Wednesday, January 11, 2012

Moore's law will still hold in ten years?

Yep, you read correctly.  Admittedly, I'm a little late to the party in writing this, but the nature magazine article references a team of scientists who've been able to create classical, nanoscale wires.  This completely defies something I've been saying for a couple of years:  that silicon power cannot survive the increasing miniaturization of transistors.

The argument runs like this:  the reason computing power doubles every 18 months is because we can inexpensively place thinner and thinner transistors onto our chips.  Currently, the transistors in the Pentium chip in your PC has a layer about twenty or so atoms thick.  Extrapolating Moore's Law out to about 2020, we get layers more in the realm of five atoms thick.  At that point, we have to abandon classical mechanics and turn to the more paradoxical laws of quantum mechanics, where the Heisenberg Uncertainty Principle kicks in.  This means that you can't quite pin down the electron; it could be inside the wire, or outside it.  In other words, you have a short circuit.

However, the Ferry team's results, if replicated, completely blow that argument out of the water.  Using phosphorus to provide electrons, they managed to show that a silicon wire only a few nanometres thick obeyed Ohm's Law (that is, the current flowing through a circuit is proportional to the voltage applied to it; the proportionality constant is expressed in terms of resistance, so V = IR).  Remember, Ohm's Law is a law of classical electrodynamics, not quantum electrodynamics.  In other words, this nanoscopic wire is completely classical, even though it should be a quantum system.  The end date for Moore's Law has thus been pushed back yet again.

Why does this occur?  After all, this flies in the face of textbook quantum mechanics.  Niels Bohr proposed a method for determining when classical mechanics must be abandoned:  take the mass m, the velocity v, and the path length d of a typical particle in the system, and calculate the product mvd.  If this product is on a lower order than Planck's constant, we must treat the system as a quantum system rather than a classical system.  Taking the mass of an electron as 9.109382×10−31 kg, the velocity as 0.97 c (as it usually is in a transistor), and the path length as
11 nm.  The product, then, is about 0.1 h, which means that the system should (barely) count as
non-classical, right?

In the Nature article, the team speculates briefly that, because the phosphorus coating used to provide
electrons is so dense, the state vectors* of the individual electrons overlap.  Presumably, they meant to
imply by this that the overlap causes a great amount of interference between electrons, and thus the
electrons decohere.  In any case, I think that this is very interesting, and that this has profound
implications for technology, if the results can be replicated.  It also reminds us to never trust our own
hypotheses; just the data.


*In this post and in future posts, I will always refer to the state vector in quantum mechanics, rather
than the more commonly-used term wave function.  This is because I believe the former term to be more
accurate:  the value referred to here is a complex number ("vector") that describes the state of the
system, and it's not even always a wave, mathematically speaking.  Hence, I shall always use the
former term, except in cases of historical context.

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