School of Mathematical Sciences Life Impact The University of Adelaide Nanocomputing memory Nanocomputing memory devices and logic gates devices and logic gates formed from carbon formed from carbon nanotubes and nanotubes and metallofullerenes metallofullerenes Nanomechanics Group, Nanomechanics Group, School of Mathematical Sciences, School of Mathematical Sciences, The University of Adelaide, The University of Adelaide, Adelaide, SA 5005, Australia Adelaide, SA 5005, Australia Richard K. F. Lee and James M. Hill 5 th – 9 th February 2012 ICONN 2012, Perth, Western Australia
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School of Mathematical Sciences Life Impact The University of Adelaide Nanocomputing memory devices and logic gates formed from carbon nanotubes and metallofullerenes.
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School of Mathematical Sciences
Life Impact The University of Adelaide
Nanocomputing memory Nanocomputing memory devices and logic gates formed devices and logic gates formed
from carbon nanotubes and from carbon nanotubes and metallofullerenesmetallofullerenes
Nanomechanics Group, Nanomechanics Group,
School of Mathematical Sciences, School of Mathematical Sciences,
The University of Adelaide,The University of Adelaide,
Adelaide, SA 5005, AustraliaAdelaide, SA 5005, AustraliaRichard K. F. Lee and James M. Hill
5th – 9th February 2012ICONN 2012, Perth, Western Australia
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
Computer size and speed
3
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=1024GB1GB=1024MB1MB=1024KB1KB=1024B
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 dS1 and dS2 on two different molecules.
€
E = Φ(ρ ij )j
∑i
∑
€
E = η1η2 Φ(ρ )dS1dS2∫∫
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=46 and B=412 determined experimentally, and using empirical combining rules, 12=(12)1/2, 12=(1+2)/2,
• Force: F=-d/d
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛−=
+−=
126
126
4
)(
ρ
σ
ρ
σε
ρρρ
BA
: well depth, : van der Waals distance
min = 21/6, min = -
• 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
€
(ρ) = −A
ρ 6 +B
ρ12
Φ f (ρ) =η f πb
ρ
A
2
1
(ρ + b)4 −1
(ρ − b)4
⎡
⎣ ⎢ ⎤
⎦ ⎥
−B
5
1
(ρ + b)10 −1
(ρ − b)10
⎡
⎣ ⎢ ⎤
⎦ ⎥
⎧
⎨ ⎪ ⎪
⎩ ⎪ ⎪
⎫
⎬ ⎪ ⎪
⎭ ⎪ ⎪
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)
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.
Nano memory device (1)
Metallofullerene (0, 0, Z)
Smaller Nanotube (rcos, rsin, z)
Larger Nanotube (Rcos, Rsin, z)
Distance for the center of the metallofullerene and
Smaller Tube: t2=r2+(Z-z)2
Larger Tube: T2=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
Egap
Emin
State |0> State |1>
Detail:
K+@C60
L1=20År=6.093ÅR=6.766Å
Force
Fcritical
Fcritical
State |0> State |1>
Detail:
K+@C60
L1=20År=6.093ÅR=6.766Å
Nano memory device (2)
External E fieldChanging 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.
Different Ion @C60 for nano memory device (2)
Ion 0(Å) (meV) (Å) Emin(eV) Egap(eV) Fcritical (eV/Å) Mass(u)