First Principle Study on Schottky Barrier at Ni/Graphene/4H-SiC Interface

High stability 4H-SiC ohmic contact is currently a key technical challenge that silicon carbide devices urgently need to overcome. It is important to reduce the Schottky barrier height (SBH) at the Ni/4H-SiC interface to optimize ohmic contact. In this paper, the mechanisms of graphene layer changing Ni/4H-SiC interface Schottky barrier height (SBH) are studied based on the first-principles method within the local density approximation. Theoretical studies have shown that graphene intercalation can reduce the SBH of Ni and 4H-SiC interfaces. The reason of SBH reduction may be that the graphene C atoms saturate the dangling bonds on the 4H-SiC surface and the influence of the metal-induced energy gap state at the interface is reduced. In addition, the new phase formed at the interface of graphene and silicon carbide has a lower work function. Furthermore, an interfacial electric dipole layer may be formed at the 4H-SiC/graphene interface which may also reduce the SBH. These results make them to be promising candidates for future radiation resistant electronics.


Introduction
Silicon carbide (SiC) has a wider bandgap, higher atomic displacement energy [1], critical breakdown field strength, saturated electron drift velocity and thermal conductivity.This determines that SiC has inherent advantages such as radiation resistance, high temperature resistance [2], low noise, high working voltage [1], high energy resolution [3] , high charge collection efficiency, and fast time response [3].High stability SiC ohmic contact is currently a key technical challenge that silicon carbide devices urgently need to overcome.The quality of ohmic contact performance directly affects the device performance [4].It is difficult for metals to directly form lower potential barriers to obtain ohmic characteristics when in contact with wide bandgap SiC.Due to the electronic affinity and surface density of states constraints of silicon carbide, the Ohmic contact resistivity formed by high-temperature annealing is high, with poor stability and low process repeatability [5].High temperature annealing can activate impurities in silicon carbide, leading to scattering of electrical signals, which limits the improvement of signal-to-noise ratio, charge collection, time resolution, and operational stability [1].
Stefan Hertel found that graphene can provide perfect ohmic contact with low-doping SiC epitaxial layers [6].Zheng Jiangshan et al. verified that applying voltage can achieve p-type ohmic contact at the metal/graphene/SiC interface [7].Ji Yuting and Jia Yuping confirmed that graphene, as an intermediate transition layer between metal and silicon carbide, can reduce the metal/4H-SiC interface barrier [8,9], form a good ohmic contact [6,[10][11][12][13], improve charge collection efficiency and time resolution [10,14,15].The reason may be that graphene can promote the formation of interfacial carbon compounds, thereby reducing the ohmic contact resistance.The graphene as an intermediate transition layer may be beneficial to reducing the SBH of the metal/4H-SiC interface and improving the ohmic characteristics.However, the relevant mechanism is not yet known and there is a lack of corresponding theoretical basis.
The metal nickel is often used as a contact metal for 4H-SiC ohmic contact.Therefore, it is of great significance to study the Schottky barrier at the Ni/Graphene/4H-SiC interface.We have studied the effect of graphene on the SBH of the Ni/4H-SiC (0001) contact interface based on first principles.The formation of interfacial chemical bonds and charge transfer were analyzed through the density of states (DOS), the partial density of states (PDOS) and differential charge density.

Calculation Method
In the paper all the models were built and optimized by using the VASP module.In the process of model optimization, generalized-gradient approximation (GGA) of the exchange-correlation functional (RPBE) at 300 K are used.The models are built at 300K temperature, so the model showed semiconductor characteristics.All calculations are carried in reciprocal space.The sampling density of point Monkhorst-Pack k-point grid was selected as 5×5×1.The cutoff energy for plane wave expansion was set to 400eV.The convergence criterion for force was less than 0.01eV/Å.The maximal displacement of atoms was less than 1×10 -3 Å.The total energy of the system was less than 2.0×10 -6 eV/atom.The internal stress between atoms was less than 0.1 GPa.The SCF tolerance was less than 1.0×10 -6 eV/atom.The structure optimization has good convergence.At this time, the structures is the most stable because of the lowest energy.

Results and discussion
The paper builds a highly symmetrical, up-and-down rectangular structure model, in which there are two layers of Ni, a single layer of graphene and four layers of SiC carbon atoms.The lattice mismatch is reasonable and the structure is stable.In order to eliminate the influence of dangling bonds on the bottom surface, the C atoms on the SiC (0001 -) surface are passivated with H atoms, and the unit cells are isolated with a 25Å vacuum layer to eliminate interactions caused by periodicity.It can be seen from the Figure 1 that graphene does not show a two-dimensional planar morphology after model optimization.This demonstrates that the interaction between carbon and carbon has changed, and it is no longer sp 2 hybridization.There is no van der Waals force between the C atoms of graphene and SiC, but the interaction with the Si atoms on the SiC (0001) plane.The Si-C distance formed by C atoms and Si atoms are 1.970Å and 1.908Å, the Ni-C distance formed by Ni atoms and C atoms are 2.115Å and 1.943Å which basically reaches the bonding distance.The optimized structure appears to be reconstructed, which is consistent with the research of Varchon F. [16].Therefore, this model is proved to be reliable.For Si and C elements, the outer s and p state electrons play a major role in the reaction, while for Ni element, the outer s, p, and d state electrons play a major role in the reaction.Figure 3 shows the DOS of these three states of electrons.4 shows that electrons overlap between graphene and Ni, and the nearby graphite gains electrons, while the adjacent graphite loses electrons.Therefore, this shows further proving that Ni does not interact with graphene.This result is consistent with the results of Shaffer [17].Because the electrons inside the metal can move freely, it can be found that a small number of electrons are lost in the lower outer layer, and some of these electrons enter the gap between the Ni layers as free electrons.Electrons transfer from Si atoms on the surface of 4H-SiC to graphene C atoms.The charge depletion region formed on the Si surface and the charge accumulation region formed on the C surface jointly form the interface electric field.This results in the formation of interface electric dipoles, and the presence of this electric field may also reduce the Schottky barrier to some extent.This also indicates the interaction with atoms in graphite rarefaction, and based on the bonding mode, it can be inferred that the two form covalent bonds, which saturate the surface hanging bonds of 4H-SiC [18].This to some extent reduces the intrinsic interface states of 4H-SiC, which is beneficial for reducing the Schottky barrier [19].This proves that graphite rarefaction interacts with Si atoms in SiC and Ni.It can be seen from the Figure 5 that the electronic states in the forbidden band of 4H-SiC gradually increase from the bottom layer to the interface layer.Interface states near the Fermi level arise from scratch, among which electronic states are the most obvious, and these interface states rapidly decay toward the interior.In the interior (second, third, and fourth layers), since there are no impurities and deformations inside the body, the electronic state that appears in the forbidden band is induced by the metal.In other words, semiconductor electronic states are affected by metal-induced energy gap states, known as intrinsic interface states, which may cause partial pinning of the Fermi level.The influence of self-induced energy gap states and the overlap of electronic states caused by interactions at the interface lead to the appearance of a very high peak near the Fermi level of the first 4H-SiC layer.

Conclusion and perspectives
In this paper, the mechanisms of graphene layer changing Ni/4H-SiC interface SBH are studied based on the first-principles method.was studied.Theoretical studies have shown that graphene intercalation can reduce the SBH of Ni and 4H-SiC interfaces.The reason of SBH reduction may be that the graphene C atoms saturate the dangling bonds on the 4H-SiC surface and the influence of the metal-induced energy gap state at the interface is reduced.In addition, the new phase formed at the interface of graphene and silicon carbide has a lower work function.Furthermore, an interfacial electric dipole layer may be formed at the 4H-SiC/graphene interface which may also reduce the SBH.These results suggesting graphene-optimized silicon carbide devices to be promising candidates for future radiation resistant electronics.

Acknowledgment
This work was supported by the National Natural Science Foundation (12305207) and the State Key Laboratory of Particle Detection and Electronics (SKLPDE-ZZ-202312)

Figure 1 .
Figure 1.Ni/Graphene/4H-SiC crystal structures The DOS and PDOS of Ni/4H-SiC and Ni/Graphene/4H-SiC is plotted in Figure 2. The conduction band minimum (CBM) and the valence band maximum (VBM) were determined by p orbit and Ni(d) orbit.Compared with the CBM of Ni/4H-SiC, the CBM of Ni/Graphene/4H-SiC shifted to the left by 0.90eV, indicating a decrease of 0.90eV in the distance between the Fermi level and the conduction band.This indicates that the single-layer graphite thin transition layer reduces the SBH of Ni and 4H-SiC by 0.90eV.

Figure 3 .
Figure 3.The local density of states of Ni/Graphene/4H-SiC: (a) The Ni atom at the top；(b) The Ni atoms near graphene; (c) The C atom near Ni in graphene; (d) The C atom near 4H-SiC in graphene; (e) C atom in 4H-SiC near graphene; (f) The bottom C atom in 4H-SiC; (g) The bottom Si atom in 4H-SiC Compared with DOS of Si atoms near the Fermi level (Ef) in the lower layer of 4H-SiC, the density of states of Si atoms near graphite rarefaction increases.The decrease of electronic states near the Fermi level in the DOS of graphene C atoms near 4H-SiC (0001).This indicates that the Si atom at the SiC (0001) interface reacts with the C atom in graphene, and the electronic states interact and overlap with each other.The DOS of C atoms near the metal Ni in graphite rarefaction increases, while the DOS of Ni atoms near the graphite rarefaction decreases.Simultaneously, the DOS of Ni atoms near graphene rarefaction decreases, indicating that there is a reaction between Ni and graphite.In order to visually display the gain and loss of electrons at the interface, the (a) and (b) sections of the Ni/Graphene/4H-SiC atomic layer were taken for differential charge density.The Figure4shows that electrons overlap between graphene and Ni, and the nearby graphite gains electrons, while the adjacent graphite loses electrons.Therefore, this shows further proving that Ni does not interact with graphene.This result is consistent with the results of Shaffer[17].Because the electrons inside the metal can move freely, it can be found that a small number of electrons are lost in the lower outer layer, and some of these electrons enter the gap between the Ni layers as free electrons.Electrons transfer from Si atoms on the surface of 4H-SiC to graphene C atoms.The charge depletion region formed on the Si surface and the charge accumulation region formed on the C surface jointly form the interface electric field.This results in the formation of interface electric dipoles, and the presence of this electric field may also reduce the Schottky barrier to some extent.This also indicates the interaction with atoms in graphite rarefaction, and based on the bonding mode, it can be inferred that the two form covalent bonds, which saturate the surface hanging bonds of 4H-SiC[18].This to some extent reduces the intrinsic interface states of 4H-