⇦Chinese Physics Letters, 2022, Vol. 39, No. 7, Article code 077102 Tailoring of Bandgap and Spin-Orbit Splitting in ZrSe$_{2}$ with Low Substitution of Ti for Zr Sheng Wang (王盛)1†, Zia ur Rehman2†, Zhanfeng Liu (刘站锋)1, Tongrui Li (李彤瑞)1, Yuliang Li (李昱良)1, Yunbo Wu (吴云波)1, Hongen Zhu (朱红恩)1, Shengtao Cui (崔胜涛)1, Yi Liu (刘毅)1, Guobin Zhang (张国斌)1, Li Song (宋礼)1*, and Zhe Sun (孙喆)1* Affiliations 1National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230029, China 2Nanoscale Synthesis & Research Laboratory, Department of Applied Physics, University of Karachi, Karachi-75270, Pakistan Received 13 April 2022; accepted manuscript online 2 June 2022; published online 27 June 2022 †Sheng Wang and Zia ur Rehman contributed equally to this work.
*Corresponding authors. Email: song2012@ustc.edu.cn; zsun@ustc.edu.cn Citation Text: Wang S, Rehman Z u, Liu Z F et al. 2022 Chin. Phys. Lett. 39 077102    Abstract Tuning the bandgap in layered transition metal dichalcogenides (TMDCs) is crucial for their versatile applications in many fields. The ternary formation is a viable method to tune the bandgap as well as other intrinsic properties of TMDCs, because the multi-elemental characteristics provide additional tunability at the atomic level and advantageously alter the physical properties of TMDCs. Herein, ternary Ti$_{x}$Zr$_{1-x}$Se$_{2}$ single crystals were synthesized using the chemical-vapor-transport method. The changes in electronic structures of ZrSe$_{2}$ induced by Ti substitution were revealed using angle-resolved photoemission spectroscopy. Our data show that at a low level of Ti substitution, the bandgap of Ti$_{x}$Zr$_{1-x}$Se$_{2}$ decreases monotonically, and the electronic system undergoes a transition from a semiconducting to a metallic state without a significant variation of dispersions of valence bands. Meanwhile, the size of spin-orbit splitting dominated by Se $4p$ orbitals decreases with the increase of Ti doping. Our work shows a convenient way to alter the bandgap and spin-orbit coupling in TMDCs at the low level of substitution of transition metals.
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 DOI:10.1088/0256-307X/39/7/077102 © 2022 Chinese Physics Society Article Text Transition metal dichalcogenides (TMDCs) have attracted widespread interest due to their potential applications in many fields. The tunable bandgap of TMDCs is one of unique properties of these materials, which makes these materials a desirable candidate for p–n junction,[1] high mobility field-effect transistors,[2–4] memory and switching devices,[5] optical and photovoltaic devices,[6] etc. Hence, bandgap engineering is one of the frontier topics in TMDCs. Physical approaches to the bandgap regulation of TMDCs, e.g., strain, and precise control of the number of layers, suffer from mechanical limitations, and chances are scarce to obtain large-sized samples. On the other hand, the ternary material is considered the most viable way to engineer the bandgap with chemical doping at the atomic level of the host lattice. It often overcomes the intrinsic limitations of the binary compounds, with the additional advantage of novel properties and functionalities induced by chemical dopants. Ternary materials, such as the ternary transition metal chalcogenides, transition metal carbides and nitrides, metal phosphorous trichalcogenides, and ternary oxides, have drawn extensive attention and exhibited properties that binary materials do not possess. Much progress has been made in ternary materials, including bandgap and phase engineering,[7,8] field-effect transistor devices,[9] valence band splitting,[10] electronics,[11] valleytronics,[12] and charge density waves.[13] Pb$_{1-x}$Sn$_{x}$Se was proved to be a desirable material for applications in photodetection and high-speed logic devices.[14] The bandgap of SnS$_{2}$ was tuned through Se doping to show appreciable properties in electronic device applications.[15,16] In ternary alloy films of Mg$_{x}$Zn$_{1-x}$O$_{2}$ and Cd$_{y}$Zn$_{1-y}$O$_{2}$, the bandgap can vary significantly from 3 eV to 4 eV.[17] In the Cu–In–Se system, by adjusting the ratio of three elements, both the bandgap and the lattice structure can be changed.[18] Upon varying doping levels, the transition from semiconductor to semi-metallic phase occurs in Mo$_{1-x}$W$_{x}$Te$_{2}$.[19] The bandgap of ZrSe$_{x}$S$_{2-x}$ varies systematically with the doping $x$.[20] These findings suggest a convenient way to adjust the bandgap in ternary materials. ZrSe$_{2}$ and TiSe$_{2}$ are isostructural, and the former is a semiconductor,[20,21] while the latter is metal.[22] Their structural, electrical, and optical properties have been extensively studied,[23–29] and there are substantial differences between them in band structures and electronic properties. The top of the valence band of TiSe$_{2}$ is very close to the Fermi level, and the bottom of the conduction band goes across the Fermi level at the $M$ point in the Brillouin zone.[30] In ZrSe$_{2}$, the top of the valence band is located at the binding energy of $-1$ eV, and the bottom of the conduction band is above the Fermi level. TiSe$_{2}$ and ZrSe$_{2}$ have the same anions with cations belonging to the fourth group, so it is desirable to tune the bandgap of ZrSe$_{2}$ with Ti substitution. We note that the cation substitution may require a large doping level to change the size of the bandgap, for instance, a doping level of $x\ge 0.5$ is needed to tune the bandgap in Mo$_{1-x}$W$_{x}$Se$_{2}$.[31,32] However, both MoSe$_{2}$ and WSe$_{2}$ are semiconductors, and the overall trend of bandgap tenability may be different from the case of Ti substitution for Zr in ZrSe$_{2}$. In this work, we synthesized a series of Ti$_{x}$Zr$_{1-x}$Se$_{2}$ ($x \le 0.1$) single crystals using the chemical vapor transport (CVT) method. The evolution of electronic structures as a function of doping was systematically studied using angle-resolved photoemission spectroscopy (ARPES). Our results reveal that ZrSe$_{2}$ could be changed from a semiconductor to a metal with low substitution of Ti element, while the overall dispersions of valence bands are sustained. With the increase of doping $x$, the gap between conduction and valence bands decreases. Though the substitution occurs at the cation sites, the spin-orbit splitting of the Se $4p$ valence bands systematically changes. Our studies suggest that by selected element substitutions in ternary TMDCs, it is convenient to tune the bandgap and spin-orbit splitting of valence bands without degrading the sample quality.
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Fig. 1. (a) Top view and side view of Ti$_{x}$Zr$_{1-x}$Se$_{2}$ lattice. (b) Single-crystal x-ray diffraction (XRD) patterns of ZrSe$_{2}$ and Ti$_{0.1}$Zr$_{0.9}$Se$_{2}$. (c) Photos of Ti$_{x}$Zr$_{1-x}$Se$_{2}$ crystals. (d) EDS data of Ti$_{0.1}$Zr$_{0.9}$Se$_{2}$, and the inset table shows the atomic ratios of various elements. [(e), (f)] Microstructural analysis of Ti$_{0.1}$Zr$_{0.9}$Se$_{2}$. (g)–(j) Elemental mapping image of Ti$_{0.1}$Zr$_{0.9}$Se$_{2}$, showing that Ti atoms are homogeneously dispersed in the ZrSe$_{2}$ lattice. (k) Resistances as a function of temperature for Ti$_{x}$Zr$_{1-x}$Se$_{2}$.
Figure 1(a) shows the structural model of Ti$_{x}$Zr$_{1-x}$Se$_{2}$, in which the dopant Ti replaces Zr atoms. Figure 1(b) shows the XRD patterns for single crystals ZrSe$_{2}$ and Ti$_{0.1}$Zr$_{0.9}$Se$_{2}$. The characteristic peaks are sharp without impurity or satellite peaks, indicating the high quality of our samples. The variation of interlayer spacing obtained from XRD is only 0.0187 Å, from 6.1843 Å in ZrSe$_{2}$ to a small value of 6.1656 Å in Ti$_{0.1}$Zr$_{0.9}$Se$_{2}$, which is negligible, suggesting that Ti atom are doped into the Zr sites. Generally speaking, intercalation can evidently enlarge the interlayer spacing and the XRD peaks shift to lower Bragg angles. For instance, only 1.3 wt% Re element intercalation in Re-intercalation ZrSe$_{2}$ significantly changed the peak positions of XRD.[21] Figure 1(c) shows the pictures of our samples with various doping levels. Energy dispersive spectrum (EDS) of nominal composition Ti$_{0.1}$Zr$_{0.9}$Se$_{2}$ is presented in Fig. 1(d), and the elemental proportion suggests that 9.5% of Zr atoms were replaced by Ti. A very small amount of Se vacancies ($\sim $2%) is very common in ZrSe$_{2}$, which may affect the carrier concentration in our samples. However, we focus on the band structures of Ti$_{x}$Zr$_{1-x}$Se$_{2}$ in this work, and the uncertainty due to Se vacancies is minimal. The microstructures of Ti$_{0.1}$Zr$_{0.9}$Se$_{2}$ [Figs. 1(e) and 1(f)] were investigated using scanning transmission electron microscopy (STEM) as well, which is highly consistent with that of ZrSe$_{2}$, indicating that Ti substitution does not affect the basic lattice structures of ZrSe$_{2}$. Moreover, STEM mapping results in Figs. 1(g)–1(j) manifest that substituted Ti atoms are dispersed homogeneously in the lattice of ZrSe$_{2}$. Figure 1(k) shows the resistances of Ti$_{x}$Zr$_{1-x}$Se$_{2}$ as a function of temperature, indicating that the Ti substitution in ZrSe$_{2}$ can induce a transition from a semiconductor to a metal. This behavior can be anticipated, since the TiSe$_{2}$ is a metal. In the crossover regime between $x=0$ and $x=0.1$, we note here that Ti$_{x}$Zr$_{1-x}$Se$_{2}$ ($x=0.02,\, 0.05$) shows a semiconducting behavior in resistance measurements, while some weak spectral weight from conduction bands becomes visible in ARPES measurements as will be shown later.
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Fig. 2. ARPES intensity of Ti$_{0.1}$Zr$_{0.9}$Se$_{2}$ at various binding energies. The data in (a)–(g) were obtained using 42 eV photons. All data were acquired at $T=30$ K. The green hexagonal box indicates the Brillouin zone. (h) Three-dimensional Brillouin zone with high-symmetry points labeled.
To obtain a deeper insight into the variations of electronic structures upon Ti substitution in ZrSe$_{2}$, we performed ARPES measurements on a series of Ti$_{x}$Zr$_{1-x}$Se$_{2}$ single crystals. In the $G$–$M$–$K$ plane, multiple bands overlap around the top of valence bands, which makes it inapplicable to quantitatively extract the size of the spin-orbit splitting. Moreover, the bottom of the conduction band is lower in the $A$–$L$–$H$ plane than that in the $G$–$M$–$K$ plane, so it is convenient to catch how the Ti doping affects the conduction band. Therefore, we focus on the data in the $A$–$L$–$H$ plane. The ARPES intensity of Ti$_{0.1}$Zr$_{0.9}$Se$_{2}$ at different binding energies is illustrated in Fig. 2. According to our previous ARPES studies of ZrSe$_{2}$,[21] we can readily determine photon energies for the specific $k_{z}$ position in $k$-space. Figures 2(a)–2(g) were taken at $k_{z} \sim \pi /c$ ($h\nu = 42$ eV). Figure 2(a) shows a small pocket at the $L$ point, which disappears at deeper binding energies, indicating it is an electron pocket originating from the bottom of conduction bands. To qualitatively evaluate the changes of band dispersions with Ti substitution, we plot in Fig. 3 the band dispersions of Ti$_{x}$Zr$_{1-x}$Se$_{2}$ ($x=0,\, 0.02,\, 0.05,\, 0.1$) along high symmetry directions. Figures 3(a1)–3(a4) show the ARPES intensities along the $A$–$L$ direction. The topmost valence band moves up as $x$ increases. The location of the top of valence bands is $-980$ meV, $-895$ meV, $-805$ meV, $-700$ meV for $x = 0$, 0.02, 0.05, 0.1 at the $A$ point, respectively. Some weak spectral weight shows up at the $L$ point in $x=0.02$. In order to make it clear, we adjusted the contrast of the spectral weight from the conduction band. Though this weak spectral weight could not clearly determine the position of the bottom of the conduction band, we argue that it can still serve as a good reference to qualitatively demonstrate the evolution of the bandgap with doping $x$. For $x=0.1$, the spectral weight at the $L$ point is much stronger, and this behavior is consistent with the resistance measurements in Fig. 1(k), indicating that ZrSe$_{2}$ turns into metal after a small amount of Ti substitution. In Fig. 3(c), we compare some characteristics of band dispersions obtained at different doping levels, which are extracted from the ARPES data in Figs. 3(a1)–3(a4). It is evident that the overall band dispersions are sustained upon Ti substitution up to $x=0.1$, though we will show later that the spin-orbit splitting varies with doping $x$. In Figs. 3(b1)–3(b4), the spectral weight of Ti$_{x}$Zr$_{1-x}$Se$_{2}$ with $x =0,\, 0.02,\, 0.05,\, 0.1$ along the $A$–$H$ direction are presented. Ti substitution induces similar behavior as observed in Figs. 3(a1)–3(a4), that is, the overall valence band dispersions remained basically the same. A comparison of the ARPES data taken from ZrSe$_{2}$ and Ti$_{x}$Zr$_{1-x}$Se$_{2}$ suggests that Ti substitution at low doping levels does not affect the band dispersions significantly, which is helpful to sustain the fundamental electronic systems. The main effect of Ti substitution is to reduce the bandgap and induce the transition of the host system from a semiconductor to a metal. A similar phenomenon has been seen in Zr$X_{2}$($X$ = Se, Te), where the substitution of the same group anion leads to a phase transition between the semiconducting phase of ZrSe$_{2}$ and the semimetallic phase of ZrTe$_{2}$.[33,34] In addition, further increasing the Ti doping level to reduce the bandgap will help us to explore the critical state where the exciton insulating behavior appears in the TiSe$_{2}$ system, though this is not out of the scope of our current studies.
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Fig. 3. (a1)–(a4) ARPES spectral weight along the $A$–$L$ direction of Ti$_{x}$Zr$_{1-x}$Se$_{2}$. (b1)–(b4) ARPES spectral weight along the $A$–$H$ direction of Ti$_{x}$Zr$_{1-x}$Se$_{2}$. The dashed lines depict characteristics of band dispersions. [(c), (d)] Characteristic dispersions from (a1)–(a4) and (b1)–(b4), respectively. To make an overall comparison, the band dispersions from $x=0.02,\, 0.05,\, 0.1$ are shifted in the energy scale, and the relative shift amounts are labeled. (e) The top of the valence band of Ti$_{x}$Zr$_{1-x}$Se$_{2}$ as a function of doping $x$, the red dashed lines are guides for the eyes.
To present the effect of Ti doping on the bandgap, we show in Fig. 3(e) the location of the top of the valence band as a function of doping $x$. Though we could not determine the gap size, it is evident that Ti substitution monotonically reduces the gap of ZrSe$_{2}$ with increasing doping. Similar behavior takes place in the ZrSe$_{x}$S$_{2-x}$ system as reported by Moustafa et al.,[20] that is, the location of the top of the valence band continuously moves to the lower binding energy with the increase of the substitution Se. The linear evolution of the binding energy may be related to a linear dependence of the bandgap as a function of the doping $x$ for this family.[20,35] Kar et al. recently reported that metal-chalcogen bond length plays a crucial role in the change of band structure of Zr$X_{2}$ ($X$ = Se and Te), which could lead to a phase transition between a semiconducting phase and a topological semimetal.[33] We argue that metal-chalcogen bond length could also play a similar role in our work. Owing to the variation between Ti–Se bond length and Zr–Se bond length, the bandgap of Ti$_{x}$Zr$_{1-x}$Se$_{2}$ could be manipulated by the change of Ti doping. This underlying mechanism provides us with a good strategy to precisely tailor the band structures of ZrSe$_{2}$. Notably, we also observed the spin-orbit splitting of the Se $4p$ orbital character at the $A$ point. In Fig. 4, we demonstrated the band dispersions of Ti$_{x}$Zr$_{1-x}$Se$_{2}$ around the $A$ point to evaluate the variation of the splitting of the Se $4p$ orbital band with Ti substitution. Previous studies concluded that the spin-orbit splitting decreases with the electronegativity values of the chalcogen atom in ZrSe$_{x}$S$_{2-x}$.[36] As shown in Fig. 4, our work shows that the size of the spin-orbit splitting also decreases with Ti substitution, though the chalcogen atom remains the same in Ti$_{x}$Zr$_{1-x}$Se$_{2}$. A similar phenomenon has also been observed in monolayer TMDCs films. Mo et al. found that the valence band splitting of monolayer WSe$_{2}$ at the $K$ point of the Brillouin zone is about 475 meV,[37] while the corresponding value of monolayer MoSe$_{2}$ is only 180 meV.[38] These studies suggest that the cation substitution in TMDCs could also tune the spin-orbit splitting of valence bands that are dominated by anion elements. In these materials, there is a hybridization of transition metal atoms' $d$ orbital and chalcogen atoms' $p$ orbital, therefore the strength of spin-orbit interaction is related to not only the chalcogen atoms but also the transition metal atoms. In Fig. 4(i), we plot the relationship between the size of the spin-orbit splitting and the Ti doping $x$, which is a guide to estimate the strength of the spin-orbit coupling (SOC) after the substitution of Ti.
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Fig. 4. (a)–(d) ARPES intensity around the $A$ point of Ti$_{x}$Zr$_{1-x}$Se$_{2}$. (e)–(h) The corresponding energy distribution curves (EDCs). The red lines in (e)–(h) represent EDCs used to obtain the size of the spin-orbit splitting. (i) The size of the spin-orbit splitting as a function of doping $x$, the red dashed lines are guides for the eyes.
In summary, we have synthesized high-quality Ti$_{x}$Zr$_{1-x}$Se$_{2}$ ($x=0,\, 0.02,\, 0.05,\, 0.1$) single crystals using the CVT method, and performed the ARPES measurements to reveal the evolution of band structures upon Ti substitution. We found that a low level of Ti substitution in ZrSe$_{2}$ can systematically control the location of the top valence band, thereby tailoring the bandgap size and realizing a transition from the semiconducting phase of ZrSe$_{2}$ to the metallic phase of Ti$_{0.1}$Zr$_{0.9}$Se$_{2}$. Meanwhile, we quantitatively studied the size of the spin-orbit splitting of valence bands and found that Ti substitution also changes the splitting size. Our studies suggest that element substitutions in ternary TMDCs are an effective approach to bandgap engineering without degrading the quality of electronic systems and host materials. Acknowledgment. This work was supported by the National Key R&D Program of China (Grant No. 2017YFA0402901), the National Natural Science Foundation of China (Grant No. U2032153), the International Partnership Program (Grant No. 211134KYSB20190063), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB25000000), and the USTC Research Funds of the Double First-Class Initiative (Grant No. YD2310002004). References p n junctions in tungsten diselenideHigh-mobility field-effect transistors based on transition metal dichalcogenidesA Ternary Alloy Substrate to Synthesize Monolayer Graphene with Liquid Carbon PrecursorElectron Doping of Ultrathin Black Phosphorus with Cu AdatomsOn the optical properties of some layer compoundsStrong Light-Matter Interactions in Heterostructures of Atomically Thin FilmsControllable synthesis of molybdenum tungsten disulfide alloy for vertically composition-controlled multilayerGrowth of Large-Area 2D MoS 2(1- x ) Se 2 x Semiconductor AlloysTwo-Dimensional Molybdenum Tungsten Diselenide Alloys: Photoluminescence, Raman Scattering, and Electrical TransportSpin-orbit engineering in transition metal dichalcogenide alloy monolayersBand Gap Engineering and Layer-by-Layer Mapping of Selenium-Doped Molybdenum DisulfidePromising valleytronic materials with strong spin-valley coupling in two-dimensional MN2 X2 (M = Mo, W; X = F, H)Charge-density waves and superlattices in the metallic layered transition metal dichalcogenidesBN-Enabled Epitaxy of Pb 1- x Sn x Se Nanoplates on SiO2 /Si for High-Performance Mid-Infrared DetectionUltra-Thin Layered Ternary Single Crystals [Sn(S x Se1− x )2 ] with Bandgap Engineering for High Performance Phototransistors on Versatile SubstratesField effect transistors with layered two-dimensional SnS2−x Sex conduction channels: Effects of selenium substitutionBand gap engineering based on MgxZn1−xO and CdyZn1−yO ternary alloy filmsOn the band gap anomaly in I–III–VI2, I–III3–VI5, and I–III5–VI8 families of Cu ternariesComposition and temperature-dependent phase transition in miscible Mo1−xWxTe2 single crystalsAngle-resolved photoemission studies of the valence bands of ZrS Se2−Band structure tailoring in ZrSe2 single crystal via trace rhenium intercalationSemimetal-to-Semimetal Charge Density Wave Transition in 1 T − TiSe 2 Hidden spin polarization in the 1 T -phase layered transition-metal dichalcogenides MX 2 ( M = Zr, Hf; X = S, Se, Te)Epitaxial ZrSe2/MoSe2 semiconductor v.d. Waals heterostructures on wide band gap AlN substratesEffects of the vacancy and doping on the electronic and magnetic characteristics of ZrSe2 monolayer: A first-principles investigationBilayer MSe2 (M = Zr, Hf) as promising two-dimensional thermoelectric materials: a first-principles studyElectronic and magnetic properties of structural defects in pristine ZrSe2 monolayerElectronic and vibrational properties of TiSe 2 in the charge-density-wave phase from first principlesEvidence for pseudo–Jahn-Teller distortions in the charge density wave phase of 1 T − TiSe 2 Dimensional Effects on the Charge Density Waves in Ultrathin Films of TiSe2Bandgap engineering of two-dimensional semiconductor materialsTwo-dimensional semiconductor alloys: Monolayer Mo1−x Wx Se2Metal-chalcogen bond-length induced electronic phase transition from semiconductor to topological semimetal in Zr X 2 ( X = Se and Te)Transition from Semimetal to Semiconductor in ZrTe2 Induced by Se SubstitutionGrowth and band gap determination of the ZrS x Se 2 − x single crystal seriesSpin orbit splitting in the valence bands of ZrSxSe2−x: Angle resolved photoemission and density functional theoryElectronic Structure, Surface Doping, and Optical Response in Epitaxial WSe2 Thin FilmsDirect observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe2
[1] Späh R et al. 1983 Appl. Phys. Lett. 43 79
[2] Podzorov V et al. 2004 Appl. Phys. Lett. 84 3301
[3] Gan W et al. 2017 ACS Nano 11 1371
[4] Koenig S P et al. 2016 Nano Lett. 16 2145
[5] Lee P A et al. 1969 J. Phys. Chem. Solids 30 2719
[6] Britnell L et al. 2013 Science 340 1311
[7] Song J G et al. 2015 Nat. Commun. 6 7817
[8] Feng Q et al. 2014 Adv. Mater. 26 2648
[9] Zhang M et al. 2014 ACS Nano 8 7130
[10] Wang G et al. 2015 Nat. Commun. 6 10110
[11] Gong Y J et al. 2014 Nano Lett. 14 442
[12] Dou K Y et al. 2020 Appl. Phys. Lett. 117 172405
[13] Wilson J A et al. 1975 Adv. Phys. 24 117
[14] Wang Q et al. 2015 Small 11 5388
[15] Perumal P et al. 2016 Adv. Funct. Mater. 26 3630
[16] Pan T S et al. 2013 Appl. Phys. Lett. 103 093108
[17] Makino Y et al. 2001 Appl. Phys. Lett. 78 1237
[18] Wasim S M et al. 2000 Appl. Phys. Lett. 77 94
[19] Lv Y Y et al. 2017 Sci. Rep. 7 44587
[20] Moustafa M et al. 2016 Appl. Surf. Sci. 366 397
[21] Rehman Z et al. 2019 Appl. Phys. Lett. 115 213102
[22] Li G et al. 2007 Phys. Rev. Lett. 99 027404
[23] Cheng C et al. 2018 Sci. Bull. 63 85
[24] Tsipas P et al. 2015 Microelectron. Eng. 147 269
[25] Gao X Y et al. 2021 Thin Solid Films 732 138790
[26] Yan P et al. 2019 RSC Adv. 9 12394
[27] Gao Y H et al. 2018 Comput. Mater. Sci. 146 36
[28] Bianco R et al. 2015 Phys. Rev. B 92 094107
[29] Wegner A et al. 2020 Phys. Rev. B 101 195145
[30] Chen P et al. 2016 Nano Lett. 16 6331
[31] Chaves A et al. 2020 npj 2D Mater. Appl. 4 29
[32] Tongay S et al. 2014 Appl. Phys. Lett. 104 012101
[33] Kar I et al. 2020 Phys. Rev. B 101 165122
[34] Muhammad Z et al. 2020 ACS Nano 14 835
[35] Moustafa M et al. 2009 Phys. Rev. B 80 035206
[36] Moustafa M et al. 2013 J. Electron Spectrosc. Relat. Phenom. 189 35
[37] Zhang Y et al. 2016 Nano Lett. 16 2485
[38] Zhang Y et al. 2014 Nat. Nanotechnol. 9 111