Temperature limits for ballistic quantization in a GaAs/AlGaAs one-dimensional constriction

One-dimensional (1D) ballistic constrictions have been made in a two-dimensional electron gas of high carrier concentration (6.5 * 10¹¹ cm^-2) and high mobility (9.5 * 10⁵ cm² V^-1 s^-1) formed at the interface of a GaAs/AlGaAs heterostructure. At least seven ballistic conductance steps were clearly observed at 4.2 K and remained discernible up to 40 K. A 1D subband spacing of 10 meV was found from the electric-field-induced half plateaux in differential conductance. The mobility and carrier concentration of the two-dimensional electron gas were also measured as functions of temperature in order to compare the relative effects on the degradation of the ballistic quantization of Fermi-Dirac broadening at the Fermi energy and the reduction in the ballistic mean free path. The close similarity between the experimental conductance characteristics and those calculated with a simple assumption of the Fermi-Dirac electron energy distribution strongly suggests that this is the principle mechanism in smearing the quantized conductance plateaux.