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Itanium Quad TukwilaTransistor Count: 2BCost: ~$50
Si Wafer with Area sufficient for2 Billion TransistorsCost: ~$0.50
Flash MemoryTransistor Count: 2BCost: ~$3
SmartPhoneCost: ~$200
Sand (Chips and Screen)Cost: ~$0
Plastic Resin / Metal OreCost: ~$4
What Drives The Cost of Placing Atoms Where We Want Them? What are The Fundamental Limits?
Fabricational Complexity
Fabricational Complexity Per Unit Cost
MpF N ln
N BLOCKS
Fabricational Complexity for N Blocks or M Types = NMln
Fabricational Cost for N Blocks = NNp
Where is the Yield Per Fabricational Step p
Complexity Per Unit CostComplexity Per Unit Time*Energy
A G C T
T C T G
C A C G
A
G
C
T
Genome (Natural)
Chemical Synthesis
Semi-conductor Chip
High Speed Offset Web TFT DVD-6
Liquid Embossing
Design Rule Smallest Dimension (microns) 0.0003 0.0003 0.1 10 2 0.25 0.2Number of Types of Elements 4 4 8 6 8 2 4Area of SOA Artifact (Sq. Microns) NA 7.E+08 7.E+10 2.E+12 1.E+12 1.E+10 8.E+09Volume of SOA Artifact (Cubic Microns) 6.E+01 5.E+06 7.E+09 2.E+12 1.E+11 7.E+12 8.E+08Number of Elements in SOA Artifact 3.E+09 7.E+04 7.E+12 2.E+10 3.E+11 2.E+11 2.E+11Volume Per Element(Cubic Microns) 2.E-08 8.E+01 1.E-03 1.E+02 4.E-01 4.E+01 4.E-03Fabrication Time(seconds) 4.E+03 2.E+04 9.E+04 1.E-01 7.E+02 3 6.E+01Time Per Element (Seconds) 1.E-06 3.E+02 1.E-08 7.E-12 2.E-09 2.E-11 3.E-10Fabrication Cost for SOA Artifact($) 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
Complexity Per Unit Cost
Printed Electronics
~Minutes ~ 3Weeks of 7x24 Processing
Lithography Printed Electronics
+
Liquid InorganicSemiconductors[1]
[1] Ridley et al., Science, 286, 746 (1999)Science 297,416 (2000)
Printing
Towards $10 Tablets & E Books
Fabricational Complexity
Fabricational Complexity Per Unit Cost
MpF ln
N BLOCKS
Fabricational Complexity for N Blocks or M Types = NMln
Fabricational Cost for N Blocks w/ Error Correction = 1Np
Where is the Yield Per Fabricational Step p
Complexity Per Unit CostComplexity Per Unit Time*Energy
A G C T
T C T G
C A C G
A
G
C
T
N Devices
Yielding N Devices with Error Correction(Why A Small Amount of Error Correction Has A Very Large Effect)
kNkN
Mk
ppMNM
NMY
)1()!(!
!][
][NY ]1[ NY ]3[ NY
Fraction of Chips with M or More Perfect Devices (i.e. N-M or Fewer Errors).
0.75 0.97 0.997 0.9998
0.5 0.85 0.97 0.99
0.25 0.60 0.84 0.95
0.1 0.33 0.60 0.80
0.01 0.06 0.16 0.32
Table 1. Yields as a function of the number of repaired errors.
]2[ NY
J. Jacobson 02/12/09
http://laser.gist.ac.kr/board/bbs/board.php?bo_table=rese_02
http://www.sdtech.co.kr/data/file/pro03/1890065063_Z6N9yvt4_EC9DB4EBAFB8ECA780_1.jpg
Error Correcting Fabrication - TFT
http://www.sdtech.co.kr/device3.html
Moore’s Law Without Moore’s 2nd Law
http://www.chipsetc.com/the-transistor.html
http://www.webenweb.co.uk/museum/comps.htm
Moore’s Law
Error Correcting Manufacturing
Super Geometric Scaling
• Error Corrected TFT• Error Corrected CMOS• Error Corrected DNA Synthesis
Exponential Resource -> Exponential Gain Linear Resource-> Exponential Gain
DNA SynthesisChemical Synthesis
(Open Loop Protection Group)Biological Synthesis
(Error Correcting Polymerase)
Error Rate: 1:102
Throughput: 300 S per Base Additionhttp://www.med.upenn.edu/naf/services/catalog99.pdf
Throughput Error Rate Product Differential: ~108
template dependant 5'-3' primer extension
5'-3' error-correcting exonuclease
3'-5' proofreading exonuclease
Example: [A] Synthesize 1500 Nucleotide Base Gene. Error Rate = 0.99(0.99)1500 ~ 10-7. [B] 3000 Nucleotide Base Gene. (0.99)3000 ~ 10-13.
Error Rate: 1:106
Throughput: 10 mS per
Base AdditionBeese et al. (1993), Science, 260, 352-355. http://www.biochem.ucl.ac.uk/bsm/xtal/teach/repl/klenow.html
Error Correcting Gene Synthesis
Nucleic Acids Research 2004 32(20):e162
Lamers et al. Nature 407:711 (2000)
X
X
X
Nucleic Acids Research 2004 32(20):e162
Error Rate 1:104
http://www.ornl.gov/hgmis/publicat/microbial/image3.html
Nature Biotechnology 18, 85-90 (January 2000)
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
photos provided by David Schwartz (University of Wisconsin, Madison)]
D. radiodurans 1.75 million rads, 0 h
D. radiodurans 1.75 million rads, 24 h
http://openi.nlm.nih.gov/imgs/rescaled512/1079854_1471-2180-5-17-11.png
Atoms: ~ 20 [C,N,O]Complexion: W~ 320 x = 32
Product: C = 4 statesx = 2
x[Product / Parts] =~ .0625
Complexity (uProcessor/program):x ~ 1K byte = 8000
Product: C = 4 statesx = 2
x[Product / Parts] =~ .00025
DNA Polymerase
Nucleotides: ~ 1000Complexion: W~41000 x = 2000 = 2Kb
Product: 107 Nucleotidesx = 2x107
x[Product / Parts] =104
x >1 Product has sufficient complexity to encode for parts / assembler
Synthetic Complexities of Various Systems
500 1000 1500 2000 2500 3000
0.2
0.4
0.6
0.8
1.0
Threshold for LifeWhat is the Threshold for Self Replicating Systems?
Measurement Theory
http://en.wikipedia.org/wiki/File:Stem-loop.svg
Error Correcting Exonuclease
(Ruler)
DNA
Number of Nucleotides
Prob
abili
ty o
f Sel
f Rep
licati
on
NN
N
N
kT
qp
qQp
kq
q
N/2
2/
2/Bond
/E-
-1 P :Yield Total
11 :Yield StepPer
:open bonds N/2 ally that Probabilit :sNucleotide N
3E e :Where
:open is bond single ay that Probabilit
Bond
Watson Crick .18 nm
How Well Can N Molecules Measure Distance?
/sandwalk.blogspot.com/2007/12/dna-denaturation-and-renaturation-and.html
Threshold length: 1541 bp for 50% yield. 379 bp for 10-6 yield.
20 40 60 80 100 120
500
1000
1500
Threshold for LifeWhat is the Threshold for Self Replicating Systems?
Measurement Theory
Number of Nucleotides m Per Building Block
Min
imum
Mac
hine
Size
N
To b
e Se
lf-Re
plic
ating
mNmN
N
N
kT
qp
qQp
kq
q
/N/2/
2/
2/
Bond/E-
-1 P :Yield Total
11 :Yield StepPer
:open bonds N/2 ally that Probabilit
bonds N/2 snucleotide N
3E e :Where
:open is bond single ay that Probabilit
Bond
Threshold for assembling blocks of m –mers (monomer, dimer , trimer etc.)The longer the block the greater the binding energy.
m N for 50% Yield Number of Build Steps
1 (A,G,T,C)
1541 1541
2 (AA,AG,AT …)
1381 691
3 (AAA,AAG…)
1286 429
10 994 100
50 564 12
100 336 4
123 245 2
Yield___ 50%___ 10%___ 1%___ 1E-6
Threshold Machine Complexity N for Self-Replication
NOTES