* Corresponding author. Tel.: #33-4-67143822; fax: #33-4- 67547134. E-mail address: varani@cem2.univ-montp2.fr (L. Varani) Physica B 272 (1999) 247}249 Thermal conductivity of nonequilibrium carriers L. Varani*, P. Gaubert, J.C. Vaissie`re, J.P. Nougier, J. Mateos, T. Gonza H lez, D. Pardo, L. Reggiani, E. Starikov, P. Shiktorov, V. Gruzhinskis Centre d'Electronique et de Micro-optoe & lectronique de Montpellier (CNRS UMR 5507), Universite & Montpellier II, 34095 Montpellier cedex 5, France Departamento de Fn & sica Aplicada, Universidad de Salamanca Plaza de la Merced s/n, 37008 Salamanca, Spain Dipartimento di Ingegneria dell+ Innnovazione ed Istituto Nazionale di Fisica della Materia, Universita % di Lecce, via Arnesano, 73100 Lecce, Italy Semiconductor Physics Institute, Goshtauto 11, 2600 Vilnius, Lithuania Abstract We present a theoretical analysis of the thermal conductivity of charge carriers in semiconductors under nonequilib- rium conditions due to an applied electric "eld. The theory is based on a correlation-function formalism which directly relates this kinetic coe$cient to four spectral densities involving carrier velocity and energy #ux #uctuations. Monte Carlo calculations performed for the cases of p-Si and n-GaAs give an evidence of a strong dependence of the thermal conductivity on increasing electric "elds.  1999 Elsevier Science B.V. All rights reserved. Keywords: Thermal conductivity; Correlation functions; Monte Carlo Calculations; Energy transport 1. Introduction Thermal conductivity of charge carriers repres- ents one of the relevant kinetic coe$cients resulting from the motion of carriers under the action of a temperature gradient [1]. In contrast to other kinetic coe$cients, its dependence on the applied electric "eld has received minor attention from the semiconductor community. This can be attributed in part to a greater interest in the electrical than in the thermal properties, and in part to the di$culty in providing the experimental counterpart of the theoretical calculations due to the prevailing con- tribution of the lattice over that of the charge car- riers. It must be stressed however that a detailed analysis of energy #ux phenomena in semiconduc- tors is a mandatory issue of to-date small-device modelling: as a matter of fact quite di!erent electri- cal characteristics have been predicted according to the speci"c model used for the nonequilibrium ther- mal conductivity [2]. The most straightforward method to obtain kin- etic coe$cients consists in modelling the linear response of the system to weak external perturba- tions such as electric "eld, gradient of temperature, gradient of chemical potential, magnetic "eld, etc. On the other hand, one can take advantage of the #uctuation}dissipation relation [3] to obtain these coe$cients from the knowledge of an appro- priate set of correlation functions without including 0921-4526/99/$ - see front matter  1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 2 7 9 - 3