Stability Analysis of Carbon Nanotube Interconnects

Abstract

This paper deals with frequency and stability response of single wall carbon nanotube bundle (SWB) and multiwall carbon nanotube bundle (MWB) at global interconnect lengths. The performance of SWB and MWB interconnects are analyzed using driver-interconnect-load system. It is analyzed that MWB interconnects are more stable than SWB interconnects. It is illustrated that stability of both SWB and MWB interconnects increases with increase in interconnect length. The analytical model for stability and frequency response using ABCD matrix has been formulated. Using frequency response, it is observed that the bandwidth of SWB and MWB interconnects are 7.94 and 22.2 GHz respectively for an interconnect length of 500 µm. The results are verified using SPICE simulations. The time delay analysis has been performed for different interconnect lengths. Further, it is investigated that delay reduces with increasing number of shells in MWB interconnect.

Appendix

$$\left. {\begin{array}{*{20}l} {A = 1 + s\left[ {\frac{{R_{{esc}} C_{{esc}} \left( {px} \right)^{2} }}{2} + R_{d} C_{d} + C_{{esc}} \left( {px} \right)\left( {R_{{lump}} + R_{d} } \right)} \right] + s^{2} \left[ {\begin{array}{*{20}l} {\frac{{L_{{esc}} C_{{esc}} \left( {px} \right)^{2} }}{2} + \frac{{R_{{esc}}^{2} C_{{esc}}^{2} \left( {px} \right)^{4} }}{{24}}} \\ {\qquad + \frac{{R_{{esc}} R_{d} C_{{esc}} C_{d} \left( {px} \right)^{2} }}{2}} \\ \end{array} } \right.} \\ {\left. {\quad \quad \; + \frac{{R_{{esc}} C_{{esc}}^{2} \left( {px} \right)^{3} \left( {R_{{lump}} + R_{d} } \right)}}{6} + R_{{lump}} R_{d} C_{d} C_{{esc}} \left( {px} \right)} \right]} \\ \end{array} } \right\}$$

(A1)

$$\left. {\begin{array}{*{20}l} {B = \left( {2R_{lump} + R_{d} + R_{esc} \left( {px} \right)} \right) + s\left[ {\frac{{R_{esc} C_{esc} \left( {px} \right)^{2} }}{2}\left( {2R_{lump} + R_{d} } \right)} \right. + 2R_{lump} R_{d} C_{d} + \frac{{R_{esc} C_{esc} \left( {px} \right)^{3} }}{6}} \\ {\quad + L_{esc} \left( {px} \right)\,\left. { + R_{lump}^{2} C_{esc} \left( {px} \right) + R_{esc} R_{d} C_{d} \left( {px} \right) + R_{lump} R_{d} C_{esc} \left( {px} \right)} \right]} \\ {\quad + s^{2} \left[ {\left( {2R_{lump} + R_{d} } \right)\left( {\frac{{L_{esc} C_{esc} \left( {px} \right)^{2} }}{2} + \frac{{R_{esc}^{2} C_{esc}^{2} \left( {px} \right)^{4} }}{24}} \right)} \right. + R_{lump} R_{d} R_{esc} C_{esc} C_{d} \left( {px} \right)^{2} } \\ {\quad + \frac{{2R_{esc} L_{esc} C_{esc} \left( {px} \right)^{3} }}{6} + \frac{{R_{esc}^{3} C_{esc}^{2} \left( {px} \right)^{5} }}{120} + \frac{{R_{lump} \text{R}_{esc} C_{esc}^{2} \left( {px} \right)^{3} }}{6}} \\ {\quad + \left. {\frac{{R_{esc}^{2} R_{d} C_{d} C_{esc} \left( {px} \right)^{3} }}{6} + R_{d} C_{d} \left( {L_{esc} + R_{lump}^{2} C_{esc} } \right)\left( {px} \right)} \right]} \\ \end{array}} \right\}$$

(A2)