Performance metrics of current transport in pristine graphene nanoribbon field-effect transistors using recursive non-equilibrium Green's function approach

Highlights

• Performance metrics of pristine GNRFETs of various dimensions with doped AGNRs contacts are explored.

• Self-consistent solutions of Poisson and Schrödinger equations within recursive NEGF is utilized.

• 7- AGNRFETs at 7 nm exhibits outstanding subthreshold swing of ~67 mV/dec and DIBL of ~54 mV/V.

• Narrower and longer devices are less affected by short-channel effects.

Abstract

Graphene nanoribbons (GNRs) are an emerging material for future nanoelectronic applications. Because GNR fabrication technology is still in an early stage, modelling of GNR field-effect transistors (GNRFETs) is significant for evaluating the performance metrics of these devices. In this study, the charge transport properties of double-gate monolayer GNRFETs with various channel widths and lengths and doped contacts are investigated. The Hamiltonian matrix of the device is derived using the nearest-neighbour tight-binding method. The self-consistent solutions of the Poisson and Schrödinger equations are obtained within a recursive non-equilibrium Green's function formalism using the successive over-relaxation method to reduce the time required for the simulation. The effects of channel length and width of the device on the electronic transport properties such as the total density of states, transmission coefficient, energy-resolved current spectrum, and current–voltage characteristics are investigated. The performance metrics of the device, including the subthreshold swing, drain-induced barrier lowering (DIBL), threshold voltage, and on/off current ratio, are computed. It is found that for narrower and longer devices, the subthreshold swing and DIBL decrease, whereas the on/off current ratio increases. In addition, when the width index is in the 3p + 1 family, the device exhibits better switching performance. 7-armchair GNRFETs at 7 nm exhibits an outstanding subthreshold swing of ~67 mV/dec and a DIBL of ~54 mV/V. Thus, the narrower and longer device is less affected by short-channel effects, and the lower leakage current during the off state enables better switching performance, making it a potential candidate for future nanoelectronic applications in low-power design.

Introduction

Transistor scaling to date has been largely governed by Moore's law, which was postulated in 1965 by Gordon Moore [1,2]. However, owing to continued miniaturisation of complementary metal–oxide–semiconductor transistors, short-channel effects and leakage current have been observed recently in sub-10-nm channel transistors [[3], [4], [5]]. The leakage current is due to the reverse-biased p-n junction current, weak inversion, and drain-induced barrier lowering (DIBL) [6]. Nanometer-size silicon-based transistors face several fundamental physical challenges such as increased power density and a corresponding increase in dissipated heat, which degrade device performance [6,7]. Carbon nanotubes and graphene have been introduced as nanoelectronic materials to replace silicon [[8], [9], [10]]. Graphene has attracted the attention of many researchers since it was introduced in 2004 owing to its promising and exotic electronic properties [11,12], such as high electron and hole mobility at room temperature [13] and high thermal conductivity [14]. Thus, graphene-based semiconductor devices have become a significant research topic. Graphene sheets that are blended with other thin film materials, not only provide mechanical support but also enhance the properties of graphene [15]. As such, we can find promising applications of graphene-based hybrid system in optoelectronic energy harvesting devices [16,17] and solar seawater desalination [[18], [19], [20]] even anti-counterfeiting applications [21,22]. As sheet of graphene is a zero-band-gap nanomaterial, it cannot be used in transistors for switching applications. Thus, the focus has shifted to graphene nanoribbons (GNRs) [23], which have electronic properties similar to those of graphene except for the presence of a band gap. GNRs can have zigzag or armchair edges, depending on the orientation of the ribbon edge [24,25]. The width of GNRs should be carefully chosen to obtain a suitable band gap value and realize transistors with extraordinary switching performance and minimal leakage current. Theoretical investigations have proved that the band gap of GNRs is inversely proportional to their width.

Many researchers consider that GNRFETs with lengths of less than 25 nm operate in the ballistic regime, and longer GNRFETs operate in the drift-diffusion regime. However, from a practical viewpoint, an ideal ballistic FET has still not been produced after two decades. Thus, it becomes very important and informative to study the quasi-ballistic GNRFETs, which has characteristics that are intermediate between the classical drift-diffusion and ideal ballistic transport regimes. In addition, modern nanoscale devices exhibit quasi-ballistic behaviour and have a finite ballistic channel resistance. Thus, it is very important to identify the effect of channel length on short-channel GNRFETs [26,27].

Goharrizi et al. investigated the electrical characteristics and switching performance of armchair-edged GNRFETs (AGNRFETs) in the presence of line edge roughness scattering [5]. Banadaki studied the static metrics and switching properties of GNRFETs in terms of the scaling effect and their width-dependent performance by employing a mode space approach [28]. Nazari et al. used methods similar to those used in our research and concluded that a GNRFETs structure with three single-vacancy defects has a higher on/off current ratio (I_ON/I_OFF) and lower subthreshold swing than a single-vacancy GNRFETs and therefore performs better [29]. Edric et al. presented the nearest-neighbour tight-binding (NNTB) Hamiltonian matrix of the channel, which is further studied and employed in this work to build a charge transport model of the GNRFETs device to study its charge transport properties [30]. Leong et al. developed a compact model that can extract interface trap level density that is known to degrade the electrical performance of GNRFETs [31].

In this work, charge transport in a double-gate monolayer GNRFETs with various channel widths and lengths and doped contacts is numerically studied in real space using the self-consistent solutions of the Poisson and Schrödinger equations within the recursive non-equilibrium Green's function (NEGF) formalism together with the successive over-relaxation (SOR) method. The NNTB method is applied to the interaction between carbon atoms. Mean free path which is the distance that a molecule travels before collisions is very important to determine the ballistic transport. However, ideal ballistics is impossible to achieve in reality. Therefore, in our modelling framework, channel between the lengths of 5 nm–10 nm is considered to be operating in quasi-ballistic transport. Carrier mobility is the speed for carriers moving in response to an electric field. In the ballistic region, the mobility of the carriers is proportional to the length of channel as demonstrated by K. Huet et al. in 2014 [32]. However, in quasi-ballistics region, small amount of scattering mechanism must be considered although it is not noticeable in short-channel device such as doping pockets, charge and neutral defects. In addition, the mobility will increase initially but reach saturation when the length increases.

This paper is organised as follows. Section 2 describes the NEGF treatment of charge transport in GNRFETs. The effects of the channel length and width on the performance of GNRFETs are presented and analysed in Section 3. Section 4 presents the conclusions obtained in this research.