Cross Talk Analysis in Carbon Nanotube Based VLSI Interconnects

Abstract

With advanced technology nodes, large number of functionalities is integrated in a Very Large Scale Integration (VLSI) chip. Thus, the density of long interconnects is increased exponentially that connect millions of active devices on a chip, is posing a serious bottleneck in terms of substantial capacitive and inductive couplings. Hence there appears a dire need to search a potential material for future generation of VLSI interconnects that will be capable of exhibiting minimized propagation delay, power dissipation and crosstalk effects. The present work explores the possibilities of alternative interconnect material for future VLSI interconnects. The most promising alternative for copper interconnects turns out to be Carbon Nanotube (CNT).A comparative analysis of the propagation delay, power dissipation, cross-talk induced noise voltage and its frequency spectrum in CMOS inverter driven global interconnects of SWCNT bundle and copper has been presented. The single interconnect as well as capacitively coupled interconnects are represented by the π-equivalent circuit of distributed RLC-model. The Driver-Interconnect-Load (DIL) model [15] of distributed RLC circuit is used for the mutually coupled interconnects. An Alpha power law model [129] is used for representing the transistor in the CMOS inverter (driver). Influence of separation between adjacent tubes of various lengths and tube diameters, on delay and power dissipation in Single Walled Carbon Nanotube (SWCNT) bundle interconnect has been analyzed at 32nm and 22nm technology nodes. The main aim of this investigation is to optimize separation distance(x) between adjacent SWCNT and tube diameter (d) for better performance. The output waveform is analytically determined using CMOS inverter driven π-equivalent RLC circuit of SWCNT bundle and copper interconnect. The results are compared with SPICE simulation results at same technology nodes. There appears good agreement between the analytical and simulation results obtained. SPICE simulation result reveals that, in terms of delay, SWCNT bundle interconnect performs better than copper interconnect if the separation between the tubes is less than a certain critical value. It has also been noted that a SWCNT bundle composed of tubes of 1nm diameter is of lower delay than copper interconnect at various interconnect lengths and higher power dissipation due to dominance of larger capacitance of SWCNT bundle. Here an analytical model is developed to extract the transient response of victim output using CMOS inverter driven π-equivalent RLC circuit of capacitively coupled interconnects of SWCNT bundle. It is observed that at 32nm and 22nm technology nodes, for capacitively coupled interconnects, the piecewise analytical results replicate the SPICE waveforms very well. Crosstalk induced, noise voltage waveform and its frequency spectrum in capacitively coupled and mutually coupled SWCNT bundle interconnects, at the far end of victim line, at 32nm and 22nm technology nodes respectively have been analyzed. The diameter dependent crosstalk induced noise voltage levels have also been evaluated for the same technology nodes. The waveform of victim output analytically determined and compared with SPICE simulation results. A similar analysis has been performed for copper interconnects and a comparison made between the results of these two analyses. The analytical and simulation results have shown good agreement, for both CNT and copper. Based on these results it is found that, compared to copper, crosstalk noise voltage levels in capacitive coupled SWCNT bundles, at the far end of victim line, are significantly low. In mutually coupled copper interconnects, width of the noise waveform is wider compared to CNT at the far end of victim line. These results have further revealed that, compared to copper interconnects, capacitively coupled interconnects of SWCNT bundle filter more noise frequency components at both 32nm and 22nm technology nodes. In addition, compared to copper, mutually coupled interconnects of SWCNT bundles suppress comparable noise components in the higher frequency range for the same technology nodes. Based on these comparative results, an improved model for extracting inter-bundle, real life, coupling capacitances between SWCNT bundles has been proposed in this present work. An investigation of the control of crosstalk induced noise voltage (functional crosstalk noise) in capacitively coupled interconnects of SWCNT bundle, at the far-end of victim line, for fixed pitch and varying interconnect dimensions, for the proposed inter coupling capacitance model and the conventional model, at 22nm technology node, have been carried out. Results reveal that, in comparison to the latter, the former provides better reduction in crosstalk induced noise voltage. A similar analysis is performed for copper interconnects. Result reveals that, compared to SWCNT bundle interconnects, copper interconnects has higher coupled noise voltage levels. Finally, an analysis of the effect of temperature, varying over a range from 300K to 500K, on the crosstalk induced noise voltage waveform and its frequency spectrum both in capacitively coupled interconnects of SWCNT bundle using an improved inter bundle coupling capacitive model and in the copper interconnects at the far end of victim line, at 22 nm technology node is carried out. Result shows that, as temperature rises from 300K to 500K, compared to copper interconnects, the crosstalk induced voltage levels at the far end of victim line in SWCNT bundle interconnect are significantly low. With rise in temperature, the coupled SWCNT bundle interconnects suppresses more frequency components of the noise voltage than the conventional metal (copper) interconnects. The result of present research emphasizes that the comparative study of crosstalk analysis in CNT and copper interconnects shall be particularly important for the deep submicron high density, high performance chips.