Volume-Controlled, Two-Carrier Currents in Solids: The Injected Plasma Case

Double injection into semiconductors and insulators is studied under conditions where the injected electrons and holes are free (injected plasma), the current is volume-controlled, i.e., determined by distributed space charge, and the current is field-driven (diffusion negligible). The major results are, assuming a one-dimensional geometry and carrier lifetime independent of injection level, for extrinsic semiconductors, (i) an extended voltage region over which $J\ensuremath{\propto}{V}^{2}$ ($J$ current density and $V$ voltage), and (ii) depression of the current, at fixed voltage, in the square-law region through increase in the number of thermal minority carriers, $J\ensuremath{\propto}|{n}_{T}\ensuremath{-}{p}_{T}|$, with ${n}_{T}$, ${p}_{T}$ the thermal-equilibrium densities of electrons and holes, respectively. This unusual behavior is shown to be a direct consequence of recombination kinetic requirements. For insulators, assuming trapping is negligible, $J\ensuremath{\propto}{V}^{3}$. A rigorous solution is obtained for the constant-lifetime problem, valid for both semiconductors and trap-free insulators. This solution furnishes a good approximation also for variable-lifetime cases, e.g., bimolecular recombination kinetics.

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