Excitonic luminescence of iodine-intercalated HfS₂

Although layered transition metal dichalcogenides (TMDs) have been well known and widely investigated for more than 50 years,¹ they emerged in the spotlight of material scientists for only over a decade.² The interest is motivated by a variety of properties, which characterize TMDs and the unique dependence of their properties on their thickness in the few-layer limit. Although about 60 layered TMDs have been recognized to date, researchers have focused mainly their attention on Mo- and W-based semiconducting compounds, which crystallize in hexagonal 2H phase.^3,4 Properties of other TMDs have been less investigated, which opens up new avenues for research. One of the materials, which recently focused the attention of researchers, is hafnium disulfide (HfS₂), a member of group IVB TMDs with octahedral coordination (hexagonal 1T, space group: P $3¯$ m1), which has recently been shown to exhibit very effective electrical and optoelectronic properties.^5,6 Its calculated carrier mobility at room temperature was shown to reach up to 1800 cm²/V s.⁷ Moreover, its band alignments have unusually large energies below the vacuum level compared to other TMDs.^8,9 This promises an unusual electronic structure of its interfaces with other layered materials, which may be important for several applications.^4,10–13 The growing interest in HfS₂ justifies a need to develop a deeper understanding of its fundamental properties.

To meet the challenge, we report on low-temperature photoluminescence (PL) of the bulk HfS₂ grown by the chemical vapor transport (CVT) method. It is shown that the PL consists of a series of well-resolved lines in the energy range of 1.4–1.5 eV. The observed emission is attributed to the recombination of bound excitons and their replicas with acoustic and optical phonons. The excitons are proposed to be bound to neutral iodine (I₂) molecules intercalated between layers of the TMD crystal. The molecules are introduced to the crystal during the growth as halogen transport agents in the CVT growth process. The presence of iodine in the crystal is confirmed by secondary ion mass spectroscopy (SIMS). We claim that the presence of intercalated halogen molecules in the CVT-grown HfS₂ crystals is more general, as similar PL spectra were also observed in other HfS₂ samples, including commercially available crystals from Osilla and 2D Semiconductors.

Bulk HfS₂ crystals, studied in this work, were synthesized by the CVT method with iodine as a transport agent.¹⁴ The reaction and growth temperatures were set to 1050 K and 950 K, respectively. The growth was performed continuously for 120 h. With higher stability of HfS₂ against iodine, CVT growth starts first at elevated temperatures. In the vapor phase, HfI and HfI₂ can also dominate the direction of the reaction. After 120 h, the reaction was stopped automatically, and the reactor was cooled down to room temperature in 5 h. High quality HfS₂ single crystals of 0.8–1 cm² size were grown in the low-temperature part of the reactor. High quality of the grown crystals was confirmed by powder x-ray diffraction (XRD) measurements found to be in perfect agreement with that of the octahedral 1T phase of HfS₂.¹⁵ 

The PL spectra were measured under laser excitation of $λ$ = 561 nm (2.21 eV) on samples placed on a cold finger of a continuous flow cryostat. The excitation light was focused by means of a 50× long-working distance objective with a 0.55 numerical aperture (NA) producing a spot of about 1 $μ$m diameter. The signal was collected via the same microscope objective (the backscattering geometry), sent through a 0.75 m monochromator, and detected by using a liquid nitrogen cooled charge-coupled device (CCD) camera. The excitation power focused on samples was kept at 100 $μ$W during all measurements to avoid local heating.

Density functional theory (DFT) calculations were conducted in Vienna Ab initio Simulation Package¹⁶ with the Projector Augmented Wave method.¹⁷ Perdew–Burke–Ernzerhof parametrization¹⁸ of general gradients approximation to the exchange-correlation functional was used. The plane waves basis cutoff energy was set to 550 eV, and a 9 $×$ 9 $×$ 6 $Γ$-centered Monkhorst–Pack k-grid sampling was applied. Geometrical structure was optimized with $10−5$ eV/Å and 0.01 kbar criteria for the interatomic forces and stress tensor components, respectively. Grimme's D3 correction was applied to describe the interlayer vdW interactions.¹⁹ Spin–orbit interaction was taken into account during geometry optimization. Phonon calculations were performed within the Parliński–Li–Kawazoe method,²⁰ as implemented in the Phonopy software.²¹ The 3 $×$ 3 $×$ 2 supercells were found sufficient to converge the interatomic force constants within the harmonic approximation. The phonon density of the states (DOS) and band structure were obtained from integration over full Brillouin zone (BZ) on a 27 $×$ 27 $×$ 18 grid.

The in-depth composition of the sample was probed using SIMS. As received, samples were transferred without special pretreatment to the analytical chamber, where the pressure was equal to 9 × 10⁻¹⁰ mbar. The distribution of elements was obtained with a time of-flight SIMS apparatus (TOF SIMS 5, ION-TOF GmbH, Germany) operating in the dual beam mode. The samples were sputtered by cesium ions (operating conditions: 1 keV, 76 nA), rastered over 200 × 200 $μ$m area. Exposed this way, internal layers of the sample were analyzed with a Bi⁺ ion beam (operating conditions: 50 × 50 $μ$m raster size, 30 keV, 1.12 pA). The internal mass calibration was performed using mass of ions always present: ³⁴S⁻, S²⁻, S³⁻, and S⁴⁻.

The PL spectrum of HfS₂ measured at T = 5 K comprises several emission lines in the energy range 1.4–1.5 eV [see Fig. 1(a)]. The general line shape of the spectrum does not change over a whole sample. The detailed analysis of the PL spectra is presented in the supplementary material. Two characteristic peaks, X₁ and X₂, appear in the spectrum at $EX1$ = 1.5184 eV and $EX2$ = 1.5021 eV. Spectrum of a similar line shape, although blueshifted by 5 meV, was also measured on the HfS₂ flake of approximately 5 nm thickness [see Fig. 1(b)]. Although the spectra are similar, the absence of the X₁ peak from the flake's spectrum can be noticed. Missing are also two other features, denoted in Fig. 1(a) with arrows. These lines are redshifted from X₁ by 10.2 meV and 25.7 meV, respectively. Similar PL spectra were also observed from other CVT-grown HfS₂ samples, including commercially available from Osilla and 2D Semiconductors.

The line shape of the PL spectra suggests their relation to excitonic recombination followed by a series of phonon replicas. To study the spectra in more detail and profit from their general resemblance over the sample of a millimeter size, 920 spectra were collected from the sample area of approximately 1 mm² (see the supplementary material for more details). A set of spectra were analyzed, and a classical coefficient of the intensity correlation was determined.²² The intensity correlation coefficient $Γ$ between intensities at different energies $α$ and $β$ can be expressed by the following formula:

where $Iiα$ and $Iiβ$ are the PL intensities in the spectrum i measured at energies $α$ and $β$⁠, respectively. The $Iα¯$ and $Iβ¯$ are the intensities averaged over all spectra at energies $α$ and $β$⁠, respectively. The false-color map of the $Γ$ coefficient for the collected PL spectra (upper panel) together with a typical PL spectrum (lower panel) is shown in Fig. 2. The coefficient exhibits values from −1 to 1, which correspond to deep blue and dark red in the figure. The coefficient $Γ$ = 1, apparent on the diagonal of the map, is related to the auto-correlation, i.e., correlation of a given emission line in the spectrum with itself. Three energy regions can be distinguished in the map with different color patterns. Most central region is limited by the energies of the X₂ emission line at $EX2$ = 1.5021 eV and E = 1.464 eV. A set of emission lines of high correlation parallel to the diagonal of the map are apparent in the region. The energy separations between the diagonal and those lines are equal to 10.4, 17.9, 28.1, and 35.3 meV. For the reason explained later in the text, we refer to them as longitudinal (LA), transverse (TA), LA + TA, and 2TA, respectively. The apparent correlation pattern at energies higher than $EX2$ is different. Lines of high correlation in that energy region are vertical. Finally, the region of the map with E < 1.455 eV corresponds to much weaker, low-energy emission, which is most likely related to intrinsic defects in the crystal lattice.²³ This low-energy emission is not addressed in this work.

Distinct properties of the X₁ and X₂ emission lines and their phonon replicas can be determined from the correlation matrix. To see the effect in more detail, we plot the correlation spectra $Γ$(E) calculated at the energies of the X₁ [panel (a)] and X₂ [panel (c)] emission lines, see Fig. 3. The PL spectrum (with both X₁ and X₂ lines) from a selected spot on the sample is also shown in Fig. 3(b). As expected, $Γ$ = 1 for the energies of the respective X₁ and X₂ emission lines, which corresponds to auto-correlation. Notably, $Γ$ = 1 for X₁ (X₂) is accompanied by $Γ$ = 0 for X₂ (X₁). This confirms the lack of correlation between the presence of X₁ and X₂ emission lines and can be compared with results shown in Fig. 1. Both peaks appear in the spectrum independently. The correlation spectra also reflect a rich structure of replicas that follow the X₁ and X₂ emission lines. There are two local maxima in the spectrum for X₁ [Fig. 3(a)], which correspond to peaks previously attributed to the phonon replicas of the X₁ line. They are referred to as X₁-LA and X₁-$Eu$(TO), and their origin will be addressed later. Similarly, several maxima in the correlation spectrum for X₂ [Fig. 3(c)] correspond to peaks apparent in the PL spectra. This allows to trace the origin of the lines to the X₂ line. The emission lines are referred to as X₂-TA, X₂-E_u(TO), X₂-(LA + TA), and X₂-2TA. There are more local maxima in the correlation spectra (mainly for the X₁ line), which cannot be directly correlated with the emission lines in the PL spectra. The absence of emission features related to those maxima is most likely due to their weak intensity and substantial broadening, which prevents their observation. One may also appreciate the local maxima of the correlation spectra at energies higher than those of the respective emission line. These two lines are referred to as X₁^* and X₂^* in Fig. 3(b). As the X₁ and X₂ lines are associated with the ground-state recombination processes, the X₁^* and X₂^* emission lines can be related to the corresponding excited states.

To support the attribution of the observed replicas of the X₁ and X₂ emission lines to particular phonons in HfS₂, DFT calculations were performed. The resulting phonon dispersion is shown in Fig. 4(a). There are three branches of acoustic vibrations: longitudinal (LA), transverse (TA), and out-of-plane (ZA) in HfS₂, as expected. Optical modes can be appreciated at energies higher than 150 cm⁻¹. The characteristic LO–TO splitting of the infrared-active E_u and A_2u modes can be appreciated. The former vibrations are active for light's electric field E $⊥$ c, while the latter ones are active for E $‖$ c in which c is normal to the layer planes. The corresponding total phonon DOS is presented in Fig. 4(b).

Three DOS maxima corresponding to acoustic vibrations are referred to as ZA (54 cm⁻¹), LA (80 cm⁻¹), and TA (148 cm⁻¹) after modes that mainly contribute to the DOS at particular energies, see Fig. 4(b). The DOS maximum at 202 cm⁻¹ can be related to the flat regions of the E_u(TO) vibration dispersion near M and L points of the BZ in bulk HfS₂. The DOS maximum at 250 cm⁻¹ corresponds to the practically dispersion-less Raman-active E_g. The peaks at even higher energy can be related to other infrared- or Raman-active vibrational modes.

The PL from bulk HfS₂ was also examined at higher temperatures—for spectra at selected temperatures, see Fig. 5. The emission lines broaden with increasing temperature and eventually quench, leaving the broad-band low-energy emission attributed to intrinsic defects in HfS₂. The temperature evolution measurements provide yet another proof of the independent origin of the X₁ and X₂ lines, since the X₁ line and its phonon replicas quench at temperatures lower than those of the X₂ line and its phonon replicas. Moreover, two high-energy features, blueshifted from the X₁ line, emerge at elevated temperatures, as can be seen in the inset in Fig. 5. The $X1*$ line (apparent in the correlation spectrum, see Fig. 3) can be associated with the X₁ emission line. The $X1*$ emission line gains its relative intensity with respect to the X₁ line with increasing temperature. Yet another emission line, denoted $X1**$⁠, can be distinguished in the figure, whose attribution to the X₁ line is confirmed by correlation analysis at elevated temperature (not shown here).

The expected energy of the $X2*$ emission line is also marked in the inset of Fig. 5. It is most likely that at elevated temperatures the $X2*$ line gives rise to the low-energy sideband of the $X1**$ peak.

The observation of the excitonic PL at approximately 1.5 eV in bulk HfS₂ and the semiconductor with indirect bandgap of approximately 2 eV might seem surprising. However, we note that similar low-temperature excitonic PL has previously been observed in 2H polytypes of molybdenum/tungsten sulfides/selenides: $MoS2$⁠:Cl₂,²³ $WS2$⁠:Br₂,²⁴ $WSe2$⁠:I₂,²⁵ or $WS2$⁠:I₂.²⁵ The reported emission spectra were attributed to excitons bound to intercalated halogen molecules and their phonon replicas with local phonons. The ability of TMDs to serve as hosts for intercalating molecules in TMDs originates from their van der Waals (vdW) gaps. Each TMD unit cell (layer) comprises planes of covalently bond transition metal atoms “encapsulated” between two chalcogenide atom planes. The layers are kept together by weaker vdW interactions and separated one from another by the vdW gap. The large electron affinity of halogen molecules results in a short range potential attracting electrons from HfS₂ layers.²³ The localized electrons interact with optically excited holes giving rise to bound excitons. Our results unambiguously point to two distinct excitonic complexes present in the structure: X₁ and X₂. Their independent characteristics were confirmed by the accidental absence of the X₁ line in the spectrum of the HfS₂ flake as well as the intensity correlation analysis (see Figs. 1 and 3). Moreover, our attribution is supported by the temperature dependence of the spectra with simultaneous quenching of the X₁ line and its X₁-LA and X₁-$Eu$(TO) replicas. In our opinion, the X₁ and X₂ emission lines correspond to neutral and charged excitons, respectively. They combine conduction and valence band carriers in HfS₂, which are bound by the iodine molecule. Microscopic-scale fluctuations in the unintentional sample doping may be responsible for the observed quenching of the X₁ emission line, in particular spots of the sample. Notably, while the intensity of the X₁ line fluctuates strongly over the sample area and quenches at some spots, the X₂ line is present in all measured spectra. This may reflect generally intermediate doping of the investigated sample (allowing for the creation of both neutral and charged complexes) with some more heavily doped spots with trions only. Assuming the attribution of the observed excitonic lines to the neutral exciton and trion, one can approximate the binding energy of the latter as $Δ$ = 16.3 meV. The attribution of the PL emission to bound excitons comprising band carriers also explains the apparent effect of the sample thinning on their energy. Thinning the TMD structure results in the energy increase in the conduction band minimum at the Q point of the BZ, which, in 2H-TMDs eventually, leads to the direct bandgap in the monolayer limit. A similar shift can be expected in bulk HfS₂, which explains the observed evolution of the spectrum with sample thickness. The attribution of the X₁ and X₂ lines to bound excitons also facilitates the analysis of their phonon replicas. The spatial location of such excitons leads to their delocalization in the momentum space. Therefore, the exciton can be coupled with phonons of the whole BZ, which explains the rich structure of the phonon replicas in the PL spectrum of the iodine-intercalated HfS₂, see Fig. 1. If one assumes the coupling of the bound excitons with phonons from the whole BZ, the phonon replica energy structure of the excitonic line should reflect the phonon DOS. In particular, the PL features corresponding to the phonon replicas of the X₁ and X₂ emission lines should be expected at the energies of the phonon DOS maxima. In fact, the PL peaks related to LA and E_u(TO) replica of the X₁ line as well as the TA, E_u(TO), LA + TA, and 2TA replica of the X₂ line (denoted in Fig. 3 with red arrows) can be clearly identified in the PL spectra. One can appreciate very good agreement of the expected energies with the actual energies of the low-energy satellites of the excitonic features, which supports their attribution to phonon replicas of the excitonic lines. In fact, most of the observed peaks can be related to the DOS maxima of HfS₂ phonons and not to local vibrations as observed in Refs. 23–25. To confirm our attribution of the observed PL to the halogen species uses as transport agents in CVT growth, SIMS was performed on the investigated crystal. Figure 6 presents the evolution of the HfS₂, sulfur (S), and iodine (I) concentrations as a function of the sputter time, which can be interpreted as a depth profile of sample. The results confirm the presence of iodine in the crystal. Furthermore, it can be seen that while the HfS₂ and S are evenly distributed throughout the crystal, iodine exhibits a higher concentration close to the sample surface, and its density is lower in the deeper parts of the sample. Due to the measured Raman scattering spectrum on the studied HfS₂ (see the supplementary material for details), we conclude that iodine atoms cannot be substitutionally incorporated into the HfS₂ layers. Consequently, as in previously investigated TMD materials,²⁵ it is most likely that the iodine is present in our samples in the form of $I2$ molecules, which reside in the vdW gaps between HfS₂ layers.

In conclusion, the optical emission from the bulk HfS₂ is reported. A series of well-resolved emission lines, observed at low temperature in the energy range of 1.4–1.5 eV, has been ascribed to bound excitons in HfS₂. Two independent series of excitonic lines followed by acoustic and optical phonon replicas have been identified using a classical analysis of the PL intensity correlations. It has been proposed that the excitonic lines are due to neutral and charged bound excitons in HfS₂. The excitons are bound by the electron-attractive potential introduced by the I₂ molecules intercalated between layers of the crystal. The I₂ molecules are introduced to the crystal during the growth as halogen transport agents in the CVT process and their presence in the crystal are confirmed by SIMS. It is believed that further investigation of the emission will provide important insight in properties of that material, and our report would trigger more theoretical studies on possible configurations of $I2$ molecules in the vdW gaps of HfS₂. More experimental efforts are also necessary to explain the structure of the excited states of the excitonic complexes. Moreover, it may be of fundamental importance as similar PL spectra were also observed from other CVT-grown HfS₂ samples, including those commercially available.

See the supplementary material for the results of the spatial mapping of the PL spectra made on the HfS₂ crystal and the analysis of the low-temperature Raman scattering spectrum of the HfS₂.

This work was supported by the National Science Centre, Poland (Grant Nos. 2017/27/B/ST3/00205 and 2018/31/B/ST3/02111). Z.M. and W.Z. acknowledge support from the National Natural Science Foundation of China (Grant No. 62150410438), the International Collaboration Project (No. B16001), and the Beihang Hefei Innovation Research Institute (Project No. BHKX-19-02). DFT calculations were performed with the support of the PLGrid infrastructure.