TY - JOUR
T1 - Nonequilibrium thermodynamic model of thermoelectricity and thermodiffusion in semiconductors
AU - Semenov, Semen N.
AU - Schimpf, Martin E.
N1 - Publisher Copyright:
© 2023 The Royal Society of Chemistry.
PY - 2023/2/8
Y1 - 2023/2/8
N2 - We present a self-consistent model rooted in nonequilibrium thermodynamics for defining concentration gradients in the electron/hole pairs and electric-field gradients in an intrinsic semiconductor created upon exposure to a temperature gradient. The model relies on the equation for entropy production expressed through phenomenological equations for the electron/hole flux, with the imposed condition that the resulting concentration profiles of the electrons and holes are identical. The chemical potentials of electrons, holes, and parent atoms of the lattice, which are contained in the flux equations, are calculated on the basis of the temperature-dependent equilibrium dissociation reaction: lattice atom ↔ electron + hole. Electron/hole concentration profiles resulting from the temperature gradient, along with the associated gradient in the electric field, are expressed through equilibrium microscopic parameters of the semiconductor, which include the effective masses of electrons and holes, the energy gap width, and the Debye temperature. The resulting expressions contain neither kinetic nor fitting parameters, and predict values in reasonable (order-of-magnitude) agreement with empirical data. Finally, the model predicts a measurable additional thermodiffusion-based Seebeck effect when the temperature difference is on the order of several tens of degrees across a nonisothermal semiconductor working as a power supply under conditions of optimal power transport.
AB - We present a self-consistent model rooted in nonequilibrium thermodynamics for defining concentration gradients in the electron/hole pairs and electric-field gradients in an intrinsic semiconductor created upon exposure to a temperature gradient. The model relies on the equation for entropy production expressed through phenomenological equations for the electron/hole flux, with the imposed condition that the resulting concentration profiles of the electrons and holes are identical. The chemical potentials of electrons, holes, and parent atoms of the lattice, which are contained in the flux equations, are calculated on the basis of the temperature-dependent equilibrium dissociation reaction: lattice atom ↔ electron + hole. Electron/hole concentration profiles resulting from the temperature gradient, along with the associated gradient in the electric field, are expressed through equilibrium microscopic parameters of the semiconductor, which include the effective masses of electrons and holes, the energy gap width, and the Debye temperature. The resulting expressions contain neither kinetic nor fitting parameters, and predict values in reasonable (order-of-magnitude) agreement with empirical data. Finally, the model predicts a measurable additional thermodiffusion-based Seebeck effect when the temperature difference is on the order of several tens of degrees across a nonisothermal semiconductor working as a power supply under conditions of optimal power transport.
UR - http://www.scopus.com/inward/record.url?scp=85148905783&partnerID=8YFLogxK
U2 - 10.1039/d2cp05065j
DO - 10.1039/d2cp05065j
M3 - Article
C2 - 36789789
AN - SCOPUS:85148905783
SN - 1463-9076
VL - 25
SP - 6790
EP - 6796
JO - Physical Chemistry Chemical Physics
JF - Physical Chemistry Chemical Physics
IS - 9
ER -