Suppose you are a particle, let’s say, an electron, and there is a barrier you have to cross that has some potential energy with it. But you don’t have enough energy to do so. So, will you be able to do this? Can you pass over the barrier without enough energy?
According to your knowledge of classical mechanics, you’ll say – No. But if you know the laws of quantum mechanics, your answer will be – “there is a certain & non-zero probability of doing that.” It is where the phenomenon of Quantum Tunneling arises.
Quantum Tunneling is the quantum-mechanical phenomenon in which the particle has a finite probability that it can cross the barrier of higher energy by tunneling instead of climbing over it. Let us understand this in much more detail.
In quantum mechanics, the wave function represents the particle. Since the particle has a wave-like nature, therefore, it must have amplitude. Thus, the square of the amplitude of this wave-function gives the probability of the position of the particle. The location at which particle is most likely to be detected is the location where the amplitude is highest.
Now, let us assume that a particle approaches the barrier having a finite Potential Energy, more than the Potential Energy of the particle. Since the particle has a wave function with it, when it goes inside the barrier, the amplitude of the wave function decreases exponentially but does not reach the zero. When the barrier width is less, then the wave function can exit the barrier and reach the other side.
Well, this does not mean that all the particles can cross the barrier and reach the other side. Means, “There is a certain probability that the particle will tunnel through the barrier and a certain probability that it will not tunnel through it.”
It is because a wave function tunnels through two boundaries and also can reflect at each of them. This behavior of the wave function inside the barrier is described by the transmission coefficient & the reflection coefficient.
Therefore, if we send several particles towards the barrier, then a few of them will tunnel through it and reach the other side while some of them will reflect back.
- The particles with higher amplitude have more probability of passing through the barrier than the particles with lower amplitude.
- The particles have more probability of passing through the barrier of narrower width than a wider one.
When a large number of particles is passing through a barrier, they can have a high probability that a few of them will pass through it even if the individual particle doesn’t have this much probability.
Therefore, tunneling of any particle depends on the probability of the particle and width of the barrier. This whole process of passing of the particle through the barrier is known as quantum-tunneling.
In classical mechanics, if the energy of the barrier is more than that of the particles, then there is no possibility that the particles will cross it. But quantum mechanics have a different perspective. It says the particle can cross the barrier only if the size of the particle is small enough.
Therefore, if you are thinking of tunneling through the wall, you cannot do that because you are not small. The particles with negligible size and wave-like nature can tunnel through a barrier.
The tunneling effect is not a hypothetical or theoretical concept. We can see this effect, not in our daily life but on some fundamental phenomena and applications. I have listed down two-three examples where tunneling is the principle concept behind them.
In the radioactive decay, the alpha particles have lower energy than the nucleus but emerge out of it because of the tunneling effect of alpha decay.
The emission of the alpha particles from a radioactive element to form a stable daughter nucleus is known as alpha decay. An alpha particle has to cross the potential barrier of the Nucleus to escape through it. But, the alpha particle does not have enough energy for this. Therefore, it undergoes quantum tunneling so that the emission takes place.
You can also see the quantum tunneling in the semiconductors. The “tunnel diode” is the semiconductor diode, which works on the principle of tunneling.
Tunnel diode is the special semiconductor diode in which the doping of the p-type and n-type regions are heavy, and the width of the junction is narrow. Therefore, the depletion region of the semiconductor is very less, and the particles can easily cross the potential barrier (depletion region) of the semiconductor.
In semiconductors, tunneling is the direct flow of electrons from the n-side to the p-side of the semiconductor so that the current will be high even when the forward-voltage is low. In this principle, the tunnel diode works.
The nuclear fusion process in the star is due to quantum tunneling but tunneling through the coulomb barrier due to electrostatic force.
The star releases the energy by nuclear fusion inside its core. The atomic nuclei have to cross the Coulomb barrier formed by the electrostatic interaction. For this, the thermal energy due to high temperature is not sufficient. Thus, a large number of nuclei cross this barrier by tunneling, although the probability of crossing this barrier is low. Thus, the star sustains for billions of years.