Carrier kinetics from the diffusive to the ballistic regime:linear response near thermodynamic equilibrium

Abstract

We present a general formalism for the calculationof correlation functions (CFs) for transport processes throughultra-small structures based on a Wigner functionrepresentation. Linear response coefficients are obtained fromthe CFs at thermal equilibrium. The formalismis applied to a finite conductor in three, two and onedimensions, where we study the transition from diffusive toballistic regimes for non-degenerate and degenerate conditions.Analytical expressions are given for the limiting cases.Electrical and thermal conductances are expressed in terms ofcharacteristic time- and lengthscales, which are the scatteringtime and the mean free path in the diffusive regime as well asthe transit time and device length in the ballistic regime. Fora 1D, degenerate, ballistic system of fermions wefind for the electrical conductance the fundamental unitG = 2e2/h, for the differential thermoelectric power a = 0 and for the thermal conductance the fundamental unit K = p2kB2T/(3h), which has been found to hold for theballistic case of bosons with zero chemical potential as well.We provide the frequency dependence of the kinetic coefficientsassociated with different timescales belonging to themicroscopic system.