school of engineering leos may 15, 20081 moore’s law and related concepts by jerome k butler...

SCHOOL OF ENGINEERINGSCHOOL OF ENGINEERING

LEOS May 15, 2008 1

Moore’s Law and Related Concepts

ByJerome K Butler

Electrical EngineeringSouthern Methodist University

Dallas, TX 75275 USA


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Who is Gordon Moore?

• Retired chairman and CEO of Intel Corp• He described in a 1965 paper how to cram

a lot of components on a silicon chip.• Moore’s Law – The number of

components on a chip double every 24 months.

• NOW: Wants to be known as anything except “Moore’s Law.”


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Greatest Inventions of 20th Century; Benefits to Society

• Medical Technology• Space Travel• Jumbo Jets• Materials Tech. (Silicon, Plastics, Matrix,…)• Nuclear Energy• Communications allowed via Microelectronics• Computer Integration in Society allowed via

Microelectronics


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Where are we headed?

• Is there something unique about the exponential growth?

• Many things show exponential growth 1. The number of homo sapiens on the

planet- 2. The Dow-Jones Industrial Average 3. The number of transistors per unit

volume-


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Dow Jones Industrial Average


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Number of Transistors


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Contemporary Circuits


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Early Circuits: The ENIAC at U. Penn ~1940


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Is this a transistor? CMOS?It does use electrons but no holes!

Occupied about 5 cubic centimeters of space!


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In the ENIACWhat about efficiency? Calculations per watt of input power?


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About size and microelectronics Where does quantum theory enter the picture?


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Moore’s Law is about Dimensions

• Length- Foot, Meter, Wavelength

• Mass- Pounds, Kilograms

• Time- Day, Year, Second

• Are there Universal Constants?

G- Gravitational Constant

c - velocity of Light

e - Charge of an electron


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MKS System is a Human Invention (Now SI)

• Length : An arbitrary quantity, foot, yard, mile - Meter standard is located in France.

• Time: An arbitrary quantity, day, month-Second standard 9 192 631 770 periods of radiation between 2 states and the ground state of cesium 133. (Not in France)

• Mass: Difficult to understand-The mass of an object is linearly related to an international prototype. (Located in France)


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What is the Linearity Constant?

• Related to F = Ma (Newtons 2nd Law)

• Mass is proportional to a standard mass times the ratio of the two accelerations

ss MaaM )/(


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The Gravitational Constant


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Natural Constants of Nature?The velocity of photons, c, is a constant.

Natural Constants Speedometer


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Who was George Johnstone Stoney?

• 1826-1911• Irish Physicist• Professor, Queens Univ

Dublin• Postulated an Electron e

(He called it an electrine.)• J.J. Thompson (1897) later

discovered the electron.


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George Stoney

• Estimated Molecules in a volume

• Similar to Avogadro Number

• 1874 – Magnitude of electronic charge

• Units became known as a coulomb

• Proposed an atom of electricity one of three fundamental physical units

• The other two being the velocity of light

• And the gravitational constant


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Stoney’s Three Constants

Produce the Universal Constants


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Are Stoney’s Constants of Nature Useful?

The numbers were so fantastically small that people lost interest and could see no practical use. Indeed, Stoney conceived the new natural numbers but even he lost interest. He then started ‘marketing’ the electrine, which he later changed the name to electron.


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Who was Max Planck?• 1858 – 1947 • German Physicist• Prof Univ. of Berlin• Explained Black-body

radiation• Defined h (Planck’s cont)• Integrated in Quantum Th.• Revived Stoney’s Work• Now Planck’s natural units


Reviving George Stoney’s work on Natural Constants

• While Stoney’s natural constants were derived from c, e, and G, Planck added his and Boltzmann’s constant:

• h = 6.626068 × 10-34 m2 kg / s

• c = 3 x 108 m/sec

• G = 6.67300 × 10-11 m3 kg-1 s-2

• k = 1.3806503 × 10-23 m2 kg s-2 K-1

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Planck’s Natural Constants

mpl (hc /G)1/ 2 5.5610 5

pl (Gh /c3)1/ 2 4.1310 33

tpl (Gh /c5)1/ 2 1.3810 43

Tpl (hc5 /Gk)1/ 2 3.51032

grams

cm

sec

Kelvin


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“These natural constants retain their natural significance as long as the law of gravity and that of propagation of light in a vacuum and the two principles of thermodynamics remain valid; they must be found always to be the same, when measured by the most widely differing intelligences according to the most widely differing methods.”

Max Planck


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Are Stoney/Planck Constants Useful Yet?

Black HoleRegion

QuantumRegion

Stoney/PlanckConstants


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Concept of Information

• How many bits can be compressed in a unit volume (1 cubic centimeter)?

• Or, how many transistors can be placed in a unit volume (1 transistor RAM)?

• Jacob Bekenstein, a black-hole physicist, calculated the maximum amount of bits, or information, that can be stored in a unit volume.


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Concept of Information cont.

• Strangely enough, the number is proportional to the area surrounding the volume!

• This idea is not good for 3D chip designs. Just use both sides of the chip for smallest volume and largest area.

• 1 bit per unit Planck area:


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Concept of Information cont.

pl

pl 1 1 10 0 0

Apl pl pl 10 66cm2

bsp = 1066 bits cm-2

The maximum bit density is bsp is now considereda natural constant just as, for example, the velocityof light, c.


Contemporary Storage Technology

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R1= 5.5 cm

R2=2.2 cm

B = 8 x 1010 bits

A = (5.52-2.52)=75 cm2

b = B/A = 1.1 x 109 bits cm-2


New Expression for Bit Density, Component Density, etc.

Let C be the cost or effort in obtaining or manufacturing memory storage devices or semiconductor devices on a piece of silicon or any type of known material. Let C0 be the cost of, say contemporary devices, then

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C C0

1 (b /bsp )2


Observation

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Consider the case for b/bsp = 0.1 so that Moore’s Law should be applicable for bit-density ratios between 0 and 0.1. Present bit densitiesare approximately 109 bits per cubic cm.

Moore’s Law is applicable when b/bsp <<1.

C0 can be the contemporary cost, energy, or some convenient metric. As the bit densityapproaches bsp the cost highly escalates.


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Observation Cont.

Therefore, how many years are needed to reach a bit density of b = 1065 ?

109 2N/2 = 1065

N = 372 years

Moore’s Law will continue for a large numberof years with no saturation until about 2380.


What about CMOS Technology?

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It is difficult to judge CMOS technology for bit storage with linear dimensions below 1 lattice constant, which is about 10-7 cm or a bit density on the order of 1014 cm-2.

Moore’s Law should last another 33 years.


Conclusions

• Moore’s Law is a very intriguing concept especially for the manufacturing industry. However, there has never been a theoretical model that shows some of the boundaries. The ideas presented here try to address a purely empirical observation.

• Stoney and Planck were two ingenious physicists that tried to address some universal constants of nature, but the subject has been an on-going topic for many years.

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• We don’t yet know how the natural constants play into the determination of information storage or for information speed such as bit periods. Is the Stoney/Planck time constant the smallest period?

• The intriguing observation is the choice of the three parameters used to define the constants, and the most puzzling is the constant of gravity.

Conclusions cont.


Acknowledgement

• John D. Barrow, “The Constants of Nature,” Pantheon Books, New York, 2002. “The numbers that encode the deepest secrets of the universe.”

• wikipedia.com

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school of engineering leos may 15, 20081 moore’s law and related concepts by jerome k butler...

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