Full counting statistics of phonon thermal transport for disordered systems

Abstract

The disorder is inevitable in the nanodevices fabrication due to the potential impurities or the intentional doping which may have significant influence on the phonon thermal transport behavior. For these disordered systems, all transport quantities of interest, such as thermal current and thermal conductance, become random variables and a full characterization of them requires higher order cumulants besides the mean value (the first order cumulant) and the variance (the second order cumulant). The current cumulants expressions could be obtained conveniently from the theory of full counting statistics by taking derivatives on the cumulants generating function. In the presence of disorders, however, large computation time is required when performing the numerical simulations using the brute force (BF) method. In order to characterize the disorder properties of quantities of interest, the previous work has proposed the FCS-CPA method which has been proved successful in calculating the electron charge current cumulants with comparable accuracy as the BF method but consuming much less time. In view of the huge similarities between the phonon and the electron systems, the FCS-CPA method will be tested on the phonon transport systems. In this thesis, a pedagogical derivation for the phonon thermal current will be given in the non-equilibrium Green's function (NEGF) theory which will serve as a cornerstone of the BF method to calculate the current cumulants. Then the FCS-CPA method in phonon systems will be presented and the numerical calculations are performed to compare the results by both methods. The numerical results demonstrate once again the accuracy and the performance of the FCS-CPA method. Also, a parallel derivation for both phonon and electron will be given in order to show the great similarities between them in the NEGF theory, which suggest that all existing techniques in the electron NEGF framework may also be applied in the phonon transport systems.