A resilient type-III broken gap Ga2O3/SiC van der Waals heterogeneous bilayer with band-to-band tunneling effect and tunable electronic property

The potential of van der Waals (vdW) heterostructure to incorporate the outstanding features of stacked materials to meet a variety of application requirements has drawn considerable attention. Due to the unique quantum tunneling mechanisms, a type-III broken-gap obtained from vdW heterostructure is a promising design strategy for tunneling field-effect transistors. Herein, a unique Ga2O3/SiC vdW bilayer heterostructure with inherent type-III broken gap band alignment has been revealed through first-principles calculation. The underlying physical mechanism to form the broken gap band alignment is thoroughly studied. Due to the overlapping band structures, a tunneling window of 0.609 eV has been created, which enables the charges to tunnel from the VBM of the SiC layer to the CBM of the Ga2O3 layer and fulfills the required condition for band-to-band tunneling. External electric field and strain can be applied to tailor the electronic behavior of the bilayer heterostructure. Positive external electric field and compressive vertical strain enlarge the tunneling window and enhance the band-to-band tunneling (BTBT) scheme while negative electric field and tensile vertical strain shorten the BTBT window. Under external electric field as well as vertical and biaxial strain, the Ga2O3/SiC vdW hetero-bilayer maintains the type-III band alignment, revealing its capability to tolerate the external electric field and strain with resilience. All these results provide a compelling platform of the Ga2O3/SiC vdW bilayer to design high performance tunneling field effect transistor.


Computational methods
First-principles Density Functional Theory (DFT) calculations have been carried out using the Vienna Ab initio Simulation Package (VASP) in the MedeA software setting 58 .To approximate the exchange-correlation potential, we adopted the Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA), while projector-augmented wave (PAW) method is employed to define the electron-nuclear interactions 59,60 .We adopted a vacuum region of around 25 Å along the Z axis to exclude the interaction between the two succeeding layers.The pane-wave cut-off energy was taken as 500 eV.We utilized a 12 × 12 × 1 Monk- horst-Pack (MP) k-point grid for geometry optimization and electronic band structure calculation, while a 24 × 24 × 1 MP grid is used to calculate the density of states (DOS) 61 .We performed Grimme's DFT-D3 method for the van der Waals correction 62 .A force convergence criterion of 0.01 eV/Å was chosen to optimize the structures while 10 -5 eV was the energy converge criterion for the self-consistent field.In addition, Density Functional Perturbation Theory (DFPT) is used to compute the dynamic stability forecasting phonon dispersion relation 63 .Charge redistribution in the heterostructure is quantitatively analyzed using Bader charge analysis 64 .

Results and discussion
The Ga 2 O 3 /SiC van der Waals (vdW) heterostructure is obtained by vertically stacking the SiC layer and Ga 2 O 3 layer.The structural, electronic property, and electron localization function (ELF) of the individual Ga 2 O 3 and SiC 2D structures are provided in the supporting information.The lattice mismatch ( ) between the two layers is 0.08%, as obtained by the relation, = a SiC −a Ga 2 O 3 a SiC +a Ga 2 O 3 × 100% , where a SiC and a Ga 2 O 3 are the optimized lattice constants of the SiC and Ga 2 O 3 monolayer, respectively.The small lattice mismatch between the two layers suggest the experimental realization of the Ga 2 O 3 /SiC vdW heterostructure.Our Ga 2 O 3 /SiC vdW bilayer is comparable to the VS 2 /Ga 2 O 3 heterostructure where the lattice mismatch between the VS 2 and Ga 2 O 3 layer is 2.17% 44 .In addition, Chen et al. studied the photocatalytic and electrical properties of the MoS 2 /Ga 2 O 3 bilayer where the lattice mismatch between the two layers was 3.31% 39 .Depending on the relative places of the different atoms of the 2D Ga 2 O 3 and SiC, four stacking patterns are considered, namely as X 1 , X 2 , X 3 , and X 4 , as shown in Fig. 1.

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The dynamic stability of the Ga 2 O 3 /SiC heterogeneous bilayer is evaluated by calculating the phonon dispersions of the bilayer.The phonon dispersion spectra of the X 1 , X 2 , X 3 and X 4 patterns are also illustrated in Fig. 1.The stacking patterns considered are dynamically stable since there is no soft frequency mode present in their phonon dispersion spectra.
The energetic stability of a bilayer structure can be assessed by obtaining the binding energy of the structure.Negative binding energy value suggests the energetic stability of the bilayer structure.The binding energy ( E B ) of the different stacking arrangements of the heterogeneous bilayer is obtained through the relation: where S denotes the interface contact area of the heterogeneous bilayer, E Ga 2 O 3 /SiC represents total energy of the Ga 2 O 3 /SiC hetero-bilayer and E Ga 2 O 3 , E SiC correspond to the energy of the free-standing Ga 2 O 3 and SiC monolayer, respectively.The binding energies of the stacking models are summarized in Table S1, ranging from − 20.48 to − 28.15 meV/Å 2 .The results suggest that all four models are energetically stable.Table S1 also enlists the optimized interlayer distances of the stacking patterns of the Ga 2 O 3 /SiC heterogeneous bilayer, extending from 3.025 to 3.546Å.The electronic band structures of the stacking models are provided in Figure S2.As Figure S2 indicates, the electronic band diagrams of the four models show metallic properties, with the VBM is above the Fermi level and the CBM is below the Fermi level.This indicates that all the stacking patterns of the Ga 2 O 3 /SiC bilayer possess type-III (broken gap) band alignment.
Among the four (dynamic stable) models, pattern X 1 is the most energetically favorable model with the minimum binding energy (− 28.15 meV/Å 2 ) and optimized interlayer distance (3.025 Å).Hence, for our subsequent study, we focus on the X 1 stacking model of the Ga 2 O 3 /SiC heterogeneous bilayer.The ELF of the Ga 2 O 3 /SiC bilayer is illustrated in Fig. 2a, where from weak interlayer interaction between the two layers can be visualized.No electron is localized at the hetero-bilayer interface, suggesting the absence of binding between the Ga 2 O 3 and SiC layer and verifying weak vdW interaction between the two layers of the Ga 2 O 3 /SiC bilayer.
Next, we study the type of band alignment, which is an important intrinsic property of the vdW bilayer heterostructure.The projected band structure and the partial density of states (PDOS) of the X 1 model of the Ga 2 O 3 /SiC bilayer structure are represented in Fig. 2b.The Fermi energy level is set to the zero value.The contribution of the Ga, O, Si and C atom in the electronic band diagram is denoted by the navy blue, cyber yellow, green and sky-blue colors, respectively.Apparently, VBM comes from the C atom of the SiC layer and is located on the K point.CBM is contributed by the O atom of the of the Ga 2 O 3 layer and located at the Ŵ point.It can be clearly observed that CBM lies below the VBM, generating a negative band gap of 0.609 eV and thus confirming a type-III (broken gap) band alignment of the Ga 2 O 3 /SiC bilayer structure.It is important to note that, these type-III vdW heterogeneous bilayers exhibit apparent negative differential resistance characteristics owing to the presence of band-to-band tunneling (BTBT) 65 .
To shed light on the physical mechanism of the broken gap band arrangement of the Ga 2 O 3 /SiC heterogeneous bilayer, schematic illustration of the band alignments of the free-standing Ga 2 O 3 monolayer, free-standing  www.nature.com/scientificreports/Fermi energy level owing to the type-III band alignment feature.This is called the BTBT phenomenon, occurring in the type-III vdW heterogeneous bilayer and suggesting its potential application in tunneling field effect transistor (TFET).
In order to reveal the charge rearrangement and the formation mechanism of the interlayer coupling of the Ga 2 O 3 /SiC heterogeneous structure, we calculated the plane-averaged charge density difference along the Z-axis as well as the three-dimensional iso-surface of the charge density difference of the heterostructure.The charge density difference of the vdW heterostructure is obtained employing the following relation: where �ρ is the charge density difference of the Ga 2 O 3 /SiC heterogeneous structure and ρ Ga 2 O 3 /SiC , ρ Ga 2 O 3 and ρ SiC denote the charge density of the bilayer heterostructure, free-standing Ga 2 O 3 layer and free-standing SiC layer, respectively.The plane-averaged charge density difference of the vdW bilayer is represented in Fig. 3a while the inset shows the 3D iso-surface of the charge density difference.The yellow color represents an increase of charge while the cyan color represents a decrease of charge.From Fig. 3a, one can clearly observe that, charge is depleted mostly from the SiC layer while it is accumulated on the Ga 2 O 3 layer, suggesting the transfer of charge from the SiC layer to the Ga 2 O 3 layer.Charge redistribution mainly occurred at the interface region of the vdW heterogeneous bilayer.In addition, Bader charge analysis is carried out to quantify the charge redistribution at the heterostructure interface which reveals that an amount of 0.079e charge is transferred from the SiC layer to the Ga 2 O 3 layer.This confirms that a built-in electric field is induced at the heterostructure interface and supports the formation mechanism stated earlier.
An important factor for the field effect transistor performance is the tunneling probability, which can be calculated from the energy barrier at the heterostructure interface.A tunneling barrier is generated by the accumulation of negative charges at the heterostructure interface.This tunneling barrier can be quantitatively illustrated in the electrostatic potential diagram, as seen in Fig. 3b 66,67 .The tunneling barrier is reduced by the type-III broken gap, resulting in a significant tunneling probability 68,69 .The following relation is utilized to calculate the tunneling probability 70 : where P TB is the tunneling probability, is the reduced Planck constant and m is the free electron mass.ω TB and TB refer to the tunneling barrier width and height, respectively and illustrated in Fig. 3b.TB is the difference in height between the maximum potentials of the vdW space and the Ga 2 O 3 monolayer while ω TB is www.nature.com/scientificreports/described as the vdW space barrier width at the maximum potential of the Ga 2 O 3 monolayer.In our calculation, we obtained 4.19 eV and 1.61 Å as the tunneling barrier height and width, respectively and the tunneling probability is 37.83%.This is higher than the tunneling probability of the InS/Au bilayer structure 71 as well as that of the KAgSe/ SiC 2 vdW heterogeneous bilayer 72 and suggests a higher efficiency in the injection of the carriers for the Ga 2 O 3 /SiC hetero-bilayer.Charge transfer across the interface of the vdW heterogeneous bilayer substantially affect the electronic properties of the hetero-bilayer, and various external factors, including biaxial strain, external electric field, as well as vertical strain can efficiently tune the electronic properties of the vdW hetero-bilayer 15,[73][74][75][76][77][78][79][80][81] .Hence, the electronic properties of the Ga 2 O 3 /SiC bilayer are systematically studied under the influence of these external factors.
In practical applications, the electronic behaviors of the two-dimensional materials and devices can be tuned by the gate voltage to address various application requirements 82 .Therefore, the influence of the gate voltage on the electronic behavior of the Ga 2 O 3 /SiC vdW hetero-bilayer is examined by applying an electric field perpendicular to the layers of the heterostructure (along the Z axis).Herein, the positive electric field points from the SiC layer to the Ga 2 O 3 layer while the negative electric field points from the Ga 2 O 3 layer to the SiC layer.The atom projected electronic band structures of the Ga 2 O 3 /SiC layer under electric fields ranging from − 0.5 to + 0.5 V/Å are illustrated in Fig. 4a. Figure 4b,c present the band edge positions and electronic band gap (E g ) under the variation of the external electric field, respectively.The broken-gap band alignment feature is well maintained within this range of external electric field.Under a positive electric field, the CBM of the bilayer contributed by the Ga 2 O 3 layer goes downward (indicated by the dashed red arrow in Fig. 4a), while the bilayer VBM contributed by the SiC layer is pushed upward (indicated by the dashed green arrow in Fig. 4a), hence increasing the magnitude of the negative electronic band gap (Fig. 4c).Alternatively, the tunneling energy window, which is the difference in energy from the VBM of the SiC layer to the CBM of the Ga 2 O 3 layer, is expanded upon the application of the positive electric field.Accordingly, there will be an increase in the quantity of electron tunneling from the VBM of the SiC layer to the Ga 2 O 3 layer CBM.Thus, the tunneling probability will be increased, which will enhance the BTBT mechanism.On the other hand, applying an external negative electric field causes the VBM of the Ga 2 O 3 /SiC bilayer heterostructure to shift downward while the CBM of the heterobilayer moves upward (Fig. 4a,b), thereby decreasing the magnitude of the negative band gap.Consequently, the tunneling window is narrowed, and this will decrease the amount of charge tunneling from the SiC layer VBM to the Ga 2 O 3 layer CBM.Thus, tunneling probability is reduced under the influence of a negative electric field and the BTBT mechanism is weakened.A similar type of phenomenon is also reported in the WTe 2 /HfS 2 vdW heterostructure studied by Lei et al. 83 .
Analysis on the direction of the applied external electric field and the intrinsic built-in electric field at the interface of the Ga 2 O 3 /SiC vdW bilayer provides an intuitive understanding of the evolution of the electronic band structure of the vdW hetero-bilayer upon the application of external electric field.The amount of charge www.nature.com/scientificreports/transfer ( q ) with respect to the applied electric field is summarized in Fig. 4d.The direction of the positive external electric field coincides with the inherently built-in electric field of the hetero-bilayer.Therefore, applying positive external electric field reinforces the inherent built-in electric field and the amount of charge transfer from SiC layer to the Ga 2 O 3 layer is significantly increased, as illustrated in Fig. 4d.This leads to an upshift in the VBM of the vdW bilayer and a downshift in the heterogeneous bilayer CBM, resulting in the tunneling window to broaden and an enhancement in the BTBT mechanism.On the other hand, negative external electric field is directed opposite to the direction of built-in electric field.Hence, negative external electric field weakens the built-in electric field and the amount of electron transfer at the interface is decreased (Fig. 4d).As a result, the tunneling energy window is reduced and the VBM moves downward while the CBM shifts upward.Moreover, we have also studied the effect of external electric fields on the structure of the Ga 2 O 3 /SiC vdW bilayer heterostructures, which is provided in the supporting information.Strain engineering is regarded as an effective approach to trigger the electronic properties of the two-dimensional materials 84,85 .Herein, the effect of vertical strain on the electronic properties of the Ga 2 O 3 /SiC vdW hetero-bilayer is studied.Vertical strain ( D ) is applied to the heterostructure through changing its interlayer distance.We introduced vertical strain ( D ) ranging from − 0.5 to + 0.4 Å to the Ga 2 O 3 /SiC vdW heterostructure.A positive value of D corresponds to tensile vertical strain while a negative value is for compressive vertical strain.Experimentally, vacuum thermal annealing or applying pressure using a scanning tunneling microscope tip can be used to modify the interlayer distance 86,87 .The evolution of the band structure under various vertical strain is shown in Fig. 5a.The electronic band diagram of the Ga 2 O 3 /SiC vdW bilayer maintains the type-III band alignment at different interlayer distances, as shown in Fig. 5a.This suggests that Ga 2 O 3 /SiC vdW bilayer's distinct band alignment can firmly tolerate vertical strain.Besides, applying compressive vertical strain causes the VBM of the SiC layer to rise while the CBM from the Ga 2 O 3 layer moves downward.This increases the magnitude of the negative band gap (Figure S4) and widens the tunneling energy window, and the BTBT effect is increased.Conversely, when tensile vertical strain is applied to the heterostructure, the SiC layer VBM pulls down at the Ŵ point while the CBM of the Ga 2 O 3 layer at the K point rises, leading to the magnitude of the E g to decrease (Figure S4) and hence narrowing the tunneling energy window.
To shed light on the effect of vertical strain on the electronic behavior of the Ga 2 O 3 /SiC bilayer heterostructure, the amount of charge transfer and the binding energy change under varying vertical strain is depicted in Fig. 5b.The binding energy of the vdW bilayer is negative under all vertical strains considered, suggesting the energetic stability of the system regardless of the vertical strain applied.Besides, when the system is without vertical strain ( D = 0), the negative binding energy is the maximum, agrees well with earlier study 88 .With the increase of the interlayer distant of the Ga 2 O 3 /SiC bilayer system, the amount of charges transferred ( q ) decreases monotonically, revealing weaker interlayer interaction while the interlayer distant is increased.3D iso-surface of the charge density difference plot of the Ga www.nature.com/scientificreports/shown in Fig. 5c, wherefrom it can be clearly visualized that, reducing the interlayer distant of the bilayer system causes increased charge redistribution at the interface of the Ga 2 O 3 /SiC bilayer.Apart from vertical strain, we also investigate the effect of biaxial strain on the electronic properties of the Ga 2 O 3 /SiC bilayer heterostructure.The biaxial strain has been incorporated to the heterostructure using the following relation: where e is the percentage of biaxial strain applied to the heterostructure, a 0 corresponds relaxed lattice constant of the system while a denotes the strained lattice constant of the heterostructure.A positive value of e corresponds to tensile biaxial strain, while a negative value refers to compressive biaxial strain.Biaxial strain ranging from − 6 to + 6% is applied to the heterostructure system.Figure 6 summarizes the results of applying biaxial strain, while the evolution of the band structure under varying percentages of biaxial strain is shown in Figure S5.Compressive biaxial strain causes both the VBM of the SiC layer and CBM of the Ga 2 O 3 layer to rise while the tensile biaxial strain pushes both the VBM and CBM of the bilayer system downward (Fig. 6a).However, in both cases, the magnitude of the negative band gap (E g ) decreases slightly from the unstrained band gap (Fig. 6b).There is a slight increase in the amount of charges transfer ( q) from the SiC layer to the Ga 2 O 3 layer with the increasing percentage of biaxial strain, as shown in Fig. 6c.Overall, Ga 2 O 3 /SiC bilayer system preserves the type-III band arrangement under varying percentages of biaxial strain, revealing that the bilayer system is capable of withstanding biaxial strain with resilience.In addition, we have also examined the dynamic stability of the Ga 2 O 3 /SiC vdW bilayer heterostructure under biaxial strain by calculating its phonon dispersion relations.The dynamic stability of the bilayer system under biaxial strain from + 6 to − 6% strain is discussed in the supporting information.
As the FE Ga 2 O 3 monolayer has two polarization states, there is another polarization state of the Ga 2 O 3 monolayer, where the middle O atom is near the upper O layer (regarded as downward polarization).Hence, another type of stacking model of the hetero-bilayer is possible when the SiC layer is stacked below the Ga 2 O 3 layer with its downward polarization state (denoted as Ga 2 O 3↓ /SiC).We also investigated the structural and electronic properties of the Ga 2 O 3↓ /SiC vdW hetero-bilayer taking a representative stacking model of the Ga 2 O 3↓ /SiC vdW heterostructure as shown in Fig. 7a.The optimized interlayer distance is 3.38 Å while the binding energy for the Ga 2 O 3↓ /SiC vdW heterostructure system is − 17.23 meV/Å 2 , indicating the energetic stability of the system.The atom projected band structure of Ga 2 O 3↓ /SiC vdW heterostructure is shown in Fig. 7b.The bilayer system shows a semiconducting property with an electronic gap of 0.243 eV.The VBM is contributed by the C atom of the SiC layer while CBM comes from the O atom of the Ga 2 O 3 layer, confirming the type-II (staggered) band alignment.Such a type-II band alignment is appealing for solar energy conversion and optoelectronic devices 89 .Therefore, Ga 2 O 3 /SiC vdW heterogeneous bilayer combines the features of the type-II and type-III band alignments when SiC layer is stacked below the Ga 2 O 3 layer considering its two different polarization states.

Conclusion
To conclude, a novel Ga 2 O 3 /SiC vdW bilayer heterostructure with inherent type-III broken gap band alignment has been revealed through first-principles DFT calculation.Negative binding energy of the Ga 2 O 3 /SiC bilayer system suggests energetic stability while the dynamic stability of the heterostructure was confirmed by the phonon dispersion spectrum.A tunneling window of 0.609 eV is created due to the overlapping band structures, fulfilling the required condition for the BTBT mechanism, enabling the charges to tunnel from the VBM of the SiC layer to CBM of the Ga 2 O 3 layer.The effect of external electric field and strain on the electronic properties of the Ga 2 O 3 /SiC vdW hetero-bilayer has been studied.External vertical electric fields and strains can be www.nature.com/scientificreports/introduced to adjust the electronic behavior of the bilayer system to enhance the BTBT effect.Positive external electric field and compressive vertical strain widen the tunneling window and enhance the BTBT effect while negative electric field and tensile vertical strain decrease the tunneling window.Under external electric field and different types of strain, the Ga 2 O 3 /SiC vdW bilayer system maintains type-III broken gap band formation, revealing that the system is capable of withstanding external electric field and strain with resilience.Another type of configuration of the bilayer, where the SiC layer is stacked below the downward polarization state of the Ga 2 O 3 layer, shows a type-II band alignment with an electronic gap of 0.243 eV.All these findings reveal that the Ga 2 O 3 /SiC vdW heterogeneous bilayer offers tremendous potential for tunneling field-effect transistor as well as multi-purpose electronic device.

Figure 2 .
Figure 2. (a) Electron localization function, (b) projected band structure and partial density of states (PDOS) of the Ga 2 O 3 /SiC vdW bilayer heterostructure.The Fermi level is set to the zero value.In the projected band diagram, the contribution from the Ga, O, Si, and C atom is represented by the navy blue, cyber-yellow, green, and sky-blue colors, respectively.(c) Band alignment of the Ga 2 O 3 and SiC layer before and after forming the Ga 2 O 3 /SiC vdW bilayer heterostructure.refers to the work-function of the material.

( 4 )Figure 3 .
Figure 3. (a) Plane-averaged charge density difference of the Ga 2 O 3 /SiC vdW bilayer heterostructure along the Z axis.The inset shows the 3D iso-surface of the charge density difference of the Ga 2 O 3 /SiC vdW bilayer heterostructure with an iso-value of 0.0005 e/ Å 3 .The yellow and cyan colors represent the accumulation and depletion of charge, respectively.(b) Electrostatic potential profile of the Ga 2 O 3 /SiC vdW bilayer heterostructure.

Figure 4 .
Figure 4. (a) Projected band diagram of the Ga 2 O 3 /SiC vdW bilayer heterostructure under different electric fields applied.(b) The change of CBM and VBM, (c) electronic band gap (E g ), and (d) charge transfer ( q ) of the Ga 2 O 3 /SiC vdW bilayer heterostructure as a function of external electric field applied along the Z axis.

2 O 3 /Figure 5 .
Figure 5. (a) Projected band diagram of the Ga 2 O 3 /SiC vdW bilayer heterostructure under various vertical strains applied to the heterostructure.The Fermi level is set to the zero value.(b)The change of the binding energy and charge transfer ( q ) of the bilayer heterostructure with respect to the vertical strain applied to it.(c) 3D iso-surface of the charge density difference of the Ga 2 O 3 /SiC vdW bilayer heterostructure under different vertical strains applied to it.The cyan and the yellow colors denote the decrease and increase of charge, respectively.

Figure 6 .
Figure 6.The change of (a) CBM and VBM position, (b) band gap (E g ), and (c) charge transfer ( q ) of the Ga 2 O 3 /SiC vdW bilayer heterostructure under various biaxial strains applied to the heterostructure.

Figure 7 .
Figure 7. (a) Stacking model of the Ga 2 O 3 /SiC vdW bilayer heterostructure considering the downward polarization state of the FE Ga 2 O 3 layer, and (b) the corresponding projected band diagram.