate the interstitial and adatom defect systems. These 29 atoms are held constant for formation energy analysis; electronic analysis contains only the atoms necessary for each point defect system.
Table 1 shows the formation energy comparison based on the calculated total energies of each respective system with total energy calculated by Equation (1). In a collective total energy analysis of pristine and defect systems, there is an inherent additional E a t o m if compared to the pristine system calculations done by previous groups due to the additional atom or vacancy. As such, the pristine system of analysis for these formation energy considerations is a 3 × 3 × 1 unit cell with a 20 Å vacuum space and an additional titanium and sulfur atom within the vacuum space. This ensures that we compare the energetic contributions solely from the interactions rather than additional or vacant atoms. Interactions between lattice and additional atoms are negligible due to a separation of no less than 7 Å between them.
Room temperature scanning tunneling microscopy (STM) on commercially synthesized high-purity bulk 1T-TiS2 crystal was performed in ultra-high vacuum. The STM tips used for these scans are electrochemically etched tungsten wire. The sample was mechanically exfoliated in air and annealed in a vacuum to 200 °C for 30 min to further remove possible contaminants. Scans were performed at room temperature using a STREAM SPM Scienta Omicron microscope and Matrix V4 Software. The constant-current mode was used to generate topography atomic resolution images on pristine TiS2. Empty state images were taken at a positive bias of V B = 200 mV and a tunneling current of I T = 0.7 nA, which resulted in the primary contrast mechanism of the STM images coming from the change in the height of the tip, which is driven by the probability of tunneling at each point across the TiS2 sample.

3. Density Functional Calculations

All calculations are performed within a cell containing a 3 × 3 × 1 monolayer TiS2 cell with a nearby titanium and sulfur atom and then moved to adjust for the type of defect system undergoing analysis, shown in Figure 2. The geometry optimization of the 1Ti-Interstitial and 1Ti-Interstitial2 systems does not place the additional titanium at a traditional interstitial site. Instead, it is placed above the sulfur plane, which is determined to be the more energetically favorable site. The position of this additional titanium interstitial minimizes the repulsive titanium–titanium forces and maximizes the attractive titanium–sulfur forces. The geometry optimization of the 1S-Adatom1 system, which has an initial configuration of a pristine lattice with additional sulfur interstitial, optimizes into a similar position as the 1S-Adatom2. Therefore, a sulfur interstitial atom is not energetically favorable to occur, which is supported by subsequent analysis, and sulfur atoms would be more likely to begin forming an adjacent TiS2 layer than settle within the lattice.
The collective analysis of formation energies suggests the Ti-Interstitial1 and Ti-Interstitial2 systems are the most favorable out of all analyzed point defects, requiring 7.064 and 7.202 less eV, respectively, to form compared to a pristine monolayer lattice, given Ti atoms availability. The S-Adatom1 and S-Adatom2 systems are also favorable relative to a pristine system, respectively, requiring 2.793 and 2.826 less eV to form, given S atoms availability. Titanium or sulfur substitutions and vacancies are not favorable compared to a pristine lattice; however, this computational method does not take into account factors such as the dynamics of thin film growth or the impact of treatment methods such as annealing. In addition, we must consider the presence of additional titanium and sulfur within the cell of analysis. While sulfur adatoms are favorable within this method of analysis, such an environment is only present under specific experimental conditions, which are likely not present during characterization or implementation within devices.
Figure 3 and Figure 4 show the pristine system calculation predicting sulfur 2p bands comprising the majority of valence band contributions, suggesting that the sulfur 2p orbitals are completely occupied within a net neutral system. The valance band maximum is located at the Γ -point, 0.05 eV below the Fermi level. The highest valence band at the M- and K-points is slightly less than 1.0 eV below the absolute maximum at the Γ -point. As such, it requires energy for occupied electronic states to move within the reciprocal space and respective real-space positions. The conduction band is comprised mainly of titanium 3d contributions, and we observe a direct band gap of 0.422 eV at the Γ -point and an indirect band gap between the sulfur 2p-dominated valance band at the Γ -point and titanium 3d-dominated conduction band at the M-point of 0.273 eV.
Regarding the Ti-interstitial band structure displayed in Figure 3, we note that the Fermi level shifts to position it within the titanium 3d bands. As such, there are occupied electronic states within the conduction band, demonstrating a local semiconductor-to-metal transition within this region and delocalized electrons. Titanium 3d bands flatten out, demonstrating that less energy is required for electrons to translate between electronic states within the lattice.
The S-vacancy band structure is similar to the Ti-interstitial structure, given that the ratio of conductive Ti-atoms to relatively less conductive S-atoms is increased. However, the Fermi level is now at a lower energetic position, so fewer delocalized electronic states are present within a neutral sample. Therefore, there is also a local semiconductor-to-metal transition; however, the metallic state is relatively weaker than that of the Ti-interstitial.

4. Scanning Tunneling Microscopy

Figure 5 demonstrates empty state topography STM images of the surface of a bulk TiS2 lattice. We recognize depressions, or darker regions, that correspond to less available empty states. The presence of fewer empty states can be correlated with atomic vacancies, which remove most available local states compared to a pristine lattice and provide a smaller probability of tunneling. STM imaging of TiS2 produces contrast mainly based on the outermost sulfur layer, where there is less distance for tunneling to occur relative to the underlying titanium layer, which supports that the depression regions shown in the images correspond to sulfur vacancies. While sulfur vacancies are not relatively favorable based on the formation energy calculations, we note that the STM scans were performed post-annealing, which provides additional energy for less favorable point defects to occur. In addition, there are factors such as dynamics during experimental growth that are not accounted for within our computational methodology.
While comparing the experimental data to the calculations is limited, the tunneling current from STM is a measurement proportional to the available states, which is correlated with the charge density as calculated through DFT. Therefore, a comparison of these STM images of the surface of a bulk TiS2 lattice to the DFT-based computational analysis conducted on monolayer TiS2 is shown by the blue insets of the images in Figure 5, which produces excellent agreement for the vacancy of S and the increased electron density of the Ti. This computational monolayer can be approximated as the surface of a bulk TiS2 sample within STM analysis, given that STM is mostly surface-sensitive and any interactions between the TiS2 layers are made through van der Waals interactions and, therefore, relatively weak. As stated in the Density Functional Calculations section, sulfur vacancies require 9.017 eV less to form from a pristine TiS2 monolayer than titanium vacancies. While sulfur vacancies are not relatively favorable based on the formation energy calculations, we note that the STM scans were performed post-annealing, which provides additional energy for otherwise unfavorable point defects to occur.
Given that the contrast from STM images comes directly from the local density of states [57] and thus electron density, we can directly compare calculated electron density maps of monolayer TiS2 with respective point defects present in the STM images of the bulk TiS2 sample. In Figure 5a, the computational monolayer with sulfur vacancy calculates a strikingly similar geometry of an electron density map to the contrast demonstrated within the STM images of the bulk TiS2. The geometry that arises from the sulfur vacancy is a result of the lack of electron density within this region, which is also reflected within the STM image.
The analysis of protrusions, or brighter regions, within the STM images is similar to that of the depression. We can conclude that brighter regions within the STM images represent relatively more electronic states available for tunneling than the other darker regions, suggesting that additional atoms within these regions contribute to an increased amount of states and, therefore, a higher probability of tunneling. The computational analysis of formation energies suggests that any additional atoms within the lattice would be titanium, which agrees with the previous literature [44,58].
While the collective formation energy analysis also predicts that additional sulfur atoms are favorable under these conditions, we acknowledge that the additional titanium atoms require between 4.238 and 4.409 less eV to occur. This collective analysis also includes additional titanium and sulfur atoms being present within the cell of analysis. While this is true depending on vacuum conditions, especially during experimental growth, this is not necessarily true during characterization or application. We also recognize that calculating the electron density map of a computational monolayer of TiS2 with the titanium interstitial provides a similar geometry to the contrast that arises within the STM imaging of Figure 5b. The geometry is a consequence of the increased electron density within the region of the additional titanium atom.

5. Discussion and Conclusions

In this paper, we demonstrate insight regarding the presence of point defects in bulk and monolayer TiS2. STM analysis of the surface of a bulk TiS2 lattice is compared to DFT calculations of monolayer TiS2, which can be approximated as the surface of a bulk TiS2 given that the interlayer van der Waals interactions within the bulk are relatively weak compared to the intralayer covalent interactions. A collective analysis methodology is proposed and implemented within the computational analysis and consequentially simulates the experimental environment present during the growth of thin films. The collective analysis implemented contrasts the chemical potential-based corrections of formation energy analysis summarized in Freysoldt et al., 2014 [56]; however, results found through the collective analysis proposed here are similar to results found in the recent literature regarding point defects within the TiS2 lattice [44,46].
We determine that additional titanium atoms are the most energetically favorable intrinsic point defect within a monolayer 1T-TiS2 lattice and sulfur atoms are more likely to be removed from the lattice and form vacancies than titanium atoms. This conclusion is based on computational formation energy analysis between a pristine monolayer and monolayers with respective point defects present. We further support these conclusions by comparing STM images of the surface of a bulk sample of TiS2 and DFT-simulated electron density maps of monolayer TiS2 with respective point defects. While sulfur vacancies are not relatively favorable based on the formation energy calculations, we note that the STM scans were performed post-annealing, which provides additional energy for less favorable point defects to occur.
The analysis of the band structure and density of states of a pristine structure compared to the favorable point defects (shown in Figure 3 and Figure 4) within the computational monolayer of TiS2 suggests that both additional titanium interstitial atoms and sulfur vacancies result in local metallic regions within an otherwise semiconducting sample. The conduction band in each of these band structures primarily contains titanium 3d contributions. In the case of a non-stoichiometric system favoring titanium to sulfur, the conduction bands are shifted to the Fermi level, indicating a greater delocalization of electrons. Overall, this indicates that the transition from semiconducting to metallic within the material may be due to point defects within the sample.
In the end, our study on the point defects in TiS2 highlights the transition between semiconducting and metallic behavior due to the modification of the crystal lattice. Future studies on the nature of these states can direct investigations into the electronic and magnetic properties of doped TiS2, which could lead to potential advancements in electronic, valleytronic, or spintronic applications.

Author Contributions

Conceptualization, P.M.C. and J.T.H.; Methodology, P.M.C. and J.T.H.; Software, J.T.H.; Validation, P.J.K., P.M.C. and J.T.H.; Formal analysis, P.J.K., P.M.C. and J.T.H.; Investigation, P.J.K., P.M.C. and J.T.H.; Resources, P.M.C. and J.T.H.; Data curation, P.J.K., P.M.C. and J.T.H.; Writing—original draft, P.J.K., P.M.C. and J.T.H.; Writing—review & editing, P.J.K., P.M.C. and J.T.H.; Visualization, P.J.K., P.M.C. and J.T.H.; Supervision, P.M.C. and J.T.H.; Project administration, P.M.C. and J.T.H.; Funding acquisition, J.T.H. All authors have read and agreed to the published version of the manuscript.

Funding

Institute for Materials Science at Los Alamos National Laboratory; 616898.

Data Availability Statement

Data is contained within the article.

Acknowledgments

The authors thank Anne Evans for her contributions in the preliminary stages of STM data acquisition and analysis. P.J.K. and J.T.H acknowledge support from the Institute for Materials Science at Los Alamos National Laboratory.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. (a) A side view of 1T and 2H structures displays the polyhedron containing the transition-metal atoms within the middle hexagonal sheet. (b) The Brillouin zone for a monolayer TiS2 crystallographic system with points of high symmetry and the Brillouin zone analysis route used for band structure calculations.
Figure 1. (a) A side view of 1T and 2H structures displays the polyhedron containing the transition-metal atoms within the middle hexagonal sheet. (b) The Brillouin zone for a monolayer TiS2 crystallographic system with points of high symmetry and the Brillouin zone analysis route used for band structure calculations.
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Figure 2. Respective lattices for each point defect system of interest before and after geometry optimization. After optimization, the initial configuration of 1S-Interstitial settles at an adatom position (in green), demonstrating that it is energetically unfavorable for sulfur to settle within the lattice. This optimized system will be referred to as 1S-Adatom1 throughout this paper, with the subscript 1 referring to an initial state of the respective initial atom (titanium (blue) or sulfur (yellow)) located at a traditional interstitial site. 1Ti-Adatom (red) settles closer to the lattice, sitting right above the top sulfur plane, versus its original adatom position. This optimized system will be referred to as 1Ti-Interstitial2, with subscript 2 indicating the initial state with the respective initial atom located at a traditional adatom site. Further analysis is addressed within the Density Functional Calculations section.
Figure 2. Respective lattices for each point defect system of interest before and after geometry optimization. After optimization, the initial configuration of 1S-Interstitial settles at an adatom position (in green), demonstrating that it is energetically unfavorable for sulfur to settle within the lattice. This optimized system will be referred to as 1S-Adatom1 throughout this paper, with the subscript 1 referring to an initial state of the respective initial atom (titanium (blue) or sulfur (yellow)) located at a traditional interstitial site. 1Ti-Adatom (red) settles closer to the lattice, sitting right above the top sulfur plane, versus its original adatom position. This optimized system will be referred to as 1Ti-Interstitial2, with subscript 2 indicating the initial state with the respective initial atom located at a traditional adatom site. Further analysis is addressed within the Density Functional Calculations section.
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Figure 3. Band structures for (a) a pristine 3 × 3 × 1 monolayer cell, indicating a semiconducting system with a band gap of 0.422 eV, (b) the 3 × 3 × 1 cell with an additional titanium atom shifts the cell to a metallic electronic ground state, and (c) a 3 × 3 × 1 cell with a sulfur vacancy that corresponds to a similar metallic shift; however, there are fewer bands present at the Fermi level.
Figure 3. Band structures for (a) a pristine 3 × 3 × 1 monolayer cell, indicating a semiconducting system with a band gap of 0.422 eV, (b) the 3 × 3 × 1 cell with an additional titanium atom shifts the cell to a metallic electronic ground state, and (c) a 3 × 3 × 1 cell with a sulfur vacancy that corresponds to a similar metallic shift; however, there are fewer bands present at the Fermi level.
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Figure 4. Top-to-Bottom: geometry-optimized lattice, local density of states, partial density of states displaying sulfur 2p orbital contributions, and partial density of states displaying titanium 3d orbital contributions. Left-to-right: pristine TiS2 cell, pristine cell with one additional titanium atom, and pristine cell with one sulfur vacancy. The orbital angular momentum (l) and magnetic (m) quantum numbers are displayed within the legends. l = 1 corresponds to the p orbital, with l = 2 corresponding to the d orbital. Respectively, m = − 1 , 0 , 1 correspond to p y , p z , p x for the sulfur-2p partial DoS, and m = − 2 , − 1 , 0 , 1 , 2 correspond to d x y , d y z , d z 2 , d x z , d x 2 − y 2 , respectively, for the titanium-3d partial DoS. Notably, the DoS contributions are stacked rather than overlapping.
Figure 4. Top-to-Bottom: geometry-optimized lattice, local density of states, partial density of states displaying sulfur 2p orbital contributions, and partial density of states displaying titanium 3d orbital contributions. Left-to-right: pristine TiS2 cell, pristine cell with one additional titanium atom, and pristine cell with one sulfur vacancy. The orbital angular momentum (l) and magnetic (m) quantum numbers are displayed within the legends. l = 1 corresponds to the p orbital, with l = 2 corresponding to the d orbital. Respectively, m = − 1 , 0 , 1 correspond to p y , p z , p x for the sulfur-2p partial DoS, and m = − 2 , − 1 , 0 , 1 , 2 correspond to d x y , d y z , d z 2 , d x z , d x 2 − y 2 , respectively, for the titanium-3d partial DoS. Notably, the DoS contributions are stacked rather than overlapping.
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Figure 5. STM images demonstrating the surface of a bulk TiS2 crystal with a sulfur vacancy (a) and an additional titanium interstitial atom (b). Scans were taken with bias voltage V b = 200 mV and tunneling current I t = 0.7 nA. These are overlaid with a DFT-based computational electron density mapping of the surface of a monolayer of TiS2 with respective point defects, specifically a single sulfur vacancy and a single additional titanium interstitial atom.
Figure 5. STM images demonstrating the surface of a bulk TiS2 crystal with a sulfur vacancy (a) and an additional titanium interstitial atom (b). Scans were taken with bias voltage V b = 200 mV and tunneling current I t = 0.7 nA. These are overlaid with a DFT-based computational electron density mapping of the surface of a monolayer of TiS2 with respective point defects, specifically a single sulfur vacancy and a single additional titanium interstitial atom.
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Table 1. Column one represents the defect system being compared to the pristine cell. E D is the total energy of the defect system and E P + 2 is the total energy of the pristine system plus additional vacuum state atoms, where the difference between this energy is the change in the interaction energy E i n t . Column two provides each system’s respective formation energy difference based on DFT calculations. Subscripts 1 and 2 indicate a system with an initial configuration of an interstitial atom and adatom, respectively.
Table 1. Column one represents the defect system being compared to the pristine cell. E D is the total energy of the defect system and E P + 2 is the total energy of the pristine system plus additional vacuum state atoms, where the difference between this energy is the change in the interaction energy E i n t . Column two provides each system’s respective formation energy difference based on DFT calculations. Subscripts 1 and 2 indicate a system with an initial configuration of an interstitial atom and adatom, respectively.
Defect E D − E P + 2  (eV)
Ti-Int1−7.064
Ti-Int2−7.202
Ti-Sub0.417
Ti-Vac15.313
S-Ada1−2.793
S-Ada2−2.826
S-Sub9.116
S-Vac6.296
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Keeney, P.J.; Coelho, P.M.; Haraldsen, J.T. Intrinsic Defect-Induced Local Semiconducting-to-Metallic Regions Within Monolayer 1T-TiS2 Displayed by First-Principles Calculations and Scanning Tunneling Microscopy. Crystals 2025, 15, 243. https://doi.org/10.3390/cryst15030243

AMA Style

Keeney PJ, Coelho PM, Haraldsen JT. Intrinsic Defect-Induced Local Semiconducting-to-Metallic Regions Within Monolayer 1T-TiS2 Displayed by First-Principles Calculations and Scanning Tunneling Microscopy. Crystals. 2025; 15(3):243. https://doi.org/10.3390/cryst15030243

Chicago/Turabian Style

Keeney, P. J., P. M. Coelho, and J. T. Haraldsen. 2025. "Intrinsic Defect-Induced Local Semiconducting-to-Metallic Regions Within Monolayer 1T-TiS2 Displayed by First-Principles Calculations and Scanning Tunneling Microscopy" Crystals 15, no. 3: 243. https://doi.org/10.3390/cryst15030243

APA Style

Keeney, P. J., Coelho, P. M., & Haraldsen, J. T. (2025). Intrinsic Defect-Induced Local Semiconducting-to-Metallic Regions Within Monolayer 1T-TiS2 Displayed by First-Principles Calculations and Scanning Tunneling Microscopy. Crystals, 15(3), 243. https://doi.org/10.3390/cryst15030243

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