# Heisenberg's uncertainty principle for electrons and atoms

Here is a video of Michio Kaku discussing Moore's Law and the quantum mechanical limits thereof.

Around the 1:30 mark he's talking about how the chips today have a layer of 20 atoms across (I'm assuming Silicon atoms?). He goes on to say that if that number drops down to 5 atoms across, QM starts to play a role and because of the uncertainty principle we don't know where the electrons are anymore. This brings up 2 questions for me:

1. Why is 5 (silicon?) atoms the mark where QM starts to take over? Is there some way to show this using equations or is this just based off empirical evidence?

2. He's talking about the size of the chips in atoms, logically, but then brings up electrons as the particles which are affected by the reducing size of the chips. This confuses me. Why does it 'matter' for the electron that the chip gets smaller in size? In order words, why aren't the electrons affected by HUP in chips with a layer of 20 atoms across, but they are affected in chips with a later of ~ 5 atoms across?

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Just as a very rough estimate, a free electron that contributes to the current in an ohmic material typically has a speed of $\sim 10^5$ m/s (much greater than the drift velocity). This is the speed corresponding to a kinetic energy of $\sim kT$. This implies a wavelength of $\sim 10$ nm, which would probably be something like $\sim 10$ times the diameter of a silicon atom. I'm not saying that this order-of-magnitude estimate is good enough to justify the specific numerical value of the relatively sharp dividing line referred to in the question, but I think this is the basic physics of it.

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Thanks, can you tell me how you got $10^5 m/s$? – user29855 Dec 17 '13 at 16:37

Voltage runs through transistors which are formed in the substrate of the IC. In order to perform logic this voltage needs to be controlled. When they get too close together then electrons can tunnel across the gap between them and you can no longer maintain control of the flow of electricity through the IC. What I expect he's saying is that within about 5 atoms quantum tunneling will allow electrons to flow freely through the material regardless of the measures taken to control its movement through the transistors.

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Well, I think QM may come into play long before the layer is 5 atoms across -- maybe not in the sense he means, but you will certainly see tunneling and such across barriers of that width. But to answer your question about the "5 atom mark", it certainly doesn't suddenly change at 5, it's probably just much stronger than at 20 atoms thick. But I can't imagine something significant changes between 6 and 5 atoms.

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There is also a question of noise. The node capacitances of memory capacitors get smaller and smaller, and the Vdd power supply Voltages have to go down because of the breakdown Voltage getting smaller, so the difference between a logical zero charge, and a logical one charge, is just a handful of electrons. And statistically the noise level will be about the square root of that number of electrons.

Eventually, you don't have any credible noise margin left.

Even today, with analog CMOS ICs, such as Op Amps, or sigma delta A-D converters, those circuits are built with transistors very much larger, than minimum size; sometimes orders of magnitude larger, to keep down analog noise levels, specially 1/f noise which constrains low frequency performance of analog ICs.

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