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As an example the band bending induced by the forming of a p-n junction or a metal-semiconductor junction can be modified by applying a bias voltage . This voltage adds to the built-in potential ( V B I {\displaystyle V_{BI}} ) that exists in the depletion region ( V B I − V A {\displaystyle V_{BI}-V_{A}} ). [ 6 ]
File: Diagram of band-bending interfaces between two different metals and two different semiconductors.jpg
Because a band diagram shows the changes in the band structure from place to place, the resolution of a band diagram is limited by the Heisenberg uncertainty principle: the band structure relies on momentum, which is only precisely defined for large length scales. For this reason, the band diagram can only accurately depict evolution of band ...
The band structure has been generalised to wavevectors that are complex numbers, resulting in what is called a complex band structure, which is of interest at surfaces and interfaces. Each model describes some types of solids very well, and others poorly. The nearly free electron model works well for metals, but poorly for non-metals.
An example band-bending diagram is shown in the figure. For convenience, energy is expressed in eV and voltage is expressed in volts, avoiding the need for a factor q for the elementary charge . In the figure, a two-layer structure is shown, consisting of an insulator as left-hand layer and a semiconductor as right-hand layer.
In insulators and semiconductors the Fermi level is inside a band gap; however, in semiconductors the bands are near enough to the Fermi level to be thermally populated with electrons or holes. "intrin." indicates intrinsic semiconductors
However, the formation of Lüders bands depends primarily on the microscopic (i.e. average grain size and crystal structure, if applicable) and macroscopic geometries of the material. For example, a tensile-tested steel bar with a square cross-section tends to develop comparatively more bands than would a bar of identical composition having a ...
Anderson's rule is used for the construction of energy band diagrams of the heterojunction between two semiconductor materials. Anderson's rule states that when constructing an energy band diagram, the vacuum levels of the two semiconductors on either side of the heterojunction should be aligned (at the same energy). [1]