The carrier statistics in a low-dimensional nanostructure with length in one or more of the three dimensions plummeting below carrier's De Broglie wavelength is investigated. The probability distribution, the Fermi level, intrinsic velocity, and energy of the carriers are sternly affected on reducing dimensionality from 3-dimensional (3-D) bulk configuration. The carrier statistics for degenerate and non-degenerate regimes for nanostructures is worked out with an emphasis to predict the ultimate carrier velocity in a high electric field. The general results presented are applicable to all materials once the carrier concentration and ambient temperature are identified.
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