Higher-Order Generalized Hydrodynamics of Carriers and Phonons in Semiconductors in the Presence of Electric Fields: Macro to Nano

TL;DR

This paper develops a higher-order generalized hydrodynamics framework to analyze carrier and phonon behavior in semiconductors under electric fields, revealing size-dependent effects from macro to nano scales.

Contribution

It introduces a novel mesoscopic hydro-thermodynamics approach of order 1 for semiconductors, capturing non-equilibrium phenomena at small scales and under electric fields.

Findings

Size reduction leads to significant deviations from classical hydrodynamics.

Maxwell times influence the dynamics of fluxes in the system.

Electric and thermal conductivities are derived for various scales.

Abstract

It is analyzed the hydrodynamics of carriers (charge and heat motion) and phonons (heat motion) in semiconductors in the presence of constant electric fields. This is done in terms of a so-called Higher-Order Generalized Hydrodynamics (HOGH), also referred to as Mesoscopic Hydro-Thermodynamics (MHT), that is, covering phenomena involving motions displaying variations short in space and fast in time and being arbitrarily removed from equilibrium, as it is the case in modern electronic devices. The particular case of a MHT of order 1 is described, covering wire samples from macro to nano sizes. Electric and thermal conductivities are obtained. As the size decreases towards the nanometric scale, the MHT of order 1 produces results that in some cases greatly differ from those of the usual hydro-thermodynamics. The so-called Maxwell times associated to the different fluxes present in MHT are evidenced and analyzed; they have a quite relevant role in determining the characteristics of the motion.