# Quantum mechanical tunneling - example from Mcintyre's book

Can someone explain what he means here:

"because the electrons inside the two materials have lower potential energy than they would in the free space between them due to the work functions of the materials."

What are the work functions?

Why there is a potential energy barrier here?

• The work function is basically the energy required to excite one electron of the material to the vaccum energy level (i.e. "extract" it from the material). The potential barrier then models the tendency of the electron to be in the materials rather than in the free space. – Lith May 25 at 12:12
• This is the best answer of the three. Thank you. So essentially the V_0 is the amount of energy it takes to excite the electrons enough to remove them from the atomic bond? – mikanim May 25 at 15:02
• Almost. It's the energy required to remove the less bounded electrons (near the Fermi level) from the surface of the material. Usually the work function is first presented to a student (at least to me) when studying the photoelectric effect. – Lith May 25 at 16:58
• Yea I learned that already. Just wanted to clarify that this V_0 is in fact the work function. Thanks. – mikanim May 25 at 17:13

The electrons contained in the sample are not tightly bound to the atoms, these are called the free electrons that can flow through a conductor and are the carriers of electric charge in a current. However to remove an electron from the sample it still requires some finite energy $$W$$ which is called the work function, as you have to work against the electric force to release them from the atoms.

Why there is a potential energy barrier here?

This is the simple barrier penetration quantum mechanical picture .

Note that the tunneling does not change the energy state, just the wavefunction, i.e. the probability.

In the image you post, because the electrons are bound within the sample and the tip they cannot go through the air. In the air they have to have an extra energy, a different energy level , than the bound levels in the material. This difference in energy levels is the barrier.

They tunnel through:

Scanning Tunneling Microscope is based on the concept of quantum tunneling. When a conducting tip is brought very near to the surface to be examined, a bias (voltage difference) applied between the two can allow electrons to tunnel through the vacuum between them.

The bias voltage brings the same energy level between the tip and the sample, and so allows the tunneling probability to be high, as in the link above .

• This doesn't answer the question. The OP wants to know why the potential has a barrier in the first place. – Ben Crowell May 25 at 14:14
• @BenCrowell I will spell lt out – anna v May 25 at 14:19
• @BenCrowell did you down vote? Is the other answer answering the question? – anna v May 25 at 14:23