Band bending refers to the local change in energy of electrons at a semiconductor junction due to space charge effects. Because the common way to visualize the electron energy states and Fermi level in a material is to draw bands on an energy vs. distance plot, band bending refers to bending in these diagrams and not in any physical form.
Band bending can occur at a material/vacuum interface or when two materials with different local work functions are placed in contact. Some examples of situations where band bending is technologically relevant are through the doping of one area of a semiconductor (to create a p-type in contact with an n-type, say) or metal-induced gap states of a metal being affixed to a semiconductor.
In general, bands will bend locally when materials come in contact, because the two Fermi levels of the materials will equilibrate to the same level through a local exchange of charge carriers (either holes or electrons). This exchange of charge changes the energies of those charge carriers who have been exchanged, giving a curvature to the energy vs. distance diagram near the junction. Knowing how bands will bend when two different types of materials are brought in contact is key to understanding whether the junction will be rectifying (Schottky) or ohmic. The degree of band bending depends on the relative Fermi levels and carrier concentrations of the materials forming the junction. In the p-type semiconductor the band bends upward, while in n-type the bend bends downward. Note that band bending is due neither to magnetic field nor temperature gradient. Rather, it only arises in conjunction with the force of the electric field.
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