Band bending

In solid-state physics, band bending refers to the process in which the electronic band structure in a material curves up or down near a junction or interface. It does not involve any physical (spatial) bending. When the electrochemical potential of the free charge carriers around an interface of a semiconductor is dissimilar, charge carriers are transferred between the two materials until an equilibrium state is reached whereby the potential difference vanishes. The band bending concept was first developed in 1938 when Mott, Davidov and Schottky all published theories of the rectifying effect of metal-semiconductor contacts. The use of semiconductor junctions sparked the computer revolution in 1990. Devices such as the diode, the transistor, the photocell and many more still play an important role in technology. Band bending can be induced by several types of contact. In this section metal-semiconductor contact, surface state, applied bias and adsorption induced band bending are discussed. Figure 1 shows the ideal band diagram (i.e. the band diagram at zero temperature without any impurities, defects or contaminants) of a metal with an n-type semiconductor before (top) and after contact (bottom). The work function is defined as the energy difference between the Fermi level of the material and the vacuum level before contact and is denoted by . When the metal and semiconductor are brought in contact, charge carriers (i.e. free electrons and holes) will transfer between the two materials as a result of the work function difference . If the metal work function () is larger than that of the semiconductor (), that is , the electrons will flow from the semiconductor to the metal, thereby lowering the semiconductor Fermi level and increasing that of the metal. Under equilibrium the work function difference vanishes and the Fermi levels align across the interface. A Helmholtz double layer will be formed near the junction, in which the metal is negatively charged and the semiconductor is positively charged due to this electrostatic induction.