1. School of Mathematical Sciences Life Impact The University of Adelaide Nanocomputing memory devices and logic gates formed from carbon nanotubes and metallofullerenes Nanomechanics Group, School of Mathematical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia Richard K. F. Lee and James M. Hill 5 th – 9 th February 2012 ICONN 2012, Perth, Western Australia

2. Overview 2 Trends in computer requirements: –Smaller in size, –Faster processing, –Increased data capacity. Nano memory devices and logic gates: –Continuous approximation, –Lennard-Jones potential, –Memory devices and logic gates. Conclusion

3. Computer size and speed 3

4. Data storage 4 Punch Card Magnetic Tape Floppy Disk Hard Disk Media (Data Size): Floppy Disk (360KB ~ 1.44MB) ZIP Disk (100MB ~ 750MB) CD/DVD/Blue-Ray (640MB ~ 50GB) Hard Disk (30MB ~ 3TB) 1TB=1024GB 1GB=1024MB 1MB=1024KB 1KB=1024B

5. Interaction energy between two molecules The non-bonded interaction energy is obtained by summing the interaction potential energy for each atom pair In continuum models, the interaction energy is obtained by averaging over the surface of each entity. where  1 and  2 are the mean atomic surface densities for each molecule, and  is the distance between two surface elements dS 1 and dS 2 on two different molecules.

6. Lennard-Jones Potential The repulsive term 1/  12, dominates at short distances, The attractive term 1/  6, dominates at large distances (weak interaction), Each atom-atom interaction is characterised by two Lennard Jones constants, A=4  6 and B=4  12 determined experimentally, and using empirical combining rules,  12 =(  1  2 ) 1/2,  12 =(  1 +  2 )/2, Force: F=-d  /d   : well depth,  : van der Waals distance  min =  2 1/6,  min = - 

7. Mathematician who held a chair of Theoretical Physics at Bristol University (1925-32) Proposed Lennard-Jones potential (1931) (October 27, 1894 – November 1, 1954) “Father of modern computational chemistry” Lennard-Jones sphere-point interaction

8. Nano memory devices (1) (2) Large energy gap (~7eV) Small energy gap (~1.1eV) (2) Originally proposed by Y-K Kwon, D Tománek and S Iijima (1999) using MD Simulations

9. Nano memory device (1) External E field Changing State Y. Chan, R. K. F. Lee, and J. M. Hill, “Metallofullerenes in composite carbon nanotubes as a nanocomputing memory device”, IEEE Transactions on Nanotechnology, 10 (2011) 947-952.

10. Nano memory device (1) Metallofullerene (0, 0, Z) Smaller Nanotube (r cos , r sin , z) Larger Nanotube (R cos , R sin , z) Distance for the center of the metallofullerene and Smaller Tube:  t 2 =r 2 +(Z-z) 2 Larger Tube:  T 2 =R 2 +(Z-z) 2 E = E m-T1 +E m-t +E m-T2 + E f-T1 +E f-t +E f-T2 F = F m-T1 +F m-t +F m-T2 + F f-T1 +F f-t +F f-T2

11. Energy E gap E min State |0>State |1> Detail: K + @C 60 L 1 =20Å r=6.093Å R=6.766Å

12. Force F critical State |0>State |1> Detail: K + @C 60 L 1 =20Å r=6.093Å R=6.766Å

13. Nano memory device (2) External E field Changing State R. K. F. Lee, and J. M. Hill, “Design of a two-state shuttle memory device”, CMC: Computers, Materials and Continua, 20 (2010) 85-100.

14. Different Ion @C 60 for nano memory device (2) Ion  0 (Å)  (meV) (Å) E min (eV) E gap (eV) F critical (eV/Å) Mass(u) K + 4.0010 3.0352 7.23235 -4.39478 1.13255 0.4692939.102 F - 2.495 0.403 7.23482 -4.36394 1.12464 0.4661519.00 Mg 2+ 0.7926 38.798 7.23466 -4.36577 1.12517 0.4663524.31 Mg 2+ 0.9929 37.944 7.23454 -4.36724 1.12556 0.4665124.31 Mg 2+ 1.0600 37.944 7.23449 -4.36783 1.12572 0.4665724.31 Cl - 2.4192 4.336 7.23422 -4.37120 1.12655 0.4669135.453 Cl - 4.40 4.332 7.23075 -4.41539 1.13776 0.4713635.453 Cl - 4.05 6.509 7.23093 -4.41263 1.13713 0.4711135.453 Cl - 4.45 4.622 7.23045 -4.41925 1.13873 0.4717435.453 Na + 3.33 0.124 7.23478 -4.36449 1.12477 0.4662022.990 Na + 2.43 2a.031 7.23450 -4.36787 1.12568 0.4665622.990 Na + 2.58 0.643 7.23472 -4.36524 1.12498 0.4662822.990 Li + 2.224 13.429 7.23381 -4.37614 1.12787 0.467346.941 I - 4.286 10.149 7.22895 -4.43797 1.14357 0.47367126.90 =L+r-Z min

15. Transfer time for nano memory device (2) Example: K + @C 60 2L=27Å, F ext =0.5eV/Å t f =2.4933ps (1ps=10 -12 s) State Switching Rate ~ 401Gbit/s

16. Nano logic gate InputOutput I1I1 I2I2 ANDORNANDNOR TTTTFF TFFTTF FTFTTF FFFFTT T = TRUE F = FALSE R. K. F. Lee, and J. M. Hill, “Design of a nanotori-metallofullerene logic gate”, (2011), submitted to IEEE Transactions on Computers.

17. Nano logic gate Maximum energy – Minimum energy < 0.011eV

18. I1I1 I2I2 Det. ANDOROR NANDNO R ++ O4O4 ++-- +- O2O2 -++- -+ O3O3 -++- -- O1O1 --++

19. Conclusion Memory devices and logic gates: –Nano size, –Electrical field control. For a fast state switching rate / time: –Light Ion, –Large external force, –Short nanotube length, –Around 400 Gbit/s.

20. 20 Acknowledgement All colleagues in the Nanomechanics Group Australian Research Council http://www.maths.adelaide.edu.au/nanomechanics/

21. Thank you! http://www.maths.adelaide.edu.au/nanomechanics/

22. References G. E. Moore, Technical Digest International Electron Devices Meeting, 21 (1975) 11-13. B. J. Cox, N. Thamwattana and J. M. Hill, Proceedings of The Royal Society A, 463 (2007) 461-476. B. J. Cox, N. Thamwattana and J. M. Hill, Proceedings of The Royal Society A, 463 (2007) 477-494. Y. Chan, R. K. F. Lee and J. M. Hill, IEEE Transactions on Nanotechnology, 10 (2011) 947-952. R. K. F. Lee and J. M. Hill, CMC: Computers, Materials and Continua, 20 (2010) 85-100. R. K. F. Lee and J. M. Hill, “Design of a nanotori-metallofullerene logic gate”, (2011), submitted to IEEE Transactions on Computers.