Defects induced changes in conduction bands of HfS2

We report on a comprehensive study of the electronic structures of the layered semiconductor 1T-HfS2 by employing angle-resolved photoemission spectroscopy (ARPES). With in-situ potassium doping, the band structures of HfS2 could be tuned, and both of the valence band and the conduction band could be observed. S vacancy defects could be induced by post-annealing of HfS2 and a certain amount of S vacancies would result in a peculiar change of the conduction band at M¯ point— the fracture of the conduction band bottom. Our results could provide key information for the defect studies and the application of HfS2.


Introduction
Since the discovery of gapless graphene [1], 2D layered transition-metal dichalcogenides (TMDs) have attracted widespread attentions due to their unique physical, electrical and mechanical properties [2,3].In particular, semiconducting sulfides and selenides of group-VIB elements, molybdenum and tungsten with three possible structures, namely the trigonal prismatic phase (1H) , octahedral phase (1T), and the deformed structure (T0), have been widely fabricated and have become the focus of researchers, including energy storage, catalysis, solar cells, phototransistors, and field-effect transistors [4][5][6][7][8].TMDs (denoted as MX 2 , where M=Metal and X=S, Se) are formed by stacked X-M-X sandwich structures that the metal atoms are sandwiched between two chalcogen layers.The atoms in the X-M-X sandwich structure are joined together by strong chemical bonding while the sandwich structures are bonded together by much weaker van der Waals type interaction [7][8][9].The weak interlayer bondings can lead to easy cleavage between the layers and give rise to form quasi-two dimensional structures [10][11][12][13][14]. Intercalants of atoms or molecules between the layers can easily affect the atomic arrangements and band fillings, leading to a transition from semiconducting to metallic behavior [15,16].In general, the properties of TMDs can be regulated by doping [17], substitution [18], strain engineering [19], stacking [20] and phase exfoliation [21].
The 1T phase HfS 2 (hereinafter referred to as HfS 2 for simplicity) is a wide studied member of TMDs family, which is a semiconductor with an indirect band gap within the infra red and the visible range (∼1 − 2 eV) [16].The room temperature carrier mobility of HfS 2 is as high as 1800 cm 2 V −1 s −1 , far exceeding the 340 cm 2 V −1 s −1 of MoS 2 [22], and it have proven to be an important candidate material for the solar energy, field-effect transistors and photovoltaics [23][24][25][26][27][28][29].Few-layer HfS 2 FET displaying a large on/off ratio has been reported [30][31][32].The heterostructures of HfX 2 (X = S, Se, Te) have been predicted to be strong absorbers of light and have be confirmed theoretically and experimentally as an efficient photocatalyst for Water Splitting [33][34][35].On the other hand, the physical properties of pristine HfS 2 may change significantly with suffering oxidation and lattice imperfections, which will also induce significant changes in the electronic structures of HfS 2 [36].Although some experimental work has studied the electronic structures of pristine and potassium-intercalated (ex-situ) bulk HfS 2 [37][38][39][40], the effect of defects on the electronic structures of HfS2 is only theoretically calculated [41][42][43][44], and the corresponding experimental work is still lacking.
In this work, we synthesized single crystals of HfS 2 with better quality, and performed systematic studies on the electronic structures of pristine HfS 2 , in-situ potassium doping HfS 2 and defective HfS 2 with S vacancies by employing angle-resolved photoemission spectroscopy (ARPES) in combination with density functional theory (DFT) calculations.The tuning of the band structures of HfS 2 by in-situ surface potassium doping is clearly observed.Interestingly, a certain amount of S vacancies in HfS 2 will result in significant changes of the conduction band of HfS 2 at the M point.

Experimental
The 1T-HfS 2 crystals were grown by adopting the chemical vapor transport method with using iodine as a transfer agent.Stoichiometric Hf (99.9%,Adamas) and S powder (99.9%,Adamas) were mixed and sealed in a quartz tube together with the iodine under a vacuum of about 10 −4 Pa.The assembly was placed into a dualtemperature zone tube furnace.One end of the quartz tube loading the starting materials was kept at 1050 • C and the other end for crystal growth was kept at 970 • C .After two weeks, large crystals of HfS 2 were obtained at the cold end of the quartz tube.Defective HfS 2 samples with S vacancies were obtained by post-annealing of the asgrown HfS 2 at 500 °C for different times in vacuum.
The electronic structures of HfS 2 were measured using a home-made ARPES with helium discharge lamp as photoelectron excitation source (photon energy hν = 21.2 eV).The HfS 2 samples for ARPES measurements were prepared in a glove box with highly purified argon atomosphere to avoid degradation of HfS 2 during the curing process of H20E silver-filled epoxy.Fresh surfaces of HfS 2 for ARPES measurements were obtained by cleaving the samples in-situ along (001) plane under a vacuum pressure better than 10 −8 Pa at room temperature.The ARPES measurements were also carried out at room temperature.The in-situ deposition of alkali metal potassium (K) was carried out using a standard commercial alkali-metal dispenser (SAES Getters).
The theoretical electronic structures of HfS 2 were obtained by relativistic first-principles calculations based on the density-functional theory (DFT) as implemented in the QUANTUM ESPRESSO code [45].In the calculations, a hybrid functional approximation for the exchange-correlation term, Heyd-Scuseria-Ernzerhof (HSE06) [46], was employed in order to get reliable gap consistent with the experiments.To describe the weak van der Waals forces, which are mainly dominant in layered materials, the dispersion corrected DFT-D3 [47] is also used.The wave function cutoff energy was chosen to be 50 Ry and the charge density cutoff energy was 400 Ry.The Brillouin zone was sampled using a 8 × 8 × 4 grid.In order to obtain the band structure and surface spectrum, a first-principles tight-binding model Hamilton based on maximally localized Wannier functions was constructed by fitting the DFT band structures using the WANNIER90 code [48].The Hf-d orbital and S-p orbital were used for the initial projection.The surface spectra of HfS 2 were calculated using the Greens function method as implemented in the WANNIERTOOLS package [49].In all calculations, spin-orbit coupling was not taken into account.

Results and discussion
HfS 2 crystallizes in a CdI 2 -PbI polytype structure (space group P m 3 1), with the lattice parameters a = b = 3.64 Å , c = 5.86 Å , α = β = 90°and γ = 120°, as illustrated in figure 1(a).The structure is formed by S-Hf-S sandwich atomic layers with the hafnium atoms locating at the center, sandwiched between two sulfur layers.Figure 1(b) shows the Raman spectra of the as-grown and defective post-annealed HfS 2 using a 532 nm wavelength laser excitation, which matches well with the previous studies [31,50].Two notable peaks located at 256 and 336 cm −1 can be attributed to E g mode which results from the in-plane vibration of S atoms, and A 1g mode which originates from the out-plane vibration of S atoms, respectively [51,52].Therefore, there is no significant difference in the Raman spectrum of pristine and defective HfS 2 with S vacancies.Figure 1(c) shows the XRD θ-2θ scan patterns on the easy-cleaved (001) surface of as-grown and defective post-annealed HfS 2 , indicating no significant changes in the crystal structure of HfS 2 .Whereas, x-ray photoelectron spectroscopy (XPS) can be used to characterize and distinguish the pristine and defective HfS 2 , as shown in figures 1(d-e).In the XPS spectrum [figure 1(d)] of the as-grown HfS 2 , only two peaks of Hf 4f, with peak at 17.18eV for Hf 4f 7/2 state and 18.84 eV for Hf 4f 5/2 state, can be observed, which is consistent with the standard spectra for HfS 2 crystal [53,54] and allows the as-grown HfS 2 to be regarded as pristine HfS 2 .Figure 1(e) shows the XPS spectrum of defective HfS 2 .Besides the two main peaks for Hf 4f 7/2 and Hf 4f 5/2 in pure HfS 2 environment, two more small peaks at 16.05eV and 17.79 eV appear, which can be attributed to 4f 7/2 and 4f 5/2 of Hf in an environment with S vacancy defects.The reason is that the S vacancies in HfS 2 will cause changes of the chemical environment of some Hf atoms, and make it shift towards the zero-valence-state environment in which the binding energies of Hf 4f 7/2 and Hf 4f 5/2 are lower.Similar behavior can be found in MoS 2 [55,56] and HfO 2 [57].Figure 1(f) shows the low energy electron diffraction (LEED) pattern of cleaved surface of HfS 2 .The sharp and clear diffraction spots indicate a well ordered and flat surface, confirming high quality of the as-grown HfS 2 .Figure 1(g) presents the calculated bulk bands of HfS 2 along some high-symmetry paths.There is an indirect gap of HfS 2 , with the valence band maximum (VBM) locating around the Γ point while the conduction band minimum (CBM) locating round the L point.
First, the electronic structures of as-grown HfS 2 were measured by ARPES, as presented in figure 2. Figures 2(a)-(c) shows constant energy mapping of HfS 2 for three selected binding energies, i.e., −1.6 (around VBM), −2.7 and −3.0 eV. Figure 2(e)-(f) shows the measured band dispersions of HfS 2 along K -G and M -G directions, respectively.It can be seen from the ARPES data that the Fermi level lies in the indirect gap and the VBM is around the binding energy of −1.5 eV.It's worth noting that the ARPES measured VBM values, including the previous reports [39,40], are all lower than the theoretically calculated one.There may be two reasons for this.First, the theoretical calculation underestimate the Fermi level, and overestimate the VBM.Second, the pristine samples still have some S vacancy defects even they are not appear in the XPS spectrum, as shown in figure 1(d).The S vacancy defects result in electron doping, raise the Fermi level and lower the VBM.Except for the difference in relative energy, the band structures of HfS 2 obtained from the theoretical calculations and ARPES experiments match satisfactorily.To show this, the binding energy of the calculated results were lowered by 1.05eV.As it can be seen, the calculated constant energy mapping shown in figure 2(d) well reproduce the corresponding ARPES result shown in figure 2(c).As shown in figure 2(g) and figure 2(h), the main features of the ARPES measured band dispersions can be well outlined by the calculated bands from ΓKM plane (k z = 0, red dashed curves) and AHL plane(k z = π, white dashed curves).The reason that the bands from k z = 0 plane and k z = π plane coexist in one ARPES-measured image is the k z broadening effect, which is common in ARPES study with low excitation photon energy [58][59][60][61].The probing depth λ is ∼5 Å for photon energy hν = 21.2eV in our work.The k z broadening, Δk z , can be estimated using Heisenberg uncertainty  (e, f) ARPES measured band dispersions of HfS 2 along K -G and M -G directions, respectively. (g, h) Same as (e, f) but overlaid with the calculated bands.The red (white) dashed curves indicate the band dispersions along the K-Γ or M-Γ (H-A or L-A).(i) ARPES measured band dispersions (left side) and the corresponding calculated k z -integrated dispersions (right side) along K -G direction. (j) Same as (i) but along M -G direction.All ARPES data were obtained at room temperature with the photon energy hν = 21.2 eV.The calculated results were shift down by 1.05 eV in energy.
principle to be Δk z = 2π/λ ∼ 1 Å −1 , which is approximately the length of k z in the first Brillouin zone of HfS 2 .Thus, the k z broadening effect covers the whole Brillouin zone and ARPES measurements integrate the bands over the whole k z window.To show more details, the comparison between the ARPES measured band dispersions and the calculated surface spectrum comprised of k z -integrated bulk bands are shown in figure 2(i) and figure 2(j).indicating good match between the ARPES experiments and the theoretical calculations.
To gain insight into the indirect band gap and the conduction bands of HfS 2 , in-situ deposition of alkali metal potassium (K) on cleaved HfS 2 surface was used to tune the band structures of HfS 2 .The evolution of the band structures of HfS 2 with increasing exposure time to potassium deposition was shown in figure 3(a).With electron doping, the overall bands move down continuously until a saturation is reached, where the VBM reaches as low as ∼ −2.23 eV.Electron doping will cause the previously unoccupied conduction bands occupied and make them visible to ARPES. Figure 3 Having established an overall understanding of the band structures of pristine HfS 2 , we now focus on the band structures of defective HfS 2 with S vacancies.Defective HfS 2 with S vacancies were obtained by postannealing process of as-grown HfS 2 .In order to catch sight of the band structures around the M point, in-situ potassium (K) doping was also used before ARPES measurements.After K doping saturation, the band structures of pristine HfS 2 and two types of defective HfS 2 were measured and shown in figure 4. As shown in figure 4(b), the valence bands of pristine HfS 2 and defective HfS 2 around G point exhibits no significant difference.However, the case of the conduction bands around M point is unusual, as shown in figure 4(a).With increasing the post-annealing time of HfS 2 , i.e., increasing S vacancies, the bottom of the conduction band gradually evolve from continuous into completely discontinuous.This phenomenon can be well reproduced for different batches of as-grown HfS 2 with appropriate changing the annealing time.The fracture of the conduction band at M point is most probably induced by S vacancies which originates from post-annealing.However, the detailed characteristics of S vacancies in HfS 2 cannot be determined at present.The mechanism how S vacancies act on the conduction bands of HfS 2 remains to be determined and needs further researches.

Conclusion
The band structures of HfS 2 were systematically studied by using angle-resolved photoemission spectroscopy (ARPES) accompanied by theoretical calculations.The band structures of intrinsically semiconducting HfS 2 could be tuned by surface potassium doping.With enough potassium doping, the whole indirect gap and the conduction bands of HfS 2 could be visible to ARPES.By ARPES measurements, the indirect gap of HfS 2 is determined to be about 2.11 eV.S vacancy defects could be introduced into HfS 2 by post-annealing in vacuum.Considerable S vacancies would cause special change in the conduction bands, i.e., the fracture of the CBM.It is worth noting that S vacancies may exist even in the as-grown HfS 2 without post-annealing and annealing would accelerate the generation of S vacancy defects.Therefore, it is necessary to pay attention to the defects that could cause electronic structure change in HfS 2 , especially in the application of field effect transistor, photovoltaic, photocatalysis and others.We hope that the studies in this work can provide some meaningful references for defect regulation and reliable and efficient material selections in semiconductor fields.

Figure 1 .
Figure 1.(a) Schematic structure of HfS 2 .The top (left) and side (right) views of layered forms are shown.(b) Raman spectra of asgrown and post-annealed HfS 2 measured with a 532 nm wavelength laser.The inset is the photograph of single crystal piece of HfS 2 , with a typical size of 3 ∼ 4 mm and red-brown color.(c) XRD θ-2θ scan patterns on the easy-cleaved (001) surface of as-grown and post-annealed HfS 2 .XPS spectrum of (d) as-grown and (e) post-annealed HfS 2 .(f) In situ LEED pattern of cleaved surface of HfS 2 .(g) Calculated bulk bands of HfS 2 along high-symmetry paths as labeled.(h) The bulk Brillouin zone (blue) and the projected surface Brillouin zone (yellow) of HfS 2 .

Figure 2 .
Figure 2. (a)-(c) Constant energy mapping of HfS 2 in the first Brillouin zone for three selected binding energies as labeled.The red lines plot the projected surface Brillouin zone.(d) Theoretically calculated constant energy mapping of HfS 2 for binding energy of -3 eV.(e, f) ARPES measured band dispersions of HfS 2 along K -G and M -G directions, respectively. (g, h) Same as (e, f) but overlaid with the calculated bands.The red (white) dashed curves indicate the band dispersions along the K-Γ or M-Γ (H-A or L-A).(i) ARPES measured band dispersions (left side) and the corresponding calculated k z -integrated dispersions (right side) along K -G direction. (j) Same as (i) but along M -G direction.All ARPES data were obtained at room temperature with the photon energy hν = 21.2 eV.The calculated results were shift down by 1.05 eV in energy.
(b) shows the band dispersions of HfS 2 along G-M after saturation of surface potassium doping, in which the gray box indicates the vicinity of the CBM.As shown in figure 3(b), the spectra weight of the conduction bands is much lower than that of the valence bands.An enlarged and contrastincreased view of the vicinity of the CBM is shown in figure 3(c), and a parabolic-like band crossing the Fermi level is clearly observed.The CBM in figure 3(c) is estimated to be ∼ −0.12 eV, and the VBM in figure 3(b) is estimated to be ∼−2.23 eV.Therefore, the indirect gap of HfS 2 is about 2.11 eV obtained from ARPES measurements.Fermi surface mapping of HfS 2 after saturation of surface potassium doping are shown in figure 3(d).The conduction bands around M points give rise to ellipsoidal electron pockets centered at M points, and they are well reproduced by theoretical calculation as shown in figure 3(e).

Figure 3 .
Figure 3. (a) Band structure evolution of HfS 2 with surface potassium (K) doping.The ARPES spectrum were taken along the G-M direction.The bands moves down with doping until reaches saturation.(b) Band dispersions of HfS 2 along G-M after saturation of surface potassium doping.(c) Enlarging and contrast increasing of the gray box in (b), which corresponds the vicinity of the CBM.And the bottom of conduction bands around M point is shown. (d) Fermi surface mapping of HfS 2 after saturation of surface potassium doping and (e) the corresponding theoretically calculated result.The red lines plot the first Brillouin zone.