Linear conductance of short semiconductor structures

We study the length dependence of the linear conductance in semiconductor samples sandwiched between two metallic contacts. In very short samples the conductance is given by the Landauer formula which accounts for the quantum-mechanical reflection in the semiconducting region. In long samples, where semiclassical transport concepts are applicable, the conductance is derived by solving the Boltzmann equation with the appropriate boundary conditions imposed by the metallic contacts. Depending on the relative magnitudes of the sample length $L$ and the carrier mean free path $l$ we can distinguish between three specific modes of the electrical transport: the ordinary collision-controlled conductance for $L\gg l$, thermionic emission for $L\sim l$, and tunneling at the Fermi level for $L\ll l$ (below $L=100\mathrm{}$ Å, typically).