Crosstalk analysis of carbon nanotube bundle interconnects
© Zhang et al; licensee Springer. 2012
Received: 28 November 2011
Accepted: 17 February 2012
Published: 17 February 2012
Carbon nanotube (CNT) has been considered as an ideal interconnect material for replacing copper for future nanoscale IC technology due to its outstanding current carrying capability, thermal conductivity, and mechanical robustness. In this paper, crosstalk problems for single-walled carbon nanotube (SWCNT) bundle interconnects are investigated; the interconnect parameters for SWCNT bundle are calculated first, and then the equivalent circuit has been developed to perform the crosstalk analysis. Based on the simulation results using SPICE simulator, the voltage of the crosstalk-induced glitch can be reduced by decreasing the line length, increasing the spacing between adjacent lines, or increasing the diameter of SWCNT.
Keywordsinterconnects carbon nanotube bundles simulation crosstalk
Due to electron scattering on copper wire surface and grain boundary, the resistivity of a copper wire will increase rapidly when the interconnect feature size becomes smaller than 45 nm . As a result, the time delay of the transmission signal will increase dramatically, which will restrict the circuit performance. Besides, as the integration density of interconnects increases, crosstalk issues will be the concerns. The crosstalk issue directly affects the circuit performance. To address the issues, carbon nanotube (CNT) interconnects have recently been proposed as ideal substitutes in future interconnect designs . CNT can be metallic or semiconducting , depending on their chiralities, and metallic CNTs are the preferred candidates for interconnect applications [4–6].
Although a few studies on the crosstalk noise of CNT-based interconnections have been reported [7, 8], the influencing factors are not fully understood. Crosstalk is the unexpected voltage noise interference due to the electromagnetic coupling of adjacent transmission lines when the signal propagates in the transmission lines. It is well known that crosstalk between interconnects may cause signal delay and glitch that may be propagated to the output of a receiver, which can cause a logic error at the output of the receiving device . Therefore, to understand the influencing factors which affect the crosstalk voltage of single-walled carbon nanotube (SWCNT) interconnects and how to decrease them are particularly important.
In this paper, the main factors affecting the crosstalk of SWCNT bundle interconnects were studied, including the influence of the SWCNTs position when their length is fixed, which was proposed for the first time. Firstly, we considered three coupled SWCNT interconnects to form a standard parallel wire architecture over a ground plane by calculating the coupling capacitances between adjacent interconnects; this model was then extended to the SWCNT bundle by calculating the corresponding parameters.
RLC equivalent circuit parameters of SWCNT
The resistance of a SWCNT contains imperfect contact resistance (RC) which is in the range of 0 to 120 KΩ, quantum resistance (RQ) (RQ = h/4e2, and scattering resistance (RS) per unit length (RS = h/(4e2·λCNT)), where h is Planck's constant, e is the charge of an electron, and λCNT is the mean free path length.
where D is the diameter, y is the distance away from a ground plane treating the CNT as a thin wire, and vF is the Fermi velocity.
For D = 1 nm and y = 1 μm, LM ≈ 1.5 pH/μm. Clearly, the magnetic inductance can be neglected.
Crosstalk modeling for CNT bundle interconnects
In practice, CNT bundles are closer to actual application than individual CNT. Here, the crosstalk modeling is being established.
where NH is the number of rows in the interconnect bundle, NW is the number of columns, and NCNT is the total number of CNTs. Since a SWCNT bundle consists of several individual SWCNT in parallel, the formulas of the resistance, inductance, and capacitance of a SWCNT bundle have been listed in previous papers .
Results and discussion
The crosstalk voltage in a SWCNT bundle depends on several factors, such as line length, the position when the length is fixed, spacing between SWCNTs, etc., which will be discussed using the RLC model, respectively. Simulations are performed using SPICE simulator.
The crosstalk problems of using SWCNT bundle as an interconnect candidate in the future design of integrated circuits have been explored in this paper. Equivalent distributed circuit parameter models of SWCNT bundle are obtained firstly, and then crosstalk issues about parallel SWCNT bundle interconnects are analyzed based on ITRS. The simulations show that significant reduction in crosstalk noise can be achieved by decreasing line length, setting the appropriate position when the length is fixed, increasing spacing between adjacent lines, increasing the diameter of SWCNT as well as selecting the appropriate frequency.
single-walled carbon nanotube.
This work is supported by the National Natural Science Foundation of China (grant no. 60806030), the Tianjin Natural Science Foundation (grant nos. 08JCYBJC14600 and 10SYSYJC27700), and the Tianjin Science and Technology Developmental Funds of Universities and Colleges (grant nos. ZD200709 and 20100703).
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