Ballistic and Dissipative Effects in Barrier-Limited Current Transport
Steady-state current transport over a simple parabolic energy barrier is studied in the context of dissipative and ballistic transport. The dissipative transport regime is described by the diffusion equation and the solution for the parabolic barrier is reviewed. The ballistic regime is treated using Euler’s equation of classical fluid mechanics. The procedure for solution of Euler’s equation for the parabolic barrier is described, and it is shown that the predicted current density is equal to approximately 1.52 times that predicted by the conventional thermionic emission theory.
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