# Zinc-Blende GeC Stabilized on GaN (001): An Ab Initio Study

Authors: J. H. Camacho-García; Ma L. Ruiz-Peralta; G. Hernández-Cocoletzi; A. Bautista-Hernández; M. Salazar-Villanueva; A. Escobedo-Morales; E. Chigo-Anota; J. C. Moreno-Hernández
Journal: Advances in Condensed Matter Physics
 (2022)

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## Abstract

First-principle calculations have been performed to explore the initial stages of the zinc blende-like germanium carbide epitaxial growth on the gallium nitride (001)-(2 × 2) surface. First, we studied the Ge/C monolayer adsorption and incorporation at high symmetry sites. Results show that the adsorptions at the top and hcp1 sites are the most stable structures of C and Ge, respectively. Different terminated surfaces were used on the GeC epitaxial growth. According to the surface formation energies, only the first two bilayers are stable; therefore, the GeC epitaxial growth is favorable only under N-rich conditions on a Ge-terminated surface and with Ge bilayers terminated. In addition, it is demonstrated that GeC bilayers on the C-terminated surfaces are unstable and preclude the epitaxial growth. Electronic properties have been investigated by calculating the density of states (DOS) and the projected density of states (PDOS) of the most favorable structures.


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## Body

## 1. Introduction

Germanium carbide (GeC) structures have attracted considerable interest because of the extensive applications in optoelectronic devices. Because they exhibit a narrow optical bandgap, they may be used in photovoltaic and infrared optical devices due to the low stress, tuned refractive index, and high absorption coefficient.First-principle calculations based on the density functional theory (DFT) have been applied extensively due to the versatility to study different materials in order to calculate electronic, optical, and magnetic properties. In this regard, DFT calculations suggest that GexC1 − x thin films possess tunable bandgap [1–5]. In addition, amorphous films have been fabricated by radio frequency (RF) reactive sputtering; the refractive index varied according to the synthesis conditions, an important feature in designing antireflection coatings [6]. Theoretical calculations have been developed to investigate the structural, electronic, optical, and magnetic properties of GeC. Majidi et al. reported DFT studies of the electronic and linear response optical properties of graphene-like XC (X = Si, Ge, and Sn) nanosheets, and the results showed a bandgap of 2.1 eV [7]. Xu et al. investigated magnetic behavior of B, N, and 3d transition metal substitutions in germanium carbide monolayers. Results indicated that impurity atoms change the magnetic moment. In the 2D-GeC system, in both substituted Ge sublattice (VGe@Ni) or C sublattice (VC@Ni), the distributions of magnetic moments are centered on Ni and the nearest Ge/C atoms [8]. The obtained magnetic nanostructures are technologically significant for applications in spintronics devices. There are several theoretical investigations of GeC in the zinc blende (zb) phase in which the reported lattice parameter values are 4.43 Ǻ–4.62 Ǻ [9–13]. The calculated band structure shows an indirect bandgap with values from 1.52 eV to 2.56 eV [14–17]. Zhang et al. [12] used the plane-wave pseudopotential (PP) approach within the density functional perturbation theory to investigate the lattice dynamics and thermodynamic properties of SiC, GeC, and SnC. The obtained phonon dispersion exhibits no imaginary phonon frequencies of zb-GeC, indicating the structural stability. Furthermore, structural parameters and electronic and chemical bonding properties of zb-GeC (100) surfaces were investigated through DFT, and results revealed that Ge-terminated surfaces exhibit metallic properties [18]. However, the experimental confirmations are not available yet.Wide-bandgap semiconductors that have bandgaps greater than 3.0 eV, such as SiC, ZnO,β-Ga2O3, and GaN [19], have received attention due to their physical properties and different applications [20]. In this regard, gallium nitride (GaN) has been applied in light-emitting diodes [21], X-ray detectors [22], and manometer devices [23]. GaN crystallizes in the wurtzite w and zinc blende phases with a0 = 3.188 Å, c = 5.185 Å, and a0 = 4.52 Å, respectively [24]. There are experimental reports confirming the existence of stable GaN in the zinc blende phase [25–28]. Growth of this material is obtained by means of thin films, on β-SiC and GaAs substrates, in the (001) direction, in a temperature range from 700°C to 200°C [25, 26]. However, Pak et al. [27] and Novikov et al. [28] demonstrated the stability at room temperature of the zb-GaN (001) films grown by the molecular beam epitaxy (MBE) technique on (001) MgO and (001) GaAs, respectively; e.g., Figure 6 in [28], shows a 100 μm-thick zinc-blende GaN layer grown on a 3-inch GaAs substrate. Results show outstanding photoluminescence (PL) emission [29], which suggests that this is a suitable material for optical applications. In addition, zb-GaN structure is isotropic, which avoids lattice mismatch between GaN and InGaN barriers in order to fabricate light-emitting diodes with higher efficiency. GaN-based UV photodetectors showed a significantly enhanced photoresponsivity near the 365 nm wavelength range (UV-A region) [30].In the case of GeC, reports show that thin film growth results in amorphous GeC. For this reason, this work explored the possibility of using GaN as a substrate to obtain an epitaxial growth of zb-GeC.The development of electronics based on gallium nitride substrates has been focused on structural defect elimination to achieve better electrical and thermal conductivities [31]. In this sense, Posadas et al. reported the fabrication of YMnO3 epitaxial thin films on w-GaN/sapphire and determined the most stable configuration from calculations of the formation energy of the interface [32]. AlxGa1 − xN ultraviolet avalanche photodiodes were grown on GaN substrates; results show that the avalanche gain is due to the low dislocation density in the bulk of GaN substrates [33]. Moreover, heterostructures of GaN with IV compounds have been studied, either theoretically or experimentally, and they are found to be stable [34–37]. Recently, electronic structure, charge transfer, and optical properties of GaN-GeC van der Waals heterostructures have been investigated using first-principle calculations; results suggest optical absorption in the visible region, which indicates that this is a promising material for photocatalytic applications [38]. In addition, tunable photocatalysis properties of GaN/GeC have been used for the production of H2 fuel [39], water splitting, and solar energy conversion. The development of new materials involves property investigation in order to reach a real application. GaN/GeC is a promising material, and since zb-GeC and GaN are materials with potential applications in different fields, it is important to study the epitaxial growth to achieve functional devices. In this regard, both compounds have the same crystal structure, and their lattice parameter mismatch is smaller than 15%; it is possible to grow GeC/GaN systems. In this work, Ge and C monolayer/bilayer formation on the GaN (001) surface was studied by first-principle calculations in order to investigate the initial stages of the zb-GeC formation. In addition, the formation energies were calculated to demonstrate the stability of the studied configurations. The density of states (DOS) and structural, thermodynamical, and electronic properties were also calculated. This paper is organized as follows: in Section 2, we briefly describe the computational methodology, results are discussed in Section 3, and finally, conclusions are presented.


## 2. Computational Methodology

Zinc-blende gallium nitride (001) surface is considered a substrate of germanium carbide (GeC). Total energy calculations have been carried out using the periodic density functional theory as implemented in the PWscf code of the Quantum ESPRESSO package [40]. Exchange-correlation interactions are approximated with the generalized gradient approximation (GGA), as stated in the Perdew–Burke–Ernzerhof (PBE) parametrization [41]. The electron-ion interactions are treated according to the pseudopotential approach, employing Vanderbilt ultrasoft pseudopotentials [42]. Electronic states are expanded in plane waves with the cutoff energy of 30 Ry and charge density of 240 Ry. For convergence in geometry optimization, all force components should be smaller than 0.026 eV/Å, and the total energy differences must be less than 0.0026 eV. A 7 × 7 × 1 Monkhorst–Pack mesh [43] has been used to sample the Brillouin zone. The surface is modeled using the supercell method. The supercell is formed by a slab (composed of 4 GaN bilayers) and a vacuum gap width greater than 15 Å. Fractional pseudo-hydrogen atoms saturate the bottom surface dangling bonds in order to eliminate the possibility of undesirable charge transfer. To determine the density of states (DOS), the k-point mesh is increased to 21 × 21 × 1.


## 3. Results and Discussion

### 3.1. Adsorption and Incorporation of the Ge and C Monolayer

Figure1 describes the non-reconstructed GaN (001)-(2 × 2) surface and the high symmetry sites in the current study. For (001) zb-like surfaces, the high symmetry sites are defined as top, hcp, fcc, and hcp1 [44]. The top site is obtained when a Ge/C monolayer (ML) is placed on top of the first Ga-ML. At the hcp site, the Ge/C atoms are adsorbed on top of the first N-ML. The fcc site is obtained when the adatoms are adsorbed over Ga atoms from the second monolayer, and the hcp1 geometry is formed when Ge/C atoms are adsorbed above the second N monolayer (Figure 1). In addition, we explored the Ge/C monolayer incorporation into the GaN (001)-(2 × 2) surface, where Ge or C atoms displace the Ga atoms, yielding Ga as the new adatoms that are adsorbed on the surface at four high symmetry sites. In order to study adsorption at high symmetry sites, layers (either C or Ge) are placed on top of the GaN substrate; then, geometry is optimized to calculate the system total energy. In these calculations, the number of atoms of the system remains constant. Whence, a comparison can be made between the total energies of each configuration. Differences among calculated energies are referred to as relative energies. The relative energy analysis is shown in Table 1. This phenomenon has been previously studied for different surfaces [44–47] since this configuration stimulates the bilayer growth in some cases.Figure 1
Schematic atomic structure for the Ga-terminated GaN (001)-(2 × 2) surface, showing high symmetry sites (top, hcp, fcc, and hcp1) for the monolayer Ge/C adsorption. (a) The top view. (b) The side view.
(a)(b)Table 1
Relative adsorption energies (eV) and the incorporation of different Ge and C coverage.
SiteRelative energySiteRelative energyGe-top0.069C-top0.000Ge-hcp0.148C-hcp1.073Ge-fcc0.104C-fcc1.022Ge-hcp10.000C-hcp10.892Ge-1st layer/Ga-top0.118C-1st layer/Ga-top0.285Ge-1st layer/Ga-hcp0.136C-1st layer/Ga-hcp0.078Ge-1st layer/Ga-fcc0.128C-1st layer/Ga-fcc0.987Ge-1st layer/Ga-hcp10.070C-1st layer/Ga-hcp10.445Zero energy (bold numbers) is the energy reference in each case.According to the results, the Ge monolayer adsorption at the hcp1 site is the most stable structure, shown in Figure2(a), whereas the Ge-ML adsorption at the hcp site is energetically unfavorable. However, the C-ML adsorption at the top site geometry is more stable than hcp, fcc, and hcp1 sites by 1.07 eV/C-atom, 1.02 eV/C-atom, and 0.89 eV/C-atom, respectively. As it is shown in Figure 2(b), the C dangling bonds at the top surface are saturated, forming C dimers with a bond length of 1.42 Ǻ. In the Ge incorporation, the hcp1 site is more stable than the top, fcc, and hcp sites by 0.048 eV/Ge-atom, 0.058 eV/Ge-atom, and 0.066 eV/Ge-atom, respectively. The hcp site exhibits as favorable geometry, followed by the top, hcp1, and fcc (hcp > top > hcp1>fcc) for the C incorporation into the GaN surface.Figure 2
(a) Ge adsorption at the hcp1 site and (b) C adsorption at the top site.
(a)(b)In addition, we have studied different Ge/C-terminated GaN (001) surfaces, which indicates that the structure is not gallium terminated; instead, the Ge/C monolayer may be grown. Figure3 shows the optimized structures, and the structural stabilities will be discussed by means of the formation energy analysis.Figure 3
Optimized structures for (a) Ge- and (b) C-terminated surfaces.
(a)(b)


### 3.2. GeC Formation

In order to investigate the epitaxial growth of GeC on the GaN (001) surface, we have used the structures of Ge/C ML adsorption and different Ge/C-terminated GaN (001) surfaces; the most stable geometries are displayed in Figure4. Figure 4(a) shows the epitaxial growth of the GeC bilayer on the Ge-terminated GaN (001) ideal surface. Adding a C monolayer to the Ge adsorption at the hcp1 site formed this structure. Figure 4(b) exhibits the C dimer formation, with a bond length of 1.47 Å, when a C monolayer is deposited on the Ge-terminated GaN surface, demonstrating that the surface reconstruction avoids the epitaxial growth because of the carbon broken bonds’ saturation [48]. Figure 4(c) corresponds to the formation of a GeC-ML on the Ge-terminated GaN surface, which is obtained when a Ge ML is added on the C dimers (Figure 4(b)). In the top view of the figure, atoms of Ge and C show a “chair” distorted configuration [49] as the Ge-Ge bond lengths (2.76 Å) are larger than the C-C bond lengths (1.35 Å) with the bond angles of 106.1°.Figure 4
Different GeC surfaces: (a) formation of a GeC bilayer on the ideal Ga-terminated surface (GaN/GeC), (b) the C dimers’ formation on the Ge-terminated surface (Ge-term-C), and (c) GeC chair-like layer.
(a)(b)(c)Figure5 shows the epitaxial growth of GeC on the Ge-terminated GaN surface. Figure 5(a) depicts a GeC bilayer, while Figure 5(b) displays the atomic structure of the double GeC bilayer formation, which as Che et al. [18] reported. Therefore, the GeC growth is more favorable on Ge-terminated surface. The bond length between Ge-C is 1.95 Å, which agrees well with previous theoretical reports [50]. Since we have surfaces with a different number of atoms to determine the most stable structure, the surface formation energy (SFE) formalism is employed as described below.Figure 5
Epitaxial growth of (a) a GeC bilayer and (b) two GeC bilayers on the Ge-terminated surface.
(a)(b)


### 3.3. Surface Formation Energy

To determine the stability of all models, we have used the surface formation energy (SFE) formalism [45–51]. In order to apply the SFE formalism, we consider thermodynamic equilibrium between the surface and the bulk. This implies that(1)μGaNbulk=μGa+μN−ΔHfGaN,with(2a)μGa≤μGabulk,(2b)μN≤μN2molecule,where μi is the chemical potential of the ith species and ΔHfGaN is the enthalpy or formation heat of GaN in the bulk structure. According to calculations, ΔHfGaN=0.9eV, in agreement with previous reports [45]. Provided that constant pressure and zero temperature are assumed, the SFE may take the following form:(3)Ef=Eslab−Eref−ΔnGaμGa−ΔnNμN−ΔnGeμGe−ΔnCμC,where Eslab is the energy of each model and Eref is the reference energy. In this case, the reference is the ideally Ga-terminated GaN (001)-(2 × 2) surface. Δni is the excess or deficit of the ith atom. The SFE is a function of the Ga chemical potential with lower limit (N-rich conditions) μGa=μGabulk−ΔHfGaN and upper limit (Ga-rich conditions) μGa=μGabulk. μGe and μC are obtained employing a diamond structure. The obtained results are shown in Figure 6; under Ga-rich conditions, the adsorption of Ge at the hcp1 site is the most stable configuration, whereas the C-terminated surface is the most unfavorable. On the contrary, the Ge-terminated surface is the most stable structure. The C adsorption structures (Figures 2(b) and 4(b)) have a gain in energy due to the rearrangement of the C atoms to form dimers, which have a bond length of 1.24 Å. However, both structures are unstable. On the contrary, Figure 6(b) shows that, under N-rich conditions, the epitaxial growth of 1 or 2 GeC-monolayers on the Ge-terminated surface is possible. However, as the GeC-ML number rises, the system becomes unstable due to an increasing SFE, which could be explained by several studies of GeC thin films [3, 4, 6, 49–54].Figure 6
Surface formation energy (SFE) as a function of the Ga chemical potential for (a) different structures and (b) epitaxial growth.
(a)(b)


### 3.4. Electronic Properties

In this section, the total density of states (DOS) and the projected density of states (PDOS) of the most stable structures are calculated to show the electronic contributions to the Fermi level.The DOS and PDOS are plotted as functions of energy, with the Fermi level being the zero energy. Notice that we outlined the contributions to the p-orbitals of each element. Figure7 shows the electronic properties of the GaN (001)-(2 × 2) clean surface; the second and third GaN bilayers show a bandgap of ≈2 eV, according to previous reports [55]. Below the Fermi level, the major contributions are given by the N-p orbitals. On the contrary, the main contribution above the Fermi level is obtained from Ga-p orbitals. However, the first GaN bilayer shows a metallic behavior due to the Ga-terminated surface.Figure 7
DOS and PDOS for the GaN (001) surface: (a), (b), and (c) exhibit the PDOS of the 1st, 2nd, and 3rd GaN bilayers, respectively. The red and blue lines correspond to Ga-p and N-p, respectively.Figure8 exhibits the DOS and PDOS of the Ge-terminated surface; the last two bilayers remain as semiconductors with a bandgap of 2 eV. Below the Fermi level, N-p orbitals make the main contribution to the DOS. In the first bilayer, the change of Ga atoms by Ge atoms does not affect the surface metallic behavior, and also, there is no dimerization due to the electronic reconstruction. Just below the Fermi level, the main contribution to the DOS is due to the N-p orbitals. An additional GeC bilayer (Figure 9) modifies the contributions on the first bilayer. Close to the Fermi level (in −1 to −2 eV range), Ge-p orbitals are the major contributors to the DOS, no change above the Fermi level is manifested, and the surface unoccupied states are the Ge-p orbitals.Figure 8
DOS and PDOS for the Ge-terminated surface: (a), (b), and (c) exhibit the PDOS for the 1st, 2nd, and 3rd GaN bilayers, respectively. The red lines correspond to Ga-p, the blue lines are the contributions of N-p, and Ge-p is represented as olive lines.Figure 9
DOS and PDOS for a bilayer GeC. The contribution of Ga-p (red lines), N-p (blue lines), Ge-p (olive lines), and C-p (wine lines) is illustrated.


## 3.1. Adsorption and Incorporation of the Ge and C Monolayer

Figure1 describes the non-reconstructed GaN (001)-(2 × 2) surface and the high symmetry sites in the current study. For (001) zb-like surfaces, the high symmetry sites are defined as top, hcp, fcc, and hcp1 [44]. The top site is obtained when a Ge/C monolayer (ML) is placed on top of the first Ga-ML. At the hcp site, the Ge/C atoms are adsorbed on top of the first N-ML. The fcc site is obtained when the adatoms are adsorbed over Ga atoms from the second monolayer, and the hcp1 geometry is formed when Ge/C atoms are adsorbed above the second N monolayer (Figure 1). In addition, we explored the Ge/C monolayer incorporation into the GaN (001)-(2 × 2) surface, where Ge or C atoms displace the Ga atoms, yielding Ga as the new adatoms that are adsorbed on the surface at four high symmetry sites. In order to study adsorption at high symmetry sites, layers (either C or Ge) are placed on top of the GaN substrate; then, geometry is optimized to calculate the system total energy. In these calculations, the number of atoms of the system remains constant. Whence, a comparison can be made between the total energies of each configuration. Differences among calculated energies are referred to as relative energies. The relative energy analysis is shown in Table 1. This phenomenon has been previously studied for different surfaces [44–47] since this configuration stimulates the bilayer growth in some cases.Figure 1
Schematic atomic structure for the Ga-terminated GaN (001)-(2 × 2) surface, showing high symmetry sites (top, hcp, fcc, and hcp1) for the monolayer Ge/C adsorption. (a) The top view. (b) The side view.
(a)(b)Table 1
Relative adsorption energies (eV) and the incorporation of different Ge and C coverage.
SiteRelative energySiteRelative energyGe-top0.069C-top0.000Ge-hcp0.148C-hcp1.073Ge-fcc0.104C-fcc1.022Ge-hcp10.000C-hcp10.892Ge-1st layer/Ga-top0.118C-1st layer/Ga-top0.285Ge-1st layer/Ga-hcp0.136C-1st layer/Ga-hcp0.078Ge-1st layer/Ga-fcc0.128C-1st layer/Ga-fcc0.987Ge-1st layer/Ga-hcp10.070C-1st layer/Ga-hcp10.445Zero energy (bold numbers) is the energy reference in each case.According to the results, the Ge monolayer adsorption at the hcp1 site is the most stable structure, shown in Figure2(a), whereas the Ge-ML adsorption at the hcp site is energetically unfavorable. However, the C-ML adsorption at the top site geometry is more stable than hcp, fcc, and hcp1 sites by 1.07 eV/C-atom, 1.02 eV/C-atom, and 0.89 eV/C-atom, respectively. As it is shown in Figure 2(b), the C dangling bonds at the top surface are saturated, forming C dimers with a bond length of 1.42 Ǻ. In the Ge incorporation, the hcp1 site is more stable than the top, fcc, and hcp sites by 0.048 eV/Ge-atom, 0.058 eV/Ge-atom, and 0.066 eV/Ge-atom, respectively. The hcp site exhibits as favorable geometry, followed by the top, hcp1, and fcc (hcp > top > hcp1>fcc) for the C incorporation into the GaN surface.Figure 2
(a) Ge adsorption at the hcp1 site and (b) C adsorption at the top site.
(a)(b)In addition, we have studied different Ge/C-terminated GaN (001) surfaces, which indicates that the structure is not gallium terminated; instead, the Ge/C monolayer may be grown. Figure3 shows the optimized structures, and the structural stabilities will be discussed by means of the formation energy analysis.Figure 3
Optimized structures for (a) Ge- and (b) C-terminated surfaces.
(a)(b)


## 3.2. GeC Formation

In order to investigate the epitaxial growth of GeC on the GaN (001) surface, we have used the structures of Ge/C ML adsorption and different Ge/C-terminated GaN (001) surfaces; the most stable geometries are displayed in Figure4. Figure 4(a) shows the epitaxial growth of the GeC bilayer on the Ge-terminated GaN (001) ideal surface. Adding a C monolayer to the Ge adsorption at the hcp1 site formed this structure. Figure 4(b) exhibits the C dimer formation, with a bond length of 1.47 Å, when a C monolayer is deposited on the Ge-terminated GaN surface, demonstrating that the surface reconstruction avoids the epitaxial growth because of the carbon broken bonds’ saturation [48]. Figure 4(c) corresponds to the formation of a GeC-ML on the Ge-terminated GaN surface, which is obtained when a Ge ML is added on the C dimers (Figure 4(b)). In the top view of the figure, atoms of Ge and C show a “chair” distorted configuration [49] as the Ge-Ge bond lengths (2.76 Å) are larger than the C-C bond lengths (1.35 Å) with the bond angles of 106.1°.Figure 4
Different GeC surfaces: (a) formation of a GeC bilayer on the ideal Ga-terminated surface (GaN/GeC), (b) the C dimers’ formation on the Ge-terminated surface (Ge-term-C), and (c) GeC chair-like layer.
(a)(b)(c)Figure5 shows the epitaxial growth of GeC on the Ge-terminated GaN surface. Figure 5(a) depicts a GeC bilayer, while Figure 5(b) displays the atomic structure of the double GeC bilayer formation, which as Che et al. [18] reported. Therefore, the GeC growth is more favorable on Ge-terminated surface. The bond length between Ge-C is 1.95 Å, which agrees well with previous theoretical reports [50]. Since we have surfaces with a different number of atoms to determine the most stable structure, the surface formation energy (SFE) formalism is employed as described below.Figure 5
Epitaxial growth of (a) a GeC bilayer and (b) two GeC bilayers on the Ge-terminated surface.
(a)(b)


## 3.3. Surface Formation Energy

To determine the stability of all models, we have used the surface formation energy (SFE) formalism [45–51]. In order to apply the SFE formalism, we consider thermodynamic equilibrium between the surface and the bulk. This implies that(1)μGaNbulk=μGa+μN−ΔHfGaN,with(2a)μGa≤μGabulk,(2b)μN≤μN2molecule,where μi is the chemical potential of the ith species and ΔHfGaN is the enthalpy or formation heat of GaN in the bulk structure. According to calculations, ΔHfGaN=0.9eV, in agreement with previous reports [45]. Provided that constant pressure and zero temperature are assumed, the SFE may take the following form:(3)Ef=Eslab−Eref−ΔnGaμGa−ΔnNμN−ΔnGeμGe−ΔnCμC,where Eslab is the energy of each model and Eref is the reference energy. In this case, the reference is the ideally Ga-terminated GaN (001)-(2 × 2) surface. Δni is the excess or deficit of the ith atom. The SFE is a function of the Ga chemical potential with lower limit (N-rich conditions) μGa=μGabulk−ΔHfGaN and upper limit (Ga-rich conditions) μGa=μGabulk. μGe and μC are obtained employing a diamond structure. The obtained results are shown in Figure 6; under Ga-rich conditions, the adsorption of Ge at the hcp1 site is the most stable configuration, whereas the C-terminated surface is the most unfavorable. On the contrary, the Ge-terminated surface is the most stable structure. The C adsorption structures (Figures 2(b) and 4(b)) have a gain in energy due to the rearrangement of the C atoms to form dimers, which have a bond length of 1.24 Å. However, both structures are unstable. On the contrary, Figure 6(b) shows that, under N-rich conditions, the epitaxial growth of 1 or 2 GeC-monolayers on the Ge-terminated surface is possible. However, as the GeC-ML number rises, the system becomes unstable due to an increasing SFE, which could be explained by several studies of GeC thin films [3, 4, 6, 49–54].Figure 6
Surface formation energy (SFE) as a function of the Ga chemical potential for (a) different structures and (b) epitaxial growth.
(a)(b)


## 3.4. Electronic Properties

In this section, the total density of states (DOS) and the projected density of states (PDOS) of the most stable structures are calculated to show the electronic contributions to the Fermi level.The DOS and PDOS are plotted as functions of energy, with the Fermi level being the zero energy. Notice that we outlined the contributions to the p-orbitals of each element. Figure7 shows the electronic properties of the GaN (001)-(2 × 2) clean surface; the second and third GaN bilayers show a bandgap of ≈2 eV, according to previous reports [55]. Below the Fermi level, the major contributions are given by the N-p orbitals. On the contrary, the main contribution above the Fermi level is obtained from Ga-p orbitals. However, the first GaN bilayer shows a metallic behavior due to the Ga-terminated surface.Figure 7
DOS and PDOS for the GaN (001) surface: (a), (b), and (c) exhibit the PDOS of the 1st, 2nd, and 3rd GaN bilayers, respectively. The red and blue lines correspond to Ga-p and N-p, respectively.Figure8 exhibits the DOS and PDOS of the Ge-terminated surface; the last two bilayers remain as semiconductors with a bandgap of 2 eV. Below the Fermi level, N-p orbitals make the main contribution to the DOS. In the first bilayer, the change of Ga atoms by Ge atoms does not affect the surface metallic behavior, and also, there is no dimerization due to the electronic reconstruction. Just below the Fermi level, the main contribution to the DOS is due to the N-p orbitals. An additional GeC bilayer (Figure 9) modifies the contributions on the first bilayer. Close to the Fermi level (in −1 to −2 eV range), Ge-p orbitals are the major contributors to the DOS, no change above the Fermi level is manifested, and the surface unoccupied states are the Ge-p orbitals.Figure 8
DOS and PDOS for the Ge-terminated surface: (a), (b), and (c) exhibit the PDOS for the 1st, 2nd, and 3rd GaN bilayers, respectively. The red lines correspond to Ga-p, the blue lines are the contributions of N-p, and Ge-p is represented as olive lines.Figure 9
DOS and PDOS for a bilayer GeC. The contribution of Ga-p (red lines), N-p (blue lines), Ge-p (olive lines), and C-p (wine lines) is illustrated.


## 4. Conclusions

We have performed ab initio calculations to investigate the initial stages of the GeC structure formation on the GaN (001)-(2 × 2) surface. The adsorption of a monolayer of C and Ge is studied. Results show that the most stable configurations correspond to the C and Ge adsorption at the top and hcp1 sites, respectively. The epitaxial growth of GeC bilayers should be obtained with a control technique of deposition since the calculated SFE shows that only the first two bilayers are stable only under N-rich conditions and on a Ge-terminated surface. Subsequently, the GeC surface becomes unstable due to the relationship between the number of layers and the SFE, in agreement with experimental reports. In addition, our results confirmed those reported by Che et al. [18], which indicate that the Ge-terminated slab surface is more stable than the C-terminated surface. On the contrary, the GeC bilayer on the C-terminated surface is unstable and, moreover, avoids the epitaxial growth provided that the carbon broken bonds saturate. The DOS graphs indicate that all the stable surfaces have a metallic behavior as no energy gap is manifested at the Fermi level.



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