On the calculation of transport integrals in lead chalcogenides

Abstract

The calculation of transport effects requires both the knowledge of some intrinsic material parameters (deformation potentials, effective masses, impurities potential well strength, etc. ) and the values of integrals, which as a rule cannot be represented by elementary functions. When a relaxation time for the carrier scattering r can be introduced, these integrals a r e of the formwhere fo is the Fermi-Dirac distribution function, and E, k(E), and m(E) are the energy, the wave number, and the effective mass of the carriers with a relevant energy dependence determined by the adopted energy dispersion law.When narrow band-gap semiconductors are concerned and Kane-type band is applicable, and on the assumption that the relaxation time depends on energy only through the density of energy states, one readily obtains the so-called generalised Fermi-Dirac integralswhere z = E KT, p= kT/E , and x = E/kT a r e the reduced Fermi energy, the non-parabolicity parameter and the dimensionless energy of the carriers (E is the band gap). These integrals were calculated by Zawadski et al. /2/ and listings for some values of z and B can be found in /3/. When p + O these integrals reduce to the ordinary Fermi-Dirac integrals, corresponding to a parabolic energy dispersion law, according to /4/

Thermoelectric Power of Solid Solutions (PbTe)1–x(Bi2Te3)x with 0 ≦ x ≦ 0.02

“…So to analyze this dependence information about the position of the Fermi level F* (the reduced Fermi level F ) for the examined solid solutions is necessary. The reduced Fermi level F is calculated from the experimental data of thermoelectric power S according to the expression [23] Here ko is the Boltzmann constant, e the electron charge, "L,"(F,D) are the modified Fermi-Dirac integrals [24] of the type…”

“…The values of the modified two-parameter Fermi-Dirac integrals "L;(F, 8) are taken from [24]. It is assumed that the direct energy gap of the solid solutions PbTe-Bi,Te, changes with temperature as the energy gap of the undoped PbTe [l].…”

Electrical Resistivity and Scattering Mechanisms of GeTe-Rich Thermoelectric Materials in the System GeTe-AgBiTe2

“…where k 0 is the Boltzmann constant, e 1:6 Â 10 À19 C is the electron charge, T is the temperature, m * d is the density-of-states effective mass of holes, m * c is the conduction effective mass of holes, h is the reduced Planck constant, r is the scattering index, and 0 L r3=2 2 F * ; b are modified Fermi-Dirac integrals of the type [8] n L m k F * ; b 3 Àk=2…”

“…According to (8), if the assumed mechanisms of carrier scattering are valid, the product r 0 L 1 2 F * ; b must be a linear function of reciprocal temperature. The product is calculated using the experimental values of r and the modified Fermi-Dirac integrals 0 L 1 2 F * ; b.…”

Electrical resistivity and thermoelectric power of (GeTe)1−x(Bi2Te3)x solid solutions (0 ≤x≤ 0.05) in the temperature interval from 80 to 350 K

“…From the experimental temperature dependence of the thermoelectric power S(T)(Fig. 2) the reduced Fermi energy F for the examined (GeTe)l -,(BiaTe3), solid solutions is calculated using the expression[14] …”