School of Mathematical Sciences
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
5th – 9th February 2012
ICONN 2012, Perth, Western Australia
Life Impact The University of Adelaide
Overview
• 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
2
Computer size and speed
3
Data storage
Floppy Disk
Punch Card
Magnetic Tape
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
4
Hard Disk
Interaction energy between
two molecules
• The non-bonded interaction energy is obtained by summing the
interaction potential energy for each atom pair
E  ( rij )
i
j
• In continuum models, the interaction energy is obtained by averaging
over the surface of each entity.

E  h1h2 
 (r)dS dS
1
2
where h1 and h2 are the mean atomic surface densities for each molecule,
and r is the distance between two surface elements dS1 and dS2 on two
different molecules.
Lennard-Jones Potential
(r) 
A
r
6

B
r12
 s 6 s 12
4e
 r
 
 r
 

     

e : well depth, s : van der Waals distance
rmin = s 21/6, min = -e
•
•
•
•
The repulsive term 1/r12, dominates at short distances,
The attractive term 1/r6, dominates at large distances (weak interaction),
Each atom-atom interaction is characterised by two Lennard Jones
constants, A=4es6 and B=4es12 determined experimentally, and using
empirical combining rules, e12=(e1e2)1/2, s12=(s1+s2)/2,
Force: F=-d/dr.
Lennard-Jones sphere-point
interaction
“Father of modern computational chemistry”
•
•
Mathematician who held a chair of
Theoretical Physics at Bristol University
(1925-32)
Proposed Lennard-Jones potential (1931)
A B

(r) 6  12
r r

A 1
1  

 
4
2
(rb) (rb)4 
hfb



)
f (r
r B 1
1 

 

10
10


5
(
r

b
)
(
r

b
)




(October 27, 1894 – November 1, 1954)
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
Nano memory device (1)
Changing State
External E field
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.
Nano memory device (1)
Metallofullerene (0, 0, Z)
Smaller Nanotube (rcosf, rsinf, z)
Larger Nanotube (Rcosf, Rsinf, z)
Distance for the center of the
metallofullerene and
Smaller Tube: rt2=r2+(Z-z)2
Larger Tube: rT2=R2+(Z-z)2
• E = Em-T1+Em-t+Em-T2 + Ef-T1+Ef-t+Ef-T2
• F = Fm-T1+Fm-t+Fm-T2 + Ff-T1+Ff-t+Ff-T2
Energy
Detail:
K+@C60
L1=20Å
r=6.093Å
R=6.766Å
Egap
Emin
State |0>
State |1>
Force
Fcritical
Detail:
K+@C60
L1=20Å
r=6.093Å
R=6.766Å
Fcritical
State |0>
State |1>
Nano memory device (2)
Changing State
External E field
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.
Ion
K+
FMg2+
Mg2+
Mg2+
ClClClClNa+
Na+
Na+
Li+
I-
r0(Å)
4.0010
2.495
0.7926
0.9929
1.0600
2.4192
4.40
4.05
4.45
3.33
2.43
2.58
2.224
4.286
Different Ion @C60 for nano
memory device (2)
e(meV)
3.0352
0.403
38.798
37.944
37.944
4.336
4.332
6.509
4.622
0.124
2a.031
0.643
13.429
10.149
l(Å)
7.23235
7.23482
7.23466
7.23454
7.23449
7.23422
7.23075
7.23093
7.23045
7.23478
7.23450
7.23472
7.23381
7.22895
Emin(eV)
-4.39478
-4.36394
-4.36577
-4.36724
-4.36783
-4.37120
-4.41539
-4.41263
-4.41925
-4.36449
-4.36787
-4.36524
-4.37614
-4.43797
l=L+r-Zmin
Egap(eV) Fcritical (eV/Å)
1.13255 0.46929
1.12464 0.46615
1.12517 0.46635
1.12556 0.46651
1.12572 0.46657
1.12655 0.46691
1.13776 0.47136
1.13713 0.47111
1.13873 0.47174
1.12477 0.46620
1.12568 0.46656
1.12498 0.46628
1.12787 0.46734
1.14357 0.47367
Mass(u)
39.102
19.00
24.31
24.31
24.31
35.453
35.453
35.453
35.453
22.990
22.990
22.990
6.941
126.90
Transfer time for nano memory
device (2)
Z min
m
dZ
tf 

2 Z min Fext  (Z  Z min )
4mZmin

Fext
Example:
K+@C60
2L=27Å, Fext=0.5eV/Å
tf=2.4933ps (1ps=10-12s)
State Switching Rate ~ 401Gbit/s
Nano logic gate
Input
Output
I1
I2 AND
OR NAND
NOR
T
T T
T
F
F
T
F F
T
T
F
F
T F
T
T
F
F
F F
F
T
T
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.
Nano logic gate
Maximum energy – Minimum energy < 0.011eV
I1 I2 Det AND O NAND NO
.
R
R
+ + O4
+
+
-
-
+ - O2
-
+
+
-
- + O3
-
+
+
-
- - O1
-
-
+
+
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.
Acknowledgement
• All colleagues in the Nanomechanics Group
• Australian Research Council
http://www.maths.adelaide.edu.au/nanomechanics/
20
Thank you!
http://www.maths.adelaide.edu.au/nanomechanics/
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.