Polarization Modulation on Charge Transfer and Band Structures of GaN/MoS₂ Polar Heterojunctions

Abstract

As important third-generation semiconductors, wurtzite III nitrides have strong spontaneous and piezoelectric polarization effects. They can be used to construct multifunctional polar heterojunctions or quantum structures with other emerging two-dimensional (2D) semiconductors. Here, we investigate the polarization effect of GaN on the interfacial charge transfer and electronic properties of GaN/MoS₂ polar heterojunctions by first-principles calculations. From the binding energy, the N-polarity GaN/MoS₂ heterojunctions show stronger structural stability than the Ga-polarity counterparts. Both the Ga-polarity and N-polarity GaN/MoS₂ polar heterojunctions have type-II energy band alignments, but with opposite directions of both the built-in electric field and interfacial charge transfer. In addition, their heterostructure types can be effectively modulated by applying in-plane biaxial strains on GaN/MoS₂ polar heterojunctions, which can undergo energy band transitions from type II to type I. As a result, it provides a feasible solution for the structural design and integrated applications of hybrid 3D/2D polar heterojunctions in advanced electronics and optoelectronics.

1. Introduction

Due to the electronegativity difference of atoms, the positive and negative charges are separated in the wurtzite GaN and nitride semiconductors, which have extensive applications in next-generation RF power amplifiers, power switches, light-emitting diodes, lasers, solar cells, photodetectors, and integrated circuits [1,2,3,4,5,6,7,8]. GaN has two distinct polarities called Ga-polarity and N-polarity along the [0001] and [000-1] directions, respectively. The lack of inversion symmetry in GaN gives rise to a large spontaneous polarization charge of ~0.029 C/m² and a polarization electric field of ~10⁷ V/cm. The surface polarity of GaN dramatically influences surface energies, growth modes, susceptibilities to chemicals, electric charge dynamics, and so on. Its strong polarization greatly influences the GaN-based electronic and optoelectronic performances by energy band tilt and charge separation or accumulation at the polar heterointerfaces, such as AlGaN/GaN, InGaN/GaN and metal-polar semiconductor Schottky interfaces.

With regard to the developing trend of 3D-to-2D miniaturization and multifunctional integration, 2D semiconductors beyond graphene have become a research hotspot due to their unique electrical, photonic, and mechanical performances [9]. There is a large number of 2D semiconductor materials widely used in field-effect transistors and optoelectronic devices, such as transition metal dichalcogenides (TMDs) [10,11], black phosphorus (BP) [12], silicene [13], and III-VI layered materials [14]. Among them, 2D TMDs show tunable bandgaps from 1.1 eV (MoTe₂) to 2.0 eV (WS₂) for highly visible and near-infrared optoelectronic response [15,16]. Meanwhile, 2D TMDs have excellent flexibility and high carrier mobility, enabling ultrathin and lightweight, flexible electronic applications [17].

Currently, 2D semiconductors are used as potential building blocks to form low-dimensional semiconductor heterostructures for improving electronic and optical performances [18,19,20,21,22], such as MoS₂/graphene [23], MoS₂/WS₂ [24], MoS₂/WSe₂ [25], and α-In₂Se₃/MoS₂ [26]. In comparison with 2D/2D architecture, mixed-dimensional 3D/2D heterostructures have greater application potential in integrating with conventional semiconductors, such as Si, GaAs, GaN, etc. In order to obtain the full utilization of the broad optical spectrum, the integration of 2D TMDs with 3D wide-bandgap GaN is a feasible solution, such as MoS₂/GaN, MoSe₂/GaN, etc. [27,28]. Desai et al. grew a homogeneous MoS₂ layer on a GaN substrate to produce a MoS₂/GaN vertical heterojunction with a type-II energy band arrangement, and showed excellent electrical rectifying characteristic and photovoltaic responsivity under monochromatic illumination [29]. Yang et al. prepared triangular MoS₂ monolayers on GaN substrates by CVD, which exhibited an indirect bandgap of MoS₂/GaN with broadband optical absorption [30]. The type-II band alignment of MoS₂/GaN helps to effectively separate the photogenerated electrons and holes, which demonstrated unique advantages for broadband photodetectors and high-efficiency solar cells [31,32,33]. Theoretically, by first-principles calculations, Gao et al. reported the MoS₂/2D GaN van der Waals (vdW) heterostructures possess a direct gap about 1.79 eV with type-II band alignment and excellent optical absorbance of approximately ~5.5 × 10⁵ cm⁻¹ [34]. It was found that changing interlayer coupling and applying external electric fields can effectively and broadly engineer its band gap and optical properties. However, 2D GaN is difficult to synthesize experimentally and does not have strong out-of-plane polarity like 3D GaN for practical polarization modulation. In addition, Sung et al. performed density-generalized function theory calculations to investigate the interfacial structures between 2D-MoS₂ and 3D-GaN [35]. It was reported that the surface states and electrical characteristics of the 2D/3D MoS₂/GaN heterostructures could be controlled by the surface terminations of GaN. However, other types of band alignments are actually needed to control carrier distribution, charge transfer, and spatial confinement of 2D/3D GaN/MoS₂ heterostructures. To date, there is still a lack of effective means, such as GaN polarity flip and strain modulation for optical emission, electrooptic conversion, and advanced energy-harvesting applications.

In this work, we constructed two types of GaN/MoS₂ (I) and (II) polar heterojunctions by manipulating the Ga-polarity and N-polarity of GaN to investigate the interfacial interactions and electronic band structures between MoS₂ and GaN, respectively. It is found that both of them are type-II energy band-aligned, with the heterojunction bandgaps of 0.87 eV and 1.53 eV for GaN/MoS₂ (I) and GaN/MoS₂ (II), respectively. Based on the differential charge density analysis, the negative charges are transferred in the opposite directions, from GaN to MoS₂ in Ga-polarity GaN/MoS₂ (I) and from MoS₂ to GaN in N-polarity GaN/MoS₂ (II), respectively. Correspondingly, the net charge transfer amounts of 0.036 e and 0.088 e demonstrates that the interfacial interaction is stronger in GaN/MoS₂ (II) than that in GaN/MoS₂ (I), which is consistent with the lower binding energy of GaN/MoS₂ (II). In addition, piezoelectric polarization of GaN has been utilized by in-plane biaxial strains to modulate the energy band configurations of GaN/MoS₂ heterojunctions, which can undergo an energy band transition from type II to type I. Therefore, the polarization modulation of GaN/MoS₂ heterojunctions provides a facile strategy for interfacial charge transfer and energy band configurations in 3D/2D polar semiconductors and device applications.

2. Computation Methods

Based on the first-principles density functional theory (DFT), our computational simulations were implemented by the Vienna ab initio simulation package (VASP) [36,37]. The heterojunction structure models were constructed by Materials Studio (MS) software. The interactions between the core and valence electrons were described by using the projector-augmented wave (PAW) method [38]. The Perdew−Burke−Ernzerhof version of the generalized gradient approximation (PBE-GGA) was selected as the electron exchange–correlation interaction functional [39], which was used for structural optimization and static self-consistent calculations. The strongly constrained and appropriately normed semilocal density (SCAN) functional was utilized to calculate the semiconductor bandgaps and electronic band structures [40]. Generally, it is efficient for accurate modeling of electronic structures of layered materials in high-throughput calculations [41]. The energy cutoff for the plane–wave basis expansion was set to be 500 eV. The Brillouin zone was sampled with a 12 × 12 × 1 Monkhorst−Pack grid. The convergence criteria of electronic and geometric optimization were 10⁻⁶ eV and 0.01 eV/Å. The algorithm selection for electronic optimization was normal. The Brillouin zone integration was performed by the Gaussian smearing (ISMEAR = 0) method with the smearing width (SIGMA) of 0.05 eV. The DFT-D3 method was used to correct interlayer vdW interactions between the MoS₂ monolayer and the GaN surface [42,43,44,45]. The vacuum space of 15 Å was adopted to avoid interactions between the periodic sheets. During the 3D/2D construction of GaN/MoS₂ heterostructures, the dangling bonds at the bottom surface of GaN layer were passivated by H atoms.

During our calculations, the initially established GaN/MoS₂ heterostructures were geometrically optimized by the lattice constants and the layer spacing. The optimized structure models were then subjected to static self-consistent calculations to obtain the charge density files. Subsequently, the SCAN generalization was used to increase the K-point grids to calculate the density of states, and the K path was set to G-M-K-G for the energy band calculation.

3. Results and Discussion

3.1. Polarity Configurations on Electronic Band Structures of GaN/MoS₂ vdW Heterostructures

As for the geometric structures of MoS₂ and GaN in Figure 1a, the 2D MoS₂ monolayer in the order of S-Mo-S arrangement has a hexagonal crystalline structure with the optimized lattice constants of a = b = 3.18 Å, while 3D wurtzite GaN has the same hexagonal structure with the optimized lattice constants of a = b = 3.21 Å. Their lattice mismatch between MoS₂ and GaN is only 0.9%, which facilitates 3D/2D heteroepitaxy for building GaN/MoS₂ heterostructures. Considering the spontaneous polarization effect of the GaN polar semiconductor along z axis, Ga-polarity and N-polarity GaN/MoS₂ heterojunctions have been constructed in the I and II stacking configurations. As shown in Figure 1b, the Ga face of GaN layer is contacted with the S atoms of MoS₂ monolayer at the GaN/MoS₂ (I) heterointerface, and, correspondingly, the N face of GaN layer is contacted with the S atoms at the GaN/MoS₂ (II) heterointerface, respectively. The lattice constants and interlayer equilibrium distances of the optimized GaN/MoS₂ unit cells are similar with a = b = 3.20 Å and d = 2.35 Å in configuration I, and a = b = 3.19 Å and d = 2.35 Å in configuration II, respectively. In order to quantitatively characterize the structural stability of GaN/MoS₂ heterojunctions, the binding energy has been calculated as follows,

$$E_b=E_{GaN/Mo{S}_2}-E_{Mo{S}_2}-E_{GaN}$$

(1)

where $E_{GaN/Mo{S}_2}$, $E_{Mo{S}_2},$ and $E_{GaN}$ are the total energies of the GaN/MoS₂ vdW heterostructures, monolayer MoS₂ and GaN, respectively. Both GaN/MoS₂ (I) and GaN/MoS₂ (II) have negative binding energies of −0.395 eV and −0.407 eV, respectively. It demonstrates that it can form stable vdW heterostructures between MoS₂ and GaN. Comparatively, MoS₂ monolayer has a stronger interfacial interaction with the N face of GaN than that with the Ga face of GaN.

Figure 2 shows the projected band structures and local density of states (LDOS) of MoS₂, GaN, and the GaN/MoS₂ (I) and (II) heterojunctions. MoS₂ has a direct bandgap of 1.75 eV with both the conduction band minimum (CBM) and valence band maximum (VBM) locating at K point, as shown in Figure 2a, which is consistent with the reported experimental values [46]. In Figure 2b, GaN shows a direct bandgap of 2.4 eV at Γ point calculated by the SCAN method, which is lower than the calculated 3.4 eV by the HSE06 method. According to LDOS diagrams, both the CBM and VBM of the isolated MoS₂ and GaN are mainly contributed by the Mo and N states, respectively.

As shown in Figure 2c,d, the energy bands of the GaN/MoS₂ heterojunctions are not a simple superposition of those of each GaN and MoS₂. The blue and red lines represent the electronic energy band weights of GaN and MoS₂, respectively. Due to the opposite polarity of GaN, the GaN/MoS₂ (I) and (II) heterojunctions have different indirect bandgaps of 0.87 eV and 1.53 eV, respectively. The CBM and VBM of GaN/MoS₂ (I) heterojunction is contributed by GaN and MoS₂, respectively. In contrast, the CBM and VBM of GaN/MoS₂ (II) heterojunction is contributed by MoS₂ and GaN, respectively. Consequently, both of them exhibit type-II band alignment, but the energy bands between MoS₂ and GaN can be reversed from Ga polarity to N polarity. Moreover, there exists an energy level located in the bandgap of the GaN/MoS₂ (II) heterojunction, as indicated by the orange arrow in Figure 2d. In combination with the LDOS analysis, it is contributed by both of MoS₂ and GaN, which may arise from the interfacial hybridization of the N-polarity surface state of GaN with MoS₂ [35]. However, the hybridization state is not observed in the Ga-polarity GaN/MoS₂ (II) configuration, which is due to the surface dangling bonds of the Ga-polarity GaN bonded with the MoS₂.

3.2. Charge Transfer Mechanisms of GaN/MoS₂ vdW Heterostructures

In addition to modulating the electronic band structures, GaN polarity also has a direct impact on the charge transfer processes. Figure 3 presents the average planar electrostatic potentials of the MoS₂ monolayer, GaN, and GaN/MoS₂ (I) and (II) heterojunctions along the z direction. The black dashed line represents the energy level of a stationary electron in the vacuum ($E_{VAC}$) and the red dashed line represents the Fermi level of the corresponding systems ($E_F)$. The work function ($\Phi$) is defined as follows:

$$\Phi =E_{VAC}-E_F$$

(2)

It is a critical parameter to get a further understanding on the physical mechanisms of the charge transfer at GaN/MoS₂ heterojunction interfaces. As shown in Figure 3a, the work function of MoS₂ monolayer is 5.85 eV. However, due to the spontaneous polarization induced by GaN layer, the different work functions at the left and right ends of the z-axis direction are 2.44 and 7.27 eV for GaN, 2.12 and 4.87 eV for GaN/MoS₂ (I), and 6.47 and 5.17 eV for GaN/MoS₂ (II) as shown in Figure 3b–d, respectively. There exists the electrostatic potential difference ($\Delta \Phi$) between the upper and lower surfaces of GaN, GaN/MoS₂ (I), and GaN/MoS₂ (II) heterojunctions. As presented by the interval of the black dashed lines in Figure 3b–d, the electrostatic potential differences are 4.83 eV between Ga-polarity and N-polarity surfaces of GaN, 2.75 eV for GaN/MoS₂ (I) and 1.3 eV for GaN/MoS₂ (II) configurations, respectively. It hence induces a polarization-induced electric field ($E_P$) according to the following equation,

$$E_P=\Delta \Phi /ed$$

(3)

where e and d are the elementary charge and the layer thickness of semiconducting materials or heterostructures, respectively. Correspondingly, the calculated polarization-induced electric fields are 0.68 V/Å, 0.23 V/Å, and 0.11 V/Å for GaN, GaN/MoS₂ (I), and GaN/MoS₂ (II), respectively. In particular, due to the polarity reversal of GaN/MoS₂ (I) and GaN/MoS₂ (II) configurations, their internal polarization-induced electric fields are in the opposite directions. In addition, the electrostatic potential differences of both configurations are lower than the difference of the isolated GaN. It demonstrates that the polarization strength in GaN has been attenuated by an interfacial depolarization effect. As a result, GaN polarity plays a great role on both the interfacial potential and internal electric field of GaN-based polar heterostructures.

Based on the above results of band structures and electrostatic potentials, Figure 4a,b shows the band alignment schematics of GaN/MoS₂ heterojunctions before contact and after contact in I and II configurations, respectively. The vacuum energy level is set to be zero as a reference. Once the GaN/MoS₂ heterostructures are formed, charge transfer will happen at the interface of GaN and MoS₂, thus achieving the same Fermi energy levels. Correspondingly, it also leads to the formation of a built-in electric field at the GaN/MoS₂ heterojunctions, which could hinder the further diffusion of electrons and holes, and eventually reach equilibrium. As compared with MoS₂, the energy bands of GaN shift downward and upward in the contacted GaN/MoS₂ (I) and GaN/MoS₂ (II) configurations in Figure 4a,b, respectively. Both the CBM and VBM of GaN are lower than those of MoS₂ in the contacted GaN/MoS₂ (I) and vice versa in the contacted GaN/MoS₂ (II). As a result, these two configurations have type-II band alignments, which could boost the spatial charge separation and reduce electron-hole recombination efficiency. Due to their opposite directions in terms of charge transfer and built-in electric field, the type and number of charge separation between GaN and MoS₂ can be directly controlled by adjusting the intrinsic polarization of GaN.

In order to quantitatively analyze the interfacial charge transfer between GaN and MoS₂ during the formation of heterojunctions, the charge density difference (Δρ) is calculated according to the following equation,

$$\Delta \rho =\rho (\mathrm{G}\mathrm{a}\mathrm{N}/{\mathrm{M}\mathrm{o}\mathrm{S}}_2)-\rho \left(\mathrm{G}\mathrm{a}\mathrm{N}\right)-\rho \left({\mathrm{M}\mathrm{o}\mathrm{S}}_2\right)$$

(4)

where ρ(GaN/MoS₂), ρ(GaN) and ρ(MoS₂) denote the charge density of the GaN/MoS₂, the freestanding GaN and MoS₂ monolayer, respectively. Figure 5 shows the plane-averaged charge density differences of GaN/MoS₂ (I) and GaN/MoS₂ (II) along the z direction. The blue and red colors indicate the charge accumulation and depletion, respectively. In Figure 5c,d the red dashed lines represent the GaN/MoS₂ interface boundaries. GaN and MoS₂ correspond to the left and right sides of the interface boundaries, respectively. As shown in Figure 5a,c, the charges are depleted in GaN and accumulated in MoS₂ at the interface of GaN/MoS₂ (I). However, the charge depletion and accumulation are the opposite at the interface of GaN/MoS₂ (II) in Figure 5b,d. These results on charge transfer are consistent with their band alignments in Figure 4. In addition, the net charge transfer amounts can be evaluated by the difference between the charge accumulation and depletion at the heterointerface. They are 0.036 e and 0.088 e in GaN/MoS₂ (I) and (II) configurations, respectively. This demonstrates that the interfacial interaction is stronger in GaN/MoS₂ (II) than that in GaN/MoS₂ (I), which is consistent with the lower binding energy of GaN/MoS₂ (II).

3.3. Strain Modulation on the Electronic Band Structures of GaN/MoS₂ vdW Heterostructures

Strain engineering is of great significance to further tailor the electronic structures and band alignments of 2D polar semiconductors and heterostructures. It can be used to modulate the polarization strength based on the piezoelectric polarization effect. Here, the in-plane biaxial strain has been applied to investigate the energy bands of GaN/MoS₂ polar heterojunctions. The in-plane biaxial strain (ε) is defined as

$$\mathsf{\epsilon }=(a-a_0)/a_0\times 100\%$$

(5)

where $a$ and $a_0$ are the lattice constants with and without strain, respectively. Figure 6 shows the projected energy bands of the GaN/MoS₂ (I) and GaN/MoS₂ (II) polar heterojunctions by tuning the in-plane biaxial strains from −10% (compressive) to 10% (tensile). The blue and red colors indicate the contributions of GaN and MoS₂, respectively. For the strained GaN/MoS₂ (I) polar heterojunction in Figure 6a, MoS₂ exhibits indirect bandgaps, with VBM at K point and CBM between K and G points under compressive strains, in contrast with CBM at K point and VBM between K and G points under tensile strains. Meanwhile, GaN keeps direct band gaps with both VBM and CBM located at G point under strains from −10% to 10%. When changing from tensile strains to compressive strains, the energy bands of GaN shift significantly upward, and its band gap values decrease gradually. For the strained GaN/MoS₂ (II) polar heterojunction in Figure 6, MoS₂ shows a direct-to-indirect band gap transition from compressive strains (−6%, −10%) to tensile strains (6%, 10%), while GaN remains a direct band gap. In contrast to that of GaN/MoS₂ (I), a new hybridized state appeared in the band gap of GaN/MoS₂ (II) as indicated by the orange arrow in Figure 6b. It is due to the electron orbital interactions between surface N atoms of N-polarity GaN and MoS₂. When applying the biaxial tensile strains, the hybridized state gradually overlaps with the downshifted conduction bands of MoS₂.

In order to further clarify the energy band alignment relationship of the GaN/MoS₂ heterojunctions under different strains, Figure 7 presents the CBMs and VBMs of MoS₂ at K point and GaN at G point as a function of biaxial strains. All the CBM and VBM values of both MoS₂ and GaN decrease under tensile strains and increase under compressive strains in GaN/MoS₂ (I) and (II) configurations. In addition, the energy band alignments between MoS₂ and GaN can be transformed from type II to type I as applying biaxial tensile strains. The controllable band transformation is favorable for charge separation, recombination, redistribution, and fast transfer processes in 3D/2D polar heterointerfaces. Comparatively, the required tensile strain for the band transformation is less in GaN/MoS₂ (II) than that in GaN/MoS₂ (I). As a result, the biaxial strains not only modulate the electronic structures of each GaN and MoS₂ layer, but also play a significant role on the interfacial band hybridization and band alignment relationship of GaN/MoS₂ polar heterojunction.

4. Conclusions

In summary, we have constructed 3D/2D GaN/MoS₂ polar heterojunctions to investigate the interfacial interactions and electronic band structures by polarization modulation. It demonstrates that the interfacial interaction is stronger in GaN/MoS₂ (II) than that in GaN/MoS₂ (I), as indicated by both the binding energy and net charge transfer amount. Both GaN/MoS₂ (I) and GaN/MoS₂ (II) have type-II band alignments, which could boost the spatial charge separation and reduce electron-hole recombination efficiency. By flipping the polarization directions of GaN, the type and number of transferred charges between GaN and MoS₂ can be directly controlled by the polarization-induced electric field. In addition, the energy band alignments between MoS₂ and GaN can be transformed from type II to type I as applying biaxial tensile strains. Thus, the polarization modulation is an effective way by which to control carrier distribution and spatial confinement for 3D/2D polar semiconductors and device applications.