Why energy bands bend near metal semiconductor junction?
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When energy bands are horizontal, energies of the valence and conduction band edges along the direction of interest are remaining constant. When the energy changes along that direction, the bands are not horizontal anymore, and are bent. Change in electrical energy over distance is also defined as electric field. So, when there is electric field present, bands are not horizontal.
Non-horizontal bands can be slanted or bent, the latter with continuous change in slope; respectively having constant or varying electric field. In an oxide with no fixed charge, electric field will be constant. However, in a semiconductor with dopant atoms which can be easily ionised, presence of any significant electric field will ionise the dopants and create fixed charges. Using Maxwell's electrostatic law (Gauss's law), these fixed charges will cause a change in electric field proportional to the magnitude of the charge. Hence, in a doped semiconductor, electric field caused bands to be not only non-horizontal but also bent.
Non-horizontal bands can be slanted or bent, the latter with continuous change in slope; respectively having constant or varying electric field. In an oxide with no fixed charge, electric field will be constant. However, in a semiconductor with dopant atoms which can be easily ionised, presence of any significant electric field will ionise the dopants and create fixed charges. Using Maxwell's electrostatic law (Gauss's law), these fixed charges will cause a change in electric field proportional to the magnitude of the charge. Hence, in a doped semiconductor, electric field caused bands to be not only non-horizontal but also bent.
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