<p>A Copper-Carbon (Cu–Carbon) hybrid interconnect has been recently proposed for future VLSI applications, offering superior electrical performance compared to traditional interconnect structures. In the present era of high operating frequency, it is important to test this new structure for noise constrained applications specifically. In this work, ABCD parameter based analytical AC model of Cu–Carbon hybrid interconnects has been developed for efficient noise estimation in nanoscale systems. Several signal transmission parameters, noise parameters and frequency dependent complex conductivity and impedances of Cu–Carbon hybrid interconnects are estimated and compared with conventional copper (Cu) interconnects and emerging alternative copper-carbon nanotube (Cu-CNT) composite interconnects. The developed model is also verified with Advanced Design System (ADS) software. Cu–Carbon hybrid interconnects have the lowest impedance among other alternative configurations. Compared to copper, Cu–Carbon hybrid interconnect (with <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2024_81729_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(F_{cnt}\)</EquationSource> </InlineEquation>=0.6) possesses <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2024_81729_Article_IEq2.gif" Format="GIF" Height="6" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sim\)</EquationSource> </InlineEquation>80% lower impedance at 100 GHz frequency. Cu–Carbon hybrid experiences lowest return loss and highest forward transmission gain as compared to Cu and Cu-CNT composite interconnects. It demonstrates <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2024_81729_Article_IEq2.gif" Format="GIF" Height="6" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sim\)</EquationSource> </InlineEquation>43% and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2024_81729_Article_IEq2.gif" Format="GIF" Height="6" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sim\)</EquationSource> </InlineEquation>48% lower <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2024_81729_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(S_{11}\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2024_81729_Article_IEq2.gif" Format="GIF" Height="6" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sim\)</EquationSource> </InlineEquation>30% and <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2024_81729_Article_IEq2.gif" Format="GIF" Height="6" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sim\)</EquationSource> </InlineEquation>38% higher <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2024_81729_Article_IEq8.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(S_{21}\)</EquationSource> </InlineEquation> values than copper at 100 GHz for single and 2-line coupled interconnects, respectively. At lower frequencies, all interconnects have comparable crosstalk noise profiles. The percentage improvement in the noise figure (in dB) and noise factor of Cu–Carbon hybrid is <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2024_81729_Article_IEq2.gif" Format="GIF" Height="6" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sim\)</EquationSource> </InlineEquation>48% and <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2024_81729_Article_IEq2.gif" Format="GIF" Height="6" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sim\)</EquationSource> </InlineEquation>98% at 100 GHz, respectively as compared with Cu interconnect. These analysis strengthens the claim of Cu–Carbon hybrid interconnect to be a worthier possibility for high frequency noise constrained applications in next-generation nanoscale systems.</p>

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ABCD parameter based analytical AC modeling of novel Cu–carbon hybrid interconnects for noise constrained nanoscale systems

  • Bhawana Kumari,
  • Manodipan Sahoo,
  • Rohit Sharma

摘要

A Copper-Carbon (Cu–Carbon) hybrid interconnect has been recently proposed for future VLSI applications, offering superior electrical performance compared to traditional interconnect structures. In the present era of high operating frequency, it is important to test this new structure for noise constrained applications specifically. In this work, ABCD parameter based analytical AC model of Cu–Carbon hybrid interconnects has been developed for efficient noise estimation in nanoscale systems. Several signal transmission parameters, noise parameters and frequency dependent complex conductivity and impedances of Cu–Carbon hybrid interconnects are estimated and compared with conventional copper (Cu) interconnects and emerging alternative copper-carbon nanotube (Cu-CNT) composite interconnects. The developed model is also verified with Advanced Design System (ADS) software. Cu–Carbon hybrid interconnects have the lowest impedance among other alternative configurations. Compared to copper, Cu–Carbon hybrid interconnect (with \(F_{cnt}\) =0.6) possesses \(\sim\) 80% lower impedance at 100 GHz frequency. Cu–Carbon hybrid experiences lowest return loss and highest forward transmission gain as compared to Cu and Cu-CNT composite interconnects. It demonstrates \(\sim\) 43% and \(\sim\) 48% lower \(S_{11}\) and \(\sim\) 30% and \(\sim\) 38% higher \(S_{21}\) values than copper at 100 GHz for single and 2-line coupled interconnects, respectively. At lower frequencies, all interconnects have comparable crosstalk noise profiles. The percentage improvement in the noise figure (in dB) and noise factor of Cu–Carbon hybrid is \(\sim\) 48% and \(\sim\) 98% at 100 GHz, respectively as compared with Cu interconnect. These analysis strengthens the claim of Cu–Carbon hybrid interconnect to be a worthier possibility for high frequency noise constrained applications in next-generation nanoscale systems.