Abstract

Using Density functional theory, I report the effects of adsorption and substitution of boron atoms on structural and electrical properties of a (10,0) carbon nanotubes (CNTs). By considering formation energy, I found that the substitution process is an exothermic process. On the opposite the adsorption process has positive formation energy. When CNT was contaminated by boron atoms, boron atoms behave as acceptors. Boron will turn the semiconducting (10,0) CNT into a metallic nanostructure. Boron induced high polarization on the tube. When boron atoms substitute with carbon atoms, the polarization is stronger in comparison when they adsorb with CNT.

1. Introduction

In the past two decades, many scientists studied various properties of carbon nanotubes (CNT). Two of the most important reasons that are fascinating scientists are the excellent physical properties and chemical stability of these structures at room temperature ^{1, 2}. The electronic properties of such materials were investigated by many scientists and it has been shown that the electronic properties of these structures strongly depend on their chirality ³. CNTs are good candidates for gas adsorption and hydrogen storage ⁴. They are good candidates for oxygen reduction in the battery industry, especially boron and nitrogen doping have shown promising results ⁵. Doping a nanostructure is a conventional method to produce secondary structures ^{6, 7}. Because the local charge distributions around dopant are changed, the secondary structure can interact with many polar and even none polar molecules. By the means of these, many processes were invented to trap molecules in bonding with CNT. The best evidence for this claim is Pt adsorption on boron-doped CNTS. Li and coworkers showed that boron-doped CNTs have a high ability of Pt adsorption ⁸. The boron doped CNTs have many interesting physical properties and many researchers have studied these properties both in theories and experiments ^{9, 10, 11}. The band gap, major career type, effective mass and other important properties of such materials are changed by doping. Recently a wide consideration of the effects of nitrogen on CNT has been published ¹². It is interesting to consider the effects of a III valent elements on the electronic properties of CNTs. In this article, I calculated electronic properties of heavily boron doped CNT. Calculating band gap, the density of states, polarization, and effective mass are the main achievement of my calculations. All of those quantities are required on theoretical calculations of heat and electron transport.

2. Computatioal Details

All calculations were performed using density functional theory (DFT) as implemented in OpenMX (Open source package for Material eXplorer) package, based on norm-conserving pseudo potentials and pseudo atomic orbital basis sets ^{13, 14} with GGA-PBE as exchange-correlation functional ¹⁵. s2p2d1 basis set and cutoff radii of 6.0 and 7.0 bohrs were adopted for carbon and boron atoms, respectively. In calculations, I have used a supercell of 25.0 ×25.0 ×21.388 ų to model a periodic (10,0) zigzag nanotube consisting of 200 carbon atoms to make sure the nanotube has no interactions with its images. The structure was fully relaxed with the criteria of 1.0×10^-8 hartrees and 1.0×10^-4 hartrees/bohr for the total energy and forces acting on atoms, respectively. An energy cutoff of 190.0 Ry was set for the convergence of the total energy in SCF iterations. The k point grid was set to 1×1×5 to sample the first Brillouin zone.

The Formation Energy of boron doped CNT is calculated as ¹⁶:

(1)

Where E_polluted is total energies of boron-doped nanotubes and µ_C and µ_B are the atomic chemical potential of boron or carbon and n is the number of boron atoms respectively. Chemical potential is calculated as the total energy per atom of the most stable structure of the elements B₄ and C₈ (unit cell of diamond) are considered as the most stable structures. In the adsorption process while removing of carbon atoms do not happen, in the equation (1) I must ignore the C chemical potential in my calculations. Cohesive energy of boron-doped CNT for substitution process is defined as:

(2)

And for the adsorption process, it is defined as:

(3)

Where n is the number of B atoms and M is the number of C atoms. The tube is free to charge and the Mulliken charge was calculated to extract the total net charges boron atoms gained from the tubes.

3. Results and Discussions

The interaction between boron and CNT should be considered in two different branches. One branch is substitution and the other is adsorption. I will discuss both in details. In comparison with nitrogen doping, readers might expect two different types of carriers. Since boron is a small element and because of the high ratio of charge per volume, it exhibits an unusual manner in different structures. As I will discuss here, I have different situations.

In this case, carbon atoms were substituted with boron atoms. As illustrated in Figure 1 all boron atoms connected to three carbon neighbors and there are not any dangling band in any cases. Since the boron is an element before carbon in the periodic table, CNTs have not strongly deformed from their pristine structure. Formation energy and cohesive energy are two helpful quantities which I can find structural properties with them. The formation energy is an energy required to produce a defect into the perfect crystal structure. Therefore bigger formation energy means more energy requires creating the structure. Negative formation energy means the process is spontaneous. Table 1 shows formation and cohesive energies. As can be seen, the substitution process is a spontaneous process because its formation energy is negative. Formation energy in the substitution process is equal to -1.42 per boron atom. As Amiri and coworkers approved before, nitrogen doping in all cases has positive formation energy ¹². But Li and Chen have shown that the co-doping of B-N on CNTs could have negative formation energy ¹⁷. So based on my calculations, I believe the source of negative energy in Li calculations, refers to boron. As Table 1 shows, the cohesive energy in the substitution process is negative and by increasing the amount of boron impurity it decreases. It means the reaction between CNT and boron is an exothermic process and it is spontaneous. Electronic properties are the next quantities that I considered. By the method I used the band gap of the pristine CNT is close to experimental data ¹². Figure 2 shows the density of state of boron doped CNT in the substitution process. As can be seen the Fermi energy (E_F=0), penetrate into valence band and this means in the substitution process I have a p-type semiconductor. It is opposite with nitrogen doping ¹². It is normal because nitrogen has an extra electron relative to carbon and in the same situation that both have three chemical bonding, an extra electron of nitrogen can be activated and release in the structure to produce an electron-rich system. In contrast, the situation is different for boron doping. Boron has one electron less than carbon. So in the same structure which both have three chemical bond, boron behaves like a hole. It is more convenient to approach these result from band energy. Figure 3 shows the band energy. As can be seen, in the substitution process the Fermi level penetrates into valence band and by increasing the concentration of boron it penetrates deeply into valence band (increasing hole concentrations). It is so constructive to calculate the net charge that boron transfer to CNT in the calculations. Table 2 contains Mulliken charges. Calculations show that each boron atom in the substitution process obtains nearly +0.45|e| charge which shows the boron atom exhibits like a positive particle or hole. But the net charge per atom decrees gradually from the CNT which contaminated by 1 atom (0.46|e|) to the CNT which contaminated by 6 atoms (0.44 |e|). The reason is referred to the interaction of boron atoms to each other but because the distance between the boron is so far to each other, the changes in net charges they obtain from the tube are close to each other. Experimental results also validate my calculations. Guire and coworkers obtained a positive value for Hall coefficient implying the presence of holes in the samples ¹⁸. As can be seen, Table 2 contains the polarization of the boron doped CNT. It was proved that pristine CNT has not any polarization ¹². The polarization of a structure is very important in gas sensing and adsorption of the gas molecule. Those structures which have more polarization can attract polar gas molecule with higher strength. As can be seen, the polarization of the boron doped structure in the substitution process has an irregular function relative to the number of boron atoms. The reason is referred to dipole cancelation of boron atoms. But in these cases, the structure that has 4 boron atoms has the highest polarization. It is better to plot the polarization respect to the number of dopants. Figure 4 shows the polarization plots vs. the number of boron atoms. As the Figure 4 shows there is a big peak in polarization plots in n=4. So I predict this concentration of boron atoms is more suitable for gas sensing devices. In comparison with nitrogen doping, there is a lesser polarization in the substitution process, but both have a maximum peak on n=4 ¹². The effective mass of hole (electron) is another important factor that is required in transport physics. The structure which has lesser effective mass has more mobility. Table 3 contains the effective mass of the structures. As can be seen, in the substitution process I have very light negative effective mass. The effective mass was calculated at k=0 for the highest valence band.

In the adsorption process, boron atoms do not replace with a carbon atom. It only adsorbs on the tube surface. Figure 5 shows the adsorbed boron atoms on the tube surface. At the beginning of simulation the position of boron atoms were settled on the center and top of honeycombs but after relaxing the system, boron atoms moved to bridge sides and made two chemical bonds with carbon atoms. The boron atoms are not placed on the tube plate and they are ejected. The angles are tangential and it is expected to obtain higher formation energy. As can be seen, the formation energy of these structures is positive (Table 1). In this state, the average of formation energy per atom is equal to +1.7 eV. In comparison to nitrogen adsorption, boron requires lesser energy to absorb. The reason behind of this refers to strong triple bonds in N₂. As Table 1 shows the cohesive energy is started from -134.31 eV for the pristine tube and is finished by -124.1eV for the n= 6 boron doped tube. It means the pristine tube is more stable than polluted one but in this case, with the same density of boron in comparison of nitrogen (ref ¹²), the structure which is polluted by boron is more stable. As I discussed on the substitution process the Fermi energy was penetrating into valence band but in the adsorption process, the Fermi energy does not penetrate anywhere (valence or conduction band). By attention to DOS plot it can be found that in this case by adding each boron atom, one energy level will appear in the band gap. By looking at the energy band diagram, it can be found that the energy level is not flat or the width of the corresponding peak on the DOS plot is not very narrow. This implies that I encountered with a heavily doped structure. By calculation the effective mass in these cases, I found that boron atom behaves like a hole and the hole has heavier mass in comparison to the substitution process. Here I calculated effective mass to that level which is more close to Fermi level. Consideration of Mulliken charges and polarization clarify an important fact. In the adsorption process in comparison to the substitution process, Mulliken charges decrease to one half. It means in this case, the amount of charge transfer to the tube is weak and each boron atom has an extra electron like as a dangling bond. Polarization consideration approves this claim. As illustrated in Figure 4 in adsorption process the polarization of doped nanotube is higher than substitution process and by changing the number of boron from 1 atom to 3 atoms it increases linearly and after that is decrease linearly which implies dipole cancelation on higher concentrations. But it is clear that this high amount of polarization is referred to a dangling bond and the higher amount of formation energy and also cohesive energy is also refer to this dinging bands.

4. Conclusions

Electronic and structural properties of boron doped CNT in substitution and adsorption process were calculated for various boron concentrations. In the substitution process boron atoms, makes 3 chemical-bonds with its carbon neighbors and because boron has a lesser electron relative to carbon when boron is substituted by carbon, it behaves like acceptor and Fermi-level moves into the valence band. On the other hand in the adsorption process, the Fermi-level did not move into valence or conduction band but the calculation of effective mass showed boron atoms behave like as acceptors. I found that substitution process is an exothermic process while adsorption process needs some energy to form or the formation energy has positive value for adsorption process. The formation energy changes with boron concentration linearly, in substitution process formation energy varies from -1.42 to -8.75 eV and in the adsorption processes it varies from 1.73 to 10.21 eV. Cohesive energy changes with boron concentration linearly and in the case of substitution process, it varies from -134.31 to –143.07 eV, on the other hand in the case of the adsorption process, it varies from -134.31 to -124.1 eV. The linear properties of formation energy and cohesive energy are referred to as boron concentration (maximum concentration of nitrogen is 3.1%). Hole effective mass in the substitution process is near -0.1me and in the adsorption process, it is near to -0.2me. Boron-doped CNTs have huge dipole moments. Because of these effects, more scientists like to use these structures as bipolar absorption based materials. Mulliken charges are considered. My calculations show that in both processes, the amount of charges that boron atoms gain from CNT in substitution process is higher than adsorption process but the polarization of CNT in adsorption process is higher than substitution process.

References