Effect of BN nanodots on the electronic properties of α- and β-graphyne sheets: a density functional theory study
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The effect of BN nanodots with hexagonal shape on the electronic properties of α- and β-graphyne sheets is investigated. The structural and electronic properties of α- and β-graphyne sheets doped with BN nanodots are studied by using density functional theory. The cohesive energies of the systems indicate all considered structures are thermally stable. It is found that hexagonal BN nanodots can effectively open the band gap in α- and β-graphyne sheets. It means BN nanodots change α- and β-graphyne sheets from semimetal to semiconductor. The BN nanodots with different sizes are considered. It is found that band gaps of the studied α- and β-graphyne sheets doped with BN nanodots increase with the increase in the size of BN nanodots. Hence, α- and β-graphyne sheets doped with BN nanodots are promising materials for use in nanoelectronic devices based on semiconductors.
KeywordsDensity functional theory Graphyne BN nanodot Band gap modification
Two-dimensional (2D) carbon-based materials have attracted considerable attention in recent decades [1, 2, 3, 4, 5]. Examples of these 2D materials are graphene and graphyne sheets [1, 2]. Graphene is a 2D hexagonal network of sp2-bonded carbon atoms . From the point of application, graphene is considered to be even more promising than other carbon-based nanostructures due to its extraordinary mechanical, thermal, electronic, and magnetic properties . Like graphene, graphyne is a one-atom-thick layer of C atoms, but it contains both sp- and sp2-hybridized C atoms [4, 5]. There are several types of graphyne. The most known graphyne are α-, β-, γ- and 6,6,12-graphyne sheets . Interestingly, it is reported that α-, β-, and 6,6,12-graphyne sheets posses amazing electronic properties similar to graphene because of their peculiar band structure featuring so-called Dirac points and cones [1, 4, 5]. At a Dirac point, the valence and conduction bands cross each other at a single point at the Fermi level. It means that these sheets are semiconductors with zero band gap, or, alternatively, as metals with zero density of states (DOS) at the Fermi level [3, 4, 5].
Although graphene and graphyne are promising materials for use in nanoelectronic, the absence of a band gap limits their applications. Many strategies such as applying external electric field, producing nanoribbons, adsorbing molecules, chemical doping, and functionalization have been proposed to introduce a band gap in graphene and graphyne [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]. In particular, many studies have been focused on the modulation of the electronic properties of these sheets by doping [8, 9, 10, 11, 12]. N and B atoms are considered as the typical electron (n-type) and hole (p-type) doping elements since they are located in the periodic table one position behind and before from C atom, respectively. B- and N-doped graphene and graphyne sheets are reported to be good semiconductors [8, 9, 10, 11, 12]. It is also found that BN co-doping is a process that opens a band gap in graphene and graphyne sheets, and changes the character of these sheets from a semimetal to a semiconductor [13, 14, 15, 16]. Recently, graphene doped with BN nanodot has been realized experimentally [16, 18, 19]. Effects of geometric shape and size of embedded BN nanodot on the electronic properties of BN-doped graphene are studied theoretically [16, 18, 19]. It is found that the band gap of graphene increases with the size of the BN nanodot, regardless of the shape of BN nanodot. Motivated by these results, we have studied possibility of band gap opening in α- and β-graphyne sheets with BN nanodots doping based on density functional theory (DFT) in the present work.
Results and discussions
The atomic structures of pristine α- and β-graphyne sheets are shown in Fig. 1. The graphyne sheets consist of both sp- and sp2-hybridized C atoms. The C–C bond between two sp-hybridized C atoms is named t (Fig. 1). The C–C bond between sp2- and sp-hybridized C atoms is labeled by s1, and the C–C bond between two sp2-hybridized C atoms is shown by s2 (Fig. 1). In α-graphyne, the single C–C (s1) and triple C–C (t) bonds are 1.39 and 1.23 Å, respectively. For β-graphyne, the triple C–C (t) bond is 1.23 Å, and the single C–C (s1 and s2) bonds are 1.34 and 1.46 Å, respectively. These values are in good agreement with those reported in previous studies [5, 32]. Our calculated cohesive energies for α- and β-graphyne sheets are − 4.87 and − 5.84 eV/atom, respectively. Hence, β-graphyne with more negative cohesive energy is more stable than α-graphyne. It is in good agreement with previous results that report the cohesive energy of graphyne decreases systematically as the ratio of sp-bonded carbon atoms increases .
The atomic structures of H1-(BN)9 and H7-(BN)42 α-graphyne sheets are shown in Fig. 3. When BN nanodots are embedded in the α-graphyne sheet, the B–C and N–C bonds are 1.51 and 1.34 Å, respectively. In both H1-(BN)9 and H7-(BN)42 α-graphyne sheets, the N–C bond lengths are shorter than the corresponding C–C bond of the pristine α-graphyne sheet (1.39 Å), while B–C bond lengths are found to be longer. It is in close agreement with the previous reported results [14, 32]. This is due to the fact that the higher electronegativity of N atoms attracts strongly the electron density compared with B atoms [14, 33]. The B–N (t) and B–N (s1) bonds are 1.27 and 1.40 Å, respectively. The cohesive energies of H1-(BN)9 and H7-(BN)42 α-graphyne sheets are calculated to understand the energetic stability of the sheets. The cohesive energies of H1-(BN)9 and H7-(BN)42 α-graphyne sheets are − 4.95 and − 5.25 eV/atom, respectively. The negative cohesive energies denote that BN doping in α-graphyne sheet is an exothermic process, and H1-(BN)9 and H7-(BN)42 α-graphyne sheets can be produced experimentally. Here, H7-(BN)42 with more negative cohesive energy is energetically more stable than H1-(BN)9.
For β-graphyne sheet, two structures named H1-(BN)9 and H3-(BN)27 are studied (Fig. 4). In the presence of BN nanodots, the B–C (s1), N–C (s1), B–N (t), and B–N (s1) bonds are 1.33, 1.54, 1.27, and 1.40 Å, respectively. Similar to α-graphyne, B–C (N–C) bond is longer (shorter) than the corresponding C–C bonds. This is due to the difference between atomic radius of B, C, and N atoms which follows trend of B < C < N. The cohesive energies of H1-(BN)9 and H3-(BN)27 β-graphyne sheets are − 5.26 and − 5.40 eV/atom, respectively. The negative cohesive energies indicate that BN doping in β-graphene is an exothermic process and the considered structures are energetically stable. It is also found that H3-(BN)27 is energetically more stable than H1-(BN)9.
It has been previously showed that α- and β-graphyne sheets have semimetallic properties. Here, the electronic properties of α- and β-graphyne sheets doped with hexagonal BN nanodots are investigated by using density functional theory calculations. For comparison, the electronic properties of graphyne-like BN sheets are also studied. The thermal stability of these sheets was confirmed by calculation of the cohesive energy. The negative cohesive energies confirm that the considered structures are thermodynamically stable. The stability of these systems is in the order of BN β-graphyne > BN α-graphyne > H3-(BN)27 β-graphyne > H1-(BN)9 β-graphyne > H7-(BN)42 α-graphyne > H1-(BN)9 α-graphyne > β-graphyne > α-graphyne. The results indicate that β-graphyne sheets are more stable than the α-graphyne sheets. In addition, the stability increases with the increase in the size of BN nanodots. To find the effect of BN nanodots on the electronic properties of the sheets, the electronic band structure and DOS of the sheets are calculated. As expected, α- and β-graphyne sheets show semimetallic behavior, while α- and β-graphyne-like BN sheets are insulator. The results reveal that BN nanodots could lead to a change in electron properties of α- and β-graphyne sheets. The BN nanodots open a band gap, and α- and β-graphyne sheets show semiconducting properties in the presence of the BN nanodots. In the studied sheets, increasing the size of the BN nanodots increases the energy band gaps. Hence, BN doping in α- and β-graphyne sheets could be utilized to open and control the band gap in graphyne sheets. Our results suggest that α- and β-graphyne sheets with BN nanodots are more proper than pristine α- and β-graphyne sheets and α- and β-graphyne-like BN sheets for use in nanoelectronic devices due to their semiconducting properties.
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