A routing algorithm for graphene nanoribbon circuit

Conventional CMOS devices are facing an increasing number of challenges as their feature sizes scale down. Graphene nanoribbon (GNR) based devices are shown to be a promising replacement of traditional CMOS at future technology nodes. However, all previous works on GNRs focus at the device level. In order to integrate these devices into electronic systems, routing becomes a key issue. In this article, the GNR routing problem is studied for the first time. We formulate the GNR routing problem as a minimum hybrid-cost shortest path problem on triangular mesh (“hybrid” means that we need to consider both the length and the bending of the routing path). We show that by graph expansion, this minimum hybrid-cost shortest path problem can be solved by applying the conventional shortest path algorithm on the expanded graph. Experimental results show that our GNR routing algorithm effectively handles the hybrid cost.

[1]  S. Xiao,et al.  Intrinsic and extrinsic performance limits of graphene devices on SiO2. , 2007, Nature nanotechnology.

[2]  Michael B. Henry,et al.  SPICE-compatible compact model for graphene field-effect transistors , 2012, 2012 IEEE International Symposium on Circuits and Systems.

[3]  Kai Chang,et al.  Resonant tunneling through S- and U-shaped graphene nanoribbons , 2009, Nanotechnology.

[4]  Martin D. F. Wong,et al.  Archer: a history-driven global routing algorithm , 2007, 2007 IEEE/ACM International Conference on Computer-Aided Design.

[5]  Kun Yuan,et al.  BoxRouter 2.0: architecture and implementation of a hybrid and robust global router , 2007, 2007 IEEE/ACM International Conference on Computer-Aided Design.

[6]  Ting-Chi Wang,et al.  NTHU-Route 2.0: A fast and stable global router , 2008, 2008 IEEE/ACM International Conference on Computer-Aided Design.

[7]  Ta-Wei Wang,et al.  NTHU-Route 2.0: a fast and stable global router , 2008, ICCAD 2008.

[8]  P. Srivastava,et al.  Band Gap Engineering in Zigzag Graphene Nanoribbons—An Ab Initio Approach , 2012 .

[9]  Jarrod A. Roy,et al.  High-performance routing at the nanometer scale , 2007, 2007 IEEE/ACM International Conference on Computer-Aided Design.

[10]  G. Fiori,et al.  Strong mobility degradation in ideal graphene nanoribbons due to phonon scattering , 2011, 1103.0295.

[11]  Carl Ebeling,et al.  PathFinder: A Negotiation-Based Performance-Driven Router for FPGAs , 1995, Third International ACM Symposium on Field-Programmable Gate Arrays.

[12]  Bing-Lin Gu,et al.  Intrinsic current-voltage characteristics of graphene nanoribbon transistors and effect of edge doping. , 2007, Nano letters.

[13]  Fujita,et al.  Edge state in graphene ribbons: Nanometer size effect and edge shape dependence. , 1996, Physical review. B, Condensed matter.

[14]  W. Duan,et al.  Towards graphene nanoribbon-based electronics , 2009, 1002.4461.

[15]  M. Fuhrer,et al.  Extraordinary Mobility in Semiconducting Carbon Nanotubes , 2004 .

[16]  Yao-Wen Chang,et al.  Multi-layer global routing considering via and wire capacities , 2008, 2008 IEEE/ACM International Conference on Computer-Aided Design.

[17]  C. T. White,et al.  Building blocks for integrated graphene circuits. , 2007, Nano letters.

[18]  Hassan Raza,et al.  Zigzag graphene nanoribbons: bandgap and midgap state modulation , 2011, Journal of physics. Condensed matter : an Institute of Physics journal.

[19]  Giuseppe Iannaccone,et al.  A SPICE-compatible model of Graphene Nano-Ribbon Field-Effect Transistors enabling circuit-level delay and power analysis under process variation , 2013, 2013 Design, Automation & Test in Europe Conference & Exhibition (DATE).

[20]  K. Jenkins,et al.  Operation of graphene transistors at gigahertz frequencies. , 2008, Nano letters.

[21]  Martin D. F. Wong,et al.  A negotiated congestion based router for simultaneous escape routing , 2010, 2010 11th International Symposium on Quality Electronic Design (ISQED).

[22]  Martin D. F. Wong,et al.  Routing with graphene nanoribbons , 2011, 16th Asia and South Pacific Design Automation Conference (ASP-DAC 2011).

[23]  Kaustav Banerjee,et al.  Carbon Nanomaterials: The Ideal Interconnect Technology for Next-Generation ICs , 2010, IEEE Design & Test of Computers.

[24]  SUPARNA DUTTASINHA,et al.  Graphene: Status and Prospects , 2009, Science.

[25]  C. Xu,et al.  Modeling, Analysis, and Design of Graphene Nano-Ribbon Interconnects , 2009, IEEE Transactions on Electron Devices.

[26]  T. Ragheb,et al.  On the modeling of resistance in graphene nanoribbon (GNR) for future interconnect applications , 2008, ICCAD 2008.

[27]  T. Ragheb,et al.  On the modeling of resistance in graphene nanoribbon (GNR) for future interconnect applications , 2008, 2008 IEEE/ACM International Conference on Computer-Aided Design.

[28]  Transfer-free fabrication of graphene transistors , 2011, 1112.4320.

[29]  S. Xiao,et al.  Intrinsic and extrinsic performance limits of graphene devices on SiO 2 , 2008 .

[30]  J. Lyding,et al.  The influence of edge structure on the electronic properties of graphene quantum dots and nanoribbons. , 2009, Nature materials.

[31]  C. Xu,et al.  Carbon Nanomaterials for Next-Generation Interconnects and Passives: Physics, Status, and Prospects , 2009, IEEE Transactions on Electron Devices.

[32]  S. Louie,et al.  Energy gaps in graphene nanoribbons. , 2006, Physical Review Letters.

[33]  Jarrod A. Roy,et al.  High-Performance Routing at the Nanometer Scale , 2008, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[34]  Jiwoong Park,et al.  Transfer-free batch fabrication of single layer graphene transistors. , 2009, Nano letters.