Yamada, T., & Sone, J. (1989). High-field electron transport in quantum wires studied by solution of the Boltzmann equation. Physical review. B, Condensed matter, 40(9), 6265–6271. doi:10.1103/PhysRevB.40.6265

 

solves the Boltzmann equation in a 1D system. Because of the inelastic optical phonon scattering, the equation does not close for one energy value. This makes the solution challenging. The solution idea is to discretize the energy space, and export or import electrons depending on drift and scattering.

 

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