Introduction

Two-dimensional (2D) materials have attracted great attention due to their unique characteristics, such as high carrier mobility, excellent mechanical properties and optical properties [1,2,3]. Transition metal 2D materials include transition metal dichalcogenides (TMDs), transition metal carbides (TMCs), transition metal oxides (TMOs) and so on. Among them, the most studied are TMDs, which have intriguing electronic, optical and thermal properties [4, 5], such as MoS2 [6,7,8,9], MoSe2 [10,11,12,13] and WSe2 [14,15,16]. However, the carrier mobility of TMDs is low, which limits their practical applications [17]. Several studies reveal that the performance of single materials can be optimized by constructing heterostructures [18,19,20,21]. The heterostructure can not only maintain the intrinsic characteristics of the single-layer material, but also obtain new electronic properties due to the interface coupling effect of the heterostructure at the interface. As a 2D transition metal dichalcogenide, MoSe2 has high absorption efficiency and is often used to construct heterostructures due to its unique lattice structure, electron transport and optical properties. For example, MoSe2@rGO cathode-coated batteries provide a higher reversible capacity and excellent cycle stability [22]. Tian et al. found that the photocatalytic activity of ZnSe/MoSe2 is four times that of ZnSe, and its photoelectric performance is also increased [23].

PC6 is a layered semiconductor material with a graphene-like structure [24], which has attracted the attention of researchers due to its extremely high intrinsic conductivity with anisotropy character and ultrahigh carrier mobility [25]. For example, it has very good application performance in the field of Li-ion batteries [26] and could be a potential reusable material as NO and NO2 sensors with high selectivity and sensitivity [27]. Unfortunately, PC6 has a lower optical absorption efficiency [24], which limits its application in optoelectronics. Therefore, we can improve its optical absorption efficiency by constructing heterostructures with MoSe2. It is well-known that the band alignment of heterojunction can be tuned by electric field and strain. For example, InSe/MoSe2 (WSe2) [28] and g-C3N4/WSe2 [29] exhibit a variety of band alignments under different external electric fields, including astraddle type-I, interlaced type-II and broken-up type-III. When biaxial strain is applied, the GaS/g-C3N4 can transition from type-I to type-II band alignment, even from semiconductor to metal under strong strain [30]. Similarly, the band edge of the blue phosphorene/C2N heterostructure can be tuned by applying biaxial strain [31]. In addition, vacancies usually play an important role in tailoring electronic, optical, and magnetic properties of semiconductors. For MoSe2, whether it is Mo-vacancy [32] or Se-vacancy [33], it should be beneficial to their potential applications in optoelectronics and nanoelectronic devices. However, the influence of different biaxial strains and electric fields on the PC6/MoSe2 heterostructure is the important points of our work.

In this paper, we establish PC6/MoSe2 heterostructure, and the structure, electronic and optical properties of the PC6/MoSe2 heterostructure are investigated using density functional theory. It turns out that the PC6/MoSe2 heterostructure exhibits a type-I band alignment. Type-I band alignment is very useful for confining electrons and holes in the same material, so type-I heterostructures are mainly used in light-emitting diodes and semiconductor lasers. The transition from type-I to type-II is completed under external electric field and strain, even from semiconductor to metal under strong strain, which provides guidance for extending the application of PC6/MoSe2 heterostructure.

Computational method

All the first-principles calculations are performed using Vienna Ab initio Simulation Package (VASP) [34, 35], and based on periodic density functional theory (DFT) [36, 37] and projector augmented wave (PAW) [38, 39] method. Since the Perdew–Burke–Ernzerhof (PBE) [40, 41] method of generalized gradient approximation usually underestimates the band gap of semiconductors, we use Heyd–Scuseria–Ernzerhof (HSE06) [42] hybrid functional to describe the electronic and optical properties of PC6/MoSe2 heterostructure. The optB88-vdW functional is selected to describe the vdW interaction in the heterojunction. The cut-off energy for the plane wave is set to 400 eV. All structures are fully relaxed, and convergence criterion of energy in the self-consistency process is set to 10–4 eV. The interaction between adjacent periodic slabs can be avoided when the vacuum layer is set to 20 Å. A Monkhorst–Pack k-point mesh of 3 × 3 × 1 is adopted to optimize the geometric structures and perform the self-consistent calculations. It is well-known that PBE usually underestimates the band gap. Therefore, we adopt the HSE functional in the following calculations. An external electric field [43, 44] is implemented by introducing a planar dipole layer, which will cause a uniform potential difference along the direction perpendicular to the heterojunction interface.

Results and discussion

Geometry and electronic structure of monolayers

The optimized crystal structures of PC6 and MoSe2 monolayers are shown in Fig. 1 with the lattice constants 6.683 Å and 3.327 Å, respectively, which are consistent with previous theoretical reports [27, 29]. The thickness of the PC6 monolayer is about 2.140 Å, because the P atoms in the graphene-like PC6 are extruded to both sides. The bond lengths in PC6 are 1.811 Å for P–C, 1.361 Å for C1-C2, 1.462 Å for C2-C3 and C4-C5 and 1.422 Å for C3-C4, while the bond length of Mo-Se is 2.547 Å in MoSe2, which are in good agreement with the literatures [24, 45].

Figure 1
figure 1

Crystal structure of single layer a PC6 and b MoSe2. Brown, purple, pink and dark green represent C, P, Se and Mo, respectively

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The band structures calculated by HSE06 are shown in Fig. 2. It is shown that both PC6 and MoSe2 are direct semiconductors, and their conduction band minimum (CBM) and valence band maximum (VBM) are located at the M point and K point with the band gaps of 0.94 eV and 1.8 eV, respectively, which is in accordance with the previous study [23, 25].

Figure 2
figure 2

Band structures of a monolayer PC6 and b monolayer MoSe2 through HSE06. The Fermi level is set to zero and indicated by the dashed line

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Geometric and electronic structure of the PC6/MoSe2 heterostructure

As mentioned above, the optimized lattice constants for the PC6 and MoSe2 monolayers are 6.67 Å and 3.33 Å, respectively. Therefore, to construct the PC6/MoSe2 heterostructure, a 2 × 2 × 1 MoSe2 supercell is used to match the 1 × 1 × 1 PC6 unit cell, as shown in Fig. 3. In this way, the lattice constant of the heterostructure is a = 6.67 Å with the lattice mismatch of only about 0.1%. Then, after geometrical relaxation, the P–C, C–C and Mo-Se bond lengths at the interface change slightly, which implies that there is little rearrangement of atoms. In order to obtain a relatively stable structure, the binding energy (Eb) of the PC6/MoSe2 heterostructure is calculated, which is defined as follows:

$$E_{{\text{b}}} = E_{{{\text{PC}}_{6} /{\text{MoSe}}_{2} }} - E_{{{\text{PC}}_{6} }} - E_{{{\text{MoSe}}_{2} }}$$
(1)

here, \({E}_{{\mathrm{PC}}_{6}/{\mathrm{MoSe}}_{2}}\) is the total energy of the PC6/MoSe2 heterostructure, while \({E}_{{\mathrm{PC}}_{6}}\) and \({E}_{{\mathrm{MoSe}}_{2}}\) are the total energies of the isolated PC6 and MoSe2 monolayers, respectively. According to Eq. (1), the binding energy of the relaxed PC6/MoSe2 heterostructure is -0.496 meV. It is well-known that a negative value of the binding energy means that the formation of the heterostructure is an exothermic process, which proves the stability of the heterostructure.

Figure 3
figure 3

a Side view and b top view of the geometry of the PC6/MoSe2 heterostructure. Brown, purple, pink and dark green represent C, P, Se and Mo, respectively

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The band structure in Fig. 4a indicates that the PC6/MoSe2 heterostructure is a semiconductor with a direct band gap of 0.88 eV, which is smaller than the band gap of single-layer PC6 (0.94 eV) and MoSe2 (1.85 eV), indicating the weak charge transfer between PC6 and MoSe2 monolayers. For further identifying the electronic properties of the PC6/MoSe2 heterostructure, the density of state (DOS) is calculated, as shown in Fig. 4b. The weak hybridization between PC6 and MoSe2 can be found, indicating that the interlayer coupling between the two layers is weak. It can be said that the intrinsic electronic properties are preserved when PC6 monolayer transforms into PC6/MoSe2 heterostructure. The DOS of PC6/MoSe2 heterostructure shows that the CBM and VBM are contributed by C-2p, so electrons and holes are confined in PC6, which means that a type-I heterostructure is formed. This type of heterostructure can be used in optoelectronic devices, such as light-emitting diodes.

Figure 4
figure 4

a Band structure and b DOS of PC6/MoSe2 heterostructure. In the band structure, blue and red lines represent the contributions of PC6 and MoSe2 layers, respectively. The Fermi level is set to zero and indicated by the dashed line

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Work function is an important factor in determining the charge transfer between layers and then may affect the band alignment of heterostructures. The work functions are 4.928 eV and 5.575 eV for the PC6 and MoSe2 monolayers, respectively. The difference between the work functions will cause electrons to flow from PC6 to MoSe2. Hence, the electrons accumulate near MoSe2, while the holes accumulate in the region of PC6, thereby forming a built-in electric field directed from PC6 to MoSe2, which may produce an extra driving force. To more clearly describe the interfacial coupling between PC6 and MoSe2, the charge density difference of the PC6/MoSe2 heterostructure is calculated as:

$$\Delta {\uprho } = \rho_{{{\text{PC}}_{6} /{\text{MoSe}}_{2} }} - \rho_{{{\text{PC}}_{6} }} - \rho_{{{\text{MoSe}}_{2} }}$$
(2)

where \({\rho }_{{\mathrm{PC}}_{6}/{\mathrm{MoSe}}_{2}}\), \({\rho }_{{\mathrm{PC}}_{6}}\) and \({\rho }_{{\mathrm{MoSe}}_{2}}\) are the charge density of PC6/MoSe2 heterostructure, single-layer PC6 and MoSe2, respectively. The charge density rearrangement can be found in both layers and the charge transfer between them can be realized, as shown in Fig. 5a. An obvious planar charge rearrangement and the transfer of electrons from PC6 to MoSe2 are observed except the vicinity of the P atoms, where the buckling exists. To further explore the properties of charge transfer, the averaged charge density difference is calculated and shown in Fig. 5b, in which the positive values indicate electron accumulation, and the negative values represent electron depletion. At the interface, the charge transfer is complicated, which is also resulted from the buckling in the structure, although a small transfer of electron from PC6 to MoSe2 can be deduced from the figure. Then, the Bader charge analysis is performed to quantitatively confirm the total value of the transferred charge, which shows that the transferred electron is 0.0173e from PC6 to MoSe2.

Figure 5
figure 5

a Charge density difference for the PC6/MoSe2 heterostructure, the cyan and yellow regions represent the charge depletion and accumulation, respectively. b The averaged charge density difference for the PC6/MoSe2 heterostructure along the Z-axis

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Effect of strain on the PC6/MoSe2 heterostructure

The electronic structural properties of heterostructures can be adjusted under biaxial strains, which have been widely used in 2D materials [46, 47]. Applying biaxial strain can improve the performance of materials, which is important for further applications [48, 49]. Therefore, the effect of biaxial strain on the performance of heterojunction is investigated. The biaxial strain of PC6/MoSe2 heterostructure can be defined as:

$${\updelta } = \left( {\frac{{a - a_{0} }}{{a_{0} }}} \right) \times 100\%$$
(3)

where a and \(a_{0}\) represent the strained and unstrained lattice constants. So as to ensure that the applied strain is within the elastic limit, the strain energy (Es) of each atom in the system is calculated,

$$E_{{\text{s}}} = (E_{{{\text{strained}}}} - E_{{{\text{unstrained}}}} )/n$$
(4)

where n is the total number of atoms in the unit. Figure 6a shows that the strain energy approximatively presents a quadratic curve in the selected range of ± 6%, which indicates that the geometry of the heterostructure is not destroyed under the biaxial strain, that is, the applied biaxial strain is reasonable and the process is completely reversible. The band gap of the heterostructure is also plotted as a function of strain in Fig. 6a. It can be seen that the band gap decreases almost linearly as the strain increases within the range of -6% ~ 5%, and it reaches the maximum value (~ 1.29 eV) under the strain of about -5%. At δ = 6%, the system undergoes a direct transition of semiconductor to metal, which means that the conductivity of the heterostructure is adjustable. Then, we focused on semiconductor and supply the band edges under the strain of -6% to 5% in Fig. 6b. Apparently, type-I band alignment is maintained from -5% to 5% strain. It is noticed that the band gaps of both the two single layers decrease from negative to positive strain by and large except in the range of great compression for MoSe2, where the band gap of PC6 is more sensitive to strain. At the meantime, it also can be seen that for both materials, the VBM hardly changes with strains, and the change of gap is basically determined by CBM. The CBM of PC6 decreases monotonically as the strain increases from negative to positive, while the CBM of MoSe2 increases monotonously from -6% to -4%, leading to a transition from type-I to type-II between -6% and -5%. In short, the strain can effectively change the type of PC6/MoSe2 heterostructure. It is useful for designing multifunctional electronic and optoelectronic devices.

Figure 6
figure 6

a In-plane biaxial strain effects on the band gap and strain energy of the PC6/MoSe2 heterostructure. b VBM and CBM levels of PC6/MoSe2 heterostructure under different applied biaxial strains. A positive value of strain indicates stretching strain. Fermi level is set to 0

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Figure 7 shows the effect of different strains on DOS. The DOS of the conduction band shifts slightly to lower energy as the positive strain increases. With the increase in negative strain, the DOS of the conduction band obviously shifts to higher energy. It is obvious for the movement of occupation by C atoms, but the movement of occupation by Mo atom is not obvious, so that Mo atoms dominate the CBM at -6%. Therefore, the band gap increase almost linearly as the strain decreases within the range of 5% ~ -6%, and it reaches the maximum value under the strain of about -5%. When PC6/MoSe2 remains type-I heterojunction, the main electronic state (C atoms) occupied at the edge of the band gap is almost the same as the case without strain in Fig. 4b. Obviously, the occupancy rate of C atoms in CBM and VBM becomes larger from positive to negative strain. As shown in Fig. 4b, the occupancy of electrons is relatively dispersed, indicating that the localization of electrons is weakened. However, strain can change the occupation of electrons, especially at -1.2 ~ -1.5 eV and 1.2 ~ 2 eV, and the sharp peaks of Mo atoms in DOS increase and the occupation of electrons gradually converges as the positive strain increases, indicating that the electrons are relatively localized. The peak value of DOS gradually decreases as the negative strain increases, especially for Se atoms.

Figure 7
figure 7

DOS of PC6/MoSe2 heterostructure at strains of a 2%, b 4%, c -2%, d -4% and e -6%. Please refer to the electronic version

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The effect of vertical strain on the band gap of the PC6/MoSe2 heterostructure is shown in Table 1. The vertical strain is defined as: \(\varepsilon =d-{d}_{0}\), where d0 = 3.7 Å is the original distance between the two layers. It is shown that the vertical strain has little effect on the band structure of the PC6/MoSe2 heterostructure, so no much work is done on it.

Table 1 Band gap of PC6/MoSe2 heterostructure under different applied vertical strains
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Effect of external electric field on the PC6/MoSe2 heterostructure

To explore the effect of external electric field on the electronic properties of the PC6/MoSe2 heterostructure, the external electric field in the range of -0.5 to 0.5 V/Å is applied on the heterostructure with the positive direction perpendicularly from MoSe2 to PC6. Figure 8 shows the variation of band edges and band gaps of PC6 and MoSe2 in the PC6/MoSe2 heterostructure under various external electric fields. It can be seen that both the VBM and CBM of MoSe2 decrease monotonically from positive electric field to negative electric field (due to potential difference of the external electric field), while that of PC6 change little especially in the range of -0.4 ~ 0.4 V/Å. So the MoSe2 layer is more sensitive to external electric field on the heterostructure. The CBM and VBM of the heterojunction are contributed by PC6 monolayer from -0.3 to 0.2 V/Å, resulting in the band gap of the heterojunction remaining almost unchanged in the range. When a positive electric field is strengthened, the CBM of MoSe2 gradually approaches the Fermi level (the Fermi level rises). Once the negative electric field exceeds 0.3 V/Å, the CBM of the heterostructure is contributed by MoSe2, and the VBM is still contributed by PC6. Finally, the transition from type-I to type-II is completed, and the spatial distribution of carriers has changed. On the other hand, when a negative electric field is strengthened, the VBM of MoSe2 gradually approaches the Fermi level (the Fermi level drops). At -0.4 V/Å, the PC6/MoSe2 heterostructure can also complete the transformation from type-I to type-II. The external electric field is considered to be a key strategy for modulating the electronic properties of PC6/MoSe2 heterostructures; thus, PC6/MoSe2 will be widely applied in nanoelectronic devices.

Figure 8
figure 8

Calculated band gap and band edge position as a function of the vertical electric field for the PC6/MoSe2 heterostructure

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Figure 9 reveals the response of the average charge density difference of the PC6/MoSe2 heterojunction with the variation of external electric field. It can be seen that the fluctuation of charge density difference along Z-axis also raises as the intensity of the electric field enhances, which can facilitate the movement of band edges and signify a more forceful interplay at the bilayer interface. However, the total value of transferred charge cannot be read directly, so the number and direction of the total charge transferred are estimated by Bader analysis and listed in Table 2. The electrons transferred from PC6 to MoSe2 increase with the intensity of the positive electric field (0.0173|e|~ 0.0658|e|). It is worth noting that in a small negative electric field, the direction of charge transfer is the same as that of under positive electric field, but the electrons transferred from PC6 to MoSe2 start to decrease, which is due to the reduced net effective internal electric field crossing the interface. After that, the PC6 layer begins to receive electrons, which indicates that the size of the built-in electric field should be between 0.2 and 0.3 V/Å when the external electric field is zero. The applied electric field can change the distribution of charge and the accumulation of carriers, which in turn helps us grasp the charge transfer mechanism. This is due to the interaction between the built-in electric field and the external electric field.

Figure 9
figure 9

Averaged charge density difference of the PC6/MoSe2 heterojunction along the Z direction under various electric field. The black vertical dash lines indicate the position of PC6 and MoSe2 layer in the heterojunction

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Table 2 Charge transfer of PC6/MoSe2 heterostructure under the different vertical electric field (positive value means losing electrons, negative value means gaining electrons)
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The optical properties of PC6/MoSe2 heterostructure

The optical absorption of the PC6/MoSe2 heterojunction has been studied since the optical properties of materials play an important role in application of optoelectronic devices. The optical absorption coefficient can be calculated as follows [50]:

$$\alpha \left( \omega \right) = \sqrt 2 \omega [\sqrt {\varepsilon_{1}^{2} \left( \omega \right) + \varepsilon_{2}^{2} \left( \omega \right)} - \varepsilon_{1} \left( \omega \right)]^{1/2}$$
(5)

where ε1(ω) and ε2(ω) are the real and imaginary parts of the dielectric function. The imaginary part of the dielectric function is calculated as follows [50]:

$$\varepsilon_{2} \left( \omega \right) = \frac{{4\pi^{2} e^{2} }}{{Vm^{2} \varpi^{2} }}\mathop \sum \limits_{{nn^{\prime}\sigma }} kn\sigma \left| {p_{i} } \right|kn^{\prime}\sigma kn^{\prime}\sigma \left| {p_{j} } \right|kn\sigma \times f_{kn} \left( {1 - f_{{kn^{\prime}}} } \right)\delta \left( {E_{{kn^{\prime}}} - E_{kn} - \hbar \omega } \right)$$
(6)

The optical absorption spectra of isolated PC6 and MoSe2 as well as the PC6/MoSe2 heterostructure are shown in Fig. 10a. It is clear that PC6 has a wider absorption range than MoSe2 in the infrared region, and the first absorption peak is also higher than MoSe2, while MoSe2 has a much larger absorption capacity in the visible and UV regions. Compared with that of the single layers, the absorption edge of the PC6/MoSe2 heterostructure has a redshift, which is more obvious compared with MoSe2 and corresponds to the change of the band gap value. Evidently, the PC6/MoSe2 heterostructure combines the advantages of the two single layers. This phenomenon can be attributed to the overlap of electronic states, which is caused by the coupling between layers. According to the report of Peng et al. [51], the optical absorption of 105 cm−1 can be regarded as a sign of effective use of solar energy. Therefore, the PC6/MoSe2 heterostructure has good utilization of solar energy.

Figure 10
figure 10

a Absorption coefficient of PC6/MoSe2 heterostructure, single-layer PC6 and MoSe2. The absorption spectra of PC6/MoSe2 heterostructure as a function of b biaxial strain and c electric field. The yellow area represents the visible light region

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Since the optical absorption spectra have the same changing trend under different biaxial strains and external electric fields, some representative results are shown in Fig. 9b, c. Successive redshifts and blueshifts can be observed with positive and negative biaxial strain, respectively, in Fig. 10b, which corresponds to the change in the band gap in Fig. 6a. As shown in Fig. 10c, it can be seen that the absorption of the heterojunction under the applied electric field has only a slight difference between 0 and 4.3 eV compared with 0 V/Å, while the heterostructure exhibits stronger UV absorption in the energy range of 4.3 to 6 eV. This is due to a new optical transition caused by electric field-induced charge transfer and interlayer coupling in the heterostructure.

Conclusion

In the work, the electronic properties of PC6/MoSe2 heterostructure under biaxial strain and external electric field are studied. It is also noticed that PC6 is more sensitive to large compressive strains, while MoSe2 is more sensitive to external electric fields. By applying biaxial strain, the band gap of the heterostructure can be adjusted approximately linearly within -5% to 5%. It can be found that the negative biaxial strain can make the PC6/MoSe2 heterostructure complete the transition from type-I to type-II, and the transition from semiconductor to metal can be achieved directly at 6%. In addition, the electric field can also significantly change the band structure of the PC6/MoSe2 heterojunction, which causes the heterojunction to undergo a transition from type-I to type-II under strong electric field. The charge transferred from PC6 to MoSe2 increases almost linearly by applying positive electric field, while if an electric field of −0.3 V/Å is applied, the direction of charge transfer changes, so the electric field can effectively adjust the charge distribution and carrier concentration. According to our results, the band alignment of the heterojunction can be adjusted under different electric fields and strains, so as to provide effective guidance for the follow-up research on the potential applications of PC6/MoSe2 heterostructure in multifunctional devices.