Abstract
A steady-state current can generate significant regions of space charge in semiconductors. A first integral is given here for the nonlinear differential equations describing the process, which should be helpful in reducing computing time for calculations. A rigorous proof is presented to show that spatially oscillating charge distributions are produced when ωpτ ≳1/2 where ωp is the plasma frequency and τ is the average scattering time. For collisionless transport, a complete analytic solution is obtained showing perfect periodicity with properties determined by the injecting contact.
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