The band-edge excitons observed in few-layer NiPS3

Band-edge excitons of few-layer nickel phosphorous trisulfide (NiPS3) are characterized via micro-thermal-modulated reflectance (μTR) measurements from 10 to 300 K. Prominent μTR features of the A exciton series and B are simultaneously detected near the band edge of NiPS3. The A exciton series contains two sharp A1 and A2 levels and one threshold-energy-related transition (direct gap, E∞), which are simultaneously detected at the lower energy side of NiPS3. In addition, one broadened B feature is present at the higher energy side of few-layer NiPS3. The A series excitons may correlate with majorly d-to-d transition in the Rydberg series with threshold energy of E∞ ≅ 1.511 eV at 10 K. The binding energy of A1 is about 36 meV, and the transition energy is A1 ≅ 1.366 eV at 300 K. The transition energy of B measured by μTR is about 1.894 eV at 10 K. The excitonic series A may directly transit from the top of valence band to the conduction band of NiPS3, while the B feature might originate from the spin-split-off valence band to the conduction band edge. The direct optical gap of NiPS3 is ~1.402 eV at 300 K, which is confirmed by μTR and transmittance experiments.


INTRODUCTION
Two-dimensional (2D) semiconductors exhibit immense functionalities and practicalities of large area 1,2 , ultra-thin 3,4 , smooth surface 5 , high carrier mobility [6][7][8] , flexible layers [9][10][11] , and thickness-tunable band-gap modulation 12,13 that have gradually received blooming attention in semiconductor technological studies and development in the post-silicon era. Among the 2D semiconductors, transition-metal dichalcogenides (TMDCs) MX 2 (M = W, Mo, Re and X = S, Se) [14][15][16][17][18] comprising a monolayer structure with X-M-X and layered III-VI compounds NX (N = Ga, In and X = S, Se, Te) [19][20][21][22][23] that are composed of fundamental units of X-N-N-X might be two of the important braches of 2D materials that require further research and development in electronics and optoelectronics devices applications. The TMDC of ReSe 2 has been proven to be a bipolar channel material for application in analog and digital integrated circuits 24 . The layered TMDCs of WSe 2 and Cr-doped WSe 2 possess the flexibility on bandgap tuning and also stacking phase change from 2H to 1T with the increase of the chromium content 25 . A plasma-treated MoS 2 device was proposed to be a multibits memory that applied for improving computation speed and data storage capacity 26 . Conversely, considering III-VI compounds, InSe has been demonstrated as a high-mobility 2D semiconductor (1006-3700 cm 2 /V-s) that is suitable for the fabrication of high-speed field-effect transistors (FETs) 7,8 . The native oxidation layer of InO x on an InSe layer could also produce artificial synapse functions in an InSe FET device 27 . The layered III-VI GaSe 1−x S x (0 ≤ x ≤ 1) series compounds are optically sensitive and can be applied in photodetectors and light-emission devices in the visible-to-ultraviolet region [28][29][30] . Recently, as an additional class of 2D layered materials with a monolayer structure between that of TMDCs and III-VI compounds, metal phosphorus trichalcogenides (also known as metal phosphotrichalcogenides) M 2 P 2 X 6 (M = V, Mn, Fe, Co, Ni, Cd, Mg, or Zn; X = S or Se) have attracted considerable attentions 31,32 . In the metal phosphotrichalcogenides M 2 P 2 X 6 , each P 2 X 6 unit has the valency of 4− [i.e., (P 2 X 6 ) 4− ]. It is necessary to have M 2 4+ ions for achieving the whole M 2 P 2 X 6 structure, e.g., Mg 2 P 2 S 6 , Zn 2 P 2 Se 6 , and Ni 2 P 2 S 6 , etc 31 .
However, the M 2 4+ ions are not usually the same metal elements, thus some of the compounds like CuInP 2 S 6 , CuCrP 2 S 6 , and AgInP 2 Se 6 , etc. also belong to the metal phosphotrichalcogenide family 32 . According to theoretical and experimental results, the bandgap values of M 2 P 2 X 6 (as well as MPS 3 ) range from 1.2 to 3.4 eV 32 , which may considerably enhance the absorption efficiency and wavelength absorption region compared with those of layered TMDCs having bandgap values of 1.2 to 2 eV. These materials typically own chemical bonding that is intermediate between covalent and ionic as well as exhibit unusual behavior of intercalation-substitution ions, which can render them suitable for applications in Li-ion batteries 33 . Moreover, some of the metal elements in this family are usually magnetic (e.g., M = Fe, Ni, Mn and Co). As these metal ions are formed in the van der Waals sheet of M 2 P 2 S 6 , each metal atom would have three equal-distance M neighbors and exhibit stable magnetic phases in the hexagonal lattice. Therefore, layered MPX 3 has been proposed to exhibit specific applications in magneto-optics 34 , magnetic storage, and 2D magnetism 35 . The Néel temperature (T N ) is an index of the magnetic transition from antiferromagnetic to paramagnetic. The values of T N are~78 K for MnPS 3 ,~123 K for FePS 3 , and~155 K for layered NiPS 3 . NiPS 3 exhibits the highest Néel temperature, and the magnetization axis of the ordered states lies along the van der Waals plane, which differs from those of layered MnPS 3 and FePS 3 with out-of-plane axial magnetization 35 .
Beyond the study of magnetic properties, few-layer semiconducting NiPS 3 also has been fabricated as an ultraviolet photoconductive photodetector with a high detectivity of 1.22 × 10 12 Jones as determined via Jones testing with a 254-nm laser 36 . The heteroatom doping of carbon on the NiPS 3 surface activates the photocatalytic activity of the basal plane and enhances the hydrogen evolution efficiency in the KOH solution 37 . The catalytic behavior of NiPS 3 also can be exploited to perform water splitting 38 . A resistive-type humidity sensor with a high sensing speed constructed using layered NiPS 3 also has been proposed 39 , and an n-channel NiPS 3 FET with an on/off ratio reaching 10 3 to 10 5 also has been reported 40 . Although a few application studies of layered semiconducting NiPS 3 have been reported, the fundamental band-edge nature and optical properties of the nickel phosphotrichalcogenide are not well understood. This in turn limits the development of electronic and optoelectronic devices prepared using NiPS 3 . Some studies have claimed that the bandgap of NiPS 3 is 1.6 eV 31,32,41 ; however, the experimental band-edge structure and excitonic transitions in layered NiPS 3 have not been explored in detail.
In this paper, the band-edge excitons of few-layer NiPS 3 are first observed by temperature-dependent microthermal-modulated reflectance (μTR) measurements in the temperature range between 10 and 300 K. Owing to the reduced dimensionality serving to weaken the dielectric screening effect of electron-hole pairs, 2D materials usually have strong Coulumbic interactions in excitons and trions, among others, to form a many-body system, thereby achieving increased excitonic (trionic) binding energy in the layer plane 42 . Excitonic transitions are thus frequently constructed and exist in 2D layered semiconductors. The most renowned cases of this include the A and B excitons that are present in layered MoS 2 12 , which are also clearly present in the entire series of Mo 1−x W x S 2 (0 ≤ x ≤ 1) layers with an energy blueshift behavior with the increase in the W content 43 . Another typical case is the five dipole excitons of E 1 ex , E 2 ex , E 3 ex , E S1 ex , and E S2 ex , respectively, with a mutual orthogonality of polarization in the layered 2D TMDCs of ReS 2 and ReSe 2 [44][45][46] . In this study, prominent and clear excitonic transitions of few-layer NiPS 3 (t = 15 ± 5 nm) are observed by μTR measurements at 10 K near the band edge. The band-edge excitons of NiPS 3 contain three excitonic features denoted as A 1 , A 2 , and E ∞ in the A series excitons, respectively, while a broadened feature correlates with the band-to-band feature of B. The A 1 , A 2 , and E ∞ μTR features display the Rydberg-series-like transitions with the first level at A 1 , the second level at A 2 , and the continuum band at E ∞ , respectively. The B μTR feature may originate from valence-band (E V ) splitting to the direct conduction-band (E C ) edge transition. The temperature dependences of the energies and broadening parameters of the A series and B obtained via μTR measurements of few-layer NiPS 3 also are analyzed. In addition, temperaturedependent transmittance (optical absorption) measurements of layered NiPS 3 are conducted to verify and identify the absorption edge and excitonic transitions of the A series from 10 to 300 K. The direct optical gap E ∞ of NiPS 3 is determined to be around 1.402 eV at 300 K. According to thickness-dependent micro-photoluminescence (μPL) measurements, an indirect-like E 3d emission peak that merged with A 1 is detected at~1.23 eV, while a direct emission of B band also appears at~1.825 eV at 300 K (i.e., t = 10-200 nm). With changing the layer thickness of NiPS 3 , the PL intensities of the E 3d emission are also changed, while the intensity of the Bband emission is unchanged from t = 10-200 nm. The Ni 3d e g * band may be located intermediate between E C of S 3p* + P 3p* + Ni 3d* and E V of Ni 3d + S 3p + P 3p to result in the E 3d indirectlike emission in the layered NiPS 3 .

RESULTS
Crystal information and structure Layered single crystals of nickel phosphotrisulfide NiPS 3 were grown by the chemical vapor transport (CVT) method using I 2 as the transport agent. Supplementary Fig. 1a in the supplementary information (SI) shows the crystal morphology of the as-grown NiPS 3 layered crystals for illustration. The outline of the layered NiPS 3 single crystals essentially reveals a hexagonal shape, and the powdered X-ray diffraction (XRD) pattern shown in Supplementary  Fig. 1b exhibits a monoclinic structure (symmetry C2/m), with calculated lattice constants of a = 5.761, b = 10.06, c = 6.576 Å, and β = 107°. These values are in agreement with results obtained previously for NiPS 3 32,47,48 . Supplementary Figs. 2-4 in the SI also include content analysis conducted by energy-dispersive X-ray analysis and structural characterization using Raman spectroscopy for comparison (see Supplementary Notes 1-2).
The A-series excitons and B band transition in NiPS 3 at 10 K Figure 1a shows the low-temperature μTR spectrum of a few-layer NiPS 3 sample (i.e., black solid line) measured at 10 K. The upper inset shows a microscope image of the few-layer NiPS 3 nanoflake exfoliated on a SiO 2 /Si substrate for the μTR experiment, while the lower inset shows the thickness information determined by atomic force microscopy (AFM). The thickness is about 23 monolayers (t = 15 ± 5 nm) of the layered NiPS 3 crystal. As shown in Fig. 1a, the black solid line is the experimental spectrum, and the green-dashed curve is the least-square fit to a first-derivative Lorentzian line-shape function appropriate for the excitonic transitions expressed as follows 49 : where i is the respective transition; A ex i and ϕ ex i are the amplitude and phase of the line shape; and E i ex and Γ ex i are the energy and broadening parameter of the interband transitions, respectively. As analyzed by the Lorentzian line-shape fitting using Eq. (1), the energy values of two prominent excitonic features (i.e., A 1 = 1.475 eV and A 2 = 1.495 eV) together with one higher-energy transition (i.e . , E ∞ at 1.511 eV) are clearly detected in the A series of few-layer NiPS 3 by μTR. One broadened μTR feature (denoted as B at~1.894 eV) is also found at the higher-energy side of NiPS 3 at 10 K. The transition amplitudes A ex i of the A series excitons gradually decrease from the maximum n = 1 level, progressing to the subsequent n = 2 transition, and finally the E ∞ feature follows the general transition probability of the exciton sequence in semiconductors. Modulated TR measurements of semiconductors have been proven to be effective for the characterization of excitons, direct band edge, and interband transitions in the semiconductor's band structure [50][51][52] . The derivative spectral line features suppress the unintentional spectral background and emphasize the direct critical-point transitions in the band structure 52 . The TR modulation spectroscopy can be regarded as a physical derivative approach to the reflectance spectrum of semiconductor dielectric function by directly applying thermal perturbation to the crystal lattice periodically (i.e., ΔR). The wellderivative ΔR signal (AC) of sample is thus measured and normalized to the sample reflectance R (DC) for obtaining ΔR/R at each wavelength using lock-in amplifier. The TR modulation spectroscopy is different from that of reflectance contrast method with firstly measuring ΔR/R = (R sample − R substrate )/R substrate 53,54 and then implementing mathematical derivative to the line shape using (d/dE) (ΔR/R) 53 . The μTR technique is directly response to the physical derivative nature of direct transitions in the band structure of the few-layer sample, and thus possesses less substrate effect coming from the SiO 2 /Si substrate. Supplementary  Fig. 5 shows the bulk TR results of NiPS 3 without any substrate. Essentially the results measured by μTR (with substrate) and measured by conventional TR (without substrate) are similar (Supplementary Note 3). As shown in Fig. 1a, the sharp features of the A series excitons and the extremely broadened B transition reveal that the A and B excitons exhibit different origins in NiPS 3 . The crystal structure of NiPS 3 can be realized as a stacking structure of one-layer trigonal (1 T) phase TMDCs such as TiS 2 . Figure 1b shows the atomic arrangements of the side (upper parts) and top (lower part) views of the layered NiPS 3 structure. As the 1T-TiS 2 stacking formula, the NiPS 3 phase is taken as the layered MS 2 (as TMDCs) with the Ti atom replaced by Ni, while 1/3 of the Ni atoms are substituted by the P-P pairs (P 2 dimers) to form P 2 S 2 + NiS 2 + NiS 2 = Ni 2 P 2 S 6 structures that connect and C.-H. Ho et al. extend to the entire lamella sheet (monolayer). This situation is clearly demonstrated in the side view of the monolayer NiPS 3 that is displayed in the upper parts of Fig. 1b. Considering the bonding structure of NiPS 3 , the P-P pairs are covalently bonded to six sulfur atoms, and each P atom is tetrahedrally coordinated with three S atoms to form opposite triangles, as shown by the 1 T phase shown in the top view of Fig. 1b. Therefore, a (P 2 S 6 ) 4− fundamental unit exists, and it requires two Ni 2+ to construct the complete Ni 2 P 2 S 6 layer compound. Because the P 2 S 2 is occupied in the 1/3 lattice of layered Ni 2 P 2 S 6 , the perfect hexagonal 1 T phase is thereby transformed into a monoclinic layered structure of C2/m symmetry. The P 2 dimers also may contribute to the band-edge electronic states of layered NiPS 3 . Therefore, the antibonding states of S 3p* + P 3p* + Ni 3d* may consist in conduction band while the valence band is composed by hybridation of Ni 3d + S 3p + P 3p bonding states. Excepting the incorporation of the P-P pairs, the band-edge contributions of electronic states in E C and E V of NiPS 3 can also refer to the TMDCs as MoS 2 55 , where the largely Mo 4d* and minor S 3p* are simultaneously consisted in the E C bottom while major Mo 4d and S 3p are positioned at the top of E V . For the spin-orbit splitting band Δ so , the band contributions may consisted of 60% Mo 4d z 2 and 40% S 3p z 55 . The main difference between the band-edge structures of MoS 2 and NiPS 3 is maybe the magnetic structure of Ni 3d states that contributed to the antiferromagnet layered NiPS 3 .
According to the analysis of exciton series A observed in Fig. 1a, a modified hydrogen Rydberg model of 2D 53 derived from 3D case 56 may be used to analyze optical transitions and to evaluate binding energy of the observed excitons. In the 2D case, the model h (μ: reduced mass) and V eÀh r ð Þ ¼ Àe 2 =ðε eff Á rÞ is the locally attractive Columbic interaction between electron and hole. The term ε eff is the effective permittivity of the material available for excitons. The 2D model of exciton predicts an excitonic binding energy expressed as follows: where n is the principal quantum number, E ∞ is the threshold energy of the excitonic sequence, and E An is the transition energy of the exciton level detected by the layered sample. According this 2D model, a typical case for estimating A series excitons in monolayer (1 L) WS 2 is E ∞ = 2.41 (±0.04) eV and binding energy E b 1 = 0.32 (±0.04) eV. However, for the thick-layer bulk case (>10 L), because the effects caused by 3D hydrogenic Hamitonian and excitonic Bohr radius, etc. the direct gap reduces to E ∞ = 2.10 eV and E b 1 decreases to 0.05 eV 53 . For the n = 2 level, the energy separation between n = 1 and n = 2 is increased with the layer thickness decreases when t ≤ 4 L. The energy splitting of n = 1 and n = 2 will remain the same in bulk case in layered WS 2 (t > 10 L) 57 . For NiPS 3 , the A series and B transitions are correlated with majorly Ni 3d states constructed in E C and E V [58][59][60][61] . The A series originates from largely d-to-d transitions correlated with the spin orientation in the antiferromagnetic NiPS 3 58 . As shown in Fig. 1a, the A 1 level is tentatively assigned to be the n = 1 level, the A 2 exciton is inferred to be the n = 2 level, and E ∞ feature is correlated with the direct band gap of NiPS 3 . The lower inset below Fig. 1a depicts the representative scheme of the A 1 , A 2 , and continuum band of bulk NiPS 3 for analog to the detected A series excitons at 10 K. The A 1 exciton of NiPS 3 has also recently been detected by PL measurement to locate between 1.475 and 1.478 eV with the thickness changing from 3 L to 8 L at 10 K 58 . For the bilayer and monolayer NiPS 3 , the PL emission of the A 1 exciton is missing to lend evidence that monolayer NiPS 3 is maybe an indirect-like 2D material. The excitonic PL emission of A 1 also showed linearlypolarized light along the crystal's a axis 58 . The polarized behavior of the A 1 exciton is different from the A series exciton in the layered MoS 2 12 . The A 1 exciton had been assigned as a Zhang-Rice triplet to a Zhang-Rice singlet transition that correlated with the spin directions in the Ni 3d states of NiPS 3 58 . Figure 1c shows the representative band scheme of NiPS 3 appropriate for the transitions of the A series and B observed in Fig. 1a by μTR. The band block array of NiPS 3 is proposed to be the S 3p* + P 3p* antibonding states combined with the lower Ni 3d* band that is positioned at the bottom of E C , whereas the fully occupied Ni 3d (t 2g + e g ) followed by the S 3p + P 3p bonding state comprises the main E V 57 . The Ni 3d electron state is d 8 , which separates into the lower fully-occupied t 2g 6 in E V (i.e., E V is mainly Ni 3d t 2g 6 + P 3p + S 3p) and the higher half-filled e g 2 band hybridization with E C (i.e., E C is major in Ni 3d* e g 2 + P 3p* + S 3p*), where P 3p z * antibonding state contributes to the E C of NiPS 3 59,60 . Not only the Ni 3d state but also the P 3p state hybridizes with the S 3p orbital still contributing to the band edge of layered NiPS 3 61 . As shown in Fig. 1c, the A series excitons of the A 1 , A 2 , and E ∞ transitions may originate from the top of E V by Ni 3d to the E C bottom of NiPS 3 , while the B feature is inferred to originate from the spin-orbital splitting of E V to the E C bottom. The transition of spin-orbital splitting band to E C is rather flat to obtain a more broadened B feature as compared to the sharp features of the A series excitons in Fig. 1a.
Temperature-dependent microthermal-modulated reflectance spectroscopy of few-layer NiPS 3 Figure 2a, b shows the temperature-dependent μTR spectra of the few-layer NiPS 3 sample in the temperature range between 10 and 300 K near the band edge. The dashed lines are the experimental spectra, and the solid curves are the least-square fits using Eq. (1). The obtained transition energies E ex i of A 1 , A 2 , E ∞ , and B transitions from 10 to 300 K are depicted in Fig. 3a and temperaturedependent broadening parameters Γ ex i of the A 1 and B μTR features are shown in Fig. 3b, respectively. The obtained transition energies of A 1 , A 2 , E ∞ , and B at 10 K are indicated by arrows in Fig. 2 Temperature-dependent μTR spectra of NiPS 3 near band edge. a Temperature dependence of the band-edge excitonic transitions of the A series and B observed in few-layer NiPS 3 via μTR measurements. The solid lines are the least-square fits of the experimental data to a derivative of the Lorentzian line-shape function in Eq. (1). b Magnification of the B transition feature in a. c 2D contour plot of the μTR spectra of the A series excitons from 10 to 300 K to illustrate the temperature-energy shift and intensity change. d Representative scheme of the experimental setup for the temperature-dependent μTR measurements.  Fig. 2a, with the increase in the temperature from 10 to 300 K in the few-layer NiPS 3 , band-edge excitons of the A series reveal energy reduction and line-shape broadened characteristics. Figure 2b shows the magnification of the μTR features of the B exciton from 1.6 to 2 eV (blue box in Fig. 2a): Energy reduction and line-shape broadened characteristics are clearly observed from 10 to 300 K. The transition amplitudes A ex i of the A series and B features in Fig. 2a, b also demonstrate degradation with the increase in the temperature. Figure 2c shows the 2D contour plot of the μTR spectra of the A series excitons, A 1 , A 2 , and E ∞ from 10 to 300 K. The energy separation of the n = 1 and n = 2 levels of NiPS 3 is about 20 meV (Fig. 2(a)). The n = 2 exciton level is ionized at T > 175 K (Fig. 2a, c). The value of the thermal energy kT (where k is the Boltzmann constant) is in agreement with the energy separation of the n = 2 level and E ∞ (~16 meV) to facilitate the thermal ionization of the A 2 exciton level. The binding energy of the A 1 level obtained from the Rydberg-series analysis of NiPS 3 in Eq. (1) is about 36 meV. Therefore, the A 1 exciton (i.e., A 1 ≅ 1.366 eV) can be detected in Fig. 2a for the layered NiPS 3 at 300 K. Figure 2d shows the representative scheme for the experimental setup of the μTR measurement for the few-layer NiPS 3 . A tungsten halogen lamp dispersed by a monochromator provided the monochromatic light, and which was then guided to a CCDequipped microscope using optical fiber. The detailed descriptions of the experimental setup are stated in "Methods" section. Figure 3a shows the experimental data points of the transition energies of the temperature-dependent A series (n = 1, n = 2, and E ∞ ) and B features in the few-layer NiPS 3 obtained by the analysis of the derivative Lorentzian line-shape fitting using Eq. (1) that was derived from Fig. 2a, b. The solid lines correspond to the least-square fits to the Varshni empirical relationship:

Temperature-dependent analysis of A series and B in NiPS 3
where i is the respective transition, E i (0) is the energy at 0 K, α i is related to the strength of the electron (exciton)-phonon interaction, and β i is closely related to the Debye temperature. Table 1 lists the obtained fitting parameters for comparison. More rapid temperature-energy shift of the E V top than that of the spin-orbital splitting in the NiPS 3 band indicates that the exciton-phonon interaction strength of the A-series are slightly larger than that of the B band transition. According to the energy difference between B and E ∞ in Fig. 3a, the spin-orbital splitting (Δ so ) of the few-layer NiPS 3 is about 0.383 eV. This value is greater than that of about 0.19 eV in the energy separation of the A and B excitons in MoS 2 62,63 . The temperature dependence of the bandedge transition energies of few-layer NiPS 3 also can be analyzed using another expression containing the Bose-Einstein occupation factor for phonons: 64 where a iB represents the strength of the electron (exciton)-phonon interaction, and θ iB corresponds to the averaged phonon temperature. Figure 3a shows the fitted results represented by the red dashed-doted curves. The obtained values of E iB (0), a iB , and θ iB also are listed in Table 1 together with the layered compounds MoS 2 , WS 2 , and Mo 0.5 W 0.5 S 2 43 , while GaAs 64 and ZnSe 65 are included for comparison. The values of the Varshni parameter α i and Bose-Einstein type constant a iB of the A series excitons (A 1 , A 2 , and E ∞ ) in NiPS 3 are greater than those of the layered TMDCs MoS 2 , Mo 0.5 W 0.5 S 2 , and WS 2 . The energy difference of the A exciton between 10 and 300 K is about 110 meV in NiPS 3 , which is greater than those of 70-80 meV for MoS 2 , Mo 0.5 W 0.5 S 2 , and WS 2 . The incorporation of the additional P 2 pairs in layered Ni 2 P 2 S 6 is potentially the main reason for causing a more rapid temperature-energy gap shift compared to the other layered TMDCs in the environment of a crystal lattice-constant change.  Figure 3b plots the analysis of the broadening parameter Γ (halfwidth at half-maximum (HWHM)) of the representative A 1 and B features in the μTR spectra of few-layer NiPS 3 between 10 and 300 K with representative error bars. The solid lines represent the least-square fitting to a Bose-Einstein-type formula, which is appropriate for the temperature-dependent line-width analysis as follows: 64,65 where Γ i0 represents the term of the line-shape broadening invoked from the mechanism of crystallinity from impurities, dislocations, electron interactions, and Auger processes, whereas the Γ iLO term is related to the electron (exciton)-longitudinal optical (LO) phonon (Frohlich) interaction. θ iLO is related to the LO phonon temperature. The obtained fitting parameters of the line-shape broadening of the A 1 and B transitions in NiPS 3 are Γ i0 = 7 ± 1 and 96 ± 10 meV; Γ iLO = 98 ± 10 and 1800 ± 800 meV; and θ iLO = 280 ± 20 and 584 ± 140 K, respectively. The considerably lower value of Γ i0 of the A 1 exciton indicates that an extremely high-quality crystal is obtained for layered NiPS 3 . The broadened B feature implies that the spin-orbital-splitting band is rather flat compared to the E V top (in k space) that exists in the band structure of NiPS 3 . Because linewidth broadening contributes more significantly than the energy shift with the change in the temperature in the NiPS 3 lattice, the θ iLO value is therefore greater than that of θ iB due to the larger averaged phonon temperature.
Transmittance and optical absorption of NiPS 3 near band edge To further identify the band-edge nature, temperature-dependent transmittance (T) measurement of a bulk NiPS 3 with a thickness of about 10 μm was conducted. Figure 4a, b show the transmittance absorption edge and μTR spectra of the A and B excitons at 10 and 300 K, respectively, together with a mathematical-derivative transmittance (ΔT) spectrum that is included for contrast. The transmittance spectrum of NiPS 3 clearly reveals the presence of the A 1 , A 2 , and E ∞ excitonic features at the absorption edge at 10 K, similar to those detected in the μTR spectrum. In addition, the ΔT spectrum in Fig. 4a reveals the same energy position and line shape of the A 1 , A 2 , and E ∞ features compared with those detected in the μTR measurement of NiPS 3 at 10 K. At 300 K, the A 2 feature is ionized, and the energy value of A 1 from μTR is about 1.366 eV. The transmittance edge is extremely close to the A 1 transition, and the ΔT spectral line shape is also similar to that of the μTR feature. These results indicate that the energies of transmittance absorption edge (measured by T) and direct band edge (measured by μTR) of bulk NiPS 3 are very close. This result is dissimilar to other TMDCs such as MoS 2 , whose transmittance absorption edge is at 1.23-1.28 eV (i.e., optical transition assisted by emission and absorption of phonons), while the direct gap is about 1.88 eV in multilayer MoS 2 66 . The energy difference between the indirect and direct bandgaps of MoS 2 is about 0.6 eV. The weakened layer-by-layer decoupling of layered NiPS 3 compared to MoS 2 may be the main reason for the small energy difference between the indirect and direct bandgaps of the layered compound. Figure 4c, d show the temperature-dependent transmittance and absorption spectra of the NiPS 3 sample from 10 to 300 K. The absorption spectrum of NiPS 3 at 10 K in Fig. 4d is also similar to previous absorption curve that detected by antiferromagnet NiPS 3 58 . The absorption edge in the temperaturedependent transmittance and absorption spectra demonstrates an energy blue-shift behavior with the decrease in the temperature from 300 to 10 K, similar to the typical trend for semiconductors. The clear A 1 , A 2 , and E ∞ transition features of the A series excitons are still observed in the low-temperature absorption spectra (T < 180 K), verifying the μTR results of fewlayer NiPS 3 in Fig. 2a. At 300 K, a shoulder peak of E ∞ ≈ 1.402 eV is still observed for NiPS 3 in Fig. 4d. This value is in good agreement with the direct band gap of the layered NiPS 3 obtained using the Rydberg series as E ∞ ≈ A 1 (1.366 eV) + E b 1 (36 meV) at room temperature.

Micro-photoluminescence result
To evaluate the origin of the band edge, thickness-dependent micro-photoluminescence (μPL) measurements of layered NiPS 3 were conducted at 300 K. Figure 5a shows the μPL spectrum of a few-layer NiPS 3 sample with a thickness of about 10 nm. Two broadened peaks at about E 3d ≈ 1.23 eV and at B ≈ 1.825 eV are observed in the μPL spectrum of few-layer NiPS 3 . The E 3d peak is strong, but it gradually decreases with the increase of thickness in Table 1. Values of the Varshni and Bose-Einstein type fitting parameters that describe the temperature dependences of the excitonic transition energies of the A 1 , A 2 , E ∞ , and B in the few-layer NiPS 3 together with those previously obtained for MoS 2 , WS 2 , Mo 0.5 W 0.5 S 2 , GaAs, and ZnSe.

Materials
Feature layered NiPS 3 (Fig. 5b), whereas the B emission peak remains at a similar PL intensity with the change in the layer thickness from 10 to 200 nm. A detailed analysis of the PL line-shape fitting of the PL spectrum in Fig. 5a reveals that the A 1 peak (at 1.366 eV) is still involved in the broadened E 3d peak. The variation of PL intensity of the E 3d peak with changing the thickness of NiPS 3 implies that multilayer NiPS 3 is maybe an indirect semiconductor with an indirect-like emission of~1.23 eV, originating from the Ni 3d e g * band to the E V transition assisted by phonons at 300 K. The indirect-like emission of a 1.3-1.4 eV peak from indirect E C valley at Σ point was usually observed in the multilayered MoS 2 (10-200 nm) on SiO 2 /Si and on Cu substrate 67 . In the lightemission process, phonons are required to conserve the momentum, and photoexcited hot electrons are injection into the lower indirect valley of E C for resulting in indirect-like emission. As shown in Fig. 4b, the transmittance absorption edge of layered NiPS 3 reveals that photons almost pass through at 1.23 eV, while this value starts to decrease until the photon energy becomes 1.366 eV (A 1 ) at 300 K. This result implies that the Ni 3d e g * states might form an intermediate band located between the main E C (P 3p* + S 3p* + Ni 3d*) and the top of E V . The lower indirect-like emission bands of the M d to d transitions of M 2 P 2 S 6 also can be observed in previous study of Cd 2 P 2 S 6 68 . The inset of Fig. 5a shows the probable band scheme of the band edge for PL band-edge emissions. The E 3d peak is an indirect-like emission caused by the intermediate band of Ni 3d e g * existed in NiPS 3 . The A 1 and B Fig. 4 The comparison of transmittance and μTR spectra in NiPS 3 . Spectral comparison of the band-edge transitions in the transmittance (T), first-derivative transmittance (ΔT), and μTR spectra at a 10 K and b 300 K. The temperature-dependent transmittance and absorption spectra of the layered NiPS 3 sample from 10 to 300 K are shown in c and d, respectively. emissions are originated from the direct E C bottom to the E V top and to the spin-split-off band below E V , respectively.

DISCUSSION
In conclusion, the band-edge excitons of A series and B transition were clearly detected and observed in the high-quality few-layer NiPS 3 grown by chemical vapor transport. The prominent excitonic sequence of A 1 , A 2 , and E ∞ transitions and one bandto-band feature of B in NiPS 3 were detected by micro-TR at 10 K. The energy values and amplitudes of the excitonic sequence A 1 , A 2 , and E ∞ followed a Rydberg series and continuum band. The excitonic binding energy of the A 1 level is about 36 meV and its transition energy is 1.366 eV at 300 K. The temperature-dependent μTR measurements of the A series and B transitions of the fewlayer NiPS 3 were conducted to verify the thermal ionization energy of the excitons and the temperature-energy shift of the 2D material from 10 to 300 K. The energy separation of the A 1 , A 2 , and E ∞ transitions was in good agreement with the corresponding ionization temperatures to sustain the detected A series excitons in NiPS 3 . In addition, band-edge excitons of the A 1 , A 2 , and E ∞ transitions were detected in the temperature-dependent transmittance and absorption spectra to identify the existence of the A series excitons in the layered NiPS 3 . The direct optical gap of few-layer NiPS 3 was determined to be E ∞ ≈ 1.402 eV at 300 K. The temperature-energy shift of the A series excitons between 10 and 300 K was faster than those of MoS 2 and WS 2 . From the μPL measurement of few-layer NiPS 3 , the indirect-like emission was observed at 1.23 eV, while a direct B band emission was observed at 1.825 eV. The indirect-like emission possibly originates from an intermediate band of Ni 3d e g * to the E V top recombination. The A series excitons come from the top of E V to the E C bottom, while the B feature is originated from the spin-split-off band to the E C transition. Based on the experimental analysis, the origin of the band-edge excitons of the layered nickel phosphorus trisulfide was realized.

Sample growth
Test samples were prepared by growing the layered single crystals of NiPS 3 via CVT with I 2 as the transport agent. First, powdered elements of Ni (99.99% purity), P (99.999% purity), and S (99.999% purity) were prepared. Second, the powder mixture of the starting materials and an appropriate amount of I 2 (10 mg/cm 3 ) were cooled with liquid nitrogen and sealed in a vacuum environment at~10 −6 Torr inside a quartz ampoule. The growth temperature was set as 800°C (heating zone) → 700°C (growth zone) with a gradient of −2.5°C/cm for the simultaneous growth in two ampoules. The reaction occurred over 336 h to grow large single crystals. After this growth, several shiny sheet-like NiPS 3 thick crystals with areas up to a scale of square centimeters were obtained. With the weakened van der Waals bonds between the layers, different layer thicknesses of NiPS 3 can be mechanically exfoliated and transferred onto a SiO 2 /Si substrate using Scotch tapes with different stickiness properties.

Microthermal-modulated reflectance
For μTR measurements, a 150-W tungsten halogen lamp served as the white light source. The white light source was dispersed by a 0.2-m Photonics International (PTI) monochromator, which was equipped with a 1200-grooves/mm grating for providing monochromatic light. The SiO 2 /Si substrate decorated with few-layer NiPS 3 (size of 0.8 × 0.8 × 0.01 cm 3 ) was closely attached onto an Au-evaporated quartz plate. The monochromatic light source was coupled onto the few-layer or multilayer sample using a silica fiber, and it passed through a light-guiding microscope (LGM) equipped with an Olympus objective lens (50×, working distance~8 mm). It served as the interconnection coupled medium between the few-layer sample and the incident and reflected lights 69 . The reflected light from the layered sample was collected by the LGM and then coupled to an EG&G HUV200B Si detector using an additional silica fiber. Optical alignment was accomplished by the XYZ adjustment of the nano-flake sample using a CCD imaging camera in the LGM. A 4-Hz heating current (~0.5 A) was periodically supplied to the Au heater for the thermal modulation of the lattice constant and band edge of the sample. Phase-sensitive detection was achieved by using an NF 5610B lock-in amplifier. A Janis open-circled liquid-helium cryostat equipped a Lakeshore 335 thermometer controller was used to facilitate temperature-dependent measurements from low temperatures to room temperature.

Optical transmission measurement
For the transmission measurement of bulk NiPS 3 sample, the same monochromatic light source as that employed for μTR was used. The layer sample of t~10 μm was closely mounted on a copper holder with a center hole of size approximately 500 μm for light transmission. The incident light was chopped at 200 Hz with an optical chopper. The transmission light of the sample was passed to an EG&G HUV200B Si photodetector. An NF 5610B lock-in amplifier was used to implement the phase-sensitive photodetection. An RMC 22 close-cycled He compressor system that was equipped with a Lakeshore 335 thermometer controller facilitated the low temperature and temperature-dependent measurements.

Micro-photoluminescence experiment
The μPL measurements were conducted in an integrated RAMaker microscope spectrometer with a 532-nm solid-state diode-pump laser as the excitation source. The same LGM setup as that used for μTR was utilized for the interconnection coupled medium between the few-layer Fig. 5 Thickness-dependent μPL result of few-layer NiPS 3 at 300 K. a μPL spectrum of the band-edge emissions of a few-layer NiPS 3 sample with a thickness of~10 nm at 300 K. The fitting curves of the PL peaks are also included. The left inset shows a microscopic image of the few-layer sample, and the right inset shows the possible band-edge scheme for the observed PL emissions. b Thickness dependence of the PL intensities of the E 3d and B peaks detected in a.