A situation can arise in semiconductors similar to the space-charge limited emission of electrons in vacuum. The theory of Shockley and Prim for this phenomenon has been extended to the high field case using the approximation that the drift velocity of the carriers is v=μ(EE₀)1/2, where μ is the low field mobility, E the electric field, and E₀ the "critical field." For this approximation the current density analogous to Child's law for a plane parallel diode is J=(2/3)(5/3)3/2KμE₀1/2Vₐ3/2w5/2, where Vₐ is the potential across a diode of thickness w and K is the dielectric constant in mks units. Good agreement between theory and experiment for hole flow in germanium at liquid air temperature has been obtained, using values of μ and E₀ obtained independently by Ryder.
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G. C. Dacey (1953) studied this question.
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