Space-Charge Limited Emission in Semiconductors

A situation analogous to thermionic emission into vacuum can occur in semiconductors. A semiconductor analog for a plane parallel vacuum diode may consist of two layers of $n$ type semiconductor bounding a plane parallel slab of pure semiconductor. The current density analogous to Child's law is $J=\frac{9\kappa {\epsilon }_0\mu V^2}{8W^3}$, where $\kappa =\mathrm{dielectric}\mathrm{constant}$, ${\epsilon }_0=\mathrm{mks}\mathrm{permittivity}$, $\mu =\mathrm{mobility}$, $V=\mathrm{applied}\mathrm{voltage}$, and $W=\mathrm{thickness}\mathrm{of}\mathrm{pure}\mathrm{region}$. The condition prevailing at the space-charge maximum is analyzed taking into account diffusion due to random thermal motion. Brief discussions are given of the effect of fixed space charge, the dependence of mobility upon electric field strength and the role of space-charge limited emission in a new class of unipolar transistors.