An analytical approach to calculate effective channel length in graphene nanoribbon field effect transistors M. Ghadiry a,⇑ , M. Nadi b , M. Bahadorian c , Asrulnizam ABD Manaf a , H. Karimi d , Hatef Sadeghi e a School of Electrical and Electronic Engineering, Engineering Campus, Universiti Sains Malaysia, Penang, Malaysia b Department of Computer Engineering, Ashtian Branch, IAU, Ashtian, Iran c Institute of Advanced Photonics Science, Nanotechnology Research Alliance, Universiti Teknologi Malaysia, 81310 Johor Bahru, Malaysia d Japan International Institute of Technology (MJIIT), Universiti Teknologi Malaysia, 54100 Kuala Lumpur, Malaysia e Lancaster Quantum Technology Center, Physics Department, Lancaster University, LA1 4YB Lancaster, UK article info Article history: Received 12 September 2012 Received in revised form 23 November 2012 Accepted 3 December 2012 Available online xxxx abstract A compact analytical approach for calculation of effective channel length in graphene nanoribbon field effect transistor (GNRFET) is presented in this paper. The modelling is begun by applying Gauss’s law and solving Poisson’s equation. We include the effect of quantum capacitance and GNR’s intrinsic carrier concentration in our model. Based on the model the effects of several parameters such as drain-source voltage, channel length, and oxide thickness are studied on the length of effective channel in GNRFETs. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction By using graphene nanoribbon it seems to be possible to make devices with channels that are extremely thin and will allow FETs to be scaled to shorter channel lengths and higher speeds without encountering the adverse short-channel effects restricting the per- formance of the existing devices. As a result, high performance lo- gic circuits such as high speed full adders could be realized [1,2]. Recently, experimental and theoretical studies such as [3–6] have shown it is possible to fabricate GNR transistors. As a result, many researchers have been attracted to this field and provided several models for GNR’s properties [7–12]. Nevertheless, there is lack of research in modelling the behaviour of GNRFET near the drain junction and the breakdown mechanism. The effective channel length is one of the most important parameters of MOSFETs showing the portion of the channel con- tributing to the properties of MOSFETs such as I–V characteristic. In order to calculate the effective channel length, the width of the drain region, where impact ionization and carrier velocity sat- uration occur, has to be computed. It controls the lateral drain breakdown [13,14], substrate current, hot-electron generation [15,16], and drain current at the drain region [17,18]. Although several models are available for saturation region of silicon-based MOSFETs such as [19,20,16,21,22], there is still plenty of room for research in modelling of this region for car- bon-based FETs. In order to gain insights into reliability issues of these devices, close analysis of this region is necessary. In addition, these kinds of models open the way to explore the possibility of designing power transistors using carbon. Since at the moment the fabrication technology is still at its very first steps, analytical modelling seems to be a useful tool in the case of examining saturation region. In this paper,s simple and compact analytical models for surface potential, lateral electric field and effective channel length are proposed and the behaviour of a general top-gate GNRFET in the saturation region is studied. 2. Effective channel length model for GNRFET with top gate A schematic cross-section of top-gated GNRFET is shown in Fig. 1, where t ox is the oxide thickness of top gate with dielectric constant of  ox ; t g , W and L are the GNR’s thickness, width and the channel length respectively. The channel is divided into two sections. Section 1 is defined be- tween drain and saturation point and Section 2 between saturation point and source junction. We begin with applying Gauss’s law in the Section 1, shown in Fig. 1. q Z x 0 Z tg 0 ðn þ NÞ dx dt ¼ Z x 0  ox n ox dx  Z tg 0  g n 0 dt þ Z tg 0  g n x dt ð1Þ where q is the charge magnitude,  g and  ox are the graphene and oxide dielectric constants, n is the intrinsic carrier concentration, 0026-2714/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.microrel.2012.12.002 ⇑ Corresponding author. Tel.: +60 127427906. E-mail address: m.hoseinghadiry@gmail.com (M. Ghadiry). Microelectronics Reliability xxx (2013) xxx–xxx Contents lists available at SciVerse ScienceDirect Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel Please cite this article in press as: Ghadiry M et al. An analytical approach to calculate effective channel length in graphene nanoribbon field effect tran- sistors. Microelectron Reliab (2013), http://dx.doi.org/10.1016/j.microrel.2012.12.002