Engineering the band gap and optical properties of a two-dimensional molybdenum carbon fluoride MXene

Using first-principles density functional theory, we investigated the electronic and optical properties of monolayer and multilayer nanosheets of molybdenum carbon fluoride (Mo₂CF₂), a two-dimensional (2D) transition-metal carbide MXene. The indirect band gap of the Mo₂CF₂ semiconductor can be engineered by controlling the number of layers where the band gap energy changes from 0.278 eV for the monolayer to 0.249 eV for the trilayer nanosheet. The decrease in band gap energy in the multilayer is due to inter­layer coupling, which splits the bands according to the number of layers. Mo₂CF₂ behaves as a metal with an anomalous dispersion and high optical conductivity at incident photon energies of 0.68–2.19, 3.49–6.68 and 7.30–8.31 eV. It has a relatively low reflectivity and is absorbing over a broad range of photon energies from about 0.429 (2890), 0.387 (3204) and 0.345 eV (3594 nm) for the monolayer, bilayer and trilayer nanosheets, respectively, achieving peak absorption in the vacuum ultraviolet region at about 7.9 eV (157 nm). The optical properties of Mo₂CF₂ can likewise be tuned by varying the number of layers. The unique behavior of its optical properties along with the ability to control its electronic and optical properties enhances the potential of 2D Mo₂CF₂ for various applications in the fields of electronics and energy storage.

1. Introduction

Since the discovery of graphene and its wonderful properties (Kaushik et al., 2019; Ostovari et al., 2018), two-dimensional (2D) materials with their extraordinary electronic, mechanical and optical properties (Georgiou et al., 2012; Tamleh et al., 2018) have attracted much research inter­est in the field of materials science. The recent discovery of a novel family of com­pounds called 2D transition-metal carbides, nitrides and carbonitrides (MXene) has gained significant attention from the scientific community and has spurred new inter­est in 2D materials (Khazaei et al., 2019; Bae et al., 2021; Naguib et al., 2013; Anasori et al., 2015). MXene has a general formula of M_n+1X_nT_x (n = 1–3), where M indicates early transition metals (e.g. Sc, Ti, V, Nb, Mo, etc.), X stands for C and/or N, and T_x represents functional groups on the surface of the MXene, such as –OH, –O or –F (Naguib et al., 2011; Hong et al., 2020; Champagne et al., 2018). MXenes have a huge potential in a wide range of applications, such as energy storage (Yorulmaz et al., 2016; Anasori et al., 2017), sensing (Sinha et al., 2018; Khazaei et al., 2012), catalysis (Peng et al., 2018; Wang et al., 2018; Li & Wu, 2019) and the development of electronic devices (Zhang & Nicolosi, 2019).

Molybdenum carbon fluoride (Mo₂CF₂) is a MXene consisting of the molybdenum (Mo) transition metal, carbon (C) and functionalized by fluorine (F). Khazaei et al. (2014) reported that a monolayer Mo₂CF₂ is an indirect band gap semiconductor with a narrow band gap of 0.27 eV and the most stable Mo₂CF₂ (hollow site–hollow site) structure is a promising thermoelectric material. Monolayer Mo₂CF₂ has many excellent properties, such as high capacity, outstanding mechanical strength and good flexibility. Therefore, this material has a great potential as an anode material for Li-ion batteries, as well as in various applications, including electronics and energy storage (Mehta et al., 2019).

Despite previous works on several MXenes, including Ti₃C₂T₂, Nb₄C₃T_x and V₂C– , with a wide variety of applications (Khazaei et al., 2019; Bae et al., 2021; Champagne et al., 2018; Mostafaei & Abbasnejad, 2021; Khan et al., 2019), research on the electronic and optical properties of Mo₂CF₂, and how the number of layers affects these properties is still lacking. The ability to control the band gap of a material is very important for its application in the field of electronic devices. As a material with exciting prospects for electronics and energy storage applications, the ability to control the electronic structure and hence the band gap of Mo₂CF₂ will greatly enhance its potential. However, the ability to control the band gap of Mo₂CF₂ has not yet been demonstrated. Therefore, this work investigates the structural, electronic and optical properties of monolayer, bilayer and trilayer nanosheets of Mo₂CF₂ (collectively referred to as 2D layered Mo₂CF₂) using first-principles calculations in the framework of the generalized gradient approximation (GGA) implemented by the Perdew–Burke–Ernzerhof (PBE) functional. Our results illustrate how the electronic structure, band gap energy and optical properties can be controlled by manipulating the number of layers in a 2D Mo₂CF₂.

2. Computational method

The crystal structures of the bulk and 2D layered Mo₂CF₂ were visualized using VESTA (Momma & Izumi, 2011). The top and side views of bulk Mo₂CF₂ are shown in Figs. 1(a) and 1(b). Bulk Mo₂CF₂ consists of a layer of C atoms sandwiched between Mo atoms and two layers of Mo atoms halogenated by F atomic layers on each side. It has a hexa­gonal structure and space group P6₃/mmc (No. 194). The side view of the relaxed configurations of the monolayer, bilayer and trilayer nanosheet is illustrated in Fig. 1. The atomic coordinates used to construct and visualize the bulk structure are Mo1 (0.333, 0.667, 0.368), Mo2 (0.667, 0.333, 0.632), C (0.000, 0.000, 0.500), F1 (0.667, 0.333, 0.184) and F2 (0.333, 0.667, 0.8156). The atomic coordinates (Wyckoff positions) and unit-cell parameters are taken from a previous report (Khazaei et al., 2014) and were optimized using the GGA–PBE functional with the convergence criterion of 510⁻⁶ eV per atom. The Mo—C and Mo—F bonds are strong, with mixed covalent, metallic and ionic characteristics. On the other hand, the F—F bonds are weaker and more reactive, allowing a monolayer to be easily exfoliated from the bulk (Zhu et al., 2017). The structure of the monolayer was constructed in VESTA starting from the 111 unit cell of the bulk crystal and making the value of the c axis five times greater than that of the bulk, thereby obtaining a 115 supercell. The number of layers was increased by adding a layer into the unit cell while keeping the lattice parameter along the c axis fixed. The structure from monolayer to multilayer is optimized every time a layer is added. The optimized unit-cell parameters are shown in Table 1.

Table 1
Calculated band gap energy, unit-cell parameters and bond lengths for the bulk and two-dimensional layered Mo₂CF₂

	Band gap energy (eV)	a = b (Å)	c (Å)	dMo—C (Å)	dMo—F (Å)
Bulk	0.237	3.2738	6.7495	2.1125	2.2960
Trilayer	0.249	3.2798	35.7058	2.1154	2.3036
Bilayer	0.258	3.2793	35.7128	2.1151	2.3032
Monolayer	0.278	3.2786	35.7215	2.1148	2.3029

Figure 1 The crystal structures of Mo2CF2 showing (a) a top view and (b) a side view of bulk Mo2CF2, and (c) a side view of the monolayer (left), bilayer (middle) and trilayer (right) nanosheets of Mo2CF2.

The electronic band structures of bulk and 2D layered Mo₂CF₂ were calculated based on density functional theory (DFT) within the generalized gradient approximation (GGA) using the Perdew–Burke–Ernzerhof (PBE) functional. The calculations were implemented in the CASTEP code (Segall et al., 2002; Accelrys, 2010) with a sufficiently high plane-wave basis cut-off of 500 eV. In all calculations, a 551 Monkhorst–Pack k-point grid was used to generate the initial charge density.

The optical properties of the bulk and 2D layered Mo₂CF₂ were extracted from the frequency-dependent com­plex di­elec­tric function after applying a scissors correction to account for the excited-state nature of the optical properties. The com­plex dielectric function represents the linear response of the system to an external electromagnetic field and consists of a real and imaginary part as follows:

where ω is the optical frequency and ɛ₁(ω) and ɛ₂(ω) are the real and imaginary parts of the dielectric function, respectively. The real part ɛ₁(ω) of the dielectric function can be obtained from the imaginary part ɛ₂(ω) using the Kramers–Kronig relationships (Hutchings et al., 1992; Kronig, 1926; Kramers, 1927).

where P is the principal value, η is an infinitesimal com­plex shift with a value of 0.1 and ω is the frequency over which the equation is being integrated. From the frequency-dependent com­plex dielectric function, other optical parameters, such as the absorption coefficient α(ω), refractive index n(ω), reflectivity R(ω) (Qiu et al., 2018) and conductivity (σ) (Accelrys, 2010), were calculated using the following equations, where c is the speed of light:

3. Results and discussion

3.1. Crystal structure and electronic band structure

The unit-cell parameters and bond lengths for the bulk and 2D layered Mo₂CF₂ are summarized in Table 1. Our result for the monolayer is in good agreement with previous reports that numerically calculated the electronic structure of monolayer Mo₂CF₂ (Khazaei et al., 2014). Experimental results for the band gap energy, unit-cell parameters, and bond lengths of bulk and 2D layered Mo₂CF₂ are still lacking.

Figs. 2(a)–2(d) show the electronic band structures of bulk and 2D layered Mo₂CF₂ calculated along the high-symmetry k-points path G–A–H–K–G–M–L–H in the first Brillouin zone. In these figures, the valence band maxima are shifted to zero energy. The band structures exhibit similar band shapes, particularly for the valence and conduction bands. All the materials are seen to be indirect band gap semiconductors. The maximum of the valence band and the minimum of the conduction band of the monolayer and multilayer are located at the k-point between G and K, while the bulk has the band gap located at the k-point between H and A.

Figure 2 Electronic band structures of (a) bulk, (b) monolayer, (c) bilayer and (d) trilayer Mo2CF2

The band gap energies of the monolayer, bilayer, trilayer and bulk Mo₂CF₂ are 0.278, 0.258, 0.249 and 0.237 eV, respectively, as summarized in Table 1. The 0.278 eV band gap energy obtained from our calculations for the monolayer is in good agreement with the previously reported band gap energy of 0.27 eV calculated using GGA–PBE (Khazaei et al., 2014). In general, the band gap energy decreases as the number of layers is increased. The decrease in band gap energy can be attributed to inter­layer coupling, which results in the splitting of the bands. As can be seen in Figs. 2(b) (monolayer), 2(c) (bilayer) and 2(d) (trilayer), band splitting increases progressively from the monolayer to the trilayer, and the splitting depends on the number of layers. As the number of layers increases, the splitting of bands due to the stronger inter­layer coupling results in a decrease in the band gap energy. In com­parison, band splitting in the bulk Mo₂CF₂ is relatively small, which indicates that the couplings in the bulk are weak van der Waals inter­actions. These results indicate that the band gap of 2D layered Mo₂CF₂ could be engineered by controlling the number of layers. The ability to manipulate the band gap energy makes Mo₂CF₂ a promising material for applications in the field of electronic devices.

The total and partial density of states for the bulk and 2D layered Mo₂CF₂ are shown in Fig. 3. The valence band maximum and conduction band minimum are mainly com­posed of Mo-d states with a small overlap with C-p and F-p states. The Mo-d states also play a dominant role in the conduction band above the Fermi level, which confirms the partially occupied Mo²⁺ 4d² orbital.

Figure 3 Total and partial density of states for (a) bulk, (b) monolayer, (c) bilayer and (d) trilayer Mo2CF2. The dashed lines represent the Fermi level.

3.2. Optical properties

Fig. 4(a) shows the real part of the dielectric function, ɛ₁(ω), for the bulk and 2D layered Mo₂CF₂. The calculated values of ɛ₁(0) are 5.76, 10.58 and 1.42 eV for the monolayer, bilayer and trilayer Mo₂CF₂, respectively. From 0 to 6 eV, the intensity of the peaks is seen to increase as the number of layers increases. The maximum value for ɛ₁(ω) is achieved at around 0.67 eV for all the materials. The higher value of ɛ₁(ω) shows a greater ability for the polarization of low incident photon energy as the number of layers increases. Moving towards higher incident photon energy, an inflection point is observed around 6 eV, where ɛ₁(ω) takes on negative values. Above 6 eV, the intensity of the peaks appears to decrease (becomes more negative) as the number of layers increases. In the photon energy inter­vals 0.68–2.19, 3.49–6.68 and 7.30–8.31 eV, the bulk and 2D layered Mo₂CF₂ behave as a metal owing to anomalous dispersion. Dispersion is the property of materials whereby the refractive index changes as a function of wavelength. In normal dispersion, the refractive index increases as the photon energy increases (wavelength decreases), meaning that longer wavelengths are bent less com­pared to shorter wavelengths. The anomalous dispersion is confirmed by the plot of the refractive index as a function of photon energy [Fig. 4(b)]. Here, the refractive index decreases as the photon energy increases in the photon energy inter­vals 0.76–2.41, 3.66–6.89 and 7.43–8.94 eV. In normal dispersion, the refractive index should increase as the photon energy increases, as observed in the ranges 0–0.76, 2.41–3.66 and 6.89–7.43 eV. It is also inter­esting to note that when the incident photon energy is greater than 8.52 eV, the value of the refractive index is less than one, which is characteristic of metals. Comparing the refractive index values of the 2D layered Mo₂CF₂, the refractive index can be increased by increasing the number of layers. These results suggest that the static dielectric constant and the optical dispersion characteristics of the 2D layered Mo₂CF₂ can also be manipulated by controlling the number of layers.

Figure 4 (a) Real part of the dielectric function [ɛ1(ω)] and (b) refractive index (n) as a function of incident photon energy for bulk and 2D layered Mo2CF2.

The imaginary part of the dielectric function, ɛ₂(ω), is shown in Fig. 5(a). This com­ponent is related to the transitions between the valence and conduction bands, and therefore to the electronic structure of Mo₂CF₂ and the absorption of the incident photons. The optical band gaps of the bulk and 2D layered Mo₂CF₂ can then be estimated from ɛ₂(ω) and these are 0.220, 0.178 and 0.136 eV for the monolayer, bilayer and trilayer Mo₂CF₂, respectively. These optical band gap energies are smaller than the electronic band gap energies obtained from the electronic structures (and summarized in Table 1). The discrepancy comes from the Coulombic inter­action between electrons in the conduction band and holes in the valence band, as well as the exclusion of excitonic effects in the approximation (Cadatal-Raduban et al., 2020). Nevertheless, a similar trend to the electronic band gap energy is observed, wherein the optical band gap decreased as the number of layers increased. Above the optical band gap energy, a sharp rise in the intensity of ɛ₂(ω) is observed, with its peak appearing at 1.12 eV for all the materials. The peak corresponds to the electron transitions between the Mo-4d states to the Mo-5d states, as indicated by the density of states of Mo₂CF₂ (Fig. 3). The absorption coefficient and extinction coefficient of bulk and 2D layered Mo₂CF₂ is shown in Figs. 5(b) and 5(c), respectively. Regardless of the number of layers, Mo₂CF₂ is seen to be absorbing over a broad range of photon energies up to the vacuum ultraviolet region (greater than 6 eV photon energy or less than 200 nm wavelength), with a lower photon energy cut-off of 0.429, 0.387 and 0.345 eV for the monolayer, bilayer and trilayer nanosheets, respectively, which is in the mid-infrared wavelength region (wavelengths of about 2890, 3204 and 3594 nm for the monolayer, bilayer and trilayer nanosheets, respectively). Its peak absorption range is in the vacuum ultraviolet region from about 6 to 11 eV (wavelengths of about 207 to 112 nm), with an absorption peak at around 7.9 eV (157 nm). The extinction coefficient measures the loss of photon energy due to absorption and scattering, and therefore mimics the trend of ɛ₂(ω). Like the trend observed for ɛ₂(ω), where the intensity of ɛ₂(ω) increased as the number of layers increased, the value of the absorption and extinction coefficients also increased as a function of the number of layers. This indicates that the absorption of Mo₂CF₂ can also be manipulated by varying the number of layers.

Figure 5 (a) Imaginary part of the dielectric function [ɛ2(ω)], (b) absorption coefficient and (c) extinction coefficient (k) as a function of incident photon energy for bulk and 2D layered Mo2CF2.

Fig. 6 shows the reflectivity of bulk and 2D layered Mo₂CF₂. The reflectivity of the bilayer and trilayer Mo₂CF₂ are 0.28 and 0.35 at 0 eV, which means that about 28 and 35% of the incident light is reflected. A relatively low reflectivity is observed as the incident photon energy increases. In general, the reflectivity has a decreasing trend at photon energies between about 5 and 12 eV (about 248 and 103 nm). As reflectivity defines the ability of a material to reflect the incident photons, Mo₂CF₂ could be suitable as an antireflective coating, especially in the vacuum ultraviolet wavelength region. Furthermore, for this purpose, a smaller number of layers appears to be more advantageous (for example, a monolayer com­pared to a trilayer) as the general trend is that the reflectivity decreases with a decrease in the number of layers.

Figure 6 Reflectivity of bulk and 2D layered Mo2CF2.

Fig. 7 shows the optical conductivity of bulk and 2D layered Mo₂CF₂. The optical conductivity is derived from ɛ₂(ω) and therefore displays a similar trend com­pared to the absorption and extinction coefficient spectra [Figs. 5(b) and 5(c)]. Optical conductivity peaks are observed around 0.76–2.41, 3.66–6.89 and 7.43–8.94 eV. The value of ɛ₁(ω) is negative [Fig. 4(a)] and the materials display anomalous dispersion [Fig. 4(b)] within these energy ranges, affirming the metallic behavior of Mo₂CF₂ at these energy ranges.

Figure 7 Optical conductivity of bulk and 2D layered Mo2CF2.

4. Conclusions

Using first principles density functional theory within the generalized gradient approximation (GGA) and the Perdew–Burke–Ernzerhof (PBE) functional, the electronic structure and optical properties of bulk and 2D layered (monolayer, bilayer and trilayer) Mo₂CF₂ were studied. The band gap energy of the 2D layered Mo₂CF₂ decreased as the number of layers increased due to inter­layer coupling, which resulted in the splitting of the bands. Investigation of the optical properties of Mo₂CF₂ revealed that it behaves as a metal with an anomalous dispersion in the photon energy inter­vals of 0.68–2.19, 3.49–6.68 and 7.30–8.31 eV. Mo₂CF₂ also exhibited a high optical conductivity within these energy inter­vals. Regardless of the number of layers, Mo₂CF₂ was seen to be absorbing over a broad range of photon energies up to the vacuum ultraviolet region (greater than 6 eV photon energy or less than 200 nm wavelength), with a lower photon energy cut-off of 0.429 (2890), 0.387 (3204) and 0.345 (3594 nm) for the monolayer, bilayer and trilayer nanosheets, respectively, which is in the mid-infrared wavelength region. Its peak absorption range is in the vacuum ultraviolet region from about 6 to 11 eV (wavelengths of about 207 to 112 nm). A relatively low reflectivity is observed as the incident photon energy increases, particularly at photon energies between about 5 to 12 eV (about 248 to 103 nm). The band gap energy, static dielectric constant, optical dispersion, absorption, extinction coefficient, reflectivity, and conductivity of the 2D layered Mo₂CF₂ can be manipulated by controlling the number of layers. The unique behavior of its optical properties along with the ability to control its electronic and optical properties indicate the huge potential of 2D layered Mo₂CF₂ for various applications in the field of electronic devices.