Fermi Energy and Temperature Dependent Performance Analysis of MLGNR Based VLSI Interconnects

Abstract

The downscaling of technology nodes leads to increase the number of active devices which are used in very large-scale integration (VLSI) for chip design industry. Longer interconnects are required to interface millions of active devices in an integrated circuit (IC). Parasitic parameters of interconnects increase linearly with an increase in the length of the interconnects. As a result, the performance of the interconnects becomes a primary focus when compared with the performance of active devices in nano-scaled technology nodes. This research discusses the conventional aluminum and copper interconnects and explored the possibilities to replace these interconnects owing to their higher resistivity, electro-migration, surface and grain boundary scatterings. With the advancement of the technology nodes, it is required to increase the current density and decrease the cross-sectional dimensions of an interconnect. Carbon nanomaterials, i.e., graphene nanoribbons (GNRs) and carbon nanotubes (CNTs), demonstrate effective electrical, thermal, and mechanical properties. The GNR and CNT are allotropes of carbons with the potential to function as interconnects in the development of an IC for the VLSI industry. Although the GNR and CNT exhibit similar properties, considering the fabrication process, graphene is more suitable and can be easily controlled when compared with CNT because of its planer nature. Further, considering the number of layers, the GNR could be divided into two types: single layer GNR (SLGNR) and multilayer GNR (MLGNR). The SLGNR shows high resistivity in contrast to the MLGNR; hence, the MLGNR is a suitable material for on-chip high-performance VLSI interconnects. The performance of MLGNR as an interconnect at global levels in on-chip VLSI IC should be studied to be employed in different applications. This research work presents the impact of Fermi energy and temperature variations on the performance of MLGNR interconnects at a global length. A Fermi energy dependent equivalent circuit model is proposed to calculate the parasitic parameters of the MLGNR interconnect. The impact of Fermi energy on the MLGNR conductivity is analyzed using mathematical equations. An increase in intercalation doping increases the Fermi energy of the MLGNR layers, which increases its conductivity. The impact of the Fermi energy variation on the parasitic parameters of the MLGNR interconnect at three different technology nodes (32nm, 22nm, and 16nm) for variable global lengths (500–2000μm) is analyzed. The performance of elite ICs is influenced under variable thermal conditions. With the downscaling of the technology nodes, the impact of temperature on interconnects becomes a major challenge in designing next generation VLSI ICs. Therefore, the impact of temperature on the performance of MLGNR functioning as an interconnect should be analyzed to estimate their actual performance under a thermally variable environment at global levels. A temperature-dependent circuit model of the MLGNR is proposed to evaluate the impedance parameters, which include the various electron–phonon scatterings as a function of temperature. The scattering mechanism in the MLGNR is of two types: electron–electron scattering and electron–phonon scattering. The electron–phonon scattering is crucial when compared with electron–electron scattering with the rise in temperature on the effective mean free path (MFP) of the MLGNR. The phonon scattering is classified into acoustic, optical, and zone boundary scatterings. The temperature-dependent effective MFP of the GNR interconnect is dominated by the acoustic scattering from low to moderate range of temperatures, i.e., from 200 to 300K. Further, at a high temperature range (300–500K), the acoustic, optical, and zone boundary scatterings impact the effective MFP of the GNR. Based on the temperature dependence, the parasitic parameters are calculated at global lengths for 32nm, 22nm, and 16nm technology nodes. The physical parameters used for the three technology nodes are obtained from the International Technology Roadmap for Semiconductors (ITRS 2013). The impact of temperature on the MFP is considered to evaluate the parasitic parameters of the MLGNR functioning as interconnects using MATLAB computing software. The effective MFP of the GNR reduces, which further dominates its own resistance at high temperatures (300‒500K) for three different technology nodes. The resistance of the MLGNR interconnect increases sharply after 300K due to the shrinking of the effective MFP for the three different technology nodes considered for the study at a global length of interconnects. To calculate and analyze the performance of the MLGNR interconnects from the delay, power dissipation, and power delay product (PDP) parameters, the simulation program with integrated circuit emphasis (SPICE) simulation tool is utilized based on Fermi energy and temperature-dependent models. The delay and PDP of the MLGNR increases with an increase in the interconnect length but decreases with a rise in Fermi energy. The Fermi energy-dependent MLGNR results are compared with the copper interconnect in terms of delay and PDP for equal length and technology nodes. Similarly, the delay and PDP increase with a rise in temperature (200‒500K) at the global length of interconnects. The temperaturedependent analytical delay model of the MLGNR interconnects is also presented, and the results obtained from the analytical delay model are compared with the simulation results. The simulation and analytical results show that the outcomes of the two models correspond well. The trend of the two models shows that the delay increases with a rise in temperature (200‒500K) for different technology nodes, i.e., 32nm, 22nm, and 16nm. Furthermore, Relative stability of MLGNR is analyzed from 500–2000µm length with respect to switching delay and observed that with increasing interconnect length switching delay increases as a result input signal damp faster which upswings the relative stability of MLGNR for all three various technological nodes. Besides, relative stability is analyzed at length 2000µm and temperature 500K of MLGNR through Nyquist plots and observed that the system will achieve stability faster as we move from 32nm to 16nm technological node due to higher values of parasitic because of the reduction in MFP of electrons. The combined impact of Fermi energy and temperature on the performance of MLGNR in delay and PDP terms at global levels for three different technology is also presented and analyzed that both delay and PDP increases with rise in temperature (200‒500K) but decreases with rise in the level of Fermi energy (0.2eV‒0.6eV). A temperature-dependent comparative analysis of the MLGNR with copper and SWCNT interconnects considering delay and PDP as performance parameters is conducted for equal length and technology nodes. Moreover, the results show that the performance of the MLGNR interconnects is much better than those of the SWCNT and copper interconnects considering the impact of Fermi energy and temperature at a global length of interconnects for 32nm, 22nm, and 16nm technology nodes. Therefore, it has been concluded that the MLGNR is an outstanding material for the fabrication of nanoelectronic ICs in thermally variable conditions.