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equivalent of leaky pipes, and the smaller the pipes are, the leakier they
get. For transistors much smaller than about 10 nm, the leakage currents are
close enough to the operational current that the device is essentially short-
circuited, and ceases to perform useful work. This is the dreaded "wall" that
chip designers have been anticipating for decades. It isn't upon us yet, but
if Moore's Law holds true until 2010, it will be.
Kastner's quiet rant continues, "Probably more important is
Moore's second law, which is the observation that the
[commercial] facilities to produce the devices double in cost every four
years. The generation of facilities built 5 years ago cost one billion
dollars each, and 100 of them were built.
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I don't know how many of the current two-billion-dollar facilities are
planned, but it seems clear that investments of this magnitude cannot be
maintained. One answer is to somehow
Hacking Matter Standing
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42
give each transistor more functionality, rather than simply increasing the
number on a chip."
Now certainly, quantum dots are very, very small. You can fit enormous
numbers of them onto a chip. But people familiar with the Boolean logic on
which computers are based see another advantage as well. Computer logic is
built up of "gates," which compare two binary values (i.e., bits, which hold
either a 0 or a 1) and make decisions based on the results. The most familiar
of these are the "AND" gate, which outputs a 1 if both of its inputs are 1,
and the "OR" gate, which outputs a 1 if either of its inputs is 1.
Logic States
A0011
B0101
O0001
u t
A
B
Out
AND
Logic States
A0011
B0101
O0111
u t
A
B
Out
OR
Figure 2-8: States of AND and OR gates
The AND gate delivers a "true" if A and B are both true. The OR gate delivers
a "true" if either A or B is true. Gates like these form the basis of most
modern computer circuits.
Many other types of gates are based on negative logic, such as the "Not-AND"
or "NAND" gate, which produces the exact opposite result from the AND gate.
Another property often employed is the exclusion of superfluous states. The
"eXclusive
OR" or "XOR" gate produces a nonzero output only when one input bit is a 1 and
the other is a 0. If both inputs are 1 or both inputs are 0, then the gate's
output will be a 0. So out of four possible states for the gate, two are the
same as for a regular OR gate, and two are reversed.
Hacking Matter Standing
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43
Logic States
A0011
B0101
O1110
u t
A
B
Out
NAND
Logic States
A0011
B0101
O0110
u t
Out
XOR
A
B
Figure 2-9: States of NAND and XOR gates
The NAND gate delivers a "true" unless A and B are both true. The
XOR gate delivers a "true" if either A or B, but not both, are true.
If these logical units seem complex, just imagine the problems of stringing
dozens, thousands, or even billions of gates together! Keeping track of such
mushrooming complexity is one of the reasons we invented computers in the
first place.
The point to remember here is that digital computers can be made, with varying
efficiency, from a variety of different gate types.
In today's microchips, binary digits are represented with switching devices
called MOSFETs, or Metal Oxide Semiconductor
Field Effect Transistors, which are easy to produce with nothing but (nearly)
two-dimensional structures of metal, insulative oxides such as SiO , and
semiconductor. Many other types of
2
switches have been used for computers, including vacuum tubes and mechanical
relays, but MOSFETs are cheaper, more reliable, and much easier to
miniaturize, so they've largely taken over the world. And because of the way
MOSFETs function, we find it easiest to build up computers out of Boolean
gates using 2-4
MOSFETs each.
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Logic States
A0011
B0101
O1001
u t
Out
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XNOR
A
B
Logic States
A0011
B0101
O1001
u t
Out
XNOR
A
B
Figure 2-10: The XNOR or Equivalence Gate
The XNOR or equivalence gate delivers a "true" if A and B have the same value
It turns out, however, that quantum-dot transistors behave as Exclusive Not Or
(XNOR) gates -- also known as "equivalence gates" because they return a
positive if the two inputs are identical, and a zero if they're different.
This structure would ordinarily require at least eight MOSFETs to assemble, so
for some types of calculations, quantum dots are around four times more
efficient than MOSFETs. For certain highly specialized uses such as error
correction circuits, they can be as much as 24 times more efficient. More
importantly, a circa
2002 MOSFET operating at 1.5 volts requires the passage of about
1000 electrons in order to change its state from "on" to "off,"
whereas Kastner's team had built a quantum-dot transistor that would change
state with the passage of a single electron.
This device led directly to the discovery of the artificial atom as an
application for quantum dots. Kastner emphasizes this point philosphically:
"As a scientist, it's my goal to understand nature. We actually stumbled onto
artificial atoms by accident, while trying to understand something else.
We're always looking for new physics, new behavior that has never been
Hacking Matter Standing
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45
seen before. Once we find it, of course, we start to daydream."
Variations on this refrain are repeated by nearly every scientist in the
field: their fertile utopia is not a set of specific commercial goals but an
endless, aimless farting around. Discovery, they insist, happens not on a
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