# Barrier Tunneling

I have some questions about barrier tunneling in a scanning tunneling microscope.

From what I know, the microscope consists of a one atom tip very close to the surface of the metal being examined. A potential difference is applied between the tip and the metal and some of the electrons manage to tunnel through the vacuum.

1) How is the potential energy barrier to the electrons formed with a vacuum?

2) How do physicists determine the energy of the electron at the negative electrode?

Could you also please give mathematical equations for barrier tunneling for cases like that of the ST Microscope where the barrier is not an electric or magnetic barrier?

## Answers and Replies

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Gokul43201 said:
Try this :

http://www.chembio.uoguelph.ca/educmat/chm729/STMpage/stmdet.htm

It's not the absolute energy but the energy difference that's important. This is simply eV, where V is the bias voltage.
Thank you.

An equation I got for the transmission coefficient(T) from Resnick-Halliday says that
T = e^-(2kl) where k is proportional to the energy difference.

Does this mean that the higher the voltage applied between the surface and the tip, the lower is the transmission coefficient?