Difference Between Tunneling and Hopping: Explained

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In summary, there is some confusion surrounding the terms "hopping" and "tunneling" in the context of transport mechanisms. While some sources consider them to be the same process, others differentiate between them. The main difference is that in hopping, the particle must have enough energy to cross the barrier, while in tunneling, the particle can cross the barrier with less energy. This distinction can be seen in examples such as heavy ions hopping in a lattice and protons tunneling through a barrier in a proton conductor. A well-known example of tunneling is the alpha particle tunneling through the coulombic barrier during alpha decay.
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In my research, I've always seen variable range and nearest neighbor hopping referred to as tunneling processes. However, I've also read papers that differentiate tunneling and hopping as two different transport mechanisms. Can someone clear this up for me? Given the context, what exactly is the difference between hopping and tunneling?
 
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In hopping, the hopping particle has to have energy greater than or equal to that of the height of the barrier in order to cross the barrier, in tunnling it can cross the barrier even with energy less than the height of the barrier.

Examples: A heavy ion (let's say anthing heavier than Lithium) usually "hops" from one site to the next in the lattice during diffusion.
On the other hand interstitial proton in proton conductor can "tunnel" through the barrier and also can hop "above" it.

A celebrated example from nuclear physics is the "tunneling" of the alpha particle through the coulombic barrier during alpha decay.
 
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Useful nucleus said:
In hopping, the hopping particle has to have energy greater than or equal to that of the height of the barrier in order to cross the barrier, in tunnling it can cross the barrier even with energy less than the height of the barrier.

This is an interesting interpretation. I don't think I've heard it expressed this way before.
 

1. What is the main difference between tunneling and hopping?

The main difference between tunneling and hopping is the mechanism by which electrons move through a material. In tunneling, electrons pass through the material's energy barriers, while in hopping, electrons move from one atom to another within the material.

2. Which process is faster - tunneling or hopping?

Tunneling is generally considered to be a faster process compared to hopping. This is because in tunneling, electrons can move through the material without having to interact with other atoms, while in hopping, electrons must interact with neighboring atoms to move through the material.

3. Can both tunneling and hopping occur in the same material?

Yes, both tunneling and hopping can occur in the same material. The prevalence of each process depends on the specific properties of the material such as its band gap, temperature, and electric field strength.

4. How do tunneling and hopping affect the conductivity of a material?

Tunneling and hopping can significantly affect the conductivity of a material. In general, materials that exhibit more tunneling will have higher conductivity, while materials that exhibit more hopping will have lower conductivity.

5. What are some applications of tunneling and hopping in science and technology?

Tunneling and hopping are important processes in many technological applications, including transistors, quantum computing, and solar cells. These processes also play a crucial role in understanding the electronic properties of materials in condensed matter physics and materials science.

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