FAB2

MAS 960 Special Topics:How To Make Something That Makes (almost) Anything

jacobson@media.mit.edu

1.Air inlets 2.Crushers 3.Ganglion 4.Multiple Visual sensors 5.Muscles 6.Pincers 7.Sensory receptors 8.Stridulatory pegs 9.Wings

Avogadro Scale Engineering~Achieving the Limits of Fabricational Complexity~

Simple molecules<1nm

IBM PowerPC 750TM Microprocessor

7.56mm×8.799mm6.35×106 transistors

Semiconductor Nanocrystal~1 nm

10-10 10-510-9 10-7 10-610-8 10-4 10-3 10-2

m

Circuit designCopper wiringwidth 0.1m

red blood cell~5 m (SEM)DNA

proteins nm

bacteria1 m

Nanotube Transistor(Dekker)

Complexity vs. Size

SOI transistorwidth 0.12m

diatom30 m

• Error Correcting Fabrication • Fault Tolerant Hardware Architectures • Fault Tolerant Software or Codes • Quantum Phase Space

Resources which increase the complexity of a system exponentially with a linear addition of

resources

Resources for Exponential Scaling

n MAJ

p

p

p

MAJMAJ

p

p

p

MAJ

p

p

p

k

Threshold Theorem - Winograd and Cowan 1963

A circuit containing N error-free gates can be simulated with probability of failure ε using O(N poly(log(⋅ N/ε))) error-prone gates which fail with probability p, provided p < pth, where pth is a constant threshold independent of N.

Number of gates consumed: k3

Find k such that NpPkk

k /3 212

2ln

ln3ln)/ln(2ln

ln

~

pN

k

)/ln(~3 NPolyk Number of Gates ConsumedPer Perfect Gate is

Caruthers Synthesis

DNA Synthesis

http://www.med.upenn.edu/naf/services/catalog99.pdf

Error Rate:1: 102

300 SecondsPer step

http://www.biochem.ucl.ac.uk/bsm/xtal/teach/repl/klenow.html

1. Beese et al. (1993), Science, 260, 352-355.

Replicate Linearly with Proofreading and Error Correction

Fold to 3D Functionality

template dependant 5'-3' primer extension

5'-3' error-correcting exonuclease

3'-5' proofreading exonuclease

Error Rate:1: 106

100 Steps per second

Fabricational Complexity

Ffab = ln (W) / [ a3 fab Efab ]

Ffab = ln (M)-1 / [ a3 fab Efab ]

•Total Complexity•Complexity Per Unit Volume•Complexity Per Unit Time*Energy•Complexity Per unit Cost

…Can we use this map as a guide towards future

directions in fabrication?

Genome (Natural)

Gene Chip (Chemical Parallel Synthesis)

Semi-conductor Chip

High Speed Offset Web TFT DVD-6

Liquid Embossing

Design Rule Smallest Dimension (microns) 0.0003 0.0003 0.1 10 2 0.25 0.2Number of Types of Elements 4 4 8 6 8 2 4Area of SOA Artifact (Sq. Microns) NA 7.E+08 7.E+10 2.E+12 1.E+12 1.E+10 8.E+09Volume of SOA Artifact (Cubic Microns) 6.E+01 5.E+06 7.E+09 2.E+12 1.E+11 7.E+12 8.E+08Number of Elements in SOA Artifact 3.E+09 7.E+04 7.E+12 2.E+10 3.E+11 2.E+11 2.E+11Volume Per Element(Cubic Microns) 2.E-08 8.E+01 1.E-03 1.E+02 4.E-01 4.E+01 4.E-03Fabrication Time(seconds) 4.E+03 2.E+04 9.E+04 1.E-01 7.E+02 3 6.E+01Time Per Element (Seconds) 1.E-06 3.E+02 1.E-08 7.E-12 2.E-09 2.E-11 3.E-10Fabrication Cost for SOA Artifact($) 1.E-07 1.E+02 1.E+02 1.E-01 2.E+03 3.E-02 2.E-01Cost Per Element 3.E-17 2.E-03 2.E-11 6.E-12 6.E-09 2.E-13 1.E-12Complexity 4.E+09 9.E+04 2.E+13 4.E+10 6.E+11 1.E+11 3.E+11Complexity Per Unit Volume of SOA(um 3̂) 7.E+07 2.E-02 2.E+03 2.E-02 5.E+00 2.E-02 3.E+02Complexity Per Unit Time 1.E+06 6.E+00 2.E+08 3.E+11 9.E+08 4.E+10 5.E+09Complexity Per Unit Cost 4.E+16 9.E+02 1.E+11 3.E+11 3.E+08 4.E+12 1.E+12Cost Per Area NA 2.E-07 2.E-09 6.E-14 2.E-09 3.E-12 3.E-11

Fabricational Complexity

Fabricational Complexity

n

n

nFAB mpF ln

1

200 400 600 800 1000

10

20

30

40

50

60

70

A

A G

G T C

A T A C G T …

A G T A G C …

p2p3p

Total Complexity:

Complexity Per Unit Cost:For given complexity n*:

Cmpf nFAB /ln

*

Where C is cost per step

Cmpf nFAB /ln

*

Fabricational Complexity

Non Error Correcting:

Triply Error Correcting:

Cmpppfn

FAB 3/ln)1(3*332

3

A G T C

A G T C

A G T C

A G T C

50 100 150 200 250 300

20

40

60

80

100

120

140

P = 0.9

n

FAB

FAB

f

f 3

p

0.86 0.88 0.92 0.94 0.96 0.98

500

1000

1500

2000

2500

3000

n = 300

50 100 150 200

0.05

0.1

0.15

0.2

0.25

0.3

FAB

FAB

f

f 3

n

P = 0.85

http://www.ornl.gov/hgmis/publicat/microbial/image3.html

[Nature Biotechnology 18, 85-90 (January 2000)]

Uniformed Services University of the Health

Deinococcus radiodurans (3.2 Mb, 4-10 Copies of Genome )

D. radiodurans: 1.7 Million Rads (17kGy) – 200 DS breaksE. coli: 25 Thousand Rads – 2 or 3 DS breaks

D. radiodurans 1.75 million rads, 24 h

D. radiodurans 1.75 million rads, 0 h

photos provided by David Schwartz (University of Wisconsin, Madison)]

Autonomous self replicating machines from random building blocks

http://alumni.media.mit.edu/~saul/PhD/videos/xtalcontrol1web.mov

Caruthers Synthesis

DNA Synthesis

http://www.med.upenn.edu/naf/services/catalog99.pdf

Error Rate:1: 102

300 SecondsPer step

http://www.biochem.ucl.ac.uk/bsm/xtal/teach/repl/klenow.html

1. Beese et al. (1993), Science, 260, 352-355.

Replicate Linearly with Proofreading and Error Correction

Fold to 3D Functionality

template dependant 5'-3' primer extension

5'-3' error-correcting exonuclease

3'-5' proofreading exonuclease

Error Rate:1: 106

100 Steps per second

Fabrication Procedure of LTPS-TFT Array for AMOLED Backplane

http://www.sdtech.co.kr/device3.html

Laser CVD Repair

http://www.sfk.com/en/packaging/pick__place/