Impact of Bundle Structure on Performance of on-Chip CNT Interconnects

Table 2

Propagation delay of various interconnects for the year 2022.

Comparison chart of propagation delay of copper versus bundled CNT interconnects as per the dimensions predicted for the year 2022; (width × height of the interconnect = 11 nm × 22 nm)
Length of the interconnect	Delay of copper (ps)	Propagation delay of various bundles interconnect geometries (ps)
		Sparsely packed bundles of CNTS	Densely packed bundles CNTs
		Randomly mixed bundles	Segregated bundles; 𝛿^#=0				Proportionately mixed bundles (all the samples of segregated bundles are mixed in equal ratio)
		𝑝=1; 𝛿=1.25; 𝐷avg=1.5; 𝐷min/𝐷max=0.35	SWCNT best 𝑝=1; 𝐷=1	SWCNT worst 𝑝=1; 𝐷=7	MWCNT best; 𝑝=1; 𝐷max 3 𝐷min 1.3 𝐷min/𝐷max=0.43	MWCNT worst; 𝑝=1; 𝐷max 7 𝐷min 6.66; 𝐷min/𝐷max=0.95	Case 1*	Case 2**	Case 3***	Case 4****
10 nm	1.14E − 1	3.39E − 4	1.13E − 5	2.47E − 3	1.15E − 04	2.47E − 3	8.83E − 4	1.14E − 3	2.85E − 4	1.50E − 3
100 nm	1.14E + 0	3.39E − 3	1.13E − 4	2.47E − 2	1.15E − 03	2.47E − 2	8.83E − 3	1.14E − 2	2.85E − 3	1.50E − 2
1 𝜇m	1.14E + 1	3.76E − 2	1.27E − 3	2.47E − 1	1.15E − 02	2.47E − 1	8.84E − 2	1.14E − 1	2.86E − 2	1.51E − 1
10 𝜇m	1.14E + 2	2.13E + 0	1.27E − 1	3.97E + 0	7.18E − 01	4.07E + 0	1.6E + 0	2.24E + 0	8.86E − 1	2.77E + 0

Case 1*: a mix segregated SWCNTs with varying diameters (𝐷=1 nm, 3 nm, and 7 nm).
Case 2**: a mix of segregated MWCNT bundles with varying 𝐷_min/𝐷_max ratio from smallest to largest.
𝐷_max 7 nm 𝐷_min 1.22 nm (𝐷_min/𝐷_max=0.17), 𝐷_max 3 nm 𝐷_min 1.3 nm (𝐷_min/𝐷_max=0.43),  𝐷_max 7 nm 𝐷_min 6.32 nm (𝐷_min/𝐷_max=0.9).
Case 3***: a mix of segregated SWCNTs with lowest diameters (1 nm and 3 nm) and segregated MWCNT bundles with lowest 𝐷_min/𝐷_max ratio—(𝐷_max 7 nm 𝐷_min 1.22 nm (𝐷_min/𝐷_max=0.17), 𝐷_max 5 nm 𝐷_min 1.26 nm (𝐷_min/𝐷_max=0.25)).
Case 4****: a mix of segregated SWCNTs with largest diameters (7 nm and 5 nm) and segregated MWCNT bundles with largest 𝐷_min/𝐷_max ratio—𝐷_max 7 nm 𝐷_min 6.32 nm (𝐷_min/𝐷_max=0.9), 𝐷_max 5 nm 𝐷_min 4.32 nm (𝐷_min/𝐷_max=0.86).
^#Standard deviation of tube diameter variations in a bundle.