**Electronic and Magnetic Properties of Stone–Wales Defected Graphene Decorated with the Half-Metallocene of** *M* **(***M* **= Fe, Co, Ni): A First Principle Study**

#### **Kefeng Xie 1,2,\*, Qiangqiang Jia 2, Xiangtai Zhang 2, Li Fu <sup>3</sup> and Guohu Zhao 1,\***


Received: 27 June 2018; Accepted: 17 July 2018; Published: 20 July 2018

**Abstract:** The geometrical, electronic structure, and magnetic properties of the half-metallocene of *M* (*M* = Fe, Co, Ni) adsorbed on Stone–Wales defected graphene (SWG) were studied using the density functional theory (DFT), aiming to tune the band structure of SWG. The introduction of cyclopentadienyl (Cp) and half-metallocene strongly affected the band structure of SWG. The magnetic properties of the complex systems originated from the 3d orbitals of *M* (*M* = Fe, Co, Ni), the molecular orbital of Cp, and SWG. This phenomenon was different from that found in a previous study, which was due to metal ion-induced sandwich complexes. The results have potential applications in the design of electronic devices based on SWG.

**Keywords:** Stone–Wales defected graphene; half-metallocene; adsorption energy; density of states; and magnetic property

#### **1. Introduction**

Graphene, which is as a typical two-dimensional (2D) material, has aroused considerable attention because of its special properties and promising potential applications in electronic devices, nanocomposites, molecule sensors, transparent electrodes in light emitting diodes (LED), and photovoltaic devices [1–4]. The typical structural defects [5] in graphene are vacancies [6], impurities [7–10], Stone–Wales (SW) defects [11–14], and pentagonal–octagonal defects [15,16]. The various defects of graphene can alter its electronic and mechanical properties significantly [5,17,18]. The most common topological defect in graphene is SW defect, which is formed by an in-plane 90◦ rotation of a C-C bond in a hexagon ring with fixing the middle point of this bond. SW defects in graphene have been studied widely because the opening band gap of electronic structure is applied to tune the band structure in the design of electronic devices [14,19–21]. SW defect is a classical topological defect in graphene and Stone-Wales graphene (SWG) includes two pairs of pentagonal–heptagonal rings. Compared to perfect graphene, SW graphene is more sensitive in absorbing mercaptan, ozone, and formaldehyde [22,23]. The interactions between graphene and different molecules are important for sensor devices based on the graphene. Therefore, experimental or theoretical research has focused on understanding the effect of the electronic and magnetic properties of graphene when molecules adsorb on graphene [24–27]. Transition metals (TMs) absorbed in carbon nanotube and graphene have

been given great attention because the absorbed TM atoms can generate novel physical, chemical, and mechanical properties [28–30].

In this study, we used first principle calculations to explore the effect of interactions between SWG and cyclopentadienyl (Cp) or half-metallocene of *M* (*M* = Fe, Co, Ni) on their electronic and magnetic properties. Moreover, the geometry and electronic structures were investigated.

#### **2. Calculation Details**

Calculations were performed using DFT with van der Waals correctionsas implemented in the CASTEP software of in Material Studio. Generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) exchange correlation function was used [31]. The SW graphene slab was a 3 × 3 × 1 supercell (9.84 × 9.84 × 15.00 Å, 32 C atoms). The cutoff energy was set to 300 eV. K point of the Brillouin zone and was sampled using 5 × 5 × 1 [32]. The energy convergence standard was 10–5 eV per atom during all structural relaxation. The forces on relaxation were less than 0.05 eV/Å. Test calculations which used a higher cutoff energy (400 eV) or a larger K point (7 × 7 × 1) between the SWG sheets were performed and showed less than 4% improvement to the simulation accuracy. Therefore, the calculation parameters were considered to be accurate. We have considered the van der Waals interaction [24,25] between the SWG and Cp. A Cp or half-metallocene was located at the center of the carbon ring of SWG. Considering the structure symmetry of SWG, the hollow sites included the centers of a pentagon ring (H1), hexagon ring (H2), and heptagon ring (H3) (Figure 1).

**Figure 1.** Optimized atomic structures of (**a**) Stone-Wales graphene (SWG) and (**b**) ferrocene.

The adsorption system stability was estimated using the absorption energy *Eads* defined as follows:

$$E\_{ads} = E\_T - E\_{SWG} - E\_{Cp} - \mu\_M$$

where *ET* is the total energy of the half-metallocene of *M* (*M* = Fe, Co, Ni) absorbed SWG; *ESWG* and *ECp* are the energy of pristine SWG and Cp, respectively; and *μ<sup>M</sup>* is the energy of metal ions in the cell.

#### **3. Results and Discussion**

#### *3.1. Adsorption Configurations and Energy*

#### 3.1.1. Adsorption of Cp in Stone-Wales Graphene (SWG)

To understand how the Cp and half-metallocene are adsorbed in SWG, their adsorption configurations were evaluated and are showed in Figure 1. The adsorption energies and value of charge transfer (*Qe*) based on the Mulliken population between SWG and adsorbate corresponding to the different adsorption configurations are listed in Table 1. We discussed the adsorption of Cp on the SWG. The calculated results indicated that Cp absorbed on H1 was the most stable. Meanwhile, the adsorption energy and the smallest distance between Cp and SWG layer is shown in Table 1. The results showed that *Eads* varied from −1.09 eV to −1.15 eV and H1 had the highest value (−1.15 eV),

which was much larger than that adsorbed in perfect graphene. The large *Eads* indicated that the presence of SW defect affected the adsorption process and enhanced the interaction between Cp and the SWG substrate. Figure 2 shows the electron density difference of SWG and Cp/SWG at H1, which indicated that a strong charge transfer process existed between Cp and SWG. *Qe* of SWG at H1 was the largest (0.51 e. In fact, the charge distribution was inhomogeneous in SWG. The pentagon ring had a positive charge, whereas the heptagon ring had a negative charge (Figure 2a). Hence, Cp had one electron (i.e., H1) that was absorbed at the site of the pentagon ring. The result was consistent with the absorption energy.



**Figure 2.** Electron density difference for (**a**) SWG and (**b**) Cyclopentadienyl (Cp)/SWG at the pentagon ring (H1).

#### 3.1.2. Adsorption of Half-Metallocene of *M* (*M* = Fe, Co, Ni) in SWG

In this section, we focus on the adsorption of half-metallocene of *M* (*M* = Fe, Co, Ni) in SWG at three different sites, as shown in Figure 3. The parameters describing the adsorption complexes are depicted in Table 1. The value of *Eads* ranged from −3.82 eV to −6.23 eV, which was larger than that of SWG. Therefore, metal ions stabilized the adsorption systems of SWG with Cp. The absorption energy had significant differences among different metal ions at the same site. Particularly, SWG-Co-Cp had the strongest *Eads*, followed by SWG-Fe-Cp and SWG-Ni-Cp. Meanwhile, for the absorption sites, Cp was located closer to the heptagon ring (H3), suggesting that the metal ions played an important role in the adsorption substrate. *M*2+ (*M* = Fe, Co, Ni) with Cp (one electron) had one positive charge, and the heptagon ring had a partial negative charge. Therefore, Cp was located closer to heptagon

ring. of SWG at H3 was the largest, which was consistent with its high adsorption energy and value of charge transfer.

**Figure 3.** Optimized atomic structures of Cp in SWG at H1 (**a**); hexagon ring (H2) (**b**) and heptagon ring (H3) (**c**).

#### *3.2. Density of States (DOS) of the SWG System*

#### 3.2.1. DOS of Cp in SWG

To understand the effect of the electronic properties when Cp absorbed on SWG, the density of states (DOS) of adsorption complexes is illustrated in Figure 4, corresponding to different absorption sites (H1, H2, and H3). The spin-up DOS (majority) and spin-down DOS (minority) were presented in each case, respectively. Pristine SWG is a zero-gap semiconductor in which the Fermi level crossed the Dirac point. In the all cases of absorption configurations, the three systems exhibited metallicity, in which the conduction band passed through the Fermi level. Moreover, the majority and minority DOS were symmetrical, which indicated that their total magnetic moment was zero because of the valence electrons arranged in pairs. From the view point of the molecular orbital, the charge transfer mechanism can be associated with the relative energy positions of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the adsorbate compared to the SWG Fermi level. If the HOMO is above the Fermi level of SWG, a charge transfer from the adsorbed molecule to SWG may occur. If the LUMO is below the Fermi level, a charge transfer from graphene to the molecule could appear [33]. The HOMO of Cp was 1.68 eV above the Fermi level, deep in the SWG valence band and its LUMO was 7.01 eV above the Fermi level, high in the conduction band of SWG. The HOMO of Cp was the orbital that has a big overlap with the DOS of SWG and thus could cause very big charge transfer value. Therefore, the Cp acted as a very strong donor in the complex systems.

#### 3.2.2. DOS of Half-Metallocene of *M* (*M* = Fe, Co, Ni) in SWG

In this part, we focus on the adsorption of half-metallocene of *M* (*M* = Fe, Co, Ni) in SWG at three different sites. The DOS and PDOS are shown in Figures 5 and 6. The results indicated the spin-up and spin-down DOS were asymmetrical, which would generate a magnetic moment. Furthermore, the magnetic moment of all complex systems was tuned by the absorption sites and different metal ions. In Cp/Fe/SWG and Cp/Co/SWG, the spin-up DOS value around the Fermi level was more than that of spin-down DOS. In Cp/Ni/SWG, the spin-up DOS value around the Fermi level was less than that of spin-down DOS. In Cp/Ni/SWG, the spin-up DOS around the Fermi level remained zero. Therefore, the zero-gap semiconductor property of the SWG was maintained in the spin-up channel. On the other hand, the spin-down channel of Cp/Ni/SWG showed a non-zero DOS around the Fermi level and metallicity was correspondingly maintained. The interaction between SWG and Fe ion induced effective shifts between the spin-up and spin-down DOS, which lead to a strong magnetic moment. Considering the strong magnetic property of Fe, Co, and Ni atoms, the spin projected density of states (PDOS) of SWG with half-metallocene of *M* (*M* = Fe, Co, Ni) was showed in Figure 6. The results indicated that the spin DOS of 3d orbital of *M*, Cp, and SWG were all asymmetric between the spin-up and spin-down DOS, which showed that the magnetic property was contributed to by the three parts. The magnetic properties of Cp and SWG were induced from magnetic metal of (*M* = Fe, Co, Ni) by charge transfer. This phenomenon was different from that in a previous study [4].

**Figure 4.** Total electronic density of states (DOS) of pristine SWG (**a**) and Cp on SWG at H1 (**b**); H2 (**c**), and H3 (**d**).

**Figure 5.** Total electronic DOS of half-metallocene of Fe (**a**–**c**), Co (**d**–**e**), and Ni (**g**–**i**) in SWG at the three hollow sites (H1, H2, and H3).

**Figure 6.** PDOS of half-metallocene of Fe (**a**–**c**), Co (**d**–**e**), and Ni (**g**–**i**) in SWG at the three hollow sites (H1, H2, and H3).

#### **4. Conclusions**

The geometrical, energetic, electronic, and magnetic properties of the half-metallocene of *M* (*M* = Fe, Co, Ni) in SWG were investigated using density functional theory (DFT) calculations. The introduction of Cp and half-metallocene increased the conductivity of SWG. Furthermore, the half-metallocene of *M* (*M* = Fe, Co, Ni), with a magnetic behavior, induced different magnetic properties of the adsorption complexes. On the basis of the PDOS results, the magnetic moments of the complex systems were contributed to by the 3d orbital of *M* (*M* = Fe, Co, Ni), molecular orbital of Cp, and SWG. Interestingly, the DOS and magnetic properties were tuned by the absorption sites of Cp and half-metallocene in SWG.

**Author Contributions:** K.X. and G.Z. conceived and designed the calculated models; K.X., Q.J., X.Z., and L.F. analyzed the data; K.X. wrote the article.

**Funding:** Support by Lanzhou City University key discipline "Analysis and Treatment of Regional Typical Environmental Pollutants"; the Project of Qinghai Science & Technology Department (No. 2016-ZJ-Y01) and the Open Project of State Key Laboratory of Plateau Ecology and Agriculture, Qinghai University (No. 2017-ZZ-17) is gratefully acknowledged. Computations were done using the National Supercomputing Center in Shenzhen, P. R. China.

**Conflicts of Interest:** The authors declare no conflicts of interest.

#### **References**


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Optical Properties of Graphene/MoS2 Heterostructure: First Principles Calculations**

**Bin Qiu 1, Xiuwen Zhao 1, Guichao Hu 1, Weiwei Yue 1,2, Junfeng Ren 1,2,\* and Xiaobo Yuan 1,\***


Received: 29 October 2018; Accepted: 19 November 2018; Published: 21 November 2018

**Abstract:** The electronic structure and the optical properties of Graphene/MoS2 heterostructure (GM) are studied based on density functional theory. Compared with single-layer graphene, the bandgap will be opened; however, the bandgap will be reduced significantly when compared with single-layer MoS2. Redshifts of the absorption coefficient, refractive index, and the reflectance appear in the GM system; however, blueshift is found for the energy loss spectrum. Electronic structure and optical properties of single-layer graphene and MoS2 are changed after they are combined to form the heterostructure, which broadens the extensive developments of two-dimensional materials.

**Keywords:** graphene/MoS2 heterostructure; optical properties; electronic structure

#### **1. Introduction**

Graphene has been popular among researchers since it was successfully exfoliated by Novoselov et al. in 2004 [1]. Graphene has excellent electrical conductivity [2], excellent mechanical strength [3,4], superior thermal conductivity [5], and high light transmittance in the visible light–infrared area [6]. Graphene has been widely used in applications such as solar cells, lighting, and touch screens [7–14]. However, graphene has been extremely limited in the research and application of some fields because of its zero band gap. One of the methods used to broaden the application of graphene is to form a multilayer structure or heterostructure. Stacking different two-dimensional materials together can form a double-layer or even multi-layer artificial material that is maintained by van der Waals interactions. Such materials are known as van der Waals heterojunctions. Surprising physical properties can be obtained by stacking two-dimensional materials of different properties together. The almost infinitely rich possibilities make the van der Waals heterojunction even more important than the two-dimensional material itself [15–18]. The large surface area, high chemical resistance, high stability, and good electrical conductivity of graphene indicate that graphene sheets are promising as substrates for improving the electrochemical and electrocatalytic properties of metal oxides and metal sulfides. Properties have already been studied in the heterostructure of Ni(OH)2/graphene [19] and SnO2/graphene [20], which indicates that the heterostructure of graphene also has great research prospects. On the other hand, heterostructures based on graphene and other two-dimensional materials, such as MoS2, will change their electronic structure and other properties, which has attracted people's attention.

MoS2 is one of the transition metal dichalcogenides (TMDs). MoS2 can appear in two-dimensional or three-dimensional forms. The direct band gap will be about 1.8 eV [21,22] when MoS2 appears as a single-layer two-dimensional material, which makes it a very good semiconductor material. Monolayers of MoS2 have many excellent properties, such as high electron mobility, low dimensionality, smooth atomic sheet [21,23], and outstanding mechanical properties [24]. Monolayers of MoS2 have

been successfully prepared due to their extraordinary properties [25] and have been extensively studied [21,26–31]. Furthermore, the heterostructure of graphene/MoS2 opens up possibilities for many applications. For example, Ma et al. [32] systematically investigated the electronic and magnetic properties of perfect, vacancy-doped, and nonmetal elements (H, B, C, N, O, and F) adsorbed MoSe2, MoTe2, and WS2 monolayers by means of first-principles calculations. In 2011, Chang et al. [33,34] successfully synthesized layered graphene or graphene nanosheet/MoS2 composites by an L-cysteine-assisted solution-phase methodand the obtained composites showed three-dimensional architecture and excellent electrochemical performances which can act as anode materials for Li-ion batteries. Soon Li et al. [35] developed a selective solvothermal synthesis of MoS2 nanoparticles on reduced graphene oxide (RGO) sheets and the MoS2/RGO hybrid exhibited superior electrocatalytic activity in the hydrogen evolution reaction. Coleman et al. [36] showed that hybrid dispersions or composites could be prepared by blending MoS2 with suspensions of graphene or polymer solutions. A recent study reported the catalytic activity of MoS2/graphene dots for an oxygen evolution reaction [37]. The above results proved that the heterostructures of GM are useful in applications ranging from electronics to energy storage.

There is still a lack of research of optical properties in GM heterostructures up to now. The heterogeneous structure of graphene has bright prospects of applications and the direct bandgap electronic structure of MoS2 is an essential property for many optical applications; so, in this paper, we explore the optical properties of GM based on density functional calculations. The structure of this paper is as follows: Section 2 gives the theoretical calculation method, Section 3 gives the result analysis, and Section 4 gives the conclusion.

#### **2. Methods**

The DFT calculations we used are performed by the VASP (Vienna ab-initio Simulation Package) software package [38,39]. The lattice constant of the MoS2 monolayer is 3.16Å, and the lattice constant of pure graphene is 2.47Å, so the supercell of MoS2 we used was 4\*4\*1, and the supercell of graphene was 5\*5\*1. The lattice mismatch ratio of the system was about 2.29%. We stacked monolayer graphene and monolayer MoS2 to form the heterostructure of GM, which is shown in Figure 1. In order to reduce the interaction between the periodic structures in the vertical direction when constructing the model, a 20Å vacuum is added. In the theoretical calculations, we use the projector-augmented wave (PAW) [40,41] method to describe the interaction between ions and electrons. At the same time, the exchange-correlation potential is selected based on the Generalized Gradient Approximation (GGA [42]) in terms of the Perdew–Burke–Ernzerhof (PBE [42]) functional, which is often used to calculate the molecular adsorption at the electrode surface. The cutting power of the plane wave is set to 500 eV. When the structure relaxes, the convergence precision of each interatomic force is 0.02 eV/Å, and the self-consistent convergence energy is not higher than 10−<sup>4</sup> eV. The Brillouin zone was summed according to the 9×9×1 Monkhorst–Pack characteristic K point. Based on the above conditions, the calculated distance between graphene and MoS2 is 3.64Å. Then, the electronic structure and the optical properties of the heterostructures are calculated. Van der Waals interactions are included in the calculations.

The optical properties can be modeled by the dielectric constant of the system. We use the superposition of Lorentz oscillators to model the complex dielectric function ε(ω) = ε1(ω)+iε2(ω) of the heterostructure, which is a function of photon energy. Generally speaking, the dielectric constant is the real part of the complex permittivity, ε1(ω). The dielectric constant is caused by various kinds of displacement polarization inside the material and represents the energy storage term of the material. The imaginary part of the complex permittivity, ε2(ω), is related to the absorption (loss or gain) of the material. The steering polarization can not keep up with the various relaxation polarizations caused

by the change of the external high-frequency electric field, and represents the loss term of the material. The formula of ε2(ω) is as follows:

$$\varepsilon\_2(\omega) = \frac{4\pi^2 e^2}{\Omega} \lim\_{q \to 0} \frac{1}{q^2} \sum\_{\varepsilon, \nu, k} 2w\_k \delta(\varepsilon\_{\varepsilon k} - \varepsilon\_{\varepsilon k} - w) \times \left< u\_{\varepsilon k} + \varepsilon\_{4\eta} |u\_{\varepsilon k}\rangle\langle u\_{\varepsilon k} + \varepsilon\_{\beta \eta} |u\_{\varepsilon k}\rangle\,^\* \tag{1}$$

The real part ε1(ω) of the dielectric function can be obtained by using the Kramers–Kroing relation,

$$\varepsilon\_1(\omega) = 1 + \frac{2}{\pi} P \int\_0^\infty \frac{\varepsilon\_2^{a\beta}(w')w'}{w'^2 - w^2 + i\eta} d\omega' \tag{2}$$

**Figure 1.** Top (**a**) and side (**b**) views of the Graphene/MoS2 (GM) heterostructure. (**c**) The differential charge density distributions of GM. Gray, purple, and yellow atoms represent C, Mo, and S atoms, respectively. Blue means loss electrons and yellow means gain electrons.

Other optical constants can also be obtained from the dielectric function. For example, the absorption coefficient α(ω), refractive index n(ω), reflectance R(ω), and energy loss spectrum L(ω) can all be derived by ε1(ω) and ε2(ω). The formulas are:

$$a(\omega) = \frac{\sqrt{2}\omega}{c} \left\{ \left[ \varepsilon\_1^2(\omega) + \varepsilon\_2^2(\omega) \right]^{\frac{1}{2}} - \varepsilon\_1(\omega) \right\}^{\frac{1}{2}} \tag{3}$$

$$\mathbf{n}(\omega) = \frac{1}{\sqrt{2}} \left\{ \left[ \varepsilon\_1^2(\omega) + \varepsilon\_2^2(\omega) \right]^{\frac{1}{2}} + \varepsilon\_1(\omega) \right\}^{\frac{1}{2}} \tag{4}$$

$$\mathcal{R}(\omega) = \left| \frac{\sqrt{\varepsilon\_1(\omega) + i\varepsilon\_2(\omega)} - 1}{\sqrt{\varepsilon\_1(\omega) + i\varepsilon\_2(\omega)} + 1} \right|^2 \tag{5}$$

$$L(\omega) = \frac{\varepsilon\_2(\omega)}{\varepsilon\_1^2(\omega) + \varepsilon\_2^2(\omega)}\tag{6}$$

#### **3. Results and Discussion**

In order to illustrate the similarities and the differences of the graphene monolayer, MoS2 monolayer, and the GM heterostructure, we first calculate the electronic structures of the three systems. The energy band structures and the electronic density of states (DOS) for the three systems are shown in Figure 2. It can be found that our calculated curves are well matched with the results of previous calculations [43,44]. As shown in Figure 2, graphene is a zero bandgap material and MoS2 is a material with a band gap of 1.73 eV. After they are stacked together to form the GM structure, as shown in Figure 1, the band gap is 3.49 meV for GM heterostructures, which can be obtained from the embedded figure in Figure 2c. Based on the interlayer interactions between G and

M, there will be a change in the on-site energy of atoms in the G layer, so the band gap opens [44,45]. The upward shift of the Dirac point of graphene with respect to the Fermi level indicates that holes are donated by the MoS2 monolayer, which can be confirmed by the charge transfer between graphene and MoS2 after stacking. Figure 1c gives the differential charge density distributions, blue means loss electrons and yellow means gain electrons. It is clear from the figure that holes in G are donated by M monolayer after the stacking. From Figure 2 we can clearly see that after the heterostructure is formed, the electronic structure changes greatly. Therefore, we speculate that the formation of the GM heterostructure will influence the optical properties compared with single-layer graphene or MoS2.

**Figure 2.** Band structure and density of states (DOS) of graphene (**a**), MoS2 (**b**) and the GM heterostructure (**c**), respectively. The embedded figure in (**c**) shows the zoom in of the band structure near Fermi Energy.

The calculated dielectric constants ε(ω) of the monolayer graphene (G), monolayer MoS2 (M), and GM heterostructure are shown in Figure 3. Figure 3a shows the parallel direction of the ε1(ω). We can clearly see from the figure that the overall trends for all systems are almost identical with only small differences. In fact, people are more interested in the changes that occur in the visible light region. In the visible light region, the value of the ε1(ω) is obviously the largest in the GM system, followed by the M system, and finally the G system. Comparing the GM and G system at the low-energy zone, it can be found that the parallel direction of ε1(ω) for the two systems not only changes at the maximum values, but also GM has an obvious blueshift of ε1(ω) relative to the G system. Figure 3b shows the ε1(ω) in the vertical direction and we find similar regularity with those of Figure 3a. Under the same analysis of the three systems in the low-energy region, we find that the most obvious change is a more obvious redshift for the GM system compared with the G system. This is because the GM system is an anisotropic material and the parallel direction of the ε1(ω) illustrates differences in the vertical and horizontal directions. Figure 3c, d shows the parallel and vertical directions of the imaginary part of the dielectric constant, respectively. Same properties between the real and the imaginary parts of ε1(ω) can be found. The peak value of the dielectric constant of the GM system has been significantly improved compared with G and M and different degrees of redshift or blueshift can also be found.

**Figure 3.** The complex dielectric constants of monolayer graphene (G), monolayer MoS2 (M) and GM systems. (**a**,**b**) represent the parallel and vertical components of the real part of the dielectric constant, (**c**,**d**) represent parallel and vertical components of the imaginary part of the dielectric constant, respectively.

Figure 4a shows the absorption coefficient α(ω) in the parallel direction. The overall change trend of the GM and M systems are similar, and the only difference is in the peak values. There are obvious differences between the GM and G systems. The α(ω) of the GM system is more volatile than the G system at the peak position. Among the three systems, GM usually has a large α(ω) value in most cases; however, in the visible region, G is slightly larger than that of the GM system. A zoom in the region between 0 and 2 eV of Figure 4a is also embedded. The value of the intersection between the reverse tangent and the x-axis is the optical band gap in the region between 0 and 2 eV in Figure 4a. It can be found from Figure 4a, that the optical band gap of G is about 0.75 eV, and the optical band gap of M is about 1.63 eV. However, the band gaps are around 0.41 eV and 1.40 eV when the system is going from G and M to GM. It is well known that a photoelectron can be excited with less energy when the optical band gap is small. The optical band gap of GM is significantly reduced, which indicates that we can use a lower energy to excite a photoelectron in GM compared with the G and M systems. The vertical direction of α(ω) is given in Figure 4b. The overall change trend of the vertical direction, α(ω), has a similar regularity compared with the parallel direction. The obvious difference is that the GM system has a large redshift in the vertical direction compared with the G system. The α(ω) is greatly improved for the GM system compared with the G and M systems, so the GM system is indeed superior to the G and M systems in terms of absorption properties.

**Figure 4.** The absorption coefficient α(ω) and the refractive index n(ω) of three systems. (**a**,**b**) represent parallel and vertical components of the absorption coefficient α(ω), (**c**,**d**) represent parallel and vertical components of the refractive index n(ω), respectively.

The parallel direction and vertical direction of the refractive index n(ω) are given in Figure 4c,d, respectively. According to the formula for calculating the refractive index, i.e., Equation (4), we can see that the refractive index is essentially related to the real and the imaginary parts of the dielectric constant. By comparing the dielectric constant of Figure 3 and the refractive index image of Figure 4, it can be found that the change trends of Figure 3a,b are similar with those in Figure 4c,d, which means that the effects of the real part of the dielectric constant on the refractive index play the leading role. We found that the n(ω), especially in the visible light range, has a large value for the GM system. The heat preservation characteristics will be good if the material has a big refractive index. This property can be applied to materials that require constant temperature conditions.

The parallel and vertical directions of the reflectance R(ω) are given in Figure 5a,b, respectively. For parallel directions, the GM system is significantly higher than those of the G and M systems, especially in the visible region. It is obvious that the GM system has a certain redshift relative to the G system, and this phenomenon is also reflected in the vertical direction. In the visible light region, the value of the GM system is also higher than those of the other two systems.

The energy loss spectra L(ω) are given in Figure 5c,d. In the parallel direction, L(ω) of the GM in the low-energy region is significantly less than those of the other two systems. Especially for the G system, the maximum energy loss in the low-energy zone reaches 2, while the GM system is around 0.3. As the energy increases, energy losses also increase. The energy loss of the GM system is concentrated inthe range of 15–20 eV, however for the G and M systems, the energy losses are concentrated in the range of 5–20 eV and they span a large energy extent. In the vertical direction, the energy losses of the three systems in the low-energy region are almost zero, indicating that the loss of power in the vertical direction is small in the low-energy region. The energy loss of the GM system is almost

concentrated between 15 eV and 18 eV, while the energy of the G and the M system are lost relatively evenly between 5 eV and 15 eV, which means that the ability to control the energy loss of the GM system is the best. In addition, the GM system is relatively blueshifted for both horizontal and vertical energy loss compared with the G and M systems.

**Figure 5.** The reflectance R(ω) and the energy loss spectrum L(ω) of three systems. (**a**,**b**) represent parallel and vertical components of the reflectance R(ω), (**c**,**d**) represent parallel and vertical components of the energy loss spectrum L(ω), respectively.

#### **4. Conclusions**

In this article, we mainly discuss the electronic structure and the optical properties of GM heterostructures from the first principles calculations. Based on the DFT theory, dielectric constant, ε(ω) absorption coefficient α(ω), refractive index n(ω), reflectivity R(ω), and energy loss spectrum L(ω) of the systems are calculated. It is found that there is indeed a clear improvement of the optical properties for the GM system comparedto the G and M systems. The band gap and the dielectric constants become large for the GM system and there are redshifts for the absorption coefficient, refractive index, and the reflectance. A blueshift is found for the energy loss spectrum in the GM system. All of the above results show that, due to the formation of the heterojunctions, the optical properties of the GM system have been significantly improved compared with the single layers, which deliversa more effective way to use two-dimensional materials in optical applications.

**Author Contributions:** B.Q. did the calculations and wrote the paper, X.Z. collected the references, G.H. prepared the figures, W.Y. and J.R. analyzed the data, X.Y. generated the research idea. All authors read and approved the final manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (Grant No. 11674197) and the Natural Science Foundation of Shandong Province (Grant Nos.ZR2018MA042).

**Acknowledgments:** This work was supported by the Taishan Scholar Project of Shandong Province. **Conflicts of Interest:** The authors declare no conflicts of interest.

#### **References**


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Graphene Schottky Junction on Pillar Patterned Silicon Substrate**

**Giuseppe Luongo 1,2,\*, Alessandro Grillo 1, Filippo Giubileo 2, Laura Iemmo 1,2, Mindaugas Lukosius 3, Carlos Alvarado Chavarin 3, Christian Wenger 3,4 and Antonio Di Bartolomeo 1,2,5,\***


Received: 29 March 2019; Accepted: 22 April 2019; Published: 26 April 2019

**Abstract:** A graphene/silicon junction with rectifying behaviour and remarkable photo-response was fabricated by transferring a graphene monolayer on a pillar-patterned Si substrate. The device forms a 0.11 eV Schottky barrier with 2.6 ideality factor at room temperature and exhibits strongly biasand temperature-dependent reverse current. Below room temperature, the reverse current grows exponentially with the applied voltage because the pillar-enhanced electric field lowers the Schottky barrier. Conversely, at higher temperatures, the charge carrier thermal generation is dominant and the reverse current becomes weakly bias-dependent. A quasi-saturated reverse current is similarly observed at room temperature when the charge carriers are photogenerated under light exposure. The device shows photovoltaic effect with 0.7% power conversion efficiency and achieves 88 A/W photoresponsivity when used as photodetector.

**Keywords:** graphene; Schottky barrier; diode; photodetector; heterojunction; MOS (Metal Oxide Semiconductor) capacitor; responsivity

#### **1. Introduction**

The discovery of two-dimensional (2D) materials such as graphene [1], MoS2 [2,3], WSe2 [4,5], phosphorene and so on [6], has attracted the interests of the scientific community in the recent years. Graphene is still one the most studied materials for its 2D honeycomb structure, high electron mobility, high electrical and thermal conduction, low optical absorption coefficient and easy fabrication methods [1,7,8]. Large graphene layers can be easily synthesized by chemical vapor deposition (CVD) and integrated into the existing semiconductor device technologies. These properties make graphene the perfect candidate to realize a new generation of transistors [9–14], diodes [15–20], chemical-biological sensors [21–23], photodetectors and solar cells [24–30]. In the recent years, a lot of activity has been focused on the graphene/silicon junction (gr/Si) as one of the simplest graphene devices offering the possibility to study the physical phenomena that occur at the interface between 2D and 3D materials [31]. The gr/Si junction usually forms a Schottky barrier and behaves as a rectifier with a current-voltage (I-V) characteristic similar to that of a metal/semiconductor Schottky diode [31,32]. Because of its particular band structure, graphene possesses low electron density of states close to the Dirac point, hence the Fermi level is highly dependent on charge transfer to or from it. In the gr/Si junction, the application of a bias affects the charge transfer process and the consequent shift of the graphene Fermi energy modulates the gr/Si Schottky barrier height, which becomes therefore bias dependent [31,32]. Indeed, adding such a feature into the standard thermionic emission (T.E.) theory provides an accurate model to describe the gr/Si experimental I-V characteristics [31,33]. Gr/Si Schottky diodes are characterized by a higher ideality factor (*n* > 2) than metal/semiconductor devices (*n* ∼ 1.3) [31]. The higher *n* arises because native oxide layers are generally formed at the interface during the graphene transfer process along with silicon interface trap states and/or metallic contamination [34,35]. Obviously, the ideality of the junction can be improved by reducing the interface defects, for instance through a suitable patterning of the substrate. Indeed, the gr/Si tip junctions that we presented in a previous work showed an ideality factor of 1.5 as the patterning of the Si substrate in a tip-array geometry reduces the probability of finding defects or contaminates at the junction, compared to a planar junction of the same area [17]. In addition to that, the tip geometry amplifies the electric field close to the junction, inducing a potential that shifts the graphene Fermi level even at low bias. We exploited such a feature to realize a bias-tunable graphene-based Schottky barrier device [17].

Modifying the substrate geometry is a viable approach to improve the gr/Si device performance or its photoresponse when used as a photodetector. We remark that the photoresponsivity of the gr/Si junction has been also improved by acting on the device structure. One possible way is to reduce the oxide layer underneath the graphene in order to create a metal/oxide/semiconductor (MOS) capacitor next to the gr/Si junction perimeter. Indeed, such an MOS capacitor plays an important role in the photo-charge collection process, by providing photogenerated carriers from the Si substrate to the junction [16,18–20,36].

In this work, we combine the tip geometry and the MOS capacitor approach, by fabricating a graphene/silicon junction on Si pillars to realize a bias-tunable Schottky diode that can be used also for photovoltaic and photodetection applications. The pillar perimeter works similarly to the nanotips in enhancing the electric field at the junction but is easier to fabricate and provides a better control of the MOS capacitor areas. We present an extensive analysis of the I-V characteristics of gr/Si pillar junction and evaluate the relevant parameters using the T.E. model and the Cheung and Cheung (C.C.) method [31,32,37]. We also investigate the photo response and the photovoltaic effect of the device using white LED light at different intensities.

#### **2. Materials and Methods**

Figure 1a shows the schematic view of the gr/Si-pillar junction. Starting from a highly n-doped silicon substrate (∼10<sup>18</sup> cm<sup>−</sup>3) three pillars with the height of <sup>∼</sup>500 nm and square sections of 30 <sup>μ</sup>m, 50 μm and 100 μm per side were patterned by photolithography (Figure 1b). In a gr/Si junction the Schottky barrier is controlled by the sharper geometries, that is by the pillar perimeter in our case. As the three pillars have similar perimeter/area ratio (∼10%), we expect that they contribute in a similar way to the junction properties. A SiO2 layer was CVD-deposited until it covered the silicon pillars. Chemical-mechanical polishing (CMP) was then used to remove the oxide layer on the top of the pillars. After that, a graphene layer was transferred from Cu foil on the pillars with a method detailed elsewhere [35].

The Raman spectrum of the graphene measured on the SiO2 and Si pillars is shown in Figure 1c. The plot shows two clear peaks at <sup>∼</sup>1568 cm−<sup>1</sup> and <sup>∼</sup>2680 cm−<sup>1</sup> which indicates that graphene is a good quality monolayer.

A gold contact (anode) was evaporated on the sample through a shadow mask. The other contact (cathode) was formed by coating silver paste on the scratched back-side of the Si substrate. The I-V measurements were performed with a Keithley Semiconductor Characterization System 4200 (SCS-4200) connected to a Janis probe station. During the measurements the sample was kept in dark and at a pressure of 1 mbar.

**Figure 1.** (**a**) Two-dimensional (2D) schematic view of the gr/Si-pillar device. (**b**) Optical microscope image of the pillars. (**c**) Raman spectroscopy of the graphene on SiO2 and Si. (**d**) The current-voltage (I-V) characteristic of the device measured from 200 K to 400 K.

#### **3. Results**

Figure 1d shows the I-V characteristics measured for the gr/Si-pillar junction at different temperatures in the range 200–400 K. From low to room temperature the gr/Si junction shows an exponential reverse current which is typical of gr/Si junctions [17]. At higher temperatures, after the initial fast growth of the ohmic regime at low bias, the reverse current exhibits a gradual weaker dependence on the bias until it becomes quasi-saturated. The I-V characteristic at room temperature shows a rectification factor of two orders of magnitude at ±1.5 V.

The exponential reverse current growth at lower temperatures in Figure 1d can be explained considering the Fermi level shift due to the graphene low density of states, which reduces the Schottky barrier in reverse bias [31]. The variation of the barrier can be contributed also by the geometry and doping level of the substrate through the image-force barrier lowering. The pillar geometry magnifies the electric field around the perimeter where a wider depletion layer is created. Such a depletion layer is mirrored by charges in graphene, which cause an up-shift of the Fermi level and a reduction of the Schottky barrier. The high doping of the Si substrate can further contribute to barrier lowering through the image force effect. Conversely, the change of behaviour at higher temperatures indicates that the augmenting thermal generation rate in the depletion layer dominates the reverse leakage current which becomes less sensitive to the bias. The slight deviation of such current from saturation can be ascribed to image force barrier lowering [38,39].

To determine the Schottky diode parameters, we use the T.E. model with voltage dependent Schottky barrier height *q*φ*<sup>B</sup>* [31], expressed by the equations:

$$I = I\_0 e^{\frac{qV}{kT}} \left(1 - e^{-\frac{qV}{kT}}\right) \tag{1}$$

$$I\_0 = AA^\* T^2 e^{-\frac{g\phi\_B}{kT}},\tag{2}$$

where *I*<sup>0</sup> is the reverse saturation current, *q* the electron charge, *n* > 1 the ideality factor, *k* the Boltzmann constant, *T* the temperature, *A* the junction area, *A*<sup>∗</sup> = <sup>4</sup>π*m*<sup>∗</sup> *ek*2 *<sup>h</sup>*<sup>3</sup> <sup>=</sup> <sup>112</sup> A cm−<sup>2</sup> <sup>K</sup>−<sup>2</sup> the Richardson constant for n-type Si (*m*∗ *<sup>e</sup>* is the electron effective mass and *h* is the Plank constant) [40]. For *qV* > *nkT*, Equations (1) and (2) can be rewritten as:

$$
\ln(I) = \ln(I\_0) + \frac{qV}{nkT} \, ^\prime \tag{3}
$$

$$
\ln\left(\frac{I\_0}{T^2}\right) = \ln(AA^\*) - \frac{q\phi\_B}{kT}.\tag{4}
$$

According to Equation (3), the straight-line fitting of the ln(I)-V characteristics for *qV* >> *kT* can be used to extrapolate the reverse current *I*<sup>0</sup> at zero bias and to estimate the ideality factor *n*. The so-obtained ideality factor as a function of temperature is shown in Figure 2a. The ideality factor at room temperature is *n* ≈ 2.6 and is a monotonic decreasing function of the temperature because several non-idealities manifest more at lower temperatures. These non-idealities include metal residues consequence of the etching process (Cu in this case) which form carrier recombination centers, interface states at the junction which lead to charge trapping and detrapping, and the presence of a native oxide layer [31,34]. The zero-bias current, *I*0, is used in the Richardson plot, ln *I*0/*T*<sup>2</sup> vs 1/*T*, shown in Figure 2b, which, according to Equation (4), yields a Schottky barrier at zero-bias of 0.11 eV and ln(*AA*<sup>∗</sup> ) = <sup>−</sup>33.72. Since the effective gr/Si junction contact area is <sup>∼</sup>1.34 · 10−<sup>2</sup> mm2, the Richardson constant is *<sup>A</sup>*<sup>∗</sup> = 1.68·10−<sup>9</sup> Acm2K−2. A possible explanation for the low Richardson constant and the ideality factor *n* > 2 is the presence of a thin oxide layer [16]. Taking into account the native oxide thickness, Equation (2) can be modified by adding a tunnelling factor as:

$$I\_0 = AA^\* \exp\left(-\chi^{\frac{1}{2}}\delta\right) \exp\left(\frac{q\phi\_B}{kT}\right) \tag{5}$$

where δ (expressed in Å) is the oxide layer thickness and χ ≈ 3 eV is the differences between the energy Fermi level and the conduction band minimum of SiO2. From Equation (5), we estimated an oxide layer of 15 Å, which is thin enough to allow a tunnelling current, but can sustain a voltage drop and affect the I-V characteristic of the junction.

**Figure 2.** (**a**) Ideality factor vs the temperature extracted from the thermionic emission (T.E.) model (**b**) Richardson plot of the ln *I*0/*T*<sup>2</sup> versus 103/*T*.

At higher positive bias (*V* - 0.8 *V*), the thermionic emission current is limited by the series resistance *RS*, which is the lump sum of contact, graphene and substrate resistances. By taking it into account, Equation (1) can be rewritten as

$$I = I \alpha^{\frac{q(V - IR\_S)}{nkT}},\tag{6}$$

And from Equation (6), two new equations can be derived when *V* − *IRS* > *nkT*/*q* [37]:

$$\frac{dV}{d(\ln(I))} = IR\_S - \frac{nkT}{q} \,\,\,\,\tag{7}$$

$$H(I) = IR\_{\mathbb{S}} + n\phi\_{\mathbb{B}\_{\prime}} \tag{8}$$

where *H*(*I*) is defined as:

$$H(I) = V - \frac{nkT}{q} \ln\left(\frac{I}{AA^\*T^2}\right). \tag{9}$$

Accordingly, the series resistance and the ideality factor can be extrapolated from the slope and the intercept of the *dVd*(ln(*I*)) vs *I* plot (Figure 3a), respectively, while the Schottky barrier can be estimated from the intercept of *H*(*I*) vs *I* plot (Figure 3b). Using this method, at room temperature, we obtain 10 MΩ series resistance and ideality factor ∼3. Figure 3c,d display the series resistance, the ideality factor and *q*φ*<sup>B</sup>* measured at different temperatures. The decreasing series resistance with increasing temperature shows the typical semiconductor behaviour. This behaviour cannot be attributed to silicon, Au or Ag paste in this temperature range [41–43]. Therefore, it can only be caused by the graphene layer. The resistance drop at high temperature and the negative *dRS*/*dT* has been reported for both exfoliated and CVD grown graphene [44–46]. The graphene semimetal behaviour has been attributed mainly to the thermally activated transport through the inhomogeneous electron-hole puddles, the formation of which is favoured by the transfer process of CVD-grown graphene [35,46].

**Figure 3.** Cheung's plot of (**a**) *dV*/*d* ln(*I*) vs *I* and (**b**) *H*(*I*) vs *I* at 300*K*. (**c**) Devices series resistance, (**d**) ideality factor and the Schottky barrier extracted from the Cheung and Cheung (CC) method versus the temperature.

Using Equations (7)–(9), we estimate *q*φ*<sup>B</sup>* at different temperatures (Figure 3d); in particular *q*φ*<sup>B</sup>* ≈ 0.11 eV at room temperature which is in agreement with the previous evaluation. The temperature growing *q*φ*<sup>B</sup>* is an indication of possible spatial inhomogeneities. The homogeneity of the barrier will be discussed later. In Figure 4a,b we show the Richardson plot at given forward and reverse biases. In forward bias, the temperature dependence of the current has a linear behaviour, which is in agreement with the T.E. theory. Contrarily, in reverse bias, the evolving behaviour of the current, from exponential to saturation trend, is reflected in the Richardson plot (Figure 4b), which for *T* ≤ 300 K is similar to the forward bias one (Figure 4a), while at higher temperature shows rising converging curves. Because of this, we consider only the lower temperature part of the curves in Figure 4b (*T* ≤ 300 K) to determinate the Schottky barrier and the ln(*AA*∗), which are displayed in Figure 4c. We highlight that the Schottky barrier increases with the applied voltage, as expected. In forward bias, the graphene Fermi energy shifts down with respect to the semiconductor energy bands, thus increasing the Schottky barrier, while the opposite occurs in reverse bias. The relative shift, and therefore the barrier variation, is enhanced by the magnified electric field of the pillar and is made possible by the depinning of the Fermi level caused by the thin interfacial oxide layer [17,40].

**Figure 4.** (**a**) Richardson plot of ln *I*/*T*<sup>2</sup> vs 10<sup>3</sup> *T* in forward and (**b**) in reverse bias. (**c**) Schottky barrier and ln(*AA*∗) respect the bias. (**d**) Schottky barrier height at zero bias as a function of temperature.

Because of the CMP treatment (see Section 2), there is a possibility that the pillar top surface is not homogeneous and there could be points where the Schottky barrier is higher or lower. Following Refs. [17,40,47], we assume that the spatial variation of the Schottky barrier can be described by a Gaussian distribution. Therefore, the temperature dependence of the barrier is expressed as:

$$
\eta \phi\_B = \eta \phi\_{BM} - \frac{q \sigma^2}{2kT} \tag{10}
$$

where *q*φ*BM* is the maximum Schottky barrier and σ is the standard deviation of the Gaussian distribution. σ characterizes the inhomogeneity of the Schottky barrier and can be extracted from a plot of *q*φ*<sup>B</sup>* vs 1/2*kT* (Figure 4d). We obtain σ = 45 meV, which is lower than those reported in literature for CVD grown graphene [48,49]. Since the graphene was CVD grown, the low standard variation can be considered as a remarkable advantage of the patterning of the substrate.

Finally, we measured the gr/Si response to light. Figure 5a shows the semi-logarithmic I-V curves of the device measured under different white LED light intensities. The responsivity <sup>R</sup> <sup>=</sup> *Ilight* <sup>−</sup> *Idark* /*Popt* (*Ilight* and *Idark* are the current measured at −1*V* under illumination and in dark, respectively) as a function of the incident light power *Popt* is shown in Figure 5b. The device presents a responsivity with a maximum of <sup>∼</sup>88 A/<sup>W</sup> at 10<sup>−</sup>5–10−<sup>4</sup> Wcm<sup>−</sup>2, which decreases at higher intensities. The reduction of the responsivity at higher intensities is due to the raising recombination rate. Indeed, at high illumination, the increasing of electron-hole pair density in the depletion layer enhances the recombination rate thus making the photocurrent deviate from its linearly behaviour as shown Figure 5c.

**Figure 5.** (**a**) I-V characteristic in semilogarithmic scale of the gr/Si pillar device measured at different intensity illumination level. (**b**) Responsivity of the gr/Si pillar device as function of the light intensity. (**c**) Photocurrent measured at −1*V* and at different light intensities in logarithmic scale. (**d**) I-V characteristic measured in dark (black line) and at 5 mWcm−<sup>2</sup> (red line).

Remarkably, the device achieves a reverse current that can be greater than the forward one. The high reverse current measured at high illumination confirms that there is a contribution to the junction current from the photogeneration occurring in the substrate areas where graphene forms a MOS capacitor with Si, as explained in previous works [16,18,36,50]. Furthermore, we note that the photogeneration has the same effect as the thermal generation in shaping the I-V curves of the device. Figure 5d shows the I-V measured in dark and under illumination at 5 mW/cm<sup>2</sup> in linear scale. A photovoltaic effect with an open circuit voltage around 0.19 *V*, which is close to the estimated Schottky barrier height, and a short circuit current of 1.8 nA, corresponding to ∼0.7% power conversion efficiency, can be clearly observed. The conversion efficiency can be improved by lowering the doping of the Si substrate, which would result in an extended depletion layer for enhanced light absorption, and by reducing the shunt and series resistance that would increase the cell fill factor.

#### **4. Conclusions**

In conclusion, we fabricated a gr/Si pillar junction that possesses both a bias-tunable Schottky barrier, remarkable photoresponse and appreciable power conversion efficiency. The reverse current

grows exponentially with reverse bias at lower temperatures, while it shows a saturation at higher temperatures or under illumination. Such behaviour has been explained by taking into account the thermo- and photo- generated charges both at the gr/Si junction and in the surrounding regions.

**Author Contributions:** A.D.B. conceived the experiment, G.L., A.G., M.L. and C.A.C. performed the experiment, G.L., L.I., F.G. and A.D.B. analysed the data, A.D.B., F.G. and C.W. contributed reagents/materials/analysis tools, G.L., F.G. and A.D.B. wrote the article.

**Funding:** We acknowledge the economic support of POR Campania FSE 2014–2020, Asse III Ob. specifico l4, D.D. n. 80, 31/05/2016 and CNR-SPIN SEED Project 2017 and Project PICO & PRO, ARS S01\_01061, PON "Ricerca e Innovazione" 2014–2020.

**Acknowledgments:** We thank Technology Department, IHP-Microelectronics, Frankfurt Oder, Germany for the fabrication of the devices.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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