The Shrinking Future

December 1996

Since at least the early Sixties, Moore's Law has been faithfully adhered to. Gordon Moore, then a grad student, later a founder of Intel, said that he expected the size of electronic circuits to shrink by half every 18 months. At the time he made his statement, a computer with a megabyte of ram and a hundred megabytes of disk space occupied the space taken up by a small house, and now of course it sits on your desk. The question has to be asked, though, just how many more generations can this continue? Physics demands that at some point, you don't get faster by just getting smaller.

The greatest intellectual achievements of the 1st half of this century are the General Theory of Relativity, which is the study of the large scale structures of the universe, and Quantum Mechanics (QM), which is the study of the extremely small structures of matter. These two theories were worked out in the first three decades of this century. The Special, and General Theories of Relativity were essentially developed solely by Albert Einstein. (It is interesting that his Nobel Prize was not for that work, but for work on the photoelectric effect, which is a QM phenomenon.) On the other hand, QM was developed by a whole cast of characters, starting with Max Planck in 1900 and continuing on to Neils Bohr, Wolfgang Pauli, Werner Heisenberg, and Paul Dirac by the end of the thirties. From these theories, we have essentially the basis of Atomic Bombs, and Integrated Circuits. Since 1930, scientists, including Einstein for the rest of his long life, have been trying to develop a Unified theory, that would incorporate both of these theories, and thus far, the attempts have been quite unsuccessful.

Until recently very few commercial products needed to worry about Relativity. Until you have something whose speed starts to approach the speed of light, you can generally ignore relativistic effects. However, the Geo Positional Satellite System, in which a series of satellites send clock signals to a ground station, from which that station can calculate its own position, do need to take account of the slowdown of the satellite clocks because of their speed relative to a point on the surface of the earth. Those satellites are indeed going only a tiny fraction of the speed of light, but the accuracy demanded from the technology is such that you have to take into account even those small time abberations.

While the principles of QM were made much use of in the Nuclear industry (bombs and electrical plants), and while they underlay much of our understanding of how electronic circuits work, you do not really observe any predicted effects until you start looking at things the size of individual atoms and electrons. QM is different from classical mechanics in that it declares that energy released from the atom is released only in discrete units, called quanta. Classical mechanics would expect a continuum of energy release. The mathematics of the old and new forms of mechanics merge together as you get to macro sizes. For instance, one of the basic tenants of QM is the Heisenberg Uncertainty Principle, which says that you cannot measure both the speed and the position of an object beyond a certain limit, that limit being Planck's Constant. That constant is so small, that it is totally lost when you are measuring the speed of a baseball. But you do have to worry about it when you are trying to measure the speed of an individual electron. And it will not be very much longer until the size of electronic circuits, if they continue to follow Moore's Law, will be approaching atomic dimensions.

Everybody who has taken an elementary physics course learns that an electron can be thought of as a discrete particle, but that it can also be thought of as a wave (eg as a photon). And there are experiments that do show this dual nature. Take a beam of electrons, and send it through a slit of sufficiently narrow size, and what you see on the other side is not a point, but a diffraction pattern characteristic of light waves and not bowling balls. That slit has to be quite narrow, because the effective wavelength of the electrons are quite small, approaching X-rays rather than visible light rays, but the effect is identical.

So, what does all this have to do with commercial electronic circuits, such as those used in computers?

Speed, essentially. We all know that the original computers, like the Univac I, were slower than the processor in your Timex watch today. We all know that just in the last few years, when you measure the original 8088 processor as a base, that the 386 is something like 15 times as fast, and the pentium is maybe 100 times as fast, and it seems like this will continue forever. The reason all these speed increases, and memory increases (going from a few thousand bytes per chip to a dozen and a half megabytes per chip) have occurred is that solid state engineers have figured out how to make the electronic traces on the silicon wafers smaller and smaller. And the smaller things get, the closer together things can be. And the closer things are, the faster they can be, because the speed is pretty much a function of how long a path an electron has to take to do whatever it has to do in its circuit.

We generally think that light zips along at a pretty good rate. In vacuum, it has a speed something like 168,272 miles per second, or just over 300,000 Km/Sec. The acerbic Commander Grace Hopper used to carry around her nanoseconds. These were pieces of wire that were 0.3 meters long, something like 11 inches. (Figure it out: 300,000 Km/Sec is 3x10+8 meters/sec, multiply that by 1x10-9 [a nano], and you get 0.3 meters/nanosecond). In a wire, electrons actually move considerably slower than the speed of light in a vacuum, somewhere between a half and a tenth as fast. Ignoring that quibble, consider the consequences of a computer with a clock rate of 100 MHZ, which is well below the rates of the desktop models being sold today, but it makes the math easier if I choose that figure. 100 MHZ is one clock tick every 10 Nanoseconds. Which means that at best, an electron can travel a total distance of 3 meters per clock tick. And we know that things are not at their best in circuits, because a) wire is not a vacuum, so you have that speed penalty, and b) each circuit element, like AND gates and all those binary adder functions, take their time tolls.

So, anyway, the total path of some electron that has to do some productive work in today's CPU tops out at about a meter or so. You have probably all seen pictures of the trace layouts in a CPU: a huge mass of wires going up, down, and through the different architectural parts of a computer chip. The width of the trace pretty much determines all the other properties of the IC. Make the trace narrower, and pretty much, you can a) make everything else closer together, and that means b) put more junk on the chip so that it can do more powerful things (eg add more memory elements to a chip).

Traces today are being laid down at about 100 NanoMeter widths. The problem is, when you get down to about 5 nm traces, you start hitting our old friend, the the wave nature of the electron, and your electron starts to take on the characteristics of a photon, and none of the technology that our Integrated Circuits use today, and have used for the last forty years, expect this to happen. All kinds of other funny things happen when you get so narrow that the electron exhibits its wave nature. Like light, an electron will reflect when it comes to a turn in the trace. Like light, it can have constructive and destructive interference patterns, which means that at some points in the path, it may simply not exist at all (destructive interference). ICs are generally based on age old principles laid down by Mr Ohm in the last century, but when you deal with the wave characteristic of an electron, what is its resistance, and can a photon have capacitance? So what, you say? What is RAM memory, but a gazillion tiny capacitors filled with electrons that Do have a known capacitance.

There is a good side to this, maybe. Up till now, the increase in functionality has come from shrinking the package. Very little research has been done on the beneficial features of a circuit that has to deal with Quantum Mechanical effects. There is some research to suggest that, using a different way of thinking about all this stuff, that other technologies will be developed that can continue Moore's Law for a while longer. There is an interesting article in Spectrum magazine (Approaching the quantum limit", July 1992) that discusses some of this very early research. The suggestion is that circuits with femtosecond (1x10-15 seconds) latency times could be developed, using QM features.

So, where are we? In something less than two orders of magnitude squeezing of the circuits, we will start to hit the quantum mechanical effects of matter. That would suggest that a 386 architecthure CPU rate of about 50 GigaHertz is the top conceivable limit using existing IC technology. However, there is some hope that other technologies, which use QM effects beneficially, can take us through another order of magnitude or so beyond that. But there is a lot of research that will have to be done before commercial products like that can be introduced.