Modeling, Analysis and Design of Doped MLGNR Interconnects for Subthreshold Circuits

Abstract

There has been a lot of research done on graphene recently as a potential new material for high speed applications. In addition to having superior transport characteristics, as the high mean free path (MFP) and high current-carrying capacity, in comparison to carbon nanotube (CNT) interconnects, graphene nanoribbon (GNR) interconnects also have advantages like simple fabrication process, improved material control, and higher reproducibility. The study of interconnect design in the sub-threshold mode of operation, where the supply voltage is kept lower than the threshold voltage, has been motivated by the expanding applications of electronic circuits, such as implantable medical devices and sensor nodes. This work delves into the intricate realm of circuit modeling and performance analysis, particularly concerning the multifaceted phenomenon of scattering. The focal points of this investigation are crosstalk and frequency response, elucidated within the context of capacitively coupled Li-doped Multi Layered Graphene Nanoribbon (MLGNR) interconnects. Notably, the exploration is centered around their operation within the sub-threshold domain. In Li doped MLGNR interconnects, the influence of process and geometrical parameter variability on the induced crosstalk is explored, as well as the applicability of dielectric inserted MLGNRs in the sub-threshold domains. Li doped MLGNR's performance is contrasted with that of traditional Cu, SWCNT, and more recent hybrid materials like HCNT, HGNR, and H Carbon. The influence of interconnect geometry on the performance of the capacitively coupled interconnects of multilayer graphene nanoribbons (MLGNRs) has been comprehensively analyzed at nanoscale dimensions. Three different interconnect geometry cases (viz., case-1, case-2, and case-3) by keeping a constant interconnect pitch and modifying the width/spacing (w/s) ratio are taken into consideration to study the effect of the interconnect geometry on the impedance characteristics of the MLGNRs. Further, the edge scattering dominant circuit modelling is presented. The results show increased penalty for crosstalk induced noise (XTIN) area and crosstalk induced delay (XTID) by including the ER-induced scattering mechanism. The results also show that the effective MFP (i.e., including the influence of edge roughness (ER) generated scatterings) dominates the XTID and noise area, as opposed to the acoustic and optical (a/o) scattering induced MFP with variations in the temperature, interconnect-width, and length. In coupled interconnects of MLGNR, the gate oxide reliability (GOR) is further examined in terms of average failure rate (AFR) for various interconnect-width, and MFP cases. The results reveal that the case-3 of interconnect geometry is found to be more affected by the GOR failure in comparison to the other cases. The shielding technique is a viable way to reduce the relative GOR failure rate. According to GOR and the estimated AFR results, average values of 0.93e-7 and 0.7e-7 are obtained in shielded and non-shielded cases as a function of interconnect-length and width. The effect of the variations in process-stimulated parameters (i.e., physical and geometrical parameters) on the resultant transient response in the MLGNR interconnects with Li doping and capacitive coupling, working in the sub-threshold domain is also being investigated. The transmission-line (TL) theory based novel analytical approach is proposed here to analyze crosstalk induced noise delay (XTIN) for the sub-threshold mode operations in coupled MLGNR interconnects. With the increment in the temperature or interconnect-length values, the crosstalk induced delay (XTID) increases however with the, dielectric thickness, interconnect- width and Fermi energy level variations, the XTID decreases. It is also important to note that the average error values for the derived Vmax and V time-duration, are not higher than 5% and 18%, respectively. This work presents an equivalent distributed temperature-dependent circuit model of coupled MLGNR interconnects that takes into account the relaxation time MFP and its effects on the line resistance (R). In terms of XTID and frequency response the performance of dielectric inserted MLGNRs, doped MLGNRs, undoped MLGNRs and copper has been examined at subthreshold operating domain. The best performance properties are offered by inserting silicon dioxide (SiO2) and hafnium oxide (HfO2) between GNR layers, in comparison with all other dielectric inserted MLGNRs in sub-threshold applications. Furthermore, the highest gain margin (58 dB) and phase margin (160 degrees) are obtained in case 5, determining the maximum stability obtained in this case. The thickness values are optimized at 43 nm, 41.1 nm, 38 nm and 36 nm in the dielectric inserted MLGNRs, doped MLGNRs, undoped GNRs and Cu based interconnects, respectively, so that the least amount of crosstalk delay is achieved in the sub-threshold working mode. Further, this work also presents the thermal crosstalk analysis and frequency response comparison of the newly proposed hybrid interconnects with that of traditional on-chip interconnects operating in the sub-threshold domain. The electrical performances of hybrid copper carbon-nanotube (HCNT), hybrid copper graphene nanoribbon (HGNR) and hybrid Copper carbon (H Carbon) interconnects are studied and further compared with that of conventional, copper (Cu), single walled CNT bundles (SWCNTs) and Li doped MLGNR interconnects in relation to dynamic and functional crosstalk results by employing the transmission line (TL) analytical model for sub-threshold applications. The frequency domain analysis also suggest that the H Carbon interconnects have the steepest and the sharpest step response with the 3-dB bandwidth obtained as 6.7586×10^10 Hz. The work presented in the thesis demonstrates that temperature, surface roughness scattering, physical and geometrical parameters, doping and physical structure play a crucial role in exploring the efficiency and reliability of MLGNR interconnects operating in the sub-threshold state.