Germanene/2D-AlP van der Waals heterostructure: Tunable structural and electronic properties

Captivating emerging properties of two-dimensional (2D) materials, mostly derived from group-IV, have recently become a fascinating research area. Some of those properties of 2D materials can rarely be obtained in their three-dimensional parent materials.^1–7 Moreover, experimental synthesis of almost all the group-IV 2D materials (i.e., graphene, silicene, germanene, stanene, and others) has been conducted.^8–14 The exotic properties of 2D materials, including high carrier mobility, profound surface activity, large quantum spin hall effect, and distinct mechanical strength,^15,16 make them well adorned for next-generation application in nanoelectronics. However, bandgap deficiency consolidates the direct incorporation of these materials into such promising applications in device technology.^17,18 Of late, the development of van der Waals heterostructures (vdWHs) using two different 2D materials in vertical stacking has opened up new possibilities for bandgap engineering and charge transfer between layers.^19–25 In this context, various vdWHs have been proposed utilizing graphene, silicene, germanene, and stanene with diverse substrate layers,^26–31 which show a decent tunable bandgap formation while pertaining to the unique 2D characteristics of these materials. Besides, a slight twist in the repeated superlattice pattern (moiré pattern³²) of the vdWHs often creates new topological phases.^23,24 Varieties of extraordinary functionalities can be achieved by deploying these vdWHs in the realization of tunneling transistors, optoelectronics, and spintronic devices.^33–36 

In recent times, interest in germanene has increased linearly to other group-IV elements since the majority of semiconductor devices to date are focused on C, Si, and Ge.³⁷ The sp²–sp³ hybridization among the germanene atoms forms a low buckled structure with a zero bandgap. Germanene^38–40 shows excitonic resonance (π → π^* excitation), which acts as a semimetallic topological insulator.⁴¹ Particularly, due to its massless Dirac fermions, high carrier mobility is obtained in germanene. The incorporation of spin-orbital coupling (SOC) into the pristine germanene structure is capable of opening up ∼24 meV of bandgap around the Fermi level.⁴² Moreover, monolayer germanene could easily be synthesized with the existing technology.^43–45 For example, germanene has been synthesized from Ge deposition onto a gold (111) surface and Ge deposition onto Al(111) single-crystal surfaces. Germanene-based van der Waals heterostructures have also been reported in several theoretical and experimental studies.^11,46 In those studies, single and composite materials, such as germanene,⁴⁷ phosphorene,⁴⁸ antimonene,⁴⁹ h-BN,⁵⁰ MoS₂,⁵¹ ZnSe,⁵² InSe,²⁸ and AlAs,⁵³ were used with germanene to form the vdWHs. The resultant heterostructures showed a remarkable bandgap opening while preserving its unique features. These studies also revealed that by forming a vdWH with a suitable substrate material, germanene properties can significantly be tuned. The investigation is going onward in search of a more prominent heterostructure of germanene that might display pristine germanene properties in an unaltered form.

On the other hand, group III-V compound semiconductors have fascinated great attention due to their promising physical properties, including high bandgaps, extremely high thermal conductivities, high melting points, low dielectrics, low densities, high bulk moduli, and good harness.^54–56 In particular, AlP is of special interest as a substrate material due to its unique properties. AlP forms a zinc-blende crystal structure at standard conditions, with an indirect bandgap of 2.45 eV between the Γ and K points.⁵⁷ AlP is distinctively used in the fabrication of transferred electron devices and infrared (IR) photodetectors.⁵⁸ Moreover, AlP can be used in LEDs and is often alloyed with other binary compounds to form newer optoelectronic devices. Investigations on the heterostructure of ZnSe/AlP,⁵⁹ CuInSe₂/AlP,⁶⁰ and GaP/ZnS/AlP⁶¹ have outlined promising improvements in the electronic and optical properties. The use of AlP as a substrate material in these heterostructure configurations offers significant bandgap creation that can be tuned by varying interlayer spacing, external strain, and electrical field. Therefore, AlP stands as competent to be used as a substrate layer while forming a 2D heterostructure.

In this work, we demonstrated a first-principles study on the electronic properties of germanene/2D-AlP vdWHs. Taking four high symmetrical stacking patterns, we analyzed the stability of the patterns as well as the electronic properties, including the band diagram, the total and partial density of states (DOS), charge density distribution, and charge density differences (CDDs) between the monolayers. We tuned the bandgap by changing the interlayer separations between the layers, varying the bi-axial strain, and applying the electric field to explore the possibility of bandgap engineering. The widely tunable bandgap of ∼200 meV–460 meV was achieved for all of these patterns. We observed an extremely high carrier mobility of about 1.5 × 10⁵ cm² V⁻¹ s⁻¹ for the germanene/2D-AlP (Ge/AlP) heterostructure. Our results propose Ge/AlP heterostructures’ versatile applicability in nanoelectronics, optoelectronics, and spintronic devices.

The structural and electronic properties of the germanene/2D-AlP heterobilayer were analyzed under the density functional theory framework utilizing the plane-wave basis set of the PWscf package of Quantum Espresso suite.⁶² To analyze the impact of the electron density on the exchange–correlation energy, the generalized gradient approximation (GGA) using the Perdew-Burke-Ernzerhof (PBE)⁶³ functional was employed. The optimum norm-conserving pseudopotential interpreted the electron–ion interactions.⁶⁴ Complying to maximum previous investigations, van der Waals weak intermolecular interaction was taken into account by incorporating semi-empirical Grimme’s density functional theory (DFT)-D2⁶⁵ method. As a sampling method for Brillouin zone integration, Methfessel–Paxton first order smooth spreading with a degauss value of 0.0005 Ry was taken. Again, to properly estimate the Brillouin zone integration, a 2D centered Monkhorst–Pack⁶⁶ k-point grid of 22 × 22 × 1 was used. The calculation precision was made up to the mark by setting the total energy convergence threshold as 10⁻⁸ a.u. The kinetic energy cutoffs were set as 50 Ry and 400 Ry for the wave functions and charge densities. The direct interaction between the monolayers of the Ge/AlP vdWH was prevented by considering a 20 Å vacuum level. The electric field was applied along the z axis by setting emaxpos and eopreg values as 0.5 Å and 0.1 Å, respectively. The structures were well relaxed to outline the interaction stability, and from therein, binding energy was calculated using

where E_b is the binding energy per germanene atom, E_Ge/AlP is the total energy of Ge/AlP vdWH, E_Ge is the total energy of the free standing germanene monolayer, E_AlP is the total energy of the free standing AlP monolayer, and N_Ge is the number of atoms contained by the germanene monolayer of the Ge/AlP heterostructure.

While calculating the influence of the applied bi-axial strain (compressive and tensile) on the Ge/AlP vdWH, the normal lattice constant (a_normal) was changed to the strained lattice constant (a_strain) due to the strain (n) by the dint of the following relation:

where the positive and negative sign refer to the tensile and compressive biaxial strain, respectively.

The curvature of the conduction band (CB) minimum and valence band (VB) maximum was analyzed to estimate effective masses of electrons and holes. The effective mass is related to the curvature of the band structure by

wherein m^* stands for the effective mass, k is the wave vector, and E(k) refers to the dispersion energy. Thus, the effective mass increases with a larger radius of the curvature at the point of interest.

Investigation on germanene/2D-AlP (Ge/2D-AlP) starts with considering free-standing germanene and AlP structures. The optimization of the low buckled germanene structure stands with a lattice constant of 4.017 Å along with 0.676 Å buckling height, where the bond-distance between Ge-Ge atoms is found to be 2.352 Å. These optimized findings on free-standing germanene match closely to previous theoretical and practical considerations.^37,47,67 The planar relaxed AlP structure configuration shows a lattice constant of 3.95 Å and fits excellently to prior studies.⁶⁸ The germanene layer’s optimized lattice constant is greater by ∼1.7% than the lattice constant of AlP. Due to this small lattice mismatch, we considered the analysis with 1 × 1 supercell periodicity of the germanene layer over a 1 × 1 AlP supercell layer having the Ge lattice constant compressed to 3.95 Å. The pathway in the structural consideration becomes viable when we compare our structural model with the AlAs/germanene vdWH as investigated by Tan et al.,⁶⁹ where ∼0.24% mismatch was obtained between the germanene and AlAs primitive cells, and a similar 1 × 1 supercell consideration was chosen. Again, for a CdS/germanene vdWH with a mismatch of ∼2.6% between the CdS and the germanene layers, Zheng et al.⁵³ considered a 1 × 1 periodicity of both the CdS and germanene structures. In the investigation of the graphene/2D-SiC vdWH, a mutual mismatch of ∼5% was assessed between the graphene (4 × 4) and 2D-SiC (3 × 3) layers during structural realization.²¹ Besides, the stanene/2D-SiC heterostructure²⁰ having ∼1% mismatch, stanene/h-BN¹⁹ with ∼7% mismatch, and bismuthene/2D-SiC²² with ∼6% mismatch were described between the two ethnic structures.

We arranged the Ge/AlP structure in four distinct and high symmetric patterns: patterns-I, II, III, and IV. Pattern-I and pattern-II are arranged in such a way that the buckle edge Ge atom is placed above the Al and P atoms. Pattern-III and pattern-IV show, respectively, to the standings where the Ge atom is placed in the middle of the AlP hexagon with a change in Al and P atoms’ lateral positions. These distinct patterns are depicted in Fig. 1.

To mark the structural stability of these representative patterns, the binding energy of the system was calculated. Figure 2 shows the change in binding energy per Ge atom with a change in interlayer distances between the germanene and AlP monolayers. The binding energy is also the key to realize the optimal spacing between the monolayers that will form the basis of the electronic realizations. To obtain the optimum distance, the interlayer spacing was varied in the range of 2.5 Å to 3.9 Å. For pattern-I, at an optimum spacing of 3.22 Å, the binding energy was obtained as −108.24 meV/Ge atom. Pattern-II reaches its convergence at 2.71 Å with binding energy as high as −196.12 meV/Ge atom. The highest binding energy of −202.72 meV/Ge atom was found at 2.91 Å for pattern-III. Pattern-IV demonstrated the lowest binding energy of −94.703 meV/Ge atom and converged at an optimum spacing of 3.28 Å. Thus, a high variation both for optimum spacing and binding energies was found for the representative patterns of the Ge/AlP heterobilayer. The binding energy also depicts the mutual interactions between the layers of a heterostructure and the influence of consisting atoms on each other. A distinct variation in the structural patterns’ binding energy also refers to the corresponding patterns’ distinctive electronic properties.

The binding energy lower than 100 meV is generally referred to as the monolayers’ weak vdW attraction forces. Such weak vdW forces were found in the stanene/MoS₂ heterostructure where a binding energy of ∼39 meV per Sn atom was obtained,⁷⁰ and similar findings were reported by Wang et al. that about 18 meV/Ų binding energy could be achieved from the germanene/h-BN heterostructure.⁵⁰ More structures such as silicene/MoSe₂⁷¹ and graphene/h-BN⁷² also constitute weak vdW forces between the monolayers. The binding energy during pattern-IV falls under 100 meV and thus refers to exhibit weak vdW force between the germanene and AlP layers. The higher binding energy is achieved for the rest of the patterns (patterns-I, II, and III). These patterns, thus, refer to the interaction that is stronger than the weak vdW forces. Investigation on heterostructures such as stanene/h-BN,¹⁹ graphene/stanene,⁷³ and bismuthene/2D-SiC²² shows binding energy as higher as 250 meV per Sn-atom, 125 meV per C-atom, and 280 meV per Bi-atom, respectively, and demonstrates that the two distinct layers that constitute the corresponding pattern are bound to each other with forces stronger than the weak vdW force. The atomic radii of the atoms (Ge, Al, and P) were considered to demonstrate whether any covalent bond is present or not. The optimized interlayer distances for the four patterns are at 3.22 Å, 2.71 Å, 2.91 Å, and 3.28 Å, respectively. The summation of the covalent radii of Ge and Al atoms (1.22 Å + 1.43 Å = 2.65 Å), as well as Ge and P atoms (1.22 Å + 1.1 Å = 2.32 Å), are smaller than any of the optimized distance, indicating no mutual contact and absence of the probability of covalent bonds. Previously, Ge/BeO vdWH also showed no such covalent bond formation.⁷⁴ Apart from that, several heterostructures of graphene and silicene have been identified in the literature on various substrates, which form no mutual covalent bonds.^21,25,66,67

Germanene is a group-IV semi-metal and akin to graphene and silicene. In the germanene lattice, Ge atoms are sp²–sp³ hybridized. The bond length in germanene is higher than graphene results in weakened overlapping of the p-orbitals; as a result, a low buckled formation has occurred. The band diagram of the free-standing germanene layer due to the touching of the π and π^* bands at K-points, as depicted in Fig. 3(a), forms a zero bandgap. The π and π^* bands construct similar Dirac cones as in graphene, which resembles previous studies.^39,41 At the Fermi level, the bands are linearly dispersed, resulting in the carriers behaving like Dirac fermions with 3.8 × 10⁵ ms⁻¹ velocity.⁷⁰ Since the spin-orbital coupling (SOC) effect dominates as the atomic mass gets heavier, we also analyzed the SOC effect on the bandgap of germanene. In our study, when SOC has been incorporated, a small bandgap of 24.4 meV is obtained at the Fermi level without any significant change in the band diagram, as depicted in Fig. 3(b). The SOC-induced bandgap of germanene is agreed well with the prior study by Liu et al.,⁴² where a bandgap of ∼23.9 meV was opened at the Dirac point. Figure 3(c) shows the band structure of the free-standing 2D-AlP layer. The optimized AlP is a planar semiconductor material with a 2.24 eV indirect bandgap between the Γ and K points. The optimized findings on AlP are also consistent with past investigations.⁸ These refer to the validity of our calculations.

Band structures for the representative patterns of our Ge/AlP heterostructure are discussed in this section. When the zero bandgap semimetallic germanene is placed in the high bandgap AlP layer’s vicinity, germanene bands get distorted. We outlined quite a distinct and intriguing bandgap and band structure for the different patterns. Pattern-II and pattern-IV exhibit quite a decent direct bandgap at Γ and K points, respectively. Herein, pattern-II possesses higher binding energy and exceeds the weak vdW force than pattern-IV. We observed an indirect bandgap opening for the rest of the patterns.

In pattern-III, an indirect bandgap was found between Γ and K points. Figure 4 shows the band diagram for these patterns and their relative density of states (DOS). For pattern-II and pattern-IV, a direct bandgap of 246.4 meV and 394.5 meV is found. For pattern-I and pattern-III, the observed indirect bandgap stands as 462.2 meV and 199.5 meV, respectively. Thus, our proposed Ge/AlP 2D-vdWH is resourceful to be applied in applications requiring direct or indirect bandgap properties. During the study of a close neighbor AlAs/germanene structure, Tan et al.⁶⁹ considered four stacking patterns AAI, AAII, ABI, and ABII, among which 494 meV indirect bandgap was observed for pattern AAI. The introduction of a bandgap by composing zero bandgap group-IV elements with high bandgap materials is familiar in the literature. A similar bandgap opening phenomenon was observed for graphene,^21,72 stanene,^19,20 and silicene.^50,71 More to that, a decent bandgap ranging from ∼100 meV to ∼300 meV was observed for eight different stacking arrangements of CdS/germanene⁵³ vdWHs. Thus, our findings are in line with previous observations.

The depiction of DOS complies with the observed band diagram of the patterns. Near the Fermi level, an absence of the state refers to a decent bandgap for the corresponding pattern. The electronic properties stand quite distinctively in regard to different stacking arrangements. Due to the interaction of differently arranged AlP atoms, the lattice symmetry of germanene is altered differently, resulting in various band structures. The band structure of pattern-II and pattern-IV maintains the Dirac cones, and energy dispersion near the Fermi level is quite linear, which might retain high electron mobility in the heterobilayer. The Heyd-Scuseria-Ernzerhof (HSE) functional was also used to analyze the experimental realization of the band structure since the PBE functional underestimates the bandgap. Using the HSE-06 functional, we obtained 497.3 meV and 273.1 meV direct bandgaps for pattern-I and pattern-II, where the band structure retains the original configurations that are obtained with the PBE functional. Again, the bandgap also increases to 219.8 meV and 414.1 meV for pattern-III and pattern-IV, respectively. Thus, an enhanced bandgap can be obtained by incorporating the HSE functional. The HSE-06 functional was also utilized during the investigation of heterostructures such as graphene/2D-SiC,²¹ h-BN,⁷⁵ and octagon-nitrogen.⁷⁶ In all the cases, the bandgap estimation increases with the HSE functional. It is thus expected that the experimental realization will offer larger bandgap values than the PBE investigations.

An intriguing electronic structure is perceived with the incorporation of SOC in the Ge/AlP structure. The relative motion of the nucleus and electrons is considered in SOC, which changes the energy level, resulting in a change in the bandgap. The difference in the band structure with SOC is demonstrated in Fig. 5. Our findings show that the bandgap reduces to 414.1 meV, 150.6 meV, 88.3 meV, and 370.4 meV from their original value of 462.2 meV, 246.4 meV, 199.5 meV, and 394.5 meV as found without SOC incorporation for patterns I–IV, respectively. The reduction in bandgap complies well with previous works.^22,62,71 Quite a significant decrease in the bandgap is obtained for the bismuthene/2D-SiC heterostructure, where the initial bandgap value of 552 meV is turned to 124 meV after the SOC influence is counted.²² Again, for silicene/MoSe₂⁷¹ and graphene/h-BN⁷² heterostructures, SOC introduces bandgap reduction. For silicene/MoSe₂,⁷¹ the bandgap reduces by 7 meV, while for graphene/h-BN⁷² it abates to almost half of the value from its original value of 44.6 meV.

To analyze the DOS in a bit more insightful manner, the total and the atom projected density of states (PDOS) are detailed in this portion. Since pattern-III demonstrates the most stable binding configuration, we have selected only pattern-III for the performance measurements in the later part. We investigated the contribution of Ge, Al, and P atoms to form the overall DOS of pattern-III, as displayed in Fig. 6. From Fig. 6(a), the Ge atom contributed dominantly near the bandgap. The quest for the orbital contribution of the atoms to the total PDOS is shown in Fig. 6(b). Taking energy levels ranging from −2 eV to 0 eV in the valence band (VB) side and 0 eV+2 eV in the conduction band (CB) side, the total and atom projected density of states are plotted. According to Fig. 6(b), the p-orbital of germanene stands to be the most prominent one in the proximity of CB-minima and VB-maxima. Thus, the p-orbital of germanene will shape the significant electronic properties of the heterostructure patterns, indicating that the germanene layer will control the properties of electron transport and carrier mobility.

Next, we investigate the charge distribution and charge density difference (CDD) between the VB and the CB. The real space charge density of the germanene and 2D-AlP layer of pattern-III at the CB and VB is demonstrated in Fig. 7(a). At the VB, the charge is confined only across the germanene layer with no significant charge contribution from the AlP layer. At the CB, the orbitals are hybridized between the monolayer atoms. The charge is thus distributed between the layers. Due to this hybridization between the layers, the AlP layer will also shape the overall electronic characteristics of the heterostructure. A significant prominent portion of charge will confine within the germanene layer only, making the germanene layer the property builder for the heterostructure pattern. Charge carriers are only offered to move through the germanene layer; thus, Ge will control the carrier’s mobility. AlP slightly contributes to the carrier transportation and controls the electronic properties, which justify the efficacy of choosing AlP as the substrate and modulator of the Ge/AlP heterobilayer.

The charge distribution between the germanene and AlP layers is also described. Figure 7(b) represents the pictorial view of the charge density difference (CDD) between the layer of the Ge/AlP heterostructure for pattern-III. The CDD plot utilized the formula

where ∇Q is the charge density difference, Q_Ge/AlP is the total charge density of the Ge/AlP heterostructure, Q_Ge is the total charge density of the germanene monolayer, and Q_AlP is the total charge density of the AlP monolayer. The greenish-blue color in Fig. 7(b) represents a depletion of charges, while reddish-yellow stands for the accumulation of charges. It is evident from Fig. 7(b) that the depletion of charges occurs at the AlP layer, whereas the germanene layer is subjected to charge accumulation. Thus, the charges are transferred from the AlP layer onto the germanene layer. Orbital overlapping of the atoms and the influence of the neighboring layer’s internal electric field might cause this charge distribution. Due to this interlayer charge transfer, a localization of charge rearrangement is observed at the interface of the Ge and AlP layers. At the germanene monolayer, the buckled and planar Ge atom does not similarly contribute to charge accumulation and causes intra-layer charge redistribution, which breaks the germanene layer’s symmetry. When the zero bandgap germanene’s lattice symmetry is broken up, the bands get distorted, resulting in an introduction of the bandgap at the Γ-point of the first Brillouin zone.

Next, we analyze the effective mass of electrons and holes of the proposed heterostructure. As depicted by the band diagrams, the VB maximum and the CB minimum retain the linear dispersion phenomenon. The curvature being dispersed is analyzed to develop the effective mass of electrons and holes for each pattern. Utilizing Eq. (3), the effective mass of electrons and holes is calculated and tabulated in Table I. Since these values are relatively small compared to the resting electron mass, the structures are highly favorable. Using the relation between the effective mass of the electron (m_e^*) and carrier mobility given by μ = $(eτme*)$⁠, an estimation of the electron’s mobility can be obtained, where e is the electron charge. Taking the scattering time (τ) of graphene⁷⁷ or silicene⁷⁸ (∼10 ⁻¹³ s) as the base, the electron mobility for patterns I–IV is found to be 0.89 × 10⁴ cm² V⁻¹ S⁻¹, 16.4 × 10⁴ cm² V⁻¹ S⁻¹, 8.44 × 10⁴ cm² V⁻¹ S⁻¹, and 2.39 × 10⁵ cm² V⁻¹ S⁻¹, respectively. The mobility of intrinsic germanene, as previously studied, is 10 × 10⁴ cm² V⁻¹ S⁻¹.⁸⁰ For pattern-II, we found higher carrier mobility than in any existing germanene heterostructure; this is true even for the intrinsic germanene structure. The bandgap of pattern-II occurs at a high symmetric Γ-point. Thus, with such a decent direct bandgap and high mobility, it stands as an intriguing resource to be used for the manufacturing of high-speed nanoelectronic devices and spintronics.

In the development of nanoelectronic devices, materials with tunable electronic properties are the essential precondition. In this part of our investigation, bandgap tuning of the Ge/AlP heterostructures is considered. Figure 8 depicts the bandgap’s variation with a change in the interlayer separation (2.5 Å to 3.9 Å) between the germanene and 2D-AlP layer of pattern-III. An extraordinary bandgap tuning capability in the range 0 eV–0.71 eV is determined. The bandgap at first slightly increases as the AlP layer comes to closer vicinity of the germanene layer. The influence of the AlP layer on the germanene layer increases when the interlayer distance is decreased from the optimized point, which distorts the lattice symmetry of the germanene, resulting in an additional bandgap level. However, with more reduction in the interlayer separation, the interlayer coupling between the germanene and AlP layer becomes significantly higher, disrupting the band structure, and as a result, the bandgap starts decreasing. The reduction in the bandgap is exhibited if the interlayer distance between the germanene and AlP is changed to a higher value than the optimized level. The higher separation between the layers causes lower mutual interaction and influence from AlP to the germanene layer. The germanene starts retaining its pristine characteristics, changing the bandgap limit back toward zero, converging to the earlier studies.^20,21,72

Afterward, the biaxial strain was incorporated into the heterostructure. The change in the bandgap with applied strain ranging from −1% (compressive) to +5% (tensile) for pattern-III is shown in Fig. 9. It can be realized that the bandgap changes quite noticeably in the range of 0 meV–290 meV. With an increase in biaxial strain from −1% to +2%, the bandgap first roughly increases, but after a further increase in tensile strain, the bandgap starts decreasing. According to Fig. 9, the bandgap can be modulated by applying both the tensile and compressive strain. The electron mobility relative to the applied biaxial strain is also shown in Fig. 9. When the curvature of the VB and CB becomes larger, the effective mass of the carriers becomes higher. For the increase in strain from −1% to +2%, the effective mass of electrons increases. Afterward, changing the tensile strain from +3% to +4% decreases the curvature of the CB, leading to the decrease in m_e^*. Thus, with the change in the strain, the electron mobility can be tuned within the range of 5 × 10⁴ cm² V⁻¹ s⁻¹ to 15 × 10⁴ cm² V⁻¹ s⁻¹.

After that, the variation of the bandgap with a change in the electric field is calculated for pattern-III. The positive electric field direction is taken from the AlP layer to the germanene layer. Increasing the electric field from −0.5 V/Å to +0.5 V/Å, the bandgap can be tuned within the range from 195 meV to 202.5 meV, as shown in Fig. 10. The effect of the electric field on the electron mobility is also depicted in Fig. 10. In general, the mobility of electrons increases with relative magnitude, with a more positive electric field being applied. The increased mobility is due to an additional electric field on the electrons. The impact of an electric field depends mainly on the distinct structural configuration. With various patterns of the germanene/2D-AlP heterobilayer, different characteristics will be exhibited. When external stimuli (i.e., biaxial-strain and vertical electric fields) are applied, we observe a distinct feature of the charge contribution from the orbitals of the Ge atom. As can be seen from Figs. 11 and 12, with no significant change in the hybridization (sp²–sp³) of the germanene layer, although with an increase in strain (Fig. 11) from 0% to 5%, the contribution of the Pyz orbital dramatically increases in both the valence and conduction bands.

Similarly, with a change in the vertical electric field from 0 to +0.3 V/Å (Fig. 12), the Pyz orbital starts dominating the other orbitals. This phenomenon continues with a larger magnitude of external stimuli. Our investigation revealed that the semiconductor–metal phase transition occurs with a change in the external stimuli (external strain and vertical electric field). The influence due to the incorporation of the external electric field has also been investigated for bilayer phosphorene,^79–81 where Le et al. demonstrated that with a vertical electrical field, both the electronic phase transition (semimetal to metal) and the magnetic phase transition (antiferromagnetic to paramagnetic to ferromagnetic)⁸² can be achieved. Moreover, the investigation with Bernal stacking bilayer h-BN and graphene⁸³ shows that an external electrical field when applied vertically to the bilayers can break the inversion symmetry; this phenomenon leads to the electronic phase transition.

Finally, we have investigated the dynamical stability of the heterostructures for the fabrication purpose. Figure 13 represents the phonon dispersion relation and vibrational density of states for pattern-III. As the rest of the patterns roughly show a negative phonon frequency near the low acoustic frequency branches, they are discarded from the analysis. Since no negative phonon frequency has been achieved, pattern-III will be mechanically stable. Thus, it can be posited from the binding energy and phonon dispersion that pattern-III will present the most stable configuration for the consideration of commercial fabrication of the proposed germanene/2D-AlP heterobilayer.

In conclusion, the first principles calculation was performed for the theoretical realization of the electronic properties of the Ge/AlP 2D heterobilayer. Four highly symmetric stacking arrangements were investigated, which demonstrate weak vdW to very strong binding forces. Each of the patterns showed distinct band structures contributing to a bandgap limit of 199.5 meV–462.2 meV. The SOC incorporation significantly reduces the bandgap by ∼20 meV–90 meV. By considering the most stable pattern, the analysis of the atom projected density of states and charge density distribution was performed. These investigations showed that the germanene layer dominates the controlling of the electron transport and high mobility. The CDD of the heterobilayer showed the charge accumulation on the germanene layer from the AlP layer, justifying the results found from PDOS and charge density calculation. Moreover, a high tuning ability with a change in bandgap from around 0 meV to 500 meV by changing the interlayer separation between the germanene and AlP layers is revealed. The bandgap can also be tuned by changing the applied bi-axial strain. With a significant change in electron effective mass with applied strain, the bandgap changes in the range 0 meV–300 meV. The sawtooth-like external electric field application results in an outstanding bandgap tunability of the considered Ge/2D-AlP heterobilayer. We observed a high electron mobility of greater than 15 × 10⁴ cm² V⁻¹ s⁻¹, which happens to be the highest compared to other prior studies. The dynamical stability of the heterobilayer was also verified by the phonon dispersion relation. A large direct bandgap, higher mobility, and extensively tunable properties observed in the germanene/2D-AlP heterostructure will pave a significant impact toward further studies on germanene based nanoelectronic devices.

The authors have no conflicts of interest to declare.

The data that support the findings of this study are available from the corresponding author upon reasonable request.