A Comparative Study on Electronic Transport Behavior of Silicene and B40-Nano Onions

Density Functional Theory is utilized to scrutinize the electronic state of silicene and boron nano-onion which is a round compact mass formed by placing an N20, C20, and B20 fullerene within its parent atom fullerene B40. The NEGF is used to investigate the quantum transport at both equilibrium and non-equilibrium. Firstly the I-V curve for both silicene and boron-based devices is studied. From the results, it is concluded that boron-based devices are better than silicene. Therefore to get deeper insights into why boron-based devices are better transport properties of boron-based devices are suited. Later on, the transport mechanism is analyzed by computing the DOS, transmission and molecular spectra, HLG, I-V curve, electron densities, and differential conductance. When the Boron nano-onion is placed between the pair of Au electrodes. The calculated results are evaluated and a comparative study is done. From the results, it is deduced that the N20 variant nano-onion has reduced the HOMO-LUMO gap (HLG) and highest value of current in comparison to other devices. Thus by infusing a smaller fullerene of N20 inside the hollow cage of B40 fullerene the amplification of current and conductance can be observed in Boron-nano-onion in comparison to other devices.


Introduction
In the last decade, remarkable advances in the field of computing have been witnessed, especially when W. Shockley, J. Bardeen, and W. Brattain invented the first transistor at Bell Labs in December 1947 [1]. Later on with the discovery of the first IC in the year 1958, followed by the invention of the first planar transistor in the same year by J. Hoerni [2][3][4]. In the last 40 years, bulk silicon has served as the most promising material for semiconductors however semiconductors have reached their physical limits. Richard P. Feynman's famous lecture in 1959, proposed "There's plenty of room at the bottom" [5]. This notion gave the idea to the electronics industry of using atoms and molecules at the microscopic level. Since then research has been carried out widely on carbon and graphene nanotubes. Later on, researchers have shown their interest in some other material i.e. silicene which has a similar atomic structure to graphene but comprises silicon atoms. The structure was first identified by Guzman-Verri & Lew Yan Voon in 2007 [6]. As silicene has a similar atomic structure to graphene but it is more advantageous than that and it can be unified with current silicon-based technology and devices. Researchers have found that the electron mobility of silicene is 2.57 × 10^5 cm 2 V −1 s −1 [7] which is greater than the electron mobility of bulk silicon i.e. 0.014 × 10^5 cm 2 V −1 s −1 [8]. Sasfan et.al has investigated the electronic structure and transport properties of silicene for gas sensor applications [9]. Dongqing Zou et al. investigated the transport properties of 6 zigzag chains of H or H 2 edge-hydro generated silicene nanoribbon and hydroxide (OH) or oxygen (O) edge-oxidized slices by forming a device [10]. They deduced that edge functional groups can personate a promising element in enhancing the electrical performance of SiNR-based devices. In 2018, M. Davoodianldalik et.al examined magnetic, electronic, and transport properties of silicene armchair nanoribbons and they found that by adding the Fe monomer to silicene sheet new properties were found which will be useful in spintronics and optoelectronic devices [11]. Q.G Jiang et al. examined the stability of silicene nanoribbons by diffusing the barriers of H atoms [12]. It was found that the amalgamation of the H atoms with silicene nanoribbons increases the stability of the system.
Apart from the engrossing material discussed, another molecule is experimentally realized by Zahi in 2014, the B 40 molecule. Zhai et al. synthesized boron fullerene (B 40 ) and demonstrated that it is a highly stable molecule [13]. Boron fullerenes are similar to carbon fullerenes as they can also be amalgamated from 2D boron sheets trailing the isolated pentagon rule [14]. B 40 cage consists of two hexagonal and four heptagonal rings which can attract both acidic and basic molecules. Various research has been carried out to elucidate its, structure, orientation, and electronic properties. Due to the exceptional properties of B 40 fullerene, it was found to be a major development in the field of molecular electronics. In the previous research work, Zhang et al. scrutinized B 40 fullerene with gold electrodes and deduced that it depicts optoelectronic properties [15]. The HLG of the B 40 molecular device is reduced considerably by adding a strontium atom, which escalates the value of current through the device [16]. Because of the existence of both acidic and basic sites, B 40 fullerene has been extensively utilized as a sensor for the detection of various toxic gases [17]. Plentiful research has been done in the field of molecular electronics based on carbon as a carbon nano-onion (CNO) yet boron fullerene (B 40 ) as boron nano-onion still needs to be explored. In this paper, we constructed a Boron Nano-Onion (BNO) by the endohedral placement of a fullerene inside parent fullerene B 40 as shown in Fig. 1. Three different fullerenes (C 20 , N 20, and B 20 ) were considered to be placed inside parent fullerene B 40 . We intend to study the transport and electronic properties of boron-based nanoonion attached to gold metallic leads and also compare it with the electron transport properties of silicene. By applying the density functional theory (DFT) as well as the nonequilibrium green function, we aim to study the I-V curve, transmission spectra, DOS, molecular energy spectrum, eigenstates, and transmission pathways.

Methodology
For a better understanding of various electronic properties, all the calculations were carried out using density functional theory (DFT) [18][19][20][21]. DFT calculations are used as implemented in the Atomistix Tool kit and its graphical interface is used for simulating all the configurations [22]. DFT is chosen among various methodologies because of its better accuracy and its persistency ranges from atoms, molecules, solids, quantum, and classical fluids. It has been generalized to investigate in many different situations: free energy at finite temperatures, multicomponent systems, time-dependent phenomena, and excited states, molecular dynamics, etc. [23]. The total energy calculations are naturally apprehended by structural deformations by solving one electron Schrodinger equation in a suitable self-consistent potential approximating the electron-electron interaction. These codes are quite accurate as they are based on vibrational theorems at least for equilibrium properties [24][25][26]. Two probe devices consist of the left metallic lead (L), central scattering region (C), and right metallic lead (R). For left/right metallic leads gold is used. A molecular junction device is formed by placing a BNO molecule between the metallic leads. The electrode length on each side is 7 Å [27]. For calculating the exchange-correlation functional generalized gradient approximation (GGA) is used as suggested by Perdew, Burke, and Ernzerhof [28]. Double zeta plus polarization basis sets were used to perform the necessary calculations.
In a two-probe configuration, the miller indices were taken as 1:1:1 [29]. The length of the unit cell along the c-direction was taken to be 45 Å because this is the minimum length needed to insert a BNO between electrodes. To perform the necessary transport calculations and study the I-V curve Landauer-Buttiker formalism has been used [30].
where V represents the applied bias voltage, μ L and μ R denotes the electrochemical potential of left and right electrodes, and T(E, V) signifies transmission function respectively. T(E, V) is the transmission function that can be demonstrated from the information of coupling amongst the (1) electrodes and the position of molecular energy levels. The transmission can be determined as follows [31].
The above equation Γ(E) demonstrates the coupling function. It provides information regarding the form of contact between the molecule and the electrodes. G M (E, V) signifies green's function. It can be assumed that devices can be divided into two interfaces, having two different chemical potentials. Thus, molecular energy levels tend to float above electrostatic potential. Conversely, it tends to float downwards. The magnitude of electrostatic potentials on both sides of electrodes can be determined as [32].
where e represents the charge on the electron, E F denotes equilibrium Fermi energy and η describes the potential profile of the molecules in two probe configurations.
Next, the transmission pathways were calculated, which describes the flow of current through the molecular junction [33]. To get an insight into electron transfer rate the local currents that are bridging between the molecule and metallic leads were investigated. Local currents for a device have been examined through electrode-molecule-electrode systems. The sum of local currents is given as: where m is atoms on one side of the electrode and n is on the other side. The transmission components are represented in form of arrows. Red arrows demonstrate the positive value of current when the transmission is from the first atom to the second atom. Blue arrows demonstrate components in opposite values, thereby reducing the net current. DFT is currently the most popular approach to compute the electronic structure of matter i.e. its calculations depend upon the number of electrons in the system, which makes it more complex and hence it requires more amount of time to carry out the simulation. Apart from that, in hybrid function by when the bond lengths is increased to large values, then fragments fail to dissociate into natural atoms [34].

Results and Discussion
First of all, the I-V curve is analyzed for both silicene and boron-based devices at various voltages ranging from -1 V to +1 V with a step size of 0.2 V. From Fig. 2, a comparison can be drawn that with an increase in bias, current decreases for silicene devices on the contrary it increases for B 40 devices. From Fig. 2, it is clear that all three molecular junctions have linear behavior, which signifies that current flows without any barrier across the junction. From the I-V curve, it is deduced that the lowest value of current is observed in the B 20 @B 40 device and the highest value for N 20 @B 40 . Also, a higher number of transmission peaks can be seen for N 20 Table 1. After analyzing the I-V curve for both the devices it is deduced that boron-based devices are better than silicene. Therefore to get deeper insights into why boron-based devices are better transport properties of boron-based devices are suited.
To understand quantum transport, it is necessary to analyze molecular junctions at various biases both in opposing directions. Thus, transmission spectra are not only analyzed at zero bias, but at various biases ranging from -1 V to +1 V with a step size of 0.2 V. From Fig. 3, we anticipate that peaks don't change their position for all three devices, but amplitude is varied. In the case of N 20 @B 40 peaks don't change their position as we move from negative bias to positive bias but interestingly amplitude of the peak is increased in positive bias at various bias voltages. Whereas in the case of C 20 @B 40 and B 20 @B 40 amplitude of the peak is highest in negative and it gets reduced as we move towards positive bias. This transport behavior can be seen in the I-V curve also.
Further, to understand transport properties at equilibrium, we firstly probe the density of states for all molecular junctions. The density of states gives information regarding the number of electron states that are vigorously taking part in transmission. Figure 4 shows the comparison between the density of states for three devices that are computed from PBE-DFT parameterization. Higher peaks are observed only on one side of the Fermi level. From the figure, it is visible that LUMO dominates the transmission for all three devices as peaks above E F are more prominent. Border peaks signify better transmission, which also gives us the information that bonding between the central molecule and metallic leads is reliable.
Furthermore, to understand the type of synergy between the molecule and electrodes at which energy transfer of electrons is prominent transmission spectra curve is analyzed at equilibrium. It is the transmission spectra that provides the information about the HLG and molecular orbitals that participate actively in transmission. Figure 5 shows the transmission spectra curves at zero bias for C 20 @B 40 , N 20 @ B 40, and B 20 @B 40 . In the case of all three devices, LUMO orbital dominates the quantum transport at E F = 0. Broader peaks above the E F can be seen in the case of B 40 N 20, thus implying stronger coupling resulting in greater transmission. Thus, the results derived from DOS and transmission spectra are in consensus.
Next, the molecular energy spectrum for C 20 @B 40 , N 20 @ B 40, and B 20 @B 40 at 0 V is considered. Table 1 gives information about HOMO, LUMO, and HLG for all the devices. From the table, it is deduced that on the placement of N 20 in the fullerene cage HLG is reduced in comparison with  These results of the molecular energy spectrum are in correlation with the deductions from DOS analysis.

Fig. 3 Transmission Spectra at various bias voltages
To investigate the lower HLG gap in N 20 @B 40 , the electron density for all three molecular junctions was contemplated. From Fig. 6, it can be seen that the electron cloud is more aligned and atoms strongly hold electron cloud in the case of nitrogen variant onion as compared to the other two onions because nitrogen has strong electro-negativity. Also, the electron density is highest in the case of the nitrogen variant, which implies that higher electron density leads to a reduced HLG gap. The results of electron density coincide with the results of the I-V curve, as nitrogen has the highest electron density as well as the highest value of current. Furthermore, the differential conductance of all three devices is calculated. From Fig. 7, it is evident that all three devices have different differential conductance. Higher value peaks are in positive bias and lower value peaks are seen in negative bias which is similar to the I-V curve in terms of the amplitude. B 40 based nano-onion with nitrogen variant is perceived to have the highest differential conductance value followed by carbon variant and boron variant have the least conductance. It is contemplated that the N 20 @B 40 device exhibits peak conductance at 0.29 V which is about 20.4μS similar to the C 20 @B 40 device conductance peak at 0.2 V which is about 16.2 μS. Hence results attained from differential conductance correspond with the results for the I-V curve and transmission pathways.
The Transmission Pathways is a quantitative alternative that separates the transmission coefficient into local bond contributions, T ij. The pathways have the ability that if the system is broken down into two parts, then pathways across the boundary between A and B sum up to the total transmission coefficient.
The local bond contributions, T ij can be both positive and negative. A negative value represents that the electron is backscattered along with the bond. In some systems, there will be a single pathway that dominates the flow of transmission whereas in other systems there will be multiple pathways that contribute to the flow of transmission. The orientation of arrows shows the flow of electrons. The red arrow corresponds to the positive value of current, whereas the blue arrow corresponds to a reduction in current. On the other hand, the purple arrow represents the backscatter of electrons. From Fig. 8, it can be seen that the case of the N 20 @B 40 onion has a greater number of red arrows which implies that transmission is positive thus leading to more value of current. In the case of C 20 @B 40 and B 20 @B 40 large number of blue and purple arrows signify a lesser value of current. Backscattering can be seen in all three molecular junction devices but N 20 @B 40 has the least amount of backscattering. From the Fig. 8, it is visualized that flow of current is mainly inside the fullerene cage. The fullerene cages of N 20 , C 20 , and B 20 act as bridges during electron transmission which contributes to more number of channels thus increasing the conductance. Our results of transmission pathways are in agreement with the current-voltage results which demonstrate that N 20 B 40 has the highest value of current.

Conclusion
In this research work, we envisage the Silicene and Boron nano-onion formulated by infusing the C 20 , N 20 , and B 20 into B 40 fullerene. DFT with NEGF duo has been utilized to calculate DOS, HLG, molecular spectrum, electron density, I-V curve, and differential conductance of C 20 @B 40 , N 20 @B 40, and B 20 @B 40 . It was found that with an increase in bias, current decreases for silicene devices on the contrary it increases for B 40 devices. These deductions are novel as the comparison of silicene with boron based fullerenes have been reported for the very first time. Also, it has been proved that boron based fullerenes are a better option to devise nano-devices for electronic applications. From investigating DOS, it is inferred that for all the devices under study, LUMO orbitals play dominance in transmission. The N 20 @B 40 nano-onion has the highest value of current ranging from −180,475.436 to 187,804.21 nA in comparison to the other two devices. This is due to the reduced HLG as well as higher electron densities. The HLG gap for the devices is calculated to be C 20 @B 40 (0.226 eV) > B 20 @B 40 (0.182 eV) > N 20 @B 40 (0.097 eV). Thus infusing N 20 in B 40 fullerene leads to improvement of current in BNO junction. This opens doors for making better nano-devices in the future with enhanced current characteristics.