The band-edge excitons observed in few-layer NiPS₃

Abstract

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 surface⁵, 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) MX₂ (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 ReSe₂ has been proven to be a bipolar channel material for application in analog and digital integrated circuits²⁴. The layered TMDCs of WSe₂ and Cr-doped WSe₂ possess the flexibility on bandgap tuning and also stacking phase change from 2H to 1T with the increase of the chromium content²⁵. A plasma-treated MoS₂ device was proposed to be a multibits memory that applied for improving computation speed and data storage capacity²⁶. Conversely, considering III–VI compounds, InSe has been demonstrated as a high-mobility 2D semiconductor (1006–3700 cm²/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 device²⁷. The layered III–VI GaSe_1−xS_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) M₂P₂X₆ (M = V, Mn, Fe, Co, Ni, Cd, Mg, or Zn; X = S or Se) have attracted considerable attentions^31,32. In the metal phosphotrichalcogenides M₂P₂X₆, each P₂X₆ unit has the valency of 4− [i.e., (P₂X₆)⁴⁻]. It is necessary to have M₂⁴⁺ ions for achieving the whole M₂P₂X₆ structure, e.g., Mg₂P₂S₆, Zn₂P₂Se₆, and Ni₂P₂S₆, etc³¹. However, the M₂⁴⁺ ions are not usually the same metal elements, thus some of the compounds like CuInP₂S₆, CuCrP₂S₆, and AgInP₂Se₆, etc. also belong to the metal phosphotrichalcogenide family³². According to theoretical and experimental results, the bandgap values of M₂P₂X₆ (as well as MPS₃) range from 1.2 to 3.4 eV³², 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 batteries³³. 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 M₂P₂S₆, each metal atom would have three equal-distance M neighbors and exhibit stable magnetic phases in the hexagonal lattice. Therefore, layered MPX₃ has been proposed to exhibit specific applications in magneto-optics³⁴, magnetic storage, and 2D magnetism³⁵. 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 MnPS₃, ~123 K for FePS₃, and ~155 K for layered NiPS₃. NiPS₃ 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 MnPS₃ and FePS₃ with out-of-plane axial magnetization³⁵.

Beyond the study of magnetic properties, few-layer semiconducting NiPS₃ also has been fabricated as an ultraviolet photoconductive photodetector with a high detectivity of 1.22 × 10¹² Jones as determined via Jones testing with a 254-nm laser³⁶. The heteroatom doping of carbon on the NiPS₃ surface activates the photocatalytic activity of the basal plane and enhances the hydrogen evolution efficiency in the KOH solution³⁷. The catalytic behavior of NiPS₃ also can be exploited to perform water splitting³⁸. A resistive-type humidity sensor with a high sensing speed constructed using layered NiPS₃ also has been proposed³⁹, and an n-channel NiPS₃ FET with an on/off ratio reaching 10³ to 10⁵ also has been reported⁴⁰. Although a few application studies of layered semiconducting NiPS₃ 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 NiPS₃. Some studies have claimed that the bandgap of NiPS₃ is 1.6 eV^31,32,41; however, the experimental band-edge structure and excitonic transitions in layered NiPS₃ have not been explored in detail.

In this paper, the band-edge excitons of few-layer NiPS₃ 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 plane⁴². 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 MoS₂¹², which are also clearly present in the entire series of Mo_1−xW_xS₂ (0 ≤ x ≤ 1) layers with an energy blue-shift behavior with the increase in the W content⁴³. Another typical case is the five dipole excitons of E₁^ex, E₂^ex, E₃^ex, E_S1^ex, and E_S2^ex, respectively, with a mutual orthogonality of polarization in the layered 2D TMDCs of ReS₂ and ReSe₂^44,45,46. In this study, prominent and clear excitonic transitions of few-layer NiPS₃ (t = 15 ± 5 nm) are observed by μTR measurements at 10 K near the band edge. The band-edge excitons of NiPS₃ contain three excitonic features denoted as A₁, A₂, and E_∞ in the A series excitons, respectively, while a broadened feature correlates with the band-to-band feature of B. The A₁, A₂, and E_∞ μTR features display the Rydberg-series-like transitions with the first level at A₁, the second level at A₂, 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 NiPS₃ also are analyzed. In addition, temperature-dependent transmittance (optical absorption) measurements of layered NiPS₃ 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 NiPS₃ 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 A₁ 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 NiPS₃, the PL intensities of the E_3d emission are also changed, while the intensity of the B-band 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 indirect-like emission in the layered NiPS₃.

Results

Crystal information and structure

Layered single crystals of nickel phosphotrisulfide NiPS₃ were grown by the chemical vapor transport (CVT) method using I₂ as the transport agent. Supplementary Fig. 1a in the supplementary information (SI) shows the crystal morphology of the as-grown NiPS₃ layered crystals for illustration. The outline of the layered NiPS₃ 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 NiPS₃^32,47,48. 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 Notes1–2).

The A-series excitons and B band transition in NiPS₃ at 10 K

Figure 1a shows the low-temperature μTR spectrum of a few-layer NiPS₃ sample (i.e., black solid line) measured at 10 K. The upper inset shows a microscope image of the few-layer NiPS₃ nanoflake exfoliated on a SiO₂/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 NiPS₃ 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 follows⁴⁹:

$$\frac{{{\Delta}{{R}}}}{{{R}}} = {\mathrm{Re}}\left[ {\mathop {\sum}\nolimits_{i = 1}^n {{{A}}_{\mathrm{i}}^{{\mathrm{ex}}}e^{ - j\phi _{\mathrm{i}}^{{\mathrm{ex}}}}\left( {{{E}} - {{E}}_{\mathrm{i}}^{{\mathrm{ex}}} + j{\Gamma}_{\mathrm{i}}^{{\mathrm{ex}}}} \right)^{ - 2}} } \right],$$

(1)

where i is the respective transition; $A_{\rm{i}}^{{\mathrm{ex}}}$ and $\phi _{\rm{i}}^{{\mathrm{ex}}}$ are the amplitude and phase of the line shape; and E_i^ex and ${\Gamma}_{\mathrm{i}}^{{\mathrm{ex}}}$ 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., A₁ = 1.475 eV and A₂ = 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 NiPS₃ by μTR. One broadened μTR feature (denoted as B at ~1.894 eV) is also found at the higher-energy side of NiPS₃ at 10 K. The transition amplitudes ${{A}}_{\mathrm{i}}^{{\mathrm{ex}}}$ 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 structure⁵². 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 well-derivative 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 SiO₂/Si substrate. Supplementary Fig. 5 shows the bulk TR results of NiPS₃ 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 NiPS₃. The crystal structure of NiPS₃ can be realized as a stacking structure of one-layer trigonal (1 T) phase TMDCs such as TiS₂. Figure 1b shows the atomic arrangements of the side (upper parts) and top (lower part) views of the layered NiPS₃ structure. As the 1T–TiS₂ stacking formula, the NiPS₃ phase is taken as the layered MS₂ (as TMDCs) with the Ti atom replaced by Ni, while 1/3 of the Ni atoms are substituted by the P–P pairs (P₂ dimers) to form P₂S₂ + NiS₂ + NiS₂ = Ni₂P₂S₆ structures that connect and extend to the entire lamella sheet (monolayer). This situation is clearly demonstrated in the side view of the monolayer NiPS₃ that is displayed in the upper parts of Fig. 1b. Considering the bonding structure of NiPS₃, 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 (P₂S₆)⁴⁻ fundamental unit exists, and it requires two Ni²⁺ to construct the complete Ni₂P₂S₆ layer compound. Because the P₂S₂ is occupied in the 1/3 lattice of layered Ni₂P₂S₆, the perfect hexagonal 1 T phase is thereby transformed into a monoclinic layered structure of C2/m symmetry. The P₂ dimers also may contribute to the band-edge electronic states of layered NiPS₃. 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 NiPS₃ can also refer to the TMDCs as MoS₂⁵⁵, 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_z² and 40% S 3p_z⁵⁵. The main difference between the band-edge structures of MoS₂ and NiPS₃ is maybe the magnetic structure of Ni 3d states that contributed to the antiferromagnet layered NiPS₃.

Fig. 1: Low-temperature excitonic series observed in NiPS₃.

a Band-edge excitons of the A series and B transition in few-layer NiPS₃ observed via μTR measurements at 10 K. Insets show the microscopic image and AFM results of the few-layer sample on an SiO₂/Si substrate. The lower inset depicts the representative scheme of Rydberg series absorption for contrast. b Atomic arrangements of the side and top views for the layered Ni₂P₂S₆ structure. c Representative band-edge scheme for the A series exciton and B transition in NiPS₃.

According to the analysis of exciton series A observed in Fig. 1a, a modified hydrogen Rydberg model of 2D⁵³ derived from 3D case⁵⁶ may be used to analyze optical transitions and to evaluate binding energy of the observed excitons. In the 2D case, the model employs an effective Hamitonian $H = - \hbar ^2 \cdot \nabla _{\mathrm{r}}^2/\mu + V_{{\rm{e - h}}}\left( r \right)$, where $\mu ^{ - 1} = m_{\rm{e}}^{ - 1} + m_{\rm{h}}^{ - 1}$ (μ: reduced mass) and $V_{{\rm{e - h}}}\left( r \right) = - e^2/(\varepsilon _{{\rm{eff}}} \cdot r)$ 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:

$$E_{\rm{b}}^{\rm{n}} = \mu \cdot e^4/\left[ {2\hbar ^2 \cdot \varepsilon _{{\rm{eff}}}^2 \cdot \left( {n - 1/2} \right)^2} \right] = E_\infty - E_{{\rm{An}}},$$

(2)

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) WS₂ is E_∞ = 2.41 (±0.04) eV and binding energy E_b¹ = 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_b¹ decreases to 0.05 eV⁵³. 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 WS₂ (t > 10 L)⁵⁷. For NiPS₃, 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 NiPS₃⁵⁸. As shown in Fig. 1a, the A₁ level is tentatively assigned to be the n = 1 level, the A₂ exciton is inferred to be the n = 2 level, and E_∞ feature is correlated with the direct band gap of NiPS₃. The lower inset below Fig. 1a depicts the representative scheme of the A₁, A₂, and continuum band of bulk NiPS₃ for analog to the detected A series excitons at 10 K. The A₁ exciton of NiPS₃ 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 K⁵⁸. For the bilayer and monolayer NiPS₃, the PL emission of the A₁ exciton is missing to lend evidence that monolayer NiPS₃ is maybe an indirect-like 2D material. The excitonic PL emission of A₁ also showed linearly-polarized light along the crystal’s a axis⁵⁸. The polarized behavior of the A₁ exciton is different from the A series exciton in the layered MoS₂¹². The A₁ 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 NiPS₃⁵⁸. Figure 1c shows the representative band scheme of NiPS₃ appropriate for the transitions of the A series and B observed in Fig. 1a by μTR. The band block array of NiPS₃ 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_V⁵⁷. The Ni 3d electron state is d⁸, which separates into the lower fully-occupied t_2g⁶ in E_V (i.e., E_V is mainly Ni 3d t_2g⁶ + P 3p + S 3p) and the higher half-filled e_g² band hybridization with E_C (i.e., E_C is major in Ni 3d* e_g² + P 3p* + S 3p*), where P 3p_z* antibonding state contributes to the E_C of NiPS₃^59,60. 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 NiPS₃⁶¹. As shown in Fig. 1c, the A series excitons of the A₁, A₂, and E_∞ transitions may originate from the top of E_V by Ni 3d to the E_C bottom of NiPS₃, 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 NiPS₃

Figure 2a, b shows the temperature-dependent μTR spectra of the few-layer NiPS₃ 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 $E_{\rm{i}}^{{\rm{ex}}}$ of A₁, A₂, E_∞, and B transitions from 10 to 300 K are depicted in Fig. 3a and temperature-dependent broadening parameters ${\Gamma}_{\rm{i}}^{{\rm{ex}}}$ of the A₁ and B μTR features are shown in Fig. 3b, respectively. The obtained transition energies of A₁, A₂, E_∞, and B at 10 K are indicated by arrows in Fig. 2a, b. The energy values are A₁ = 1.475 eV, A₂ = 1.495 eV, E_∞ = 1.511 eV, and B = 1.894 eV, respectively. As shown in Fig. 2a, with the increase in the temperature from 10 to 300 K in the few-layer NiPS₃, 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 $A_{\rm{i}}^{{\rm{ex}}}$ 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, A₁, A₂, and E_∞ from 10 to 300 K. The energy separation of the n = 1 and n = 2 levels of NiPS₃ 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 A₂ exciton level. The binding energy of the A₁ level obtained from the Rydberg-series analysis of NiPS₃ in Eq. (1) is about 36 meV. Therefore, the A₁ exciton (i.e., A₁ ≅ 1.366 eV) can be detected in Fig. 2a for the layered NiPS₃ at 300 K. Figure 2d shows the representative scheme for the experimental setup of the μTR measurement for the few-layer NiPS₃. A tungsten halogen lamp dispersed by a monochromator provided the monochromatic light, and which was then guided to a CCD-equipped microscope using optical fiber. The detailed descriptions of the experimental setup are stated in “Methods” section.

Fig. 2: Temperature-dependent μTR spectra of NiPS₃ near band edge.

a Temperature dependence of the band-edge excitonic transitions of the A series and B observed in few-layer NiPS₃ 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. 3: Temperature dependence energies and broadening parameters of the A series and B features obtained by μTR.

a Temperature-dependent transition energies of the A series and B features obtained by μTR measurements. The symbols are the data points, solid lines are the least-square fits of the Varshni type, and dashed lines are those of the Bose–Einstein fitting. b Temperature dependence of the line-width broadening parameter of the A₁ and B features obtained by μTR experimentation.

Temperature-dependent analysis of A series and B in NiPS₃

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 NiPS₃ 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:

$$E_{\rm{i}}\left( T \right) = E_{\rm{i}}\left( 0 \right) - a_{\rm{i}} \cdot T^2/(\beta _{\rm{i}} + T),$$

(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 NiPS₃ 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 NiPS₃ 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 MoS₂^62,63. The temperature dependence of the band-edge transition energies of few-layer NiPS₃ also can be analyzed using another expression containing the Bose–Einstein occupation factor for phonons:⁶⁴

$$E_{\rm{i}}\left( T \right) = E_{{\rm{iB}}}\left( 0 \right)-a_{{\rm{iB}}} \cdot \left\{ {1 + 2/[\exp (\theta _{{\rm{iB}}}/T) - 1]} \right\},$$

(4)

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 MoS₂, WS₂, and Mo_0.5W_0.5S₂⁴³, while GaAs⁶⁴ and ZnSe⁶⁵ are included for comparison. The values of the Varshni parameter α_i and Bose–Einstein type constant a_iB of the A series excitons (A₁, A₂, and E_∞) in NiPS₃ are greater than those of the layered TMDCs MoS₂, Mo_0.5W_0.5S₂, and WS₂. The energy difference of the A exciton between 10 and 300 K is about 110 meV in NiPS₃, which is greater than those of 70–80 meV for MoS₂, Mo_0.5W_0.5S₂, and WS₂. The incorporation of the additional P₂ pairs in layered Ni₂P₂S₆ 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.

Table 1 Values of the Varshni and Bose–Einstein type fitting parameters that describe the temperature dependences of the excitonic transition energies of the A₁, A₂, E_∞, and B in the few-layer NiPS₃ together with those previously obtained for MoS₂, WS₂, Mo_0.5W_0.5S₂, GaAs, and ZnSe.

Figure 3b plots the analysis of the broadening parameter Γ (half-width at half-maximum (HWHM)) of the representative A₁ and B features in the μTR spectra of few-layer NiPS₃ 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

$${\Gamma}_{\rm{i}}\left( T \right) = {\Gamma}_{{\rm{i0}}} + {\Gamma}_{{\rm{iLO}}}/[\exp (\theta _{{\rm{iLO}}}/T) - 1],$$

(5)

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 A₁ and B transitions in NiPS₃ 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 A₁ exciton indicates that an extremely high-quality crystal is obtained for layered NiPS₃. 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 NiPS₃. Because linewidth broadening contributes more significantly than the energy shift with the change in the temperature in the NiPS₃ 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 NiPS₃ near band edge

To further identify the band-edge nature, temperature-dependent transmittance (T) measurement of a bulk NiPS₃ 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 NiPS₃ clearly reveals the presence of the A₁, A₂, 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 A₁, A₂, and E_∞ features compared with those detected in the μTR measurement of NiPS₃ at 10 K. At 300 K, the A₂ feature is ionized, and the energy value of A₁ from μTR is about 1.366 eV. The transmittance edge is extremely close to the A₁ 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 NiPS₃ are very close. This result is dissimilar to other TMDCs such as MoS₂, 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 MoS₂⁶⁶. The energy difference between the indirect and direct bandgaps of MoS₂ is about 0.6 eV. The weakened layer-by-layer decoupling of layered NiPS₃ compared to MoS₂ 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 NiPS₃ sample from 10 to 300 K. The absorption spectrum of NiPS₃ at 10 K in Fig. 4d is also similar to previous absorption curve that detected by antiferromagnet NiPS₃⁵⁸. The absorption edge in the temperature-dependent 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 A₁, A₂, 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 few-layer NiPS₃ in Fig. 2a. At 300 K, a shoulder peak of E_∞ ≈ 1.402 eV is still observed for NiPS₃ in Fig. 4d. This value is in good agreement with the direct band gap of the layered NiPS₃ obtained using the Rydberg series as E_∞ ≈ A₁ (1.366 eV) + E_b¹ (36 meV) at room temperature.

Fig. 4: The comparison of transmittance and μTR spectra in NiPS₃.

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 NiPS₃ sample from 10 to 300 K are shown in c and d, respectively.

Micro-photoluminescence result

To evaluate the origin of the band edge, thickness-dependent micro-photoluminescence (μPL) measurements of layered NiPS₃ were conducted at 300 K. Figure 5a shows the μPL spectrum of a few-layer NiPS₃ 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 NiPS₃. The E_3d peak is strong, but it gradually decreases with the increase of thickness in layered NiPS₃ (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 A₁ 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 NiPS₃ implies that multilayer NiPS₃ 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 MoS₂ (10–200 nm) on SiO₂/Si and on Cu substrate⁶⁷. In the light-emission 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 NiPS₃ reveals that photons almost pass through at 1.23 eV, while this value starts to decrease until the photon energy becomes 1.366 eV (A₁) 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 M₂P₂S₆ also can be observed in previous study of Cd₂P₂S₆⁶⁸. 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 NiPS₃. The A₁ and B 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.

Fig. 5: Thickness-dependent μPL result of few-layer NiPS₃ at 300 K.

a μPL spectrum of the band-edge emissions of a few-layer NiPS₃ 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.

Discussion

In conclusion, the band-edge excitons of A series and B transition were clearly detected and observed in the high-quality few-layer NiPS₃ grown by chemical vapor transport. The prominent excitonic sequence of A₁, A₂, and E_∞ transitions and one band-to-band feature of B in NiPS₃ were detected by micro-TR at 10 K. The energy values and amplitudes of the excitonic sequence A₁, A₂, and E_∞ followed a Rydberg series and continuum band. The excitonic binding energy of the A₁ 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 few-layer NiPS₃ 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 A₁, A₂, and E_∞ transitions was in good agreement with the corresponding ionization temperatures to sustain the detected A series excitons in NiPS₃. In addition, band-edge excitons of the A₁, A₂, 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 NiPS₃. The direct optical gap of few-layer NiPS₃ 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 MoS₂ and WS₂. From the μPL measurement of few-layer NiPS₃, 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.

Methods

Sample growth

Test samples were prepared by growing the layered single crystals of NiPS₃ via CVT with I₂ 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 I₂ (10 mg/cm³) 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 NiPS₃ 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 NiPS₃ can be mechanically exfoliated and transferred onto a SiO₂/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 SiO₂/Si substrate decorated with few-layer NiPS₃ (size of 0.8 × 0.8 × 0.01 cm³) 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 lights⁶⁹. 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 NiPS₃ 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 NiPS₃ sample, the incident and reflected (scattered) lights, and the charge-coupled-device (CCD) spectrometer. The laser power was 5 mW, and the laser spot size was 3–5 μm. The measurements were obtained from 1.1 to 2.25 eV.