Transfer matrix model of multilayer graphene nanoribbon interconnects

Abstract

A general, algorithmic and exact transfer matrix model is presented for multilayer graphene nanoribbon (MLGNR) interconnects that is based on multi transmission line method (MTLM). In the proposed transfer matrix formulation the effect of Fermi level shift in GNR layers is considered. Also the capacitive and inductive coupling between the GNR layers is regarded in this matrix model. Moreover, in order to get the precise results, the block number parameter for distributed property of the interconnects is proposed for the first time. The straightforward, general and algorithmic format of the proposed matrix model causes it to be used for different technology nodes and length of the interconnects. Moreover any variation in the physical parameters can be involved simply in this formulation. Using this matrix model, one can examine different analytical prospects such as Nyquist, Bode, and Nichols stability criteria, zero and poles and step time responses for on-chip MLGNR interconnects, implemented for integrated circuit applications. Also this matrix model can be used in circuit simulators such as HSPICE in order to simulate the VLSI-ULSI circuits. As the couple of examples, we have extracted Nyquist diagrams and step time responses for 10nm, 14nm, and 22nm technology nodes. The results show that relative stability of MLGNR interconnects increases with increasing technology node and interconnect length. The results demonstrate a considerable difference between the responses obtained using traditional MLGNR interconnect formulation and the exact proposed matrix model.