Electrical field and biaxial strain tunable electronic properties of the PtSe₂/Hf₂CO₂ heterostructure

Abstract

The structure and electronic properties of two-dimensional vertical van der Waals PtSe₂/Hf₂CO₂ heterostructure have been investigated based on first-principles calculations. The results show that the PtSe₂ and Hf₂CO₂ monolayers form a type-I heterostructure with both the conduction band minimum (CBM) and valence band maximum (VBM) located at the Hf₂CO₂ layer. The electronic properties of PtSe₂/Hf₂CO₂ heterostructure can be effectively adjusted by applying external electric field or biaxial strain. The transition in band alignment from type-I to type-II can be manipulated by controlling the strength and direction of the electric field. Additionally, the transition from type-I to type-II have also taken place under the strains, and the band gap of the PtSe₂/Hf₂CO₂ heterostructure decreases with increasing the compressive or tensible strain. Under a strong strain of −8%, the PtSe₂/Hf₂CO₂ heterostructure can transform from semiconductor to metal. These findings provide a promising method to tune the electronic properties of PtSe₂/Hf₂CO₂ heterostructure and design a new vdW heterostructure in the applications for electronic and optoelectronic devices.

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1. Introduction

Two-dimensional (2D) van der Waals (vdW) materials with atomic layer thickness and tunable band gap have attracted great attention.^1,2 van der Waals heterostructures, fabricated by vertically stacking two different 2D materials together,^3–5 not only maintain the individual electronic properties of each material because of the weak interaction between layers, but also have some new physics at the interface,⁶ which offer a novel platform for innovative devices and applications, such as solar cells,⁷ tunneling transistor memory devices,⁸ etc. According to the band alignment, the vdW heterostructures can be classified as three types: type-I (straddling gap), type-II (staggered gap), and type-III (broken gap).⁹ In type-I heterostructures, both the conduction band minimum (CBM) and the valence band maximum (VBM) are located in the same material with the narrower bandgap. The quantum confinement of electrons and holes in the same region facilitates their radiative recombination, which is desirable in light-emitting-diodes (LEDs).¹⁰ For type-II heterostructure, the CBM and VBM exist in different layers, where the electrons and holes are spatially separated, thereby greatly decreasing the probability of recombination and facilitating efficient electron–hole separation for light detection and harvesting, which are highly desirable for photocatalytic and photovoltaic devices.^11,12 Different from type-I and type-II heterostructures, for type-III heterostructures, the VBM and CBM of one layer are both above the CBM of the other one,¹³ enabling a nonoverlapping band offset between two semiconductors that facilitates the transport of charge carriers from one energy band to another via a quantum tunneling process.^14,15 This band-to-band tunneling (BTBT) makes type-III vdW heterostructures well-suited for tunnel devices with high-speed operation and low-power consumption, such as TFETs or Esaki diodes.¹⁶ Notably, the types and the electronic properties of vdW heterostructure can be modulated by various methods, such as coupling interlayer distances,¹⁷ applying external electric fields,¹⁸ and applying biaxial strain,¹⁹ to obtain unique structures and performances. These charming findings suggest that stacking 2D materials into vdW heterostructures provides an effective way to design novel artificial materials with special characteristics.

Since Yury Gogotsi et al. successfully synthesized Mxenes in 2011,²⁰ the 2D MXene have attracted much interest from researchers, owing to its unique physicochemical characteristics and wide range of applications in supercapacitors,²¹ batteries,²² sensors,²³ catalysis,²⁴ optoelectronics.²⁵ Hf₂CO₂ is a classical MXene with a band gap of 1.0 eV (PBE) and 1.75 eV (HSE06).²⁶ It has a low thermal expansion coefficient, high carrier mobility, and high thermal conductivity,²⁷ which make it have promising applications in optoelectronics,²⁸ solar cells,²⁹ and gas sensors.³⁰ Inheriting the properties of isolated Hf₂CO₂, the Hf₂CO₂-based vdW heterostructures for opto-electronic device applications have also been investigated extensively. For example the Hf₂CO₂/MoS₂,³¹ Hf₂CO₂/WS₂,³² and Hf₂CO₂/GaN³³ vdW heterostructures have been suggested as potential photocatalysts for overall water splitting with appropriate band structure and high carrier mobility.

PtSe₂, as one kind of transition-metal dichalcogenide (TMDC), has attracted intense interest. It has a graphene-like structure with high stability³⁴ semimetallic electronic structures, and excellent photoelectric properties.³⁵ Additionally, external electric field³⁶ and strain³⁷ can effectively regulate its electronic properties, and make the indirect–direct bandgap transition and semiconductor-semimetal transition happen. These excellent characteristics of PtSe₂ monolayer have enabled its potential applications in various devices, including field effect transistors, gas sensors, and photocatalysts.^38–41

Although the preliminary researches on the electronic properties of the Hf₂CO₂-based and PtSe₂-based vdW heterostructures have maken great progresses, the study on the properties of PtSe₂/Hf₂CO₂ vdW heterostructure is very scarce. Therefore, in this work, the PtSe₂/Hf₂CO₂ heterostructure has been investigated via first-principles calculations. The effects of stacking pattern, external electric field, and biaxial strain on the electronic properties of the PtSe₂/Hf₂CO₂ vdW heterostructure were discussed. Our research results show that the PtSe₂/Hf₂CO₂ vdW heterostructure exhibits a type-I band alignment (straddling gap), which can offer the application for LEDs. We have also found that the applied external electric fields and biaxial strains are efficient means ofor adjusting its electronic properties, which can broaden the application of PtSe₂/Hf₂CO₂ vdW heterostructure. Our results are expected to provide theoretical guidance for the design of flexible nano-electronic or optoelectronic devices based on the PtSe₂/Hf₂CO₂ vdW heterostructure.

2. Computational method

All structure relaxations and electronic property calculations in our work were performed using density functional theory (DFT)⁴² in conjunction with plane-wave ultrasoft pseudopotential, as implemented in the Vienna ab initio simulation package (VASP).⁴³ The generalized gradient approximation (GGA) of the Perdew–Burke–Ernzerhof (PBE) function was employed to express the exchange–correlation energy.⁴⁴ The cut-off energy was set to 500 eV, and the first Brillouin zone sampling was carried out by using 4 × 4 × 1 for structure optimization and using 6 × 6 × 1 for electronic properties calculations, respectively. The lattice parameters and ionic positions were fully relaxed until the total energies and forces were less than 10⁻⁶ eV and 0.02 eV Å⁻¹, respectively. To avoid spurious interactions between periodic neighbour structures, a vacuum thickness of 20 Å was chosen. Besides, a dispersion-corrected DFT method of Grimme (DFT-D3) was employed to correctly describe the effect of a vdW interaction.⁴⁵ As the PBE functional usually underestimates the band gap value, the Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional was adopted for comparison.

3. Results and discussions

3.1. The pristine PtSe₂ and Hf₂CO₂ monolayers

Fig. 1a and b display the optimized structures of individual PtSe₂ and Hf₂CO₂ single layers. The relaxed lattice parameters of the pristine PtSe₂ and Hf₂CO₂ monolayers are 3.745 and 3.265 Å, respectively, which very well agree with the values in earlier theoretical and experimental findings.^32,37 The energy band structures of pristine PtSe₂ and Hf₂CO₂ monolayers are shown in Fig. 1c and d. Both PtSe₂ and Hf₂CO₂ monolayers exhibit indirect band gaps of 1.398/1.990 eV and 0.988/1.749 eV calculated by PBE/HSE06 functionals, respectively. The valence band maximum (VBM) and conduction band minimum (CBM) of PtSe₂ are located at Γ and Γ–M, respectively, while the VBM and CBM of Hf₂CO₂ are located at Γ and M, respectively. Fig. 1e demonstrates that in the PtSe₂ monolayer, the CBM is mainly contributed by the Se-p and Pt-d states, while the VBM is largely contributed by the Se-p state. Fig. 1f shows that in the Hf₂CO₂ monolayer, the VBM is contributed by Hf-d state, and the CBM is primarily contributed by the C-p state. These calculated outcomes are consistent with previous studies.^32,33,46,47

Fig. 1 (a) and (b) Top and side views of PtSe₂ and Hf₂CO₂ monolayers. (c) and (d) The band structures calculated by the PBE and HSE06 methods, respectively. (e) and (f) Corresponding partial densities of states (PDOS) of the primitive cells of PtSe₂ and Hf₂CO₂ monolayers, calculated by PBE method.

3.2. Structural and electronic properties of PtSe₂/Hf₂CO₂ vdW heterostructures

The supercell of PtSe₂ and 2 × 2 supercell of Hf₂CO₂ are used to construct the PtSe₂/Hf₂CO₂ heterostructure. The lattice mismatch is only 0.29%, making it more possible to achieve experimental synthesis of the PtSe₂/Hf₂CO₂ heterostructure. In Fig. 2, three distinct stacking configurations of PtSe₂/Hf₂CO₂ heterostructure were studied. These configurations were created by shifting the relative positions of two layers in the horizontal direction. The binding energy E_b were calculated to estimate the thermodynamic stability of the system. It is defined as follows:

E_b = [(E_total − E_PtSe2 − E_Hf2CO2)/S] (1)

where E_total, E_PtSe2and E_Hf2CO2 represent the total energy of the heterostructure, PtSe₂ monolayer, and Hf₂CO₂ monolayer, respectively, and S is the interface area of the heterostructure. The optimized lattice parameters, interlayer distances, bond lengths, and calculated binding energies are listed in Table 1. The results demonstrated no significant variation in the bond length of these three structures, and the interlayer distances are approximately 3.1 Å. The calculated binding energies E_b are −23.082, −22.959 and −22.887 meV Å⁻² for stacking I, II, and III patterns, respectively, which are lower than PtSe₂/GaN, PtSe₂/Arsenene, and etc.,^48–53 confirming that PtSe₂/Hf₂CO₂ bilayer forms a stable vdW heterostructure. In addition, the band gaps of stacking I to III are 0.965, 0.964, and 0.957 eV respectively, calculated by the PBE method, as shown in Fig. S2.† Therefore, it can be concluded that the structural and electronic properties of PtSe₂/Hf₂CO₂ vdW heterostructure are not sensitive to diverse stacking patterns. For the ease of analysis, stacking I has been selected for subsequent calculations due to its relatively small binding energy.

Fig. 2 Top and side views of three different stacking configurations of the PtSe₂/Hf₂CO₂ heterostructure: (a) stacking I, (b) stacking II, (c) stacking III.

Table 1 Lattice parameter (a), bond length (L_x–x), band energy (E_g), interlayer distance (d) and binding energy (E_b)

System	Type	a (Å)	LPt–Se (Å)	LHf–O (Å)	LHf–C (Å)	PBE/HSE06 Eg (eV)	d (Å)	Eb (meV Å^−2)
PtSe2	—	3.748	2.528	—	—	1.398/1.990	—	—
Hf2CO2	—	3.265	—	2.100	2.335	0.988/1.749	—	—
PtSe2/Hf2CO2	I	6.492	2.529	2.096	2.324	0.965/1.788	3.105	−23.082
	II	6.491	2.529	2.094	2.328	0.964/—	3.126	−22.959
	III	6.491	2.530	2.094	2.327	0.957/—	3.130	−22.887

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Fig. 3a and b show the band structures of the PtSe₂/Hf₂CO₂ heterostructure with stacking I configuration, calculated by the PBE/HSE06 functional. Both the CBM and the VBM are contributed by Hf₂CO₂ layer. The band gap of the heterostructure is respectively 0.965/1.788 eV using PBE/HSE06 functional. Fig. 3c displays the band-resolved charge densities of the CBM and VBM for the PtSe₂/Hf₂CO₂ vdW heterostructure. The results indicate that the PtSe₂/Hf₂CO₂ vdW heterostructure exhibits a type-I band alignment. Besides, we found that the PBE functional has indeed underestimated the band gap value, but the band structure obtained from PBE has almost exhibited the same trend to that obtained from HSE06 functional.

Fig. 3 (a) and (b) The projected band structures of PtSe₂/Hf₂CO₂ heterostructure calculated by PBE and HSE06 method, respectively, the Fermi level is set as zero, the red and blue lines represent PtSe₂ and Hf₂CO₂, respectively. (c) The partial charge densities corresponding to the VBM and CBM of the PtSe₂/Hf₂CO₂ heterostructure.

Next, the work function is employed to deeply understand the band alignment of the PtSe₂/Hf₂CO₂ vdW heterostructure. The definition of work function (Φ) is

Φ = E_vac − E_F (2)

where E_vac and E_F represent the vacuum level and Fermi level, respectively. The calculated work function of the PtSe₂ layer and the Hf₂CO₂ layer are 6.03 and 5.67 eV, respectively, shown in Table 2. The electrons move from Hf₂CO₂ layer to the PtSe₂ layer due to the smaller work function of Hf₂CO₂ layer, resulting in an electric field (E_in) in the interlayer, which, in turn, impedes the transfer of charge and ultimately establishes an electrostatic equilibrium, as shown in Fig. 4a. As a result of charge transfer, the Fermi level of the PtSe₂ layer moves up while the Fermi level of the Hf₂CO₂ layer goes down for equilibrium Fermi level. Consequently, the work function of the heterostructure is calculated to be 5.83 eV.

Table 2 Edges of VBM and CBM and work function for materials

System		VBM (eV)	CBM (eV)	Work function (eV)
Isolated	PtSe2	−4.25	−6.24	6.03
	Hf2CO2	−4.28	−0.68	5.67
PtSe2/Hf2CO2	PtSe2	−4.28	−6.08	5.83
	Hf2CO2	−4.23	−6.29

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Fig. 4 (a) The band alignment of PtSe₂/Hf₂CO₂ vdW heterostructure., and E_g are the band gaps of PtSe₂ layer, Hf₂CO₂ layer and PtSe₂/Hf₂CO₂ heterostructure, respectively. (b) The side and top views of the 3D isosurface with charge density difference for PtSe₂/Hf₂CO₂ heterostructure. The cyan and yellow regions represent the electrons depletion and accumulation, respectively. The charge density value corresponding to the isosurfaces drawn is 0.805e Å⁻³. (c) The planar-averaged charge density difference for PtSe₂/Hf₂CO₂ heterostructure.

To visualize the charge transfer and charge redistribution, the differential charge density (Δρ) have been studied. The Δρ was determined as:

Δρ = ρ_PtSe2/Hf2CO2 − ρ_PtSe2 − ρ_Hf2CO2 (3)

where ρ_PtSe2/Hf2CO2, ρ_PtSe2, and ρ_Hf2CO2 are the charge densities of the PtSe₂/Hf₂CO₂ heterostructure and isolated PtSe₂ and Hf₂CO₂ monolayers, respectively. The 3D charge density difference is depicted in Fig. 4b, with the cyan area signifying electron gain and the yellow area signifying electron loss. The electrons and holes are located on the PtSe₂ layer and Hf₂CO₂ layer, respectively. The planar-averaged differential charge density is described in Fig. 4c. Positive and negative values reflect charge accumulation and depletion, respectively. At the surface of PtSe₂/Hf₂CO₂ heterostructure, electrons acculmulated on the PtSe₂ side and depleted on the Hf₂CO₂ side, indicating electron transfer from the Hf₂CO₂ layer to the PtSe₂ layer after the two layers contact.

3.3. Effect of external electric field

In order to explore the possible application of the PtSe₂/Hf₂CO₂ vdW heterostructure, we have modulated the electronic properties by applying external electric field. Considering that although the PBE functional underestimates the bandgap, it is still able to predict the correct trend in bandgap variation and to properly demonstrate the physical mechanisms. Therefore, we adopted the PBE functional in the following calculations due to the high computational cost of HSE06.

The direction of E_ext from the Hf₂CO₂ layer to the PtSe₂ layer is taken as the positive direction (shown in Fig. 5a) and the E_ext ranging from −0.7 to 0.7 V Å⁻¹ is applied. Fig. 5a and b show the band gap and band edges (VBM, CBM) as a function of the applied electric field. When the negative E_ext is applied, a transition from type-I to type-II occurs at −0.2 V Å⁻¹, and the band gap value decreases linearly with increasing the negative electric field. In the type-II heterostructure induced by negative electric field, the CBM and VBM are dominated by PtSe₂ and Hf₂CO₂ layers, respectively, as shown in Fig. 6d. Under the influence of the positive E_ext, the transition from type-I to type-II takes place at 0.1 V Å⁻¹. However, in contrast to the case of the negative electric field, the CBM and VBM of the type-II heterostructure are dominated by Hf₂CO₂ and PtSe₂, respectively, as shown in Fig. 6e. And the band gap value decreases linearly with increasing the positive electric field. The linear variations of band gaps with E_ext can be attributed to the Stark effect.⁵⁵

Fig. 5 (a) The band gap evolution of PtSe₂/Hf₂CO₂ heterostructure as a function of E_ext. The inset shows directions of build-in electric field, negative and positive external electric field. (b) The band edge evolution of PtSe₂/Hf₂CO₂ heterostructure as a function of E_ext.

Fig. 6 (a) Type-II band alignment under a negative external electric field. (b) Type-I band alignment without an external electric field, and (c) Type-II band alignment under a positive external electric field. and are the quasi-Fermi levels of PtSe₂ and Hf₂CO₂ layers in the heterostructure, respectively. (d), (e) The band structures of PtSe₂/Hf₂CO₂ heterostructure under the negative of −0.2, −0.4 and −0.7 V Å⁻¹, and positive electric fields of 0.1, 0.4 and 0.7 V Å⁻¹, respectively, where the red and blue dots represent PtSe₂ and Hf₂CO₂, respectively. The green arrow lines denote the CBM and VBM.

When applying a negative E_ext, the total electric field is weakened due to the opposite direction of the built-in and external electric field. In this case, the drift of electrons from the Hf₂CO₂ layer to the PtSe₂ layer is further strengthened, resulting in a downward shift of the quasi-Fermi level of the Hf₂CO₂ layer and an upward shift of the quasi-Fermi level of the PtSe₂ layer, shown in Fig. 6a. As shown in Fig. 6c, when the positive E_ext is applied, the built-in electric field and external electric field have the same direction, and the total electric field is enhanced, causing an upward of and a downward of . The response of the electrical properties of PtSe₂/Hf₂CO₂ heterostructure to E_ext makes the PtSe₂/Hf₂CO₂ heterostructure exhibit potential applications in FETs and MEMS.

The distinct responses of the electronic properties of PtSe₂/Hf₂CO₂ heterostructure to positive and negative electric fields can be attributed to the charge transfer and redistribution between the PtSe₂ and Hf₂CO₂ layers. Therefore, the planar-average charge density difference of heterostructure under different E_ext is plotted in Fig. 7. The positive and negative values reflect electrons accumulation and depletion, respectively. It can be obviously seen that the number of accumulated electrons at the PtSe₂ side increases with the enhanced strength of the negative E_ext, while the number of depleted electrons near the Hf₂CO₂ surface decreases with the positive E_ext increasing from 0.1 to 0.4 V Å⁻¹, then the electrons accumulation occurs at E_ext = 0.5 V Å⁻¹, and the number of accumulated electrons increases with the enhanced strength of the positive E_ext.

Fig. 7 The planar-averaged difference charge density of the PtSe₂/Hf₂CO₂ heterostructure with various E_ext.

3.4. Effect of biaxial strain

Biaxial strain has also been regarded as a powerful tool for tuning the electronic properties of 2D materials and vdW heterostructures. In this work, the electronic properties of PtSe₂/Hf₂CO₂ heterostructures have been investigated under a series of biaxial strains ranging from −8% to 8%, with a step of 2%. Fig. 8a depicts the strain energy (E_S), checked by E_S = E₁ − E₀, in which E₁ and E₀ are its total energies of strained and original structures with no strain applied, respectively. The E_S increases quadratically with strain, indicating that all strains studied are below the elastic limit and are therefore fully reversible.^54,56

Fig. 8 (a) Strain energies at various biaxial strains ranging from −8% to 8%. (b) and (c) The band gap and band edge evolution of PtSe₂/Hf₂CO₂ heterostructure as a function of biaxial strains.

Fig. 8b and c illustrate the evolution of the bandgap and the band edges (CBM and VBM) of PtSe₂/Hf₂CO₂ heterostructure as a function of the strain. The two inset plots illustrate the two different type-II band alignments. One can see that the band gap of PtSe₂/Hf₂CO₂ heterostructure decreases with increasing the compressive strain. When the compressive strain is increased to −4%, a type-I to type-II band alignment transition takes place, and the CBM and VBM are contributed by Hf₂CO₂ layer and PtSe₂ layer, respectively, then a semiconductor-to-metal transition occurs when the compressive strain is increased to −8%. On the contrary, the PtSe₂/Hf₂CO₂ heterostructure is transformed to a type-II heterostructure when the PtSe₂/Hf₂CO₂ heterostructure is increase to 2%, in which the CBM and VBM are located in PtSe₂ layer and Hf₂CO₂ layer, respectively. To further unravel the modulation mechanism of strain effects on electronic properties of PtSe₂/Hf₂CO₂ heterostructure, the electronic band structures under different strains are plotted in Fig. 9. After application of −2% compressive strain, the VBM of PtSe₂ layer increases, closing to the VBM of Hf₂CO₂ layer. When the compressive strain is increased to −4%, the VBM of PtSe₂ layer continue to increase, higher than the VBM of Hf₂CO₂ layer, resulting in a type-I to type-II transition. With the compressive strain increased to −8%, the VBM of PtSe₂ layer is higher than the CBM of Hf₂CO₂ layer, a semiconductor-to-metal occurs. Besides, we found that the band gap of PtSe₂ layer increases then decreases while the band gap of Hf₂CO₂ layers decreases with increasing the compressive strain. For the tensile strain, the CBM of Hf₂CO₂ layer greatly increases at the strain of −2%, thus changes the CBM of the heterostructure from Hf₂CO₂ to PtSe₂ layer. As a result, a type-I to type-II transition takes place. With the increase of the tensible strain, the CBM of PtSe₂ layer decreases, inducing the decrease of the bandgap of PtSe₂/Hf₂CO₂ heterostructure. In addition, we found that the bandgap of Hf₂CO₂ layers increases while the bandgap of PtSe₂ layers decreases with increasing the tensible strain.

Fig. 9 (a) The electronic band structures of PtSe₂/Hf₂CO₂ heterostructure under compressive strains in the range of −2% to 8%. (b) The electronic band structures of PtSe₂/Hf₂CO₂ heterostructure under tensile strains in the range of 2% to 8%. The red circles represent the band of PtSe₂ layer, and the blue circles represent the band of Hf₂CO₂ layer.

4. Conclusions

In this work, the structural and electronic properties of PtSe₂/Hf₂CO₂ heterostructures have been systematically investigated using first principles calculations. The PtSe₂/Hf₂CO₂ bilayer forms a stable vdW heterostructure. In equilibrium PtSe₂/Hf₂CO₂ heterostructures, both the CBM and VBM are donated by the Hf₂CO₂ layer, resulting in a type-I band alignment, which can be utilized in LEDs or other optoelectronic devices. It has been also demonstrated that the electronic properties of PtSe₂/Hf₂CO₂ vdW heterostructure are insensitive to diverse stacking patterns whereas external electric field and biaxial strain have been proved to be efficient methods for modulating the electrical properties of PtSe₂/Hf₂CO₂ heterostructure. Both the external electric field and biaxial strain can induce type-I to type-II band alignment transition, which facilitate the separation of photoexcited electrons and holes, enabling high efficiency optoelectronics and solar energy conversion. Furthermore, the band gap of PtSe₂/Hf₂CO₂ heterostructure decreases with increasing the strength of external electric field or biaxial strain after the occurrence of type-I to type-II transition. In addition, a semiconductor-to-metal transition takes place under the strong compressive strain of −8%. According to our results, the PtSe₂/Hf₂CO₂ heterostructure will present abundant opportunities for the application of flexible electronic and optoelectronic nano-devices.

Conflicts of interest

There are no conflicts to declare.

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Footnote

† Electronic supplementary information (ESI) available. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d3ra04363k

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