Analysis of Stability in Carbon Nanotube and Graphene Nanoribbon Interconnects

This paper analyzes the stability of carbon nanotube (CNT) and graphene nanoribbon (GNR) based interconnects for future VLSI technology node. We have analyzed both Bode and Nyquist stability of single-wall CNT, multi-wall CNT, GNR, and copper based interconnect systems. The stability analysis is performed for different interconnect systems for 16nm ITRS technology node. It is shown that densely packed single-wall CNT bundle based interconnect has highest gain margin for a wide range of interconnect length (1 m to 100 m) as compared to the other interconnect systems. Index Terms—Carbon nanotube (CNT), graphene nanoribbon (GNR), stability. I. INTRODUCTION With the advancement of VLSI Technology the interconnect dimensions are reduced from micron to submicron range and submicron to nanometer range. In the nanometer regime the traditional copper based interconnects will suffer serious problems due to increased resistivity and susceptibility to electromigration. The carbon nanotube (CNT) and graphene nanoribbon (GNR) are proposed as the possible replacement for traditional copper (Cu) based interconnect systems (1). CNT and GNR can support large current densities and have long mean free paths. In this paper we have analyzed Bode and Nyquist stabilities in different CNT and GNR interconnect systems and compared the results with that of Cu based interconnects. The paper is organized as follows. Section II describes the formulation of transfer function of interconnects systems in s-domain. Analysis of Bode stability and Nyquist Stability is presented in Sections III and IV. The results are presented in Section V, followed by the conclusions in Section VI. II. TRANSFER FUNCTION FORMULATION To investigate the stability of CNT and GNR based interconnect system, we have formulated the transfer function of the interconnect system. We have modeled the interconnect system by a bundle of single-wall CNT, multi-wall CNT, and GNR. The dimensions of the interconnect are obtained from the ITRS corresponding to 16 nm technology node. Fig. 1 illustrates the RLC network interconnect systems. The RLC