Modeling and Analysis of High Frequency Interconnects Using Doped Multilayer Graphene Nanoribbon

Abstract

The increasing need for faster communication and computing systems has created a demand for interconnects capable of handling sharper signal transitions and operating at higher frequencies. At the same time, driven by the need for enhanced performance, the semiconductor industry has aggressively scaled down the size of devices and interconnects. However, the continuous evolution and rapid scaling of device integration technology, have led to significant performance challenges for conventional copper (Cu) based high-speed on-chip interconnects. Hence, researchers are on a quest to find a suitable alternative that addresses these limitations while ensuring efficient and reliable performance in future high-speed, nanoscale systems. Recently, intercalation-doped multilayer graphene nanoribbons (MLGNRs) have emerged as a promising alternative for Cu interconnects, offering remarkable electronic, transport, mechanical, and thermal properties. However, despite the promising enhancements offered by intercalation doping, the practical application of MLGNR as on-chip interconnects is limited by extrinsic scatterers and skin effect at high frequencies, thereby aggravating signal integrity issues and compromising the overall performance, functionality, and reliability of high-speed systems. Further research is crucial to mitigate these challenges and fully realize the potential of MLGNR for high-speed on-chip interconnects. In this thesis, an impedance model is developed by incorporating the scattering-limited realistic effective mean free path (MFP), λR(T), for various configurations of MLGNR interconnects to extract frequency-independent circuit parameters. The MLGNR configurations include undoped MLGNR (viz., horizontal top-contact (HTC), horizontal side-contact (HSC), and vertical top-contact (VTC)), and intercalation-doped HTC-MLGNR (with AsF5, FeCl3, and Li dopants). The optimistic intrinsic-phonon-limited effective MFP, λP(T), for perfect MLGNR is also considered for impedance analysis. The circuit parameters for MLGNR variants are analyzed and compared to mixed carbon nanotube (MCNT) bundles, and smooth and rough Cu variants across a temperature range of 300 K to 500 K. Further, the impact of corrugation amplitudes (10 pm to 170 pm) on the circuit parameters of MLGNR and Cu interconnects are analyzed at 300 K. The findings indicate that the extrinsic scattering sources, particularly structural edge roughness (SER) of GNR and corrugations of dielectric surface, significantly increase the resistance of both undoped and doped MLGNR interconnects compared to Cu variants. Subsequently, a methodology incorporating the scattering-limited realistic effective MFP and a finite-thickness-dependent skin effect model is proposed for extracting the frequency-dependent impedance of MLGNR interconnects. By employing the proposed methodology, the frequency-dependent characteristics of circuit parameters for MLGNR interconnects are obtained and compared with MCNT bundle and Cu interconnects over a frequency range of 1 GHz - 104 GHz at a temperature of 300 K. The results show that due to skin effect at high frequencies, more pronounced impact of scatterers is observed, thereby exacerbating effective resistance of MLGNR interconnects. After establishing the scattering-limited, frequency-independent impedance model, this work performs a temperature-dependent comparative analysis of MLGNR, MCNT bundles, and Cu interconnects in capacitively coupled configurations. Using SPICE simulations, crosstalk-induced delay is evaluated, revealing that MLGNR variants outperform MCNT bundles and Cu interconnects for λP(T), but show inferior performance compared to Cu for λR(T). Among MLGNR and MCNT bundle interconnects, lithium intercalation-doped HTC-MLGNR (Li-D HTC-MLGNR) achieves the lowest crosstalk-induced delay for both λP(T) and λR(T). An ABCD parameter-based analytical model further examines transient response, 3-dB bandwidth, and relative stability, showing MLGNR’s superior stability despite Cu's advantage in step response and bandwidth. Moreover, Li-D HTC-MLGNR interconnects, without SER and placed on substrates like Silicon carbide (SiC) and Boron Nitride (BN), exhibit faster rise times than Cu counterparts. These findings underscore the need to eliminate scattering sources like SER and corrugations on dielectric surface for MLGNR's practical on-chip applications. Furthermore, the frequency-dependent circuit parameters are employed for evaluating frequency varying crosstalk-induced delay, overshoot amplitude, and overshoot width for MLGNR interconnects using SPICE simulations for frequency range of 1 GHz to 104 GHz. Comparisons with MCNT bundles and Cu interconnects reveal that MLGNR and MCNT bundles, for λR(T) and placed on Silicon dioxide (SiO2), exhibit inferior performance compared to Cu variants due to skin effect and scatterers. However, optimized Li-D HTC-MLGNR (O-Li-D HTC-MLGNR) placed on SiC, in the absence of substrate polar phonons (SPPs) and SER, demonstrates the minimal impact from frequency variations and skin effect, and superior performance. Therefore, to benefit from the advantages of MLGNR-based interconnects at high frequencies, intercalation doping with Li, utilizing SiC as dielectric, and eliminating scatterings with rough edges and substrate SPPs are desired. Subsequently, the frequency-dependent traits of crosstalk-induced delay and noise area, and the mean time to failure due to electromigration (EM-MTF) are analyzed for O-Li-D HTC-MLGNR interconnects under the influence of scatterers, skin effect, and process and temperature variations. As a result of variations in process parameters and temperature, the O-Li-D HTC-MLGNR exhibits an increase in variations of crosstalk-induced delay and noise area, accompanied by a reduction in variations of EM-MTF as the frequency increases. The impact of process and temperature variations gets enhanced at higher frequencies for O-Li-D HTC-MLGNR and, hence, must be eradicated for reliable interconnect design and operation. Finally, a MLGNR-based single-tier on-chip nanoscale via-interconnect scheme (VIS) is proposed, which combines the Li-D VTC-MLGNR via and Li-D HTC-MLGNR interconnect, as a prospect for monolithic 3D (M-3D) ICs. To go beyond the simplifying assumptions of perfect MLGNR and conventional skin effect, this study incorporates the impact of extrinsic scatterers in a realistic MLGNR and considers the one-dimensional skin depth formula for MLGNR-based interconnect and via. A combined equivalent circuit model is developed to analyze the challenges induced by crosstalk effects in perfect and realistic MLGNR VIS. The results show that for width in the range of 5 nm - 30 nm, perfect VIS outperforms realistic VIS in terms of crosstalk-induced delay. Moreover, at high frequencies ranging from 1 GHz-104 GHz with a width of 16 nm, realistic VIS demonstrates a performance decline of 243.18% (5.3934×103%) for l=4.8 µm (1 mm), respectively, in comparison to perfect VIS. Hence, in order to leverage the potential of MLGNR-based VIS for M-3D ICs at high frequencies, it is imperative to integrate Li-intercalation doping and mitigate the impact of extrinsic scatterers in MLGNR.