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Local density of states (LDOS) is a physical quantity that describes the density of states, but space-resolved. In materials science, this term is useful when interpreting the data from an STM, since this method is capable of imaging electron densities of states with atomic resolution. According to crystal's structure, this quantity can be predicted by computational methods, as for example with density functional theory.
LDOS in solid state devices
Local density of states can be used to gain keen insights into a solid-state device. For example, the figure on the right illustrates LDOS of a transistor as it turns on and off in a ballistic simulation. The LDOS has clear boundary in the source and drain, that corresponds to the location of bandedge. In the channel, the DOS is increasing as gate voltage increase and potential barrier goes down.
In optics and photonics the concept of local density of states refers to the states that can be occupied by a photon. For light it is usually measured by fluorescence methods, near-field scanning methods or by cathodoluminescence techniques.