**Abstract**

Due to its properties, graphene is considered a revolutionary material for the future, and as a two-dimensional material it has received a lot of research attention over the last two decades. For graphene to be used in different technologies such as solar cells, much more work needs to be done to understand its properties and engineer its properties by combining it with other materials such as semiconductors. This research work reports computational investigation of the electronic and optical properties of Ti and Ru mono-doped and co-doped graphene. Geometry optimizations for the electronic and optical properties were performed by first-principles calculations based on density functional theory. Various supercells of graphene were modeled and optimized, and their properties were calculated. The results show that different graphene supercells have different electronic and optical properties. The energy bandgap of pure graphene is zero, and after doping with Ti and Ru it increases to 0.550 eV, and 0.786 eV, respectively. The co-doped graphene bandgap is 0.272 eV. The calculated optical properties showed that doping graphene with Ti and Ru shifts the absorption from the visible to the near-infrared region, and these results open possibilities of using doped graphene as a semiconductor material.

**Keywords:** graphene, density functional theory, bandgap, doping, optical properties

## **1. Introduction**

Graphene has sparked great interest in recent decades due to its remarkable electrical and optical capabilities, as demonstrated by a groundbreaking experiment in graphene research in 2004 [1]. Graphene is a honeycomb-shaped two-dimensional sheet crystalline structure of atomically thick sp2-hybridized carbon (each carbon fortifies covalently with three other carbon atoms) [2–5]. It serves as a building block for various carbon dimensionalities, such as zero-dimensional Buckyball, onedimensional nanotube, and three-dimensional graphite [2]. A pristine graphene has zero bandgap, because its conduction and valence bands meet at a single location at the Dirac points [6–12]. Graphene is considerably stable due to the tight packing of carbon atoms and hybridization of sp2, but only when the graphene size is smaller

than 20 nm; otherwise, it is thermodynamically unstable [13, 14]. The classification of graphene as a metal, nonmetal, or semimetal is still up for discussion [13].

The properties of graphene depend on the number of graphene layers. A pristine graphene, for example, has a theoretical surface area of 2630 m<sup>2</sup> g<sup>1</sup> , which is more than the surface area of carbon nanotubes (100–1000 m<sup>2</sup> g<sup>1</sup> ) [15, 16]. Furthermore, as compared to graphene with a few layers, a single-layer graphene has a higher surface area [14]. According to numerous studies, graphene has a high charge carrier mobility of 250,000 cm2 v<sup>2</sup> s <sup>1</sup> at room temperature [5, 17, 18]. Furthermore, each layer of graphene absorbs up to 2.3% of the incident light with a reflectance of less than 0.1% [6]. As a result, it has a very high optical transparency of 97.7% as well as a high degree of flexibility [6, 19]. At room temperature, a single-layer graphene has a high thermal conductivity of 3000–5000 Wm<sup>1</sup> K<sup>1</sup> [20]. Other properties include an electrical conductivity of 6000 S cm<sup>1</sup> [21] and a Young's modulus of 1.0 TPa [22].

Graphene offers potential application in areas such as high-speed electronics, data storage, liquid crystal display (LCD) smart windows, organic light emitting diode (OLED), supercapacitors, solar cells, and electrochemical sensing [19, 23]. The combination of high electrical conductivity, chemical and thermal stability, and outstanding stretchability provides significant benefits for employing graphene as a transparent conductor in organic electronic devices. It is mostly used as a hybrid with other materials to enhance the properties of other materials making them stronger, valuable, and light weight [24–28]. Studies have shown that the number of graphene layers, defects in graphene layers, various concentrations of graphene, and different sizes of graphene have impact on properties of graphene [28–32]. Graphene has been modified in various ways to broaden its application in a variety of fields. One method to modify graphene is to introduce foreign elements into it to tempt its electronic properties. Mukherjee and Kaloni investigated the effect of boron and nitrogen doping on graphene. Their calculations showed that N-doped graphene had a Dirac point shift below the Fermi level and B-doped graphene had a Dirac point shift above the Fermi level, resulting in a bandgap opening. The opening of the bandgap appears at the Fermi level for co-doped graphene [33]. Sara Varghese *et al.* investigated the structural, energetic, and electronic properties of graphene doped with boron and nitrogen atoms at different doping concentrations. They observed that doping increases the bandgap and decreases the energetic stability [34]. Olaniyan *et al.* conducted a systematic study of the stability, electronic, and optical properties of mono- and co-doped graphene with beryllium and nitrogen. Be-N was found to be more stable than Be-doped graphene. The study also shows that when graphene is doped with Be and N, it transforms from semi-metallicity to semi-conductivity [35]. Despite the substantial amount of work that has been put into the theory and experimentation of doped graphene, there are still a great many applications that have not been fulfilled. As a result, research into doped graphene systems with superior performance continues to be pushed forward.

First-principle calculations are used in this study to evaluate several graphene supercells and examine the effects of those supercells on the electrical and optical properties of graphene material. In addition, it investigates how the electrical and optical properties of graphene change when doped with titanium or ruthenium and a combination thereof.

## **2. Computational details**

Geometry optimizations for the electronic and optical properties were performed by the first-principle calculations based on DFT implemented in the Material Studio

*Structural, Electronic, and Optical Properties of Mono- and Co-Doped Graphene with Ti… DOI: http://dx.doi.org/10.5772/intechopen.106143*

CASTEP code, using the generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE), norm-conserving pseudopotential, periodic boundary conditions, and space group of P6/mmm. The k point was set at 6x6x1 with a cutoff energy of 350 eV and energy tolerance of 1.0x10–6 eV. The force tolerance was set at 0.03 eV, the displacement tolerance 0.0001 Å, and convergence threshold of 1.0x10<sup>6</sup> eV/atoms.
