Barrier-limited transport in semiconductor devices

Current transport over a simple parabolic barrier is studied using the diffusion theory (dissipative transport) and the kinetic theory (ballistic transport). The solution of the diffusion equation for the barrier-limited case shows that the current density is inversely proportional to the width of the barrier. The solution of the kinetic theory, described by Euler's equation of classical fluid mechanics, gives a current density that is independent of the width of the energy barrier, and which is equal to 1.52 times the current density obtained from the thermionic emission theory. Euler's equation and the diffusion equation may be naturally combined into a single transport equation, and the current density derived from this equation shows the effects of both the ballistic and dissipative limits. The ballistic limits are of significance for the operation of the permeable base transistor and similar devices.