Band bending
Encyclopedia
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 function
s are placed in contact. Some examples of situations where band bending is technologically relevant are through the doping 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 level
s of the materials will equilibrate to the same level through a local exchange of charge carrier
s (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.
Space charge
Space charge is a concept in which excess electric charge is treated as a continuum of charge distributed over a region of space rather than distinct point-like charges...
effects. Because the common way to visualize the electron energy states and Fermi level
Fermi level
The Fermi level is a hypothetical level of potential energy for an electron inside a crystalline solid. Occupying such a level would give an electron a potential energy \epsilon equal to its chemical potential \mu as they both appear in the Fermi-Dirac distribution function,which...
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 function
Work function
In solid-state physics, the work function is the minimum energy needed to remove an electron from a solid to a point immediately outside the solid surface...
s are placed in contact. Some examples of situations where band bending is technologically relevant are through the doping one area of a semiconductor (to create a p-type
P-type semiconductor
A P-type semiconductor is obtained by carrying out a process of doping: that is, adding a certain type of atoms to the semiconductor in order to increase the number of free charge carriers ....
in contact with an n-type
N-type semiconductor
N-type semiconductors are a type of extrinsic semiconductor where the dopant atoms are capable of providing extra conduction electrons to the host material . This creates an excess of negative electron charge carriers....
, say) or metal-induced gap states
Metal-induced gap states
In bulk semiconductor band structure calculations, it is assumed that the crystal lattice of the material is infinite. When the finite size of a crystal is taken into account, the wavefunctions of electrons are altered and states that are forbidden within the bulk semiconductor gap are allowed at...
of a metal
Metal
A metal , is an element, compound, or alloy that is a good conductor of both electricity and heat. Metals are usually malleable and shiny, that is they reflect most of incident light...
being affixed to a semiconductor
Semiconductor
A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...
.
In general, bands will bend locally when materials come in contact, because the two Fermi level
Fermi level
The Fermi level is a hypothetical level of potential energy for an electron inside a crystalline solid. Occupying such a level would give an electron a potential energy \epsilon equal to its chemical potential \mu as they both appear in the Fermi-Dirac distribution function,which...
s of the materials will equilibrate to the same level through a local exchange of charge carrier
Charge carriers in semiconductors
There are two recognized types of charge carriers in semiconductors. One of them is electrons, which carry negative electric charge. In addition, it is convenient to treat the traveling vacancies in the valence-band electron population as the second type of charge carriers, which carry a positive...
s (either holes
Electron hole
An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice...
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
Walter H. Schottky
Walter Hermann Schottky was a German physicist who played a major early role in developing the theory of electron and ion emission phenomena, invented the screen-grid vacuum tube in 1915 and the pentode in 1919 while working at Siemens, and later made many significant contributions in the areas of...
) or ohmic
Ohmic contact
An ohmic contact is a region on a semiconductor device that has been prepared so that the current-voltage curve of the device is linear and symmetric. If the I-V characteristic is non-linear and asymmetric, the contact is not ohmic, but is a blocking or Schottky contact...
. The degree of band bending depends on the relative Fermi levels and carrier concentrations of the materials forming the junction.