Kinetic model of thermotransport in semiconductors

Kinetic theory of thermotransport of polar semiconductors: Degenerate limit

“…Those are chosen to describe the macroscopic state of electrons in the carrier transport process. The usual procedure to obtain a semiconductor generalized hydrodynamics scheme consists in constructing a hierarchy of balance equations, for the complete set of relevant variables, starting from the semiclassical Boltzmann transport equation(BTE) [1]. These hydrodynamic type equations constitute a closed set of balance equations for the relevant variables, once the higher order moments and the production terms have been completely evaluated.…”

“…We use an expansion in terms of the basic fields coming from the maximum entropy principle [1,2]. In the semiclassical model, we are considering here, the weight function is a local Fermi-Dirac distribution function.…”

“…The condition given above also appears in Ref. [1] with respect to the Onsager symmetry relations that must be satisfied by the transport coefficients. This relation expresses that only some values of ϕ make true the symmetry condition, i.e.…”

“…The relaxation times The closure of the above set of generalized hydrodynamic evolution equations was done using a non equilibrium distribution function, which must be at least an approximate solution of the Boltzmann transport equation. We use an expansion in terms of the basic fields coming from the maximum entropy principle [1,2]. In the semiclassical model, we are considering here, the weight function is a local Fermi-Dirac distribution function.…”

“…here we have represented as Σ 0 the absolute thermopower coefficient, λ 0 the thermal conductivity, Π 0 is the Peltier coefficient, and ρ 0 the electric resistivity coefficient. These kinetic thermotransport coefficients can be expressed in terms of the different relaxation times as follows, 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 When written in this form, the well known relationship between them, Π 0 = T Σ 0 , can only be satisfied if we impose the following general symmetry condition [1], (K B T/ϕ)(τ Q /τ JQ ) = −1/2. Let us note that these thermoelectric coefficients represent only the contributions coming from some specific interaction between electrons and the lattice phonons.…”