First-Principles Calculations on Atomic and Electronic Properties of Ge/4H-SiC Heterojunction

First-principles calculation is employed to investigate atomic and electronic properties of Ge/SiC heterojunction with different Ge orientations. Based on the density functional theory, the work of adhesion, relaxation energy, density of states, and total charge density are calculated. It is shown that Ge(110)/4H-SiC(0001) heterointerface possesses higher adhesion energy than that of Ge(111)/4H-SiC(0001) interface, and hence Ge/4H-SiC(0001) heterojunction with Ge[110] crystalline orientation exhibits more stable characteristics. The relaxation energy of Ge(110)/4H-SiC(0001) heterojunction interface is lower than that of Ge(111)/4H-SiC(0001) interface, indicating that Ge(110)/4H-SiC(0001) interface is easier to form at relative low temperature. The interfacial bonding is analysed using partial density of states and total charge density distribution, and the results show that the bonding is contributed by the Ge-Si bonding.


Introduction
SiC semiconductor has become one of the most excellent materials for ultraviolet-sensitive devices owing to its wide bandgap [1,2]. However, it is not sensitive to the infrared and visible light region. Ge/SiC heterojunction was employed to solve the problem, in which the Ge layer of micronanostructure was used as an absorption layer for nearinfrared (NIR) light [3]. By using the Ge/SiC heterojunction, SiC-based NIR light-operated device could be realized. The Ge/4H-SiC heterostructures are prepared by using low pressure chemical vapor deposition (LPCVD) on 4H-SiC(0001) substrates. Details of the growth process could be found in [4][5][6]. However, the lattice mismatch between Ge(111) primitive cell ( Ge(111) = 4.000Å) and 4H-SiC(0001) primitive cell ( 4H-SiC(0001) = 3.078Å) is as large as 23.0%, which can cause distortion or even dislocation near the interface, leading to a poor crystalline quality of the Ge epilayer. Hence, it is necessary and imperative to investigate the atomic and electronic properties of the Ge/SiC heterojunction.
First-principles calculation based on density functional theory (DFT) has been widely used as an important microscopic study method in recent years. The first-principles calculation can be implemented to predict material properties and, consequently, a lot of valuable results have been achieved. Li et al. [7] used the first-principles method to investigate the interface adhesion energy, interface energy, interface fracture toughness, and electronic structure of the -SiC(111)/ -Ti(0001) heterojunction. Six kinds of Cterminated -SiC(111)/ -Ti(0001) models were established to study the effect of stack position and inclination angle on interface bonding and fracture toughness. Lin et al. [8] investigated the atomic structures and electronic properties of interfaces between aluminum and four kinds of ceramics with different orientations. They discovered that aluminum metal carbide interface is more stable than aluminum metal nitrides interface and, moreover, the (111) interfaces were found to possess the largest adhesion energy. He et al. [9,10]   the Si-terminated Si(111)/6H-SiC(0001) heterojunction has higher adhesion energy and lower relaxation degree than Cterminated Si(111)/6H-SiC(0001) heterojunction. Xu et al. [11] have studied interfacial properties and electronic structure of Al(111)/4H-SiC(0001) interface.
In this paper, we present first-principles calculations of adhesion energy, relaxation energy, density of states, and total charge density of Ge(111)/4H-SiC(0001) interface and Ge(110)/4H-SiC(0001) interface, while analysing the electronic structure, geometry property, and the corresponding physical picture. Furthermore, the first-principles methods are used to investigate the structure of Ge/SiC heterointerface, which can provide a theoretical basis for the growth of Ge/SiC heterojunctions in experiment.

Methods
All the calculations in this work were implemented by using the Cambridge Serial Total Energy Package (CASTEP) Code [12,13], which are based on the density functional theory (DFT) [14]. Generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) scheme was employed to describe the exchange-correlation functional [15]. By comparing the lattice constants of GGA(PBE) and local density approximation (LDA) [16] with Caperlay-Alder Perdew-Zunger (CA-PZ) approximation algorithms, it is shown that the deviation of GGA(PBE) is smaller than that of LDA(CA-PZ). Therefore, the GGA-PBE function is implemented in the following Ge/4H-SiC(0001) heterojunction calculation. In order to make the system stable and the calculation speed optimal, plane wave cut-off energy was selected as 550 eV for a bulk, a surface, and an interface. The sampling of irreducible edge of Brillouin zone was performed with a regular Monkhorst-Pack grid with 7 × 7 × 7 k points for the bulk and 5 × 5 × 1 k points for the surface and interface, respectively. The SCF convergence threshold was 2.0 × 10 −6 eV/atom, and the convergence tolerance for energy was selected as 2.0 × 10 −5 eV/atom. The force tolerance, stress, and displacement tolerance were set as 0.05 eV/Å, 0.1 GPa, and 0.002Å, respectively. To avoid interaction between surface atoms, a vacuum layer of 13Å was selected for each surface and interface system.  Figure 3. Both of the Ge(111)/4H-SiC(0001) and Ge(110)/4H-SiC(0001) heterostructures have the same optimized interlayer distances of 2.30Å. Similar conclusions are given in [17].

Adhesion Energy and Relaxation Energy.
To gain an insight into the binding strength of the interface, we calculated the work of adhesion ( ad ), which is defined as the reversible work to separate an interface into two free surfaces given by the difference in total energy between the interface and its initial isolated slabs according to the following formula [18][19][20]: where Ge and SiC are the total energy of Ge slab and SiC slab, where one slab remained and the other is replaced by 4 Advances in Condensed Matter Physics   vacuum in the same supercell, respectively. Ge/4H-SiC denotes the total energy of the interface system, is the number of atoms at the interface in the model, and is the interfacial area. Based on (1), the variable values are obtained and listed in Table 2.
In addition, the relaxation energy relaxion can be determined by an expression as follows: where total and total are the total energies of the unrelaxed and relaxed interface systems, respectively, and is the number of atoms in the system. Based on (2), the variable values are obtained and listed in Table 3. Table 2 shows that the bonding energy of the unrelaxed interface is smaller than that of the relaxed one, indicating that the relaxed interface is more stable. It is also shown that the adhesion energy of Ge(110)/4H-SiC(0001) interface is higher than that of the Ge(111)/4H-SiC(0001) interface, indicating that Ge(110)/4H-SiC(0001) heterointerface is more energetically stable than Ge(111)/4H-SiC(0001) heterointerface. As shown in Table 3, the relaxation energy of Ge(110)/4H-SiC(0001) interface is lower than that of Ge(111)/4H-SiC(0001) interface, suggesting that Ge(110) films are easier to deposit on 4H-SiC(0001) substrates at relative low temperatures, which is consistent with the conclusions in [6].
The influence of relaxation on the atom positions at the Ge/4H-SiC interfaces is investigated. Figures 4(a)  . The first and second layers of atoms at the interface severely deviate from the equilibrium position. Approaching to the bulk materials, the deviations decrease drastically, suggesting that, as the interface formed, merely one or two layers of atoms at the interface were significantly influenced. In the meantime, one can also observe that at the interface the variation of Ge atoms is larger than that of SiC atoms, indicating that the relaxation occurs mainly on the Ge side. It is shown that the variation of atoms in Figure 4(d) is larger than that in Figure 4(c), which is attributed to the fact that the lattice mismatch in the direction is greater than that in the direction at the Ge(110)/4H-SiC(0001) interface. However, the variation of the atoms in Figure 4(g) is almost the same as that in Figure 4(h), since the lattice mismatch in the direction is commensurate to that in the direction at the Ge(111)/4H-SiC(0001) interface. appears between interfacial Ge and Si atom at the Ge(111)/4H-SiC(0001) interface, indicating that Ge-Si bonding is formed at the interface. The charge density difference of Ge(111)/4H-SiC(0001) interface is displayed in Figure 5  Advances in Condensed Matter Physics density of states at the interface is influenced by the bulk materials on both sides. As shown in Figure 6(a), on the Ge side, the significant peaks appear in the ranges from −12.5 eV to −6 eV, −6 eV to −5 eV, −5 eV to 1 eV, and 1 eV to 2.5 eV. The densities of states from −12.5 eV to −6 eV and 1 eV to 2.5 eV originate mainly from the Ge-4s, −5 eV to 1 eV is mainly from the Ge-4p, and the Ge-4s and Ge-4p are mixed to the density of states from −6 eV to −5 eV, indicating the presence of Ge-Ge bonds. The density of states from −16 eV to −13 eV is mainly originated from the C-2s and Si-3s, −13 eV to −10 eV is mainly associated with the C-2s and Si-3p, −10 eV to −7.5 eV is mostly related to the C-2p and Si-3s, and −7.5 eV to 0 eV is largely originated from the C-2p and Si-3p. By comparing with the bulk material, the distribution of density of states at the heterointerface shifts toward low energy slightly. Furthermore, by comparing the Ge(110)/4H-SiC(0001) and Ge(111)/4H-SiC(0001) heterointerfaces, for the first Ge layer of Ge slab and the first Si layer of 4H-SiC slab, several distinct resonance peaks appear in the range of −4 eV to 0 eV as well. As shown in Figure 6(b), Ge(111)/4H-SiC(0001) heterointerface significant resonance peaks appear as well. The peaks mainly originate from the orbital hybridization of Si-3p and Ge-4P, indicating the formation of Ge-Si bond at the interface.

Conflicts of Interest
The authors declare that they have no conflicts of interest.