Relaxation of Energy and Momentum in an Carrier-Phonon System

A. Rossani

Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi, Torino, Italy.

DOI: 10.4236/jmp.2012.38103                

Abstract

If electrons (e) and holes (h) in metals or semiconductors are heated to the temperatures Te and Th greater than the lattice temperature Tp, the electron-phonon interaction causes energy relaxation. In the non-uniform case a momentum relaxation occurs as well. In view of such an application, a new model, based on an asymptotic procedure for solving the generalized kinetic equations of carriers and phonons is proposed, which gives naturally the displaced Maxwellian at the leading order. After that, balance equations for the electron number, hole number, energy densities, and momentum densities are constructed, which constitute now a system of five equations for the electron chemical potential, the temperatures and the drift velocities. In the drift-diffusion approximation the constitutive laws are derived and the Onsager relations recovered.

Keywords

Energy; Momentum

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	A. Rossani, A. M. Scarfone, “Generalized Kinetic Theory of Electrons and Phonons: Models, Equilibrium, Stability,” Physica B: Condensed Matter, Vol. 334, 2003, pp. 292-297. doi:10.1016/S0921-4526(03)00079-6
[2]	I. Koponen, “Thermalization of an Electron-Phonon System in a Non-Equilibrium Statecharacterized by Fractal Distribution of Phonon Excitations,” Physical Review E, Vol. 55, No. 6, 1997, pp. 7759-7762.
[3]	A. Rossani, “Generalized Kinetic Theory of Electrons and Phonons,” Physica A: Statistical Mechanics and its Applications, Vol. 305, No. 1-2, 2002, pp. 323-329. doi:10.1016/S0378-4371(01)00682-3
[4]	A. M. Anile and S. Pennisi, “Thermodynamic Derivation of the Hydrodynamical Model for Charge Transport in Semiconductors,” Physical Review B, Vol. 46, No. 20, 1992, pp. 13186-13193.
[5]	A. Rossani, G. Spiga, A. Domaingo, “Band-Trap Capture and Emission in the Generalized Kinetic Theory of Elec- trons and Holes,” Journal of Physics A: Mathematical and General, Vol. 36, No. 48, 2003, Article ID: 11955. doi:10.1088/0305-4470/36/48/004
[6]	N. B. Abdallah, P. Degond and S. Genyeis, “An Energy-Transport Model for Semiconductors Derived from the Boltzmann Equation,” Journal of Statistical Physicss, Vol. 84, No. 1-2, 1996, pp. 205-231. doi:10.1007/BF02179583
[7]	A. Rossani and G. Spiga, “Auger Effect in the Generalized Kinetic Theory of Electrons and Holes,” Journal of Mathematical Physics, Vol. 47, No. 13, 2006, Article ID: 013301. doi:10.1063/1.2161020
[8]	N. B. Abdallah and P. Degond, “On a Hierarchy of Ma- croscopic Models for Semiconductors,” Journal of Mathematical Physics, Vol. 37, No. 7, 1996, pp. 3306-3333. doi:10.1063/1.531567