Ballistic electrons in an inhomogeneous submicron structure: Thermal and contact effects

For a simple submicron semiconductor structure we have calculated exactly the electron distribution $f(v,x)$ within a relaxation-to-local-equilibrium assumption for the collision term of the Boltzmann equation. This is the first calculation of the electron distribution in an inhomogeneous semiconductor. Large applied voltages produce a substantial ballistic peak in $f(v,x)$. But at all voltages contact inhomogeneities and local heating (and cooling) produce an I-V characteristic only weakly dependent on the scattering rate.