Fermi Velocity and Effective Mass Variations in ZGaN Ribbons: Influence of Li-Passivation

The paper presents the structural stability and electronic properties of Zigzag Gallium Nitride nano ribbons(ZGaNNR) by considering the lithium(Li) atom by employing density functional theory (DFT). Li atom has been considered as a passivating element at various symmetric sites. By using Li atoms, a significant impact has been observed on the structural and electronic characteristics of ZGaNNRs. Bare@edges_both structure emerged to be the most energetically stable among other structures. For Li-passivation@edge_Ga structures, the minimum band gap has been noticed for III-V group family of nanoribbons. Interestingly, other structures of ZGaNNRs turn metallic nature irrespective of the Li site. Further, Li-bare@edge_N structure possesses the highest Fermi velocity as compared to other structures. This is useful for designing high speed interconnect applications. Further, we investigated the effective mass of various Li-ZGaNNR structures using standard two probe models. The effective mass of H-bare@edge_N structure reveals the highest effective mass in both valence and conduction bands. The proposed work proves the high capability towards the designing of the nano-scale devices.


I. INTRODUCTION
Considering the III generation era of semiconductor devices in the nano-scale regime, mainly nitrides (GaN, AIN and BN) have gained both technological and scientific attention in recent years [1], [2]. Many researchers explored the Gallium nitride nanoribbon(GaNNR) as a replacement of CMOS technology due to its wider band gap, steep reverse breakdown voltage, good thermal and chemical stability [3]- [10]. Yogi et al. investigated the electronic properties of Cl decorated AGaNNRs [11]. Switching phenomena and effect of NDR have been examined by Inge et al. using ZGaNNR by edge fluorination [12]. Ismil et al. and Xu et al. studied optical, electronic properties and also synthesized GaN [13], [14]. Sanjay et al. used the gallium particle trapping effect to synthesize GaN nanoparticles [15]. GaN nanoparticles are synthesized by using pulsed laser deposition, nonthermal plasma method and ammonobasic reactive sublimation [16], [17]. Thermal conductivity, phonon, analysis of charge states and noise properties have been investigated using GaNNRs [18]- [20]. Power amplifier, gunn diode, high temperature The associate editor coordinating the review of this manuscript and approving it for publication was Yee Sin Ang . applications have been designed using GaN [21]- [23]. Mohamed Azize et al. designed high electron mobility transistors using GaNNR [24]. Mina Rais et al. used GaN as an electromechanical material [25]. Other GaN nanocomposites such as nanoribbons [26], [27], nanobelts [28], and nanotubes [29] have been synthesized. Electronic properties are studied with edge hydrogenation for graphene nanoribbons [30]. Spin states are used for ZGNR to finding outs the opto-mechanical properties [31]. Cu adsorption at different sites of AGNR structures exhibit metallic nature [32]. The qualitative characteristics of the band structures have been altered due to fluorine (F) edge functionalization [33]. The band gaps in graphene nanoribbons can be modulated with passivation techniques, and would also turn some structures metallic in nature [34]. On the other hand, exploring the effective mass and Fermi velocity of monolayer ZGaN would be useful for exploring nano-scale semiconductor devices.

II. COMPUTATIONAL DETAIL
The paper investigated the structural and electronic properties of various Li-ZGaNNRs using first-principle methods by employing DFT. ATK-VNL tool is used for calculating all parameters of ZGaNNRs [35]. Nanoribbons with the width N z =6 is considered to examine the effect of Li interactions. Local-density approximations (LDA) is chosen to include the exchange-correlation [36]. For the geometrical optimization, the mess cut-off energy of 100 Ry and 1 × 1 × 100 k-points sampling is used for the periodicity in the brillouin zone. The transport characteristics are investigated under the NEGF framework. The current is obtained using a two probe model using Landauer Buttiker formula [37].

III. RESULTS AND DISCUSSION
A. STRUCTURAL PROPERTIES Various Li-passivation ZGaNNR structures are considered to analyse the thermostatic stability of GaNNRs. Figure 1(a)-(f) depict the optimized geometries of considered structures. All considered Li-passivation ZGaNNRs undergo structural changes after optimization and also noticed the change in bond length between the atoms. Table 1 summarizes the reduction or elongation of a bond length. In optimization, bond length analyses reveal that the highest edge restoration occurs at the ribbon's Ga edge with Li atom and it is increased from 1.6Å to 2.64Å for the N z =6. To investigate structural stability, we examined the binding energy (E bi ) per Li atom of considered structures. Table 2 summarizes the E bi calculations. E bi has been analyzed using a E bi = [E t -n Ga E Ga -n N E N -n H E H -n Li E Li ]/N t , where E t , E Ga implies the total energy of Li-ZGaNNRs and single isolated Ga atom and E Li , E H and E N signifies the single atom energy of Li, hydrogen and nitrogen atoms respectively. n Ga , n N , n H , n Li are the number of atoms of the respective energy. Further N t is the total number of atoms in considered ribbon. We have varied the ZGaNNR width from 2 to 6 of various Li-ZGaNNRs to investigate binding energy and band gap. It is shown in Table 2 and Table 3. From Table 2, It is observed that width N z =6 structures possesses   Furthermore, Li-passivation@edge_Ga structure emerged as the most stable structure among other Li-ZGaNNRs.

B. ELECTRONIC PROPERTIES
The electronic properties of Li-ZGaNNRs are analyzed using E-k diagrams and DOS profiles. As seen in Figure 2(f), the metallic behavior is observed in Bare@edges_both ZGaNNR due to partially induced electronic bands and these bands are arising from dangling bonds on two side edges of the ZGaNNR. For Li-passivation@edges_both ZGaNNR, the chemical bond is formed in between Li and the edge of N/Ga atoms that saturates one dangling bond on the edge of Ga and N atom. The residual dangling bond at the Ga and N edges are present at the Fermi level as seen in Figure 2  which clearly indicates the semi-conducting behaviour as shown Figure 2(b). This is due to π and π * bonds of N and Ga atoms. The closing of the bandgap for Li-bare@edge_N and H-bare@edge_N structures are due to edge dangling bonds at the sites of N and Ga atoms and also noticed the presence of electronic band states around the zero Fermi level. The calculated E-k diagrams and their DOS profiles are shown in Figure 2(d-e) and Figure 3(d-e).

C. VARIATION OF FERMI VELOCITY AND EFFECTIVE MASS
A very simple way to calculate the Fermi velocity in a Dirac material is using the energy dispersion relation. The conductivity is independent of the band slope value at the Fermi level due to linear dispersion near the origin of ribbons. Another way to detect the change in the Fermi velocity is to apply Li-passivation on ZGaNNRs and also inject carriers from Li atoms to GaNNRs. With this, the conductance should increase as a function of the applied Li passivation due to the wave vector mismatch. When the position of the Li atom changes the Fermi velocity also changes. The Fermi velocity is estimated using the standard two probe models [38].   Fermi velocity(V f ) increases with increasing Li atoms in the ZGaNNR structures. Li-bare@edge_N structure possesses the highest V f (8.04 × 10 4 m/s) as compared with other structures. This is useful for designing high speed interconnect applications. Generally, Fermi velocity is inversely proportional to the quantum capacitance and kinetic inductance for designing high speed interconnect applications. In order to get the low inductive coupling and capacitive delay, the Fermi velocity should be high. It can be noticed from Table.4 that Li-bare@edge_N structure is the strong contender for designing nanoscale interconnect circuits. The characteristic lateral confinement of charge carriers in ZGaNNRs causes a non-zero effective charge carrier mass, which impacts on charge carrier mobility in these devices. Such a system emphasizes the importance of charge transport in order to promote future GaN based technology. Greater effective masses are observed due to the lattice Li passivation that induces quasi-particles, resulting in decreased charge mobility. In this regard, the carrier's effective mass of ZGaNNR is a main factor to design and improve GaN-based devices. Further, we investigated the effective mass (m*/m 0 ) of various Li-ZGaNNR structures using standard two probe model.
The calculated effective mass (m*/m 0 ) for the Li-passivated ZGaNNRs shown in Table 4. The effective mass of H-bare@edge_N structure reveals the highest effective mass in both valence (0.282) and conduction (0.107) bands. This helps to design the future low bias nano-scale semiconductor devices. The m* is calculated using a relation of energy and momentum is obtained from (2)

D. TRANSPORT PROPERTIES
In this section, the transport characteristics of various Li-passivated-ZGaNNRs with N z = 6 are investigated using standard two probe models. Evaluated using self-consistent methods and used bias sampling step size of 0.1V for 0 to 1V. For pristine ZGaNNR, the current-voltage curve clearly indicates that the current is rapidly enhanced during low bias, reaching a maximum value at 1.0V. The peak current around 2.5µA reaches with a voltage of 1.0V. This linearity is due to good ohmic interaction between Ga-N bonds. Further, we found Li-bare@edge_N structure is not conducting current at initial voltage up to 0.7V and afterwards its amplitude rises sharply. Li-passivation@edge_Ga structure conducts less current due to less numbers of H-atom presence in the scattering region. Li-passivation@edges_both, H-bare@edge_N and Bare@edges_both structures of ZGaNNRs exhibit NDR behaviour shown in Figure 4. The current-voltage characteristics of Bare@edges_both ZGaNNR shows that the current increased rapidly during initial positive bias, reaches at a bias of 0.6V and then decreases with an increase in voltage, showing NDR behavior. The peak current of 29.8µA was found at 0.6V and then current begins to decrease beyond 0.6V. Understanding the effect of NDR, by analyzing transmission curves, varies as a result of the voltage applied. At 0.6V, the bias window reveals a peak propagation direction with a current of approximately 29.8µA. Decreasing in current has been observed during a reduction in electron flow in the model. The NDR effect of the proposed model could be utilized in various applications. Further, we investigated the I-V characteristics of the H-bare@edge_N ZGaNNR. Current is enhanced at an initial positive bias, reached peak at 0.61V and then gradually decreases with a rise in voltage, shows a NDR effect. Further Li-passivation@edges_both ZGaNNR structure increases its current at the initial stage at 0.3V and then current decreases with a rise in voltage, indicating a NDR behavior. Figure 4 and 5 depict i-v characteristics and transmission spectra of considered Li-passivated ZGaNNRs.

IV. CONCLUSION
In this work, investigations of various Li- He has served the Defence Research and Development Organization (DRDO), for a short period before moving to the National Institute of Technology Rourkela, in 1989. He has supervised 16 Ph.D. students and published over 60 articles in refereed journals besides more than 150 conference papers. His research interests include adaptive signal processing, fuzzy systems, wireless communication, and machine learning for wireless communication networks, and related fields. He was a recipient of the prestigious Common-Wealth Scholarship. VOLUME 9, 2021