Thermally Aware Modeling and Analysis of Mixed CNT for Future Nanoscale Technology Nodes

Abstract

With the upgrades in technology, the number of functionalities is escalating on advanced integrated chips. In this trend, the number of global interconnects that helps to join these circuit chips is also increasing. Global interconnects are long interconnects that run globally across the chip and help to associate global signals like a clock, power, and round to all modules. In this way, the parasite associated with longer interconnects increases, and ultimately the performance of interconnects is degraded at scaled nodes. So, an indispensable need of the hour demands a suitable material that can be employed for interconnect applications in the coming times. Carbon nanotubes have been advised as the best alternative to copper interconnects, which suffered from electromigration, grain boundary scattering, and surface roughness after 45nm technology node. Because carbon nanotubes possess notably good electrical, mechanical, and thermal properties, they can easily oust copper for interconnect applications. Formed with the layer of carbon in the form of graphite and rolled up in a cylindrical shape, carbon nanotubes are classified into single-walled carbon nanotubes (single layer of graphite), multi-walled carbon nanotubes (multiple layers of graphite rolled concentrically) and double-walled carbon nanotube (two layers of graphite rolled concentrically). Since a single carbon nanotube offers a high value of resistance, the bundle of interconnect is made by placing nanotubes parallelly in the bundle. Interconnects can be well presented by transmission lines with distributed impedance parameters and are driven by CMOS transistors (using the alpha-power law model). A quick and concise comparative analysis has been done between copper and carbon nanotubes to determine impedance parameters, propagation delay, power dissipation, and power-delay product. It has been analyzed that carbon nanotubes offer better performance than copper at global lengths. The present work focuses on a new mixed class of carbon nanotubes which are formed by changing different positions of multi-walled and double-walled carbon nanotubes. The equivalent circuit parameters of mixed carbon nanotubes are extracted with the help of single conductor models of multi-walled and double-walled carbon nanotubes. Their impedance parameters are determined to obtain the output waveform analytically and to study the effect of delay, power, and power-delay product. The simulated results of various mixed carbon nanotubes comprising multi-walled and double-walled carbon nanotubes are then compared with existing carbon nanotubes and copper. The results in the present work present that concerning delay at the final output, the power dissipated and power-delay product, multi and double-walled carbon nanotube bundled structure in which double-walled carbon nanotubes are located in the center and multi-walled carbon nanotubes are placed along the periphery of the bundle yield the best performance among all other interconnect materials. The presence of double-walled carbon nanotubes in the center helps in good conductivity and multi-walled carbon nanotubes along the periphery help in the decreasing coupling, thus these two properties of the bundle come up together to perform better than other counterparts. A brief analysis of crosstalk’s effect (both dynamic and functional crosstalk) is also performed for mixed carbon nanotube bundled structures at 32nm, 22nm, and 16nm technology nodes. The stability also helps in determining the performance of the circuit. The stability of multi-walled and double-walled carbon nanotube bundled structures is also determined with the help of rise time, peak overshoot, and Nyquist plots. The effect of temperature is also added up to analyze the performance of interconnect materials. The temperature is varied from 200 Kelvin to 500 Kelvin. Different types of electron phonons scattering phenomena (acoustic scattering till 300K and optical scattering at 300K and beyond) are encountered with the increase in temperature which tends to lower the effective mean free path of the conducting electrons. Results also demonstrate that with the inclusion of the effect of temperature, the delay of global interconnects increases and degrades their performance. The result of the proposed models is also compared with the mixed CNT models existing in the literature. Analytical formulations are done to obtain delay readings and are compared with simulated delay readings. Based on the results presented, it is found that the mixed carbon nanotube bundle structure (with multi-walled carbon nanotubes in the center and double-walled carbon nanotubes along the the periphery of the bundle) outperforms all carbon nanotube bundles (MWCNTs, SWCNTs, DWCNTs) and copper at scaled technology nodes in terms of delay, power, and power-delay product. The results emphasize that the study of mixed carbon nanotube bundled structures for interconnects shall be important and useful good-performance integrated chips at advanced nano regime nodes.