Tunnel Effect

Author: Arpan Dey

Everything, no matter how strange, is reduced to probability by quantum mechanics.

In this article, we will discuss tunnel effect in quantum physics. Before we start, let us address a common misconception.

Does the ‘many-worlds’ interpretation indicate that everything must occur in some parallel reality?

Well, no. That is a common misconception. Everything for which the Schrödinger equation predicts a non-zero probability must occur, but that is not everything. For instance, a single quark can’t directly turn into a lepton, since they are elementary particles.

You must have heard of things like the possibility of a prisoner escaping through the prison walls. The probability for such things to occur in the case of macroscopic objects is negligible, so to speak, zero. But at the quantum level, everything is different, as different as can be, perhaps.

A particle without the energy to pass over a potential barrier may still tunnel through it. It is impossible in the case of the hypothetical infinite well, for even if penetration occurs, the width of the well walls is infinite. So, the particle can’t make it through.

But the tunnel effect occurs in finite wells. For instance, in the case of alpha particles emitted by certain radioactive nuclei. An alpha particle whose kinetic energy is only a few mega electron volts, is able to escape from a nucleus whose potential wall is 25 MeV high. The probability of escape is so small that the alpha particle might have to strike the wall as many as over 10^38 times before it emerges. The phenomenon of alpha decay beautifully verifies the counter-intuitive predictions of quantum theory.

The quantum tunnel effect has important applications in the semiconductor industry. For instance, the Zener diode, a type of p-n junction diode, which is used in voltage-regulation circuits, uses the concept of quantum tunneling. The Zener diode works on the principle of avalanche multiplication and Zener breakdown. Zener breakdown involves the tunneling of valence-band electrons on the p-side of the junction to the conduction band on the n-side even though these electrons don’t have enough energy to first enter the conduction band. Due to this, there is a sudden abrupt increase in the reverse current on reaching a particular voltage.

So then, can we walk through walls? Theoretically, yes! So how are we to walk through walls? It all depends on probability. Quantum mechanics allows tunneling. A particle, if bombarded toward a wall, has a very less but non-zero probability of ending up on the other side of the wall. But if a human body is to tunnel through a wall, each and every particle would need to tunnel, all at exactly the same time, to the other side of the wall. To start with, the probability of a single particle doing this is unimaginably small. Thus, the probability of all the particles of your complex body doing this is almost zero. Also, all the particles must do it at the same time, if you are to end up in a good condition on the other side!