Self-assembly using Ramanujan Graphs

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					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
                                       10

        Ti


                        Current (mA)
                                        5


                                        0


                                       -5


        Pt                      -10

                                            -2.0   -1.0   0.0     1.0
      Device =
Molecule + Electrodes                               Voltage (V)
       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-
                                                                                                                     RESET




                                                                                                                                                  RESTORE
                                                                                                                                                  & INVERT
                                                                                                                                         ENABLE
               MOLECULAR SWITCH LATCH: EXPT DATA




                                                                                                                                 SET 1
                                                                                                                                 SET 2
                                                                                                      2        C1
                                                   Clock /
                                                   control                                            1

                                                  C1    C2                                            0




                                                                                    Controls (V)
                                                                                                      -1
                                         SW1        SW2
                                                                                                      1
                       E                                                                                       C2
                                                                                                      0
            D                                                     Q
                                                                                                      -1
         Data                                                     Data
         input                                                    out                                 -2

                                                                                                     0.5

                                                                                                    0.25




                                                                                        Data (V)
                                                                                                       0
                     SW1                              200   SW2
               500                                                                                             Test 1
                                                                                                   -0.25
                                                                                                                     input +0.5V
Current (uA)




                                                      100                                           -0.5             out -0.46V

                0                                                                                   0.5        Test 2
                                                                                                                    input -0.5V
                                                       0                                           0.25             out +0.50V




                                                                                     Data (V)
          -500                                                                                        0
                                                     -100
                                                                                                   -0.25
                           -1         0       1              -1        0        1                   -0.5
                                Voltage (V)                       Voltage (V)
                                                                                                           0        2        4       6     8      10         12
                                                                                                                                  Time (s)
                     Expt: Latch works!

              0.5

              0.4    Trial 1            Signal restoration
              0.3    3
                                        Inversion, if desired
                                        >100mV operating margin
              0.2    5
Voltage (V)




              0.1

              0.0

              -0.1

              -0.2   6
                                        No nanoscale transistor!
              -0.3   4

              -0.4   2

              -0.5
                     Input     Output
                                          J. Appl. Phys. Feb 1, 2005
Random Demultiplexer
                                                                                                                                                                                                                                                                                                                                        VA                    VB                  VC


                                                                                                                                                                                                                                                                                                                                                                                         NAND
                                                                                                                                                                                                                                                                                                                                                                                            Output


                                     4


                                     3
                                             C20




                                             17                                                                  O
                                                                                                                                     HP crossbar switches & circuits
                                                                                                                                     7

                                                                                                                                     6

                                                                                                                                     5
                                                                                                                                     4
                                                                                                                                           ‘C2
                                                                                                                                                                                         -0.10




                                                                                                                                                                                         -0.12
                                                                                                                                                                                                                                                                                                                             R

                                                                                                                                                                                                                                                                                                                                   Driving
                                                                                                                                                                                                                                                                                                                                  Junction A
                                                                                                                                                                                                                                                                                                                                                         Driving
                                                                                                                                                                                                                                                                                                                                                        Junction B
                                                                                                                                                                                                                                                                                                                                                                            Receiving
                                                                                                                                                                                                                                                                                                                                                                            Junction C

                                                                                                                                                                                                                                                                                                                          Figure 1. A 1×3 array of inverting hysteretic resistor latches. This tiny
                      Current (mA)




                                     2        16                                                                         C           3
                                                                                                                                                                                         CH                                                                                                                               serial logic array is sufficient for implementation of a NAND gate.
                                                                                                                                           0’
                                                                                                             HO                          2
                                                                                                                                                                                           3
                                                                                                                                             1




                                                                                                                                                                           Current (A)
                                                                                                                                                                                                                                                                                                                                   16 k
                                     1
                                                                                                                                                                                         -0.14
                                     0              10
                                                                                                                     Al
                                                                                                              2
                                                                                                                     Ti
                                     -1                 9                                      10             1
                                                                                                                      LB                                            V
                                                                                                                                                                        C20_1 -0.16
                                                                                                                     5Pt 10
                                                                                                              0
                                                            8
                                                                                                                0                                     15

                                          -1.5      -1.0                                     -0.5     0.0       0.5 SiO2
                                                                                                                       1.0                            1.5
                                                                                                  Voltage (V)
                                                                                                                     Si
                                                                Current density (10 A/cm )




                                                                                                                                                                                         -0.18
                                                            2




                                                                                                0
                                                                                                                                                                                                                                            1 1.0 2
                                                            3




                                                                                                                                                                                                 -3       -2    -1     0
                                                                                                                                                                                                               Voltage (V)
                                                                                                                                                                        C20_2
100                                                                                                                                                                                                                                          0.5
                                            ( A · C) + B




                                                                                                                                                                                                                             Current (mA)
                                                                                             -10
                                                     10 July 2001                                                                                                                                                                              0
                                                     7 Jan 2004
                                                                                                                                                                        C20_3
                                                                                                                                                                                                                                             -0.5
                                                                                                                                                                                                                                                                                 1k                                                                   2005
Output Voltage (mV)




                                                                                             -20
                                                                                                                                                                                                 Pt

                                                                                                                                                                                                                                                                                                                                               (ITRS 2018)
                                                                                                                                                                                                                                             -1.0
                                                                                                                                                                                 TiAl                     TiAl
                                                                                                                                                                                                                                                      -0.5       0         0.5
                                                                                                                                                                                                                                                             Voltage (V)
                                                                                                                                                                                                 Pt
                                     VT
                                                                                                            -2                                   -1                   0                               1
                                                                                                                                                             Voltage (V)



                        0
                                                                                                                                                                                                                    64
                                                                                                                                                                                                                                                                                                   2004
                                            [000]

                                                    [100]

                                                                                   [010]

                                                                                                    [001]

                                                                                                                 [110]

                                                                                                                             [101]

                                                                                                                                         [011]

                                                                                                                                                  [111]

                                                                                                                                                            [000]




                                                                                  Boolean inputs [ A B C ]




                                                                                                                         1
                                                                                                                                                                                                                                                                                                0.5

                                                                                                                                                                                                                                                                                                0.4    Trial 1




                                                                                                                                                                                                                                                    2003
                                                                                                                                                                                                                                                                                                0.3    3

                                                                                                                                                                                                                                                                                                0.2    5
                                                                                                                                                                                                                                                                                  Voltage (V)




                                                                                                                                                                                                                                                                                                0.1

                                                                                                                                                                                                                                                                                                0.0

                                                                                                                                                                                                                                                                                                -0.1

                                                                                                                                                                                                                                                                                                -0.2   6




                                                                                                                             2002
                                                                                                                                                                                                                                                                                                -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

				
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posted:7/3/2012
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