Transcript Self-assembly using Ramanujan Graphs

Nanoscale Self-Assembly
A Computational View
Philip Kuekes
Quantum Science Research
HP Labs
What’s Cooking?
Everybody likes Recipes
Two Challenges for Nanoelectronics
•Invent a new switching device
•Develop a new fabrication process
Examine Architecture First
HPL Teramac
multi-architecture computer
•
106 gates operating
at 106 cycle/sec
•
100 times workstation
performance
•
Largest defect-tolerant
computer ever built
•
220,000 (3%) defective
components
Defect Theology
• Original Sin
• Redemption Through Good Works
• Guilt by Association
Redundant Testing
PASS
PASS
PASS
FAIL
PASS
PASS
FAIL
PASS PASS
PASS
Defect Tolerance for Free
• CMOS Technology –
Configuration bit >20 x wire crossing area
• Molecular Technology –
Configuration bit smaller than wire crossing
Teramac Crossbar Architecture
Memory
0
Switch
Teramac crossbar
Rotaxane Molecular Switch
-Prof. Fraser Stoddart, UCLA
4PF6-
+
N
N
+
N
N+
N
+
CH2OH
C.P. Collier, E.W. Wong et al.
Experimental Realization of a
Molecular-Tunneling Switch
Ti
Pt
Device =
Molecule + Electrodes
Current (mA)
10
5
0
-5
-10
-2.0
-1.0
0.0
Voltage (V)
1.0
Moletronics Architecture
•
•
•
•
Wires
Memories
Logic
Integrated Circuits
Crossbar at 17 nm half-pitch
width
Smallest virus 30-42 nm
hepatitis B
Parallel ErSi2 wires grown by self-assembly
2 nm width with a nine nanometer separation
Logic Array Design
U
V
W
X
Y
Z
a
b
c
d
e
f
Y = (U AND V) OR (W AND X)
Z = V+ C = V-
RESTORE
& INVERT
ENABLE
1
Controls (V)
SW1
C1
2
Clock /
control
C1
C2
SET 1
SET 2
RESET
MOLECULAR SWITCH LATCH: EXPT DATA
SW2
E
0
-1
1
C2
0
D
Data
input
Q
Data
out
-1
-2
200
SW1
Data (V)
0.5
SW2
0
Test 1
input +0.5V
out -0.46V
-0.25
100
-0.5
Test 2
input -0.5V
out +0.50V
0.5
0
0
Data (V)
Current (uA)
500
0.25
-500
-100
-1
0
Voltage (V)
1
0.25
0
-0.25
-1
0
Voltage (V)
1
-0.5
0
2
4
6
8
Time (s)
10
12
Expt: Latch works!
Voltage (V)
0.5
0.4
Trial 1
0.3
3
0.2
5
Signal restoration
Inversion, if desired
>100mV operating margin
0.1
0.0
-0.1
-0.2
6
-0.3
4
-0.4
2
No nanoscale transistor!
-0.5
Input
Output
J. Appl. Phys. Feb 1, 2005
Random Demultiplexer
VA
VB
VC
NAND
HP crossbar switches & circuits
Output
R
C20
7
4
4
C
3
‘C2
0’
1
1
10
9
-1
8
-1.0
-0.14
C20_1 -0.16
15
1.5
-0.18
0
-3
-2
1 1.0 2
-1
0
Voltage (V)
C20_2
0.5
Current (mA)
( A · C) + B
-10
10 July 2001
7 Jan 2004
0
1k
C20_3
Output Voltage (mV)
-0.5
Pt
-20
TiAl
TiAl
-0.5
0
Voltage (V)
[000]
[011]
[101]
-1
[110]
[001]
[010]
[100]
[000]
-2
[111]
VT
2005
-1.0
0
(ITRS 2018)
0.5
Voltage (V)
Pt
0
Receiving
Junction C
16 k
V
3
2
Current density (10 A/cm )
-1.5
Al
2
Ti
10
1
LB
0
0
5Pt 10
-0.5
0.0
0.5 SiO
1.0
2
Voltage (V)
Si
CH
3
1
64
2004
Boolean inputs [ A B C ]
0.5
1
2003
Voltage (V)
0
Driving
Junction B
Figure 1. A 1×3 array of inverting hysteretic resistor latches. This tiny
serial logic array is sufficient for implementation of a NAND gate.
-0.12
2
Current (A)
Current (mA)
O
17
16
HO
100
Driving
Junction A
5
3
2
-0.10
6
0.4
Trial 1
0.3
3
0.2
5
0.1
0.0
-0.1
2002
-0.2
6
-0.3
4
-0.4
2
-0.5
Input
Output
How does a Molecular
Computer
Grow Up?
• Conventional Computer
Teacher
• Low Bandwidth Link
• Initially Stupid Molecular
Student
I Get By With A Little Help
From My Friends
• Tutors
• Doctors
Complexity
• Self Assembly &
Thermodynamics
• Arbitrary Graphs
Tradeoffs
• Cost of doing the chemistry
• Cost of doing the computing
The Pure and the Grubby
The Math
- Expanders
- Cayley Graphs
- Ramanujan Graphs
Today
• Physical Scientists can only do very simple
self-assembly
• Mathematicians can create interesting
complex structures with very simple
generators
The new capability
• Combine the simple physical processes with
the mathematical constructions
• Nanoscale self-assembled systems with
enough complexity to do useful
computation.
The Physics
•
•
•
•
•
Self-Assembled DNA Nanostructures
Self-Assembled Surface Chemistry
Viral Self-Assembly
Molecular Electronic Circuit Assembly
DNA-linked Nano-particle Structures
The Math
Advantages of Simple
Construction
•
•
•
•
amenable to self-assembly
short explicit description
highly-connected
sparse
Physical Structures
Not Just Abstract Graphs
• defect-tolerance
• efficiently embedded in three-dimensional
space
• relatively short edge-lengths.
Algorithmic Manufacturing
•Local rules
•Global structure
Feedback and the Way Forward
•Computer Code
•Biology
• Chemistry, Physics, Materials Science
Feedback and the Way Forward
•Computer Code
•Biology
• Chemistry, Physics, Materials Science
Reaction Diffusion
Stealing from Biology
DNA and Proteins
versus Cells
Logic Design as Geometry
Spatial Structure
Controlled diffusion
Compartments as wires
Organelles
Garbage Collection
Ubiquitin
Apoptosis
Mass transport
The Best of Both Worlds
Self-assembly
Adaptive External
Programming
Self-disassembly
Tradeoffs
• Cost of doing the chemistry
• Cost of doing the computing