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A high-field domain is a band of elevated field orthogonal to the equi-current lines, and seen in photoconductive CdS and monochromatic light at the band edge as dark band was discovered by Böer, using the Franz–Keldysh effect. Such domains must appear whenever the conductivity decreases stronger than linearly. This can be caused by the field dependence of the carrier density, as observed in copper-doped CdS caused by Frenkel Poole excitation of holes, causing faster electron recombination, known as field quenching. These high-field domains, now referred to as Böer domains, or by field dependence of the mobility, caused by excitation of electrons into higher conduction bands with lower mobility as observed in GaAs, called the Gunn effect. The high-field domains can be identified by periodical field oscillations between high and low values, as shown in Fig. 1.
Many other crystals show such domains by typical current oscillations. The high-field domains in copper doped CdS can be easily observed by the Franz–Keldysh effect as stationary, adjacent to the cathode or moving. These are analyzed as another example below.
Theory: Stationary high-field domains can be analyzed from the transport- and Poisson equations:
d n d x = e k T {\displaystyle {\frac {dn}{dx}}={\frac {e}{kT}}\left} and d F d x = e ϵ ϵ 0 {\displaystyle {\frac {dF}{dx}}={\frac {e}{\epsilon \epsilon _{0}}}\left}
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