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Quantum tunneling is a fascinating phenomenon of quantum mechanics that allows particles, like electrons, to pass through barriers that would be insurmountable in classical physics. Imagine an electron facing a hill (energy barrier) that it does not have enough energy to climb over. In classical physics, the electron would remain stuck on one side. However, in quantum mechanics, there is a chance that the electron can "tunnel" through the barrier to the other side, even though it does not have enough energy to go over it.

This counterintuitive event occurs because, at the quantum level, particles have wave-like properties, described by a probability wave function. If the wave function extends through the barrier, there is a finite probability that the particle can appear on the other side. The larger the barrier, the smaller this probability becomes, as the wave function decreases exponentially inside the barrier. This tunneling effect is crucial to the operation of the scanning tunneling microscope (STM), allowing it to sense atomic features by measuring tunneling current.

Tunneling current is a key concept in understanding how scanning tunneling microscopes (STMs) work. It is the flow of electrons across a very narrow vacuum gap between the microscope's probe and the sample surface. Despite the lack of direct contact between the two, electrons can still move from one to the other via quantum tunneling. This current is highly sensitive to the gap width and changes exponentially with it.

• Increased Gap: The tunneling current decreases significantly, as the probability of electrons tunneling through the barrier drops exponentially.
• Decreased Gap: The tunneling current increases dramatically because the electron's wave function has a better chance to extend through and emerge on the other side of the gap.

The ability to detect even slight changes in tunneling current makes the STM a powerful tool for imaging surfaces at the atomic level.

Gap width in the context of a scanning tunneling microscope refers to the distance of the vacuum gap between the microscope's probe tip and the surface of the sample it is examining. This parameter is crucial because it determines how likely quantum tunneling is to occur. A smaller gap width results in a higher probability of tunneling, leading to an increased tunneling current.

Understanding the sensitivity of the tunneling current to changes in the gap width is essential for operating STMs effectively. A decrease in the gap width results in a substantial increase in tunneling current due to the enhanced probability of electron leakage across the gap. Conversely, increasing the gap width reduces this probability and the resulting current. By precisely controlling the gap width, STMs can generate detailed atomic-scale images, allowing researchers to study the surface properties and structures of various materials.