Scanning tunneling microscope (STM) is a powerful technique for viewing surfaces at the atomic level. Its development in 1981 earned its inventors, Gerd Binnig and Heinrich Rohrer (at IBM Zürich), the Nobel Prize in Physics in 1986  . STM probes the density of states of a material using tunneling current. For STM, good resolution is considered to be 0.1 nm lateral resolution and 0.01 nm depth resolution . The STM can be used not only in ultra high vacuum but also in air and various other liquid or gas ambients, and at temperatures ranging from near zero kelvin to a few hundred degrees Celsius .
The STM is based on the concept of quantum tunnelling. When a conducting tip is brought very near to a metallic or semiconducting surface, a bias between the two can allow electrons to tunnel through the vacuum between them. For low voltages, this tunneling current is a function of the local density of states (LDOS) at the Fermi level, Ef, of the sample . Variations in current as the probe passes over the surface are translated into an image. STM can be a challenging technique, as it requires extremely clean surfaces and sharp tips.
Tunnelling is a functioning concept that arises from quantum mechanics. Classically, an object hitting an impenetrable wall will bounce back. Imagine throwing a baseball to a friend on the other side of a mile high brick wall, directly at the wall. One would be rightfully astonished if, rather than bouncing back upon impact, the ball were to simply pass through to your friend on the other side of the wall. For objects of very small mass, as is the electron, wavelike nature has a more pronounced effect, so such an event, referred to as tunneling, has a measurable probability .
Electrons behave as beams of energy, and in the presence of a potential U(z), assuming 1-dimensional case, the energy levels ψn(z) of the electrons are given by solutions to Schrödinger’s equation,