Study on schottky barrier of Cu/Graphene/4H-SiC interface based on first principles

High stability 4H-SiC ohmic contact is currently a key technical challenge that silicon carbide devices urgently need to overcome. In the paper, the interfacial structures, atomic interactions and Schottky barrier height (SBH) of Cu/Graphene/4H-SiC were studied using the first-principles method. According to research, the SBH for Cu/G/4H-SiC is lower than the SBH for Cu/4H-SiC. The reasons for this phenomenon mainly include the following: 1. The graphene C atoms saturate the dangling bonds on the 4H-SiC surface and the influence of the metal-induced-gap-states (MIGS) at the interface is decreased. 2. A new phase is formed by inserting graphene between the Cu and 4H-SiC have low work functions. 3. An interfacial-electric-dipole layer (IEDL) formed at the interface of 4H-SiC and graphene may also reduce the SBH. These results make them to be promising candidates for future radiation resistant electronics.


Introduction
Silicon carbide has potential to be used for fast particle detection in radiation environment because of its wider band gap and high electron mobility [1][2][3] .High stability 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 to directly form ohmic contact between metals and wide band gap 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.High temperature annealing will activate impurities in silicon carbide, and the activated impurities will cause electrical signal scattering, which limits the improvement of the signal noise ratio (SNR), charge collection, time resolution and operational stability [1] .
Stefan Hertel found that graphene can provide perfect ohmic contact with SiC epitaxial layers [5] .Zheng Jiangshan et al. verified that applying voltage can achieve p-type ohmic contact at the metal/graphene/SiC interface [6] .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, form a good ohmic contact, improve charge collection efficiency and time resolution [7] .The graphene insertion layer can form carbon compounds at the interface between the metal and silicon carbide, thereby reducing the ohmic contact resistance.Graphene as an intermediate transition layer may be beneficial to reducing the SBH of the Cu/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.
In this paper, in order to explain the Schottky barrier reduction mechanism, we optimize the cell structure based on first principles, analyze the band gap, density of states (DOS) and differential charge density to study the SBH of Cu/Graphene/4H-SiC.

Calculation method
The paper builds a highly symmetrical, up-and-down rectangular structure model, in which there are two layers of Cu, monolayer graphene and four layers of 4H-SiC carbon atoms.In order to eliminate the influence of dangling bonds on the bottom, 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.The lattice mismatch is reasonable and the structure is stable.The lattice optimization values are in the table1: Table 1.The optimization parameters.

Analysis and discussion
Figure 1.Cu/Graphene/4H-SiC crystal structure.Figure 1 show that the optimized-graphene by the model does not a two-dimensional planar form.This demonstrates that the interaction between carbon and carbon has changed, and it is no longer sp 2 hybridization.The Si-C distance formed by C atoms and Si atoms is 2.087Å, which basically reaches the bonding distance.The optimized structure appears to be reconstructed, which is consistent with the research of Varchon F. [8] .Therefore, this model is proved to be reliable.The bottom C in 4H-SiC; (g) The bottom Si in 4H-SiC.Figure 3 show the density of states for Cu/Graphene/4H-SiC.The electronic structure of epitaxial growth monolayer graphene is obviously different from that of the free-state graphene.Epitaxially grown monolayer of graphene exhibit a large gap and a fixed Fermi level with a less dispersive electron state.For the Si plane, the Fermi level is near the conduction band, and for C plane, the Fermi level is in the band gap.These electron states are determined by the dangling bonds on the surface.That is, the Si surface is determined by the Si dangling bonds, and the C surface is determined by the C dangling bonds.Compared with the density of states for Si atoms near the Fermi level (E f ) in the lower layer of 4H-SiC, the DOS 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 at the 4H-SiC (0001) interface reacts with the C atom in graphene, and the electronic states interact and overlap with each other.The DOS of the C atom near the metal Cu in graphite has little change compared to the DOS of the Cu atom near the graphite.The DOS of the two layers of metal at the top did not change significantly, indicating that there is no reaction between Cu and graphite.In order to visually display the gain and loss of electrons at the interface, the (a) and (b) interfaces of the Cu/Graphene/4H-SiC atomic layer are taken for differential charge density.The Figure 4 shows that there is no electron overlap between graphene and Cu, further proving that Cu does not interact with graphene.The mismatch between graphene and silicon carbide lattice and the polarization of the 4H-SiC itself result ICAMIM-2023 Journal of Physics: Conference Series 2720 (2024) 012001 IOP Publishing doi:10.1088/1742-6596/2720/1/0120014 in charge transfer between graphene and substrate.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.According to the bonding mode, it can be inferred that the two forms a covalent bond, which saturates the surface overhang bond of 4H-SiC [9] .This to some extent reduces the intrinsic interface states of 4H-SiC, which is beneficial for reducing the Schottky barrier [10] .This proves that graphite rarefaction interacts with Si atoms in 4H-SiC, but does not interact with metal Cu.   5 show the DOS and PDOS of atoms in each layer for Cu/Graphene/4H-SiC.We can see 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) there are no impurities and deformation, but electronic states still appear.The intrinsic interface states 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 the paper, the interfacial structures, atomic interactions and Schottky barrier height (SBH) of Cu/Graphene 4H-SiC were studied based on the first-principles method.The results show that the SBH for Cu/G/4H-SiC is lower than the SBH for Cu/4H-SiC.There are several reasons for this phenomenon.Firstly, the graphene C atoms saturate the dangling bonds on the 4H-SiC surface and the influence of the metal-induced-gap-states (MIGS) at the interface is decreased, so the Schottky barrier is lowered.Secondly, a new phase is formed by inserting graphene between the Cu and 4H-SiC have low work functions.Finally, an interfacial-electric-dipole layer (IEDL) formed at the interface of 4H-SiC and graphene may also reduce the SBH.These results make them to be promising candidates for future radiation resistant electronics.

Figure 3 .
Figure 3. Density of states for Cu/Graphene/4H-SiC: (a) The Cu at the top; (b) The Cu near graphene; (c) The C near Cu in graphene;(d) The C near 4H-SiC in graphene; (e) C in 4H-SiC near graphene; (f)The bottom C in 4H-SiC; (g) The bottom Si in 4H-SiC.Figure3show the density of states for Cu/Graphene/4H-SiC.The electronic structure of epitaxial growth monolayer graphene is obviously different from that of the free-state graphene.Epitaxially grown monolayer of graphene exhibit a large gap and a fixed Fermi level with a less dispersive electron state.For the Si plane, the Fermi level is near the conduction band, and for C plane, the Fermi level is in the band gap.These electron states are determined by the dangling bonds on the surface.That is, the Si surface is determined by the Si dangling bonds, and the C surface is determined by the C dangling bonds.Compared with the density of states for Si atoms near the Fermi level (E f ) in the lower layer of 4H-SiC, the DOS 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 at the 4H-SiC (0001) interface reacts with the C atom in graphene, and the electronic states interact and overlap with each other.The DOS of the C atom near the metal Cu in graphite has little change compared to the DOS of the Cu atom near the graphite.The DOS of the two layers of metal at the top did not change significantly, indicating that there is no reaction between Cu and graphite.In order to visually display the gain and loss of electrons at the interface, the (a) and (b) interfaces of the Cu/Graphene/4H-SiC atomic layer are taken for differential charge density.The Figure4shows that there is no electron overlap between graphene and Cu, further proving that Cu does not interact with graphene.The mismatch between graphene and silicon carbide lattice and the polarization of the 4H-SiC itself result

Figure 4 .
Figure 4. Cu/Graphene/4H-SiC: (a) a section differential charge density; (b) b section differential charge density.Figure5show the DOS and PDOS of atoms in each layer for Cu/Graphene/4H-SiC.We can see 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) there are no impurities and deformation, but electronic states still appear.The intrinsic interface states 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.

Figure
Figure 4. Cu/Graphene/4H-SiC: (a) a section differential charge density; (b) b section differential charge density.Figure5show the DOS and PDOS of atoms in each layer for Cu/Graphene/4H-SiC.We can see 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) there are no impurities and deformation, but electronic states still appear.The intrinsic interface states 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.