A Cost-Effective Long-Wave Infrared Detector Material Based on Graphene@PtSe₂/HfSe₂ Bidirectional Heterostructure: A First-Principles Study

Abstract

The Graphene@PtSe₂ heterostructure is an excellent long-wave infrared detection material. However, the expensive cost of PtSe₂ prevents its widespread use in infrared detection. In this paper, Hf was used to partially replace Pt to form Graphene@(PtSe₂)_n(HfSe₂)_4−n (n = 1, 2, and 3) bidirectional heterostructures consisting of graphene and lateral PtSe₂/HfSe₂ composites based on first-principles calculations. Then, the new bidirectional heterostructures were compared with heterostructures formed by graphene with pure MSe₂ (M = Pt, Hf). It was found that the band gaps of the bidirectional heterostructures were between those of Graphene@PtSe₂ and Graphene@HfSe₂. Among these heterostructures, the Graphene@(PtSe₂)₃(HfSe₂)₁ bidirectional heterostructure has almost the same optical absorption properties in the infrared wavelength region of 1.33~40 µm as the Graphene@PtSe₂ heterostructure, and it improves the absorption in the near-infrared wavelength region of 0.75~1.33 µm. Such a designment may bring the material costs down (since PtSe₂ costs approximately five times more than HfSe₂). This study on the designment of the bidirectional Graphene@(PtSe₂)₃(HfSe₂)₁ heterostructure also illustrates a cost-effective design method for Pt-based IR detectors.

1. Introduction

Transition metal dihalides (TMDs) have been investigated intensely in recent years, due to their fascinating electrical [1,2], mechanical [3], and optical characteristics [4,5]. They could provide the basic building blocks for a new generation of nanoelectronic devices based on 2D van der Waals (vdW) crystals [6,7]. Motivated by their prominent properties, numerous studies have been focused on the research of vdW heterostructures, such as PtSe₂/GaAs [8], MoS₂/WSe₂ [9], graphene/MoS₂ [10], and WSe₂/HfSe₂ [11]. It is widely demonstrated that constructing hybrid heterostructures is a potential way to fabricate nanoelectronic and optoelectronic devices with excellent performance [12,13].

Notably, PtSe₂ is an attractive material for broadband mid-infrared detectors due to its relatively high carrier mobility, superior ambient stability, and narrow-band structure [14,15]. Since it was discovered in 2004 [16], graphene has been widely used in a large variety of fields, owing to its mechanical as well as optical properties and high conductivity [17,18,19,20,21,22,23,24,25]. There are two components to graphene’s low energy conductivity: intraband and interband contributions [26,27]. According to the zero gap of graphene, which limits its development and applications, Luo et al. [28] proposed that, by creating a Gr@PtSe₂ van der Waals heterostructure, the zero band gap of graphene could be opened, thus further expanding its response range. Later, Long et al. [29] experimentally corroborated Luo et al.’s proposal. They found that Gr@PtSe₂ shows a strong optical response (300 mA/W) at long wavelengths of 10.6 µm, indicating that it is a highly competitive candidate for long-wavelength infrared detectors. However, the high cost of PtSe₂ prevents its widespread use in photodetectors [30,31]. Is there a method to lower the cost without compromising performance? Doping is an effective method [32,33]. It has been reported that HfSe₂, with the same structure as PtSe₂, has greater carrier mobility, good optical sensitivity, and a low cost [34,35]. Similar to PtSe₂, HfSe₂ can also open the band gap of graphene [36]. Despite the fact that Zr and Hf have almost similar properties [37], Hf has better infrared light absorption properties (Figures S1 and S2). Therefore, we propose partially replacing Pt with Hf in order to reduce the cost of Gr@PtSe₂ materials.

Based on first-principles calculations, we investigated the structural, electrical, and optical properties of bidirectional heterostructures composed of graphene and lateral PtSe₂/HfSe₂ composites. We considered three cases with Hf doping ratios (Hf replacing Pt) of 75%, 50%, and 25% for (PtSe₂)_n(HfSe₂)_4−n (n = 1, 2, and 3), and the bidirectional heterostructures were Graphene@(PtSe₂)_n(HfSe₂)_4−n (n = 1, 2, and 3), abbreviated below as Pt_nHf_4−n and Gr@Pt_nHf_4−n, respectively. For comparison purposes, the results of heterostructure simulations for the production of graphene and pure PtSe₂ or HfSe₂ monolayers were also considered. We discovered that a bidirectional Gr@Pt₃Hf₁ heterostructure constituted of a partial (25%) substitution of Pt with Hf is an effective method of reducing material costs.

2. Computational Methods

The calculations were carried out utilizing a first-principles framework with a plane-wave basis set, as implemented in the Vienna Ab initio Simulation Package (VASP) code (VASP.5.4.4, Dr. Georg Kresse, Vienna, Austria) [38,39] and based on density functional theory under the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional [40]. Grimme’s van der Waals correction (DFT-D3 with pair approximation [41]), which could offer a fair description of long-range vdW interactions, has been used in order to accurately characterize weak van der Waals interactions [42]. To prevent artificial interactions between periodic pictures, the z-direction vacuum space is adjusted to 25 Å. The kinetic energy cutoff for the plane waves is set at 520 eV. Brillouin zone integration is performed using 3 × 4 × 1 Monkhorst–Pack k-grids for structure optimization and energy calculation, while 4 × 7 × 1 Monkhorst–Pack k-grids are used for the calculation of optical properties. The geometric structures are completely relaxed until the energy and forces are converged to 10⁻⁶ eV and 0.01 eV/Å, respectively.

The optical propagation across a material is described using the dielectric function and the absorption coefficient [43,44,45]. The formula is as follows:

$$\epsilon (\omega )={\epsilon }_1(\omega )+i{\epsilon }_2(\omega )$$

(1)

The dielectric function, $\epsilon$, is composed of two components: the real portion, ${\epsilon }_1$, and the imaginary part, ${\epsilon }_2$. The real component denotes the material’s ability to retain energy and is calculated using the Kramers–Kronig formula:

$${\epsilon }_1(\omega )=1+\frac{2}{\pi }P{\displaystyle {\int }_0^{\infty }\frac{{\epsilon }_2^{\alpha \beta }\left({\omega }^{\prime }\right){\omega }^{\prime }}{{\omega }^{\prime 2}-{\omega }^2+i\eta }}d{\omega }^{\prime },$$

(2)

where P stands for the integral’s primary value [46].

The loss factor is represented by the imaginary component, ${\epsilon }_2$, in the following equation:

$${\epsilon }_2(\omega )=\frac{4{\pi }^2{e}^2}{\Omega }\underset{q\to 0}{\lim }{\displaystyle \sum _{c:v:k}2}{\omega }_k\delta \left({ϵ}_{ck}-{ϵ}_{vk}-\omega \right)\times \langle u_{ck+e_{\alpha }q}\mid u_{vk}\rangle {\langle u_{ck+e_{\beta }q}\mid u_{vk}\rangle }^{*},$$

(3)

where Ω represents the volume, α and β represent the Cartesian components, e_α and e_β represent the unit vectors, υ and c represent matrix elements of the transition from the valence band state ($u_{\upsilon k}$) to the conduction band state ($u_{ck}$), and ${\epsilon }_{ck}$ and ${\epsilon }_{uk}$ represent the energies of the conduction and valence bands, respectively [46].

The absorption coefficient, α(ω), is derived from the above two equations [46]:

$$\alpha (\omega )=\frac{\sqrt{2}\omega }{c}{\left\{{\left[{\epsilon }_1^2(\omega )+{\epsilon }_2^2(\omega )\right]}^{\frac{1}{2}}-{\epsilon }_1(\omega )\right\}}^{\frac{1}{2}}$$

(4)

3. Results

3.1. Geometrical Structures

The optimized lattice constants of graphene, 1T-PtSe₂, and 1T-HfSe₂ were 2.460 Å, 3.727 Å, and 3.752 Å, respectively, which are generally consistent with previous research [47,48]. The lattice mismatch of 0.66% for MSe₂ (M = Pt, Hf) demonstrates that the lattice mismatch of PtSe₂ and HfSe₂ was suitable for the construction of transverse heterojunctions using a monolayer of these two materials as substrates. To lessen the impact on the computations caused by the symmetry of the hexagonal phase structure, as seen in Figure S3, the hexagonal cell was transformed into a rectangular lattice cell. As shown in Figure 1, the long-edge lattice constants in the cut structure are represented by a, while the short-edge lattice constants are represented by b. The bidirectional Gr@Pt_nHf_4−n heterostructure was constructed using the most stable stacking technique [28]. To construct the Pt_nHf_4−n lateral heterostructures, we used a 2 × 2 supercell, and a 3 × 3 graphene monolayer was chosen to match the 2 × 2 Pt_nHf_4−n lateral heterostructures.

The stable structural information of Gr@Pt_nHf_4−n is shown in

Table 1. The lattice constants (Å), bond lengths (Å) of Pt–Se and Hf–Se, and lattice mismatch ratios of Gr@Pt_nHf_4−n.

Materials	Gr@PtSe2	Gr@Pt1Hf3	Gr@Pt2Hf2	Gr@Pt3Hf1	Gr@HfSe2
Lattice constants (Å)	a = 12.84 b = 7.41	a = 12.79 b = 7.42	a = 12.78 b = 7.42	a = 12.77 b = 7.41	a = 12.85 b = 7.43
dPt-Se (Å), dHf-Se (Å)	2.52, -	2.55, 2.67	2.54, 2.67	2.53, 2.63	-, 2.70
Lattice mismatch ratios	0.54%	1.4%	1.4%	1.4%	1.3%

. As shown in Table 1, the bidirectional structure Gr@Pt_nHf_4−n had a stretched Pt–Se bond and a compressed Hf–Se bond compared to Gr@PtSe₂ and Gr@HfSe₂, resulting in decreased lattice constants for Gr@Pt₁Hf₃, Gr@Pt₂Hf₂, and Gr@Pt₃Hf₁. To quantitatively evaluate the interaction between the graphene and Pt_nHf_4−n, the interface binding energy (E_Δ) was also calculated according to the expression below:

$$E_{\mathsf{\Delta }}=\left(E_{Gr@P{t}_{n}H{f}_{4-n}}-E_{P{t}_{n}H{f}_{4-n}}-E_{Gr}\right)/N_C,$$

(5)

where E_{Gr@PtnHf4−n}, E_PtnHf4−n, and E_Gr are the total energies of the bidirectional heterostructures of Gr@Pt_nHf_4−n, isolated lateral heterostructures of the Pt_nHf_4−n monolayer, and isolated graphene monolayer, respectively. N_C is the number of carbon atoms in the supercell. The binding energy per C atom, as a function of the interlayer distance (d) for Gr@Pt_nHf_4−n, Gr@PtSe₂, and Gr@HfSe₂, is plotted in Figure 2. As observed in Figure 2, −E_Δ is negative, indicating that the heterostructure arrangement between the graphene monolayer and the Pt_nHf_4−n substrate was stable, and the binding energy varied significantly as the interlayer distance between the graphene and Pt_nHf_4−n layers varied. The most stable interlayer distances for Gr@Pt_nHf_4−n varied between 3.3~3.5 Å, and Gr@Pt₃Hf₁ had lower binding energy than Gr@Pt₁Hf₃ and Gr@Pt₂Hf₂ for a given interlayer distance. In addition, when the structure was stable, the binding energy of Gr@Pt₃Hf₁ was lower than that of Gr@Pt₁Hf₃ and Gr@Pt₂Hf₂. Graphene adsorbed better on Pt₃Hf₁ substrates than on Pt₁Hf₃ and Pt₂Hf₂ substrates, as shown by the higher energy stability level of Gr@Pt₃Hf₁.

3.2. Electronic Structures of Gr@Pt_nHf_4−n

The electrical structure of Gr@Pt_nHf_4−n is investigated in this section. The overall characteristics of the band structure obtained from the PBE and HSE06 generalization calculations were similar, except that the band gap value obtained from the HSE06 generalization calculations was almost doubled. Additionally, constrained by computing resources, mostly PBE was used in the following computations. The band structures (Figure 3), the total density of states (TDOS), and the projected density of states (PDOS) of monolayer Pt₁Hf₃, Pt₂Hf₂, Pt₃Hf₁, graphene, PtSe₂, and HfSe₂ were determined (Figure 4). In Figure 3d, the band structure of pristine graphene shows a typical Dirac point located at the point of the Brillouin zone. The projected density of states (PDOS) illuminates that the states of graphene are delocalized around the Fermi level. The band structure of Pt_nHf_4−n exhibits semiconductor characteristics.

Next, the projected band structure of the five heterostructures, Gr@Pt₁Hf₃, Gr@Pt₂Hf₂, Gr@Pt₃Hf₁, Gr@PtSe₂, and Gr@HfSe₂, were calculated. Compared to Figure 3, the band structure of the Gr@Pt_nHf_4−n bidirectional heterostructures were almost a superposition of two monolayer bands, indicating that the bidirectional heterostructure preserves the good electronic characteristics of its monolayer material and also extends the enriched properties. As seen in Figure 5, the band gaps of Gr@PtSe₂ and Gr@HfSe₂ were 0.0203 eV and 0.0853 eV, respectively. This is in broad accord with previously published calculations [28,36]. Band gaps of the combined structure of Gr@Pt₁Hf₃, Gr@Pt₂Hf₂, and Gr@Pt₃Hf₁ were 0.0182 eV, 0.0351 eV, and 0.0397 eV, respectively. According to the calculations, the band gaps of the bidirectional heterostructures, Gr@Pt₁Hf₃, Gr@Pt₂Hf₂, and Gr@Pt₃Hf₁, were all between the band gaps of Gr@PtSe₂ and Gr@HfSe₂. The results showed that the band gaps of the bidirectional heterostructures grew progressively as the percentage of Pt increased, with Gr@Pt₁Hf₃ and Gr@Pt₂Hf₂ showing an indirect band gap between point Y and point Γ, while Gr@Pt₃Hf₁ exhibited a direct band gap at point Γ.

For the bidirectional heterostructures of Gr@Pt_nHf_4−n, with the Bader charge analysis (

Table 2. Interfacial distance, d (Å), and acquired charges, (e), of graphene in the fully optimized configurations of the Gr@Pt₁Hf₃, Gr@Pt₂Hf₂, Gr@Pt₃Hf₁, Gr@PtSe₂, and Gr@HfSe₂ heterostructures, respectively.

Materials	d (Å)	Acquired Charges in Graphene (e)
Gr@Pt1Hf3	3.42	−0.20
Gr@Pt2Hf2	3.31	−0.26
Gr@Pt3Hf1	3.27	−0.28
Gr@PtSe2	3.46	−0.32
Gr@HfSe2	3.41	−0.12

), we find the electronic charge transfer from graphene to the top Se atoms when graphene adheres to Se-terminated substrates. A more evident view of the charge redistribution and transfer between the graphene and Pt_nHf_4−n polar surface can be obtained by calculating the charge density differences before and after the charge transfer. Such a charge density difference (Δρ) can be calculated using the following equation:

$$\mathsf{\Delta }\rho (z)={\rho }_{Gr@P{t}_{n}H{f}_{4-n}}-{\rho }_{P{t}_{n}H{f}_{4-n}}-{\rho }_{Gr},$$

(6)

where ρGr@Pt_nHf_4−n, ρPt_nHf_4−n, and ρ_Gr are the total plane-averaged electron densities of the bidirectional heterostructures of Gr@Pt_nHf_4−n, the individual lateral heterostructures of Pt_nHf_4−n, and the graphene monolayer, respectively, which are shown in Figure 6. The charge rearrangements following the development of the heterostructures, as seen in Figure 6, indicate that the charge transfers in the five structures are comparable and mostly occur near the interface (interlayer transfer). In these heterostructures, electrons are lost on the graphene side, while they are mostly grouped on the Pt_nHf_4−n side, with a tiny amount clustered on the graphene side. It is found that Δρ(z) < 0 near the graphene and Δρ(z) > 0 at the top of the Se atoms of the Pt_nHf_4−n slab substrate. This implies that the electrons are transferred from the graphene to the Pt_nHf_4−n layer, resulting in electron–hole (e–h) separation. A polarized field pointing from the graphene layer to the Pt_nHf_4−n substrate is generated. In each of the five configurations, there is a distinct transfer of electrons from graphene to Pt_nHf_4−n, but the charge collected on the Pt_nHf_4−n differs. In short, as long as the graphene monolayer adheres to the Pt_nHf_4−n substrate, electrons will gather in the region near the Pt_nHf_4−n, while holes will accumulate on the graphene monolayer, generating e–h pairs.

3.3. Optical Properties of Gr@Pt_nHf_4−n

In 2D vdW heterojunctions, it is known that interfacial interaction, charge redistribution, and e–h pair separation are often followed by an enhancement in optical transitions [49]. With the help of e–h pair separation, the light absorption coefficient may increase in the heterostructures. Figure 7 depicts the optical characteristics of the Gr@PtSe₂, Gr@HfSe₂, and Gr@Pt_nHf_4−n heterostructures. Compared to Gr@PtSe₂ and Gr@Pt_nHf_4−n, Gr@HfSe₂ has poor optical absorption properties. Moreover, as the amount of Pt in the Gr@Pt₁Hf₃, Gr@Pt₂Hf₂, and Gr@Pt₃Hf₁ bidirectional heterostructures increases, the peak value of the optical absorption coefficient in the 1.3~40 µm wavelength region rises progressively, particularly in the 0.75~1.33 µm wavelength region, while the peak optical absorption values of Gr@Pt₃Hf₁ and Gr@PtSe₂ are similar. The enhanced light absorption may be ascribed to the increased density of Pt and Se states at the bottom of the conduction band. As mentioned before, the holes and electrons of the e–h pairs are located at the graphene monolayer and the Pt_nHf_4−n substrate, respectively. Under normal IR light, electrons in the p_z-orbital of graphene are excited to the d-orbitals of the Pt atoms and the p-orbitals of the Se atoms of the conduction band of the Pt₃Hf₁ substrate. In Figure 6, charge redistribution and transfer occur at the top of the Pt_nHf_4−n substrate in Gr@Pt_nHf_4−n. The charge decreases mostly near the C atoms and subsequently increases at the top of the Se atoms, forming e–h pairs at the interface. Consequently, a polarized field is generated, which guides the orientation of the graphene to the Pt_nHf_4−n [50]. It should be noted that the light absorption enhancement of the Gr@Pt₃Hf₁ heterostructure is larger than that of the Gr@Pt₁Hf₃ and Gr@Pt₂Hf₂ heterostructures, and it may also be related to the lower interlayer distance at the surface of the Gr@Pt₃Hf₁ heterostructure. Charge transport is affected by the relatively strong interlayer interaction between the graphene and Pt₃Hf₁ layers. This indicates that the interaction intensity between the interfaces in a heterostructure may also be an important factor in improving the optical absorption coefficient. We conclude that the interlayer coupling in the bidirectional heterojunction Gr@Pt_nHf_4−n is stronger and that the IR light absorption performance is greater with higher Pt concentrations.

The IR absorption fluctuation patterns of the five heterostructures in the 0.75~1.33 µm IR wavelength region show comparable properties. Combining the band structures of the bidirectional heterostructure of Gr@Pt_nHf_4−n (Figure 5a–c), we observed that the reduced band gaps of Gr@Pt₁Hf₃, Gr@Pt₂Hf₂, and Gr@Pt₃Hf₁ will increase their absorption coefficients in the near-infrared to a visible red range relative to Gr@PtSe₂. Particularly, in the 1.3~40 µm IR wavelength region, the optical absorption coefficient of Gr@Pt₃Hf₁ is larger than that of Gr@PtSe₂ in the near-infrared to visible red-light range (Figure 8). In combination with PDOS (Figure 8c,e), the peak of DOS at 0.6~1.2 eV for Gr@Pt₃Hf₁ is more than that of Gr@PtSe₂, and the interval corresponds to the region in which the optical absorption coefficient of Gr@Pt₃Hf₁ is greater than that of Gr@PtSe₂. Therefore, we propose that doping Hf atoms may be the reason why the electronic state of Gr@Pt₃Hf₁ is more active, leading to a relatively strong absorption peak in the 1.3~40 µm IR wavelength region of its absorption spectrum. This provides Gr@Pt₃Hf₁ to replace Gr@PtSe₂ in the NIR detector, allowing the detection range to be expanded from the NIR to the visible red range. Our findings indicate that the absorptive properties of Gr@Pt₃Hf₁ in the NIR range are almost the same as those of Gr@PtSe₂, but the absorptive properties in the 0.75~1.33 µm wavelength region in the NIR are greater than those of Gr@PtSe₂. This shows that the bidirectional heterostructure of Gr@Pt₃Hf₁ is a cost-effective design method.

4. Conclusions

In conclusion, we have analyzed the electrical and optical characteristics of the bidirectional heterostructure of Gr@Pt_nHf_4−n using first-principles calculations. It was found that the bidirectional heterostructures of Gr@Pt_nHf_4−n had similar band structures, and that the band gap of graphene was opened by Pt_nHf_4−n in the presence of an inhomogeneous electrostatic potential generated by Pt_nHf_4−n. The charge was transferred from graphene to Pt_nHf_4−n, and a polarized field was generated at the interface between graphene and Pt_nHf_4−n. As the percentage of Pt in Gr@Pt_nHf_4−n increased, the band gaps of Gr@Pt₁Hf₃, Gr@Pt₂Hf₂, and Gr@Pt₃Hf₁ continued to expand, and the infrared light absorption performance also improved. In particular, the optical absorption capacity of the Gr@Pt₃Hf₁ structure was equivalent to that of Gr@PtSe₂ in the near-infrared 1.3~40 µm range of wavelength, while it was superior to Gr@PtSe₂ in the near-infrared to the visible red-light wavelength band of 0.75~1.33 µm. These theoretical findings imply that the Gr@Pt₃Hf₁ structure is a design method that is equivalent to the Gr@PtSe₂ structure in terms of near-infrared detection performance, which may efficiently decrease material costs and expand the near-infrared light detection interval. These findings show that the bidirectional heterostructure of Gr@Pt₃Hf₁ may apply to large-scale infrared photodetectors.