Carrier drift velocity in semiconducting strings

The carrier drift velocity in a 1D semiconducting sample attached to electrodes is derived from the Luttinger model, where the electric field generated by image charges within the electrodes is explicitly taken into account. If the length of the electrode is small enough compared to the sample length, the drift velocity vd can be estimated as vd≃(4e2/h)(1/εs), where e, h, and εs are the elementary charge, the Planck constant, and the dielectric constant of the semiconductor, respectively. Compared to the experimental values of vd, the obtained relationship for vd is found to be still valid for a 3D sample in the large limit of the external field.