QM DISCUSSION #2 Good evening everyone. Tonights topic in Quantum Mechanics is something used in real applications: Quantum Mechanical Tunneling. This situation applies to electrons or any small particles that impinge upon either a material barrier or an energy force potential, like the electrical force field of matter. The things that are important are the mass of the particle, the kinetic energy of the particle, the strength of the potential energy gradient, and the thickness of the potential gradient (essentially a distance). Now remember from our introduction that in QM, waves are interpreted as “probability densities”, where the places where the wave has more area are larger probabilities that the particle is in that area at any arbitrary time. So imagine an electron or some other particle moving through space and time in a wave toward a solid object or force field that has an energy potential that the particle must cross. The wave changes shape at the interface, according to the probability waves, modified by the strength of the barrier potential and the distance that must be traveled. Clearly, the amount of particles on the right side of the barrier is lower, the balance of particles remaining on the left side in the “reflected” or “standing wave” of the probabilities that remain on the outside of the barrier, right? So why is this notion important? TRANSISTORS. The computer you are using to read this post are dependent on something called a CMOS transistor. You can now imagine that if there are many electrons (or some other particle), we can say there is some effective current through the barrier, right? These currents move through the structures of our transistors, dissipating electrical energy as they move. But remember that the “Controlled” movement of electrons is what allows us to construct computers. Matter is effectively porous, and electrons “leak” out of the pathways we create for several reasons I wont go into here. But from what we discussed above, that the “distance” in a system is a factor, it becomes clear that as lengths get smaller, the danger of quantum mechanical tunneling increases, right? Quantum Tunneling can occur in ANY DIRECTION in 3-dimensions. But our chips depend on an essential 2-D confinement. So now, you know why our computer designers are running into problems making microprocessor chips smaller and smaller. New CPUs commonly have pathways as narrow as 22 nm (yes, nanometers!). We can place more than 2.2 Billion transistors on a single chip. We can see that 22 nm are well within a couple orders of magnitude of the structural sizes of the semiconductor lattice. We have been forced to reduce voltages within chips to reduce the potential differences that would cause the electrons to leak or “tunnel” out of the prescribed pathways. There, now you know why computers made with Silicon are hitting their physical limits. And it had to do with QUANTUM MECHANICS!
Posted on: Sun, 05 Oct 2014 03:53:34 +0000
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