A Generalized Roosbroeck-Schockley Relation for III-Nitrides in Far-from-Equilibrium Conditions
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A Generalized Roosbroeck-Schockley Relation for III-Nitrides in Far-from-Equilibrium Conditions A. R. Vasconcellos,1 R. Luzzi,1 C. G. Rodríguez,2 V. N. Freire,3 A. P. da Costa4 1 Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, 13083-970 Campinas, São Paulo, Brazil 2 Departamento de Física, Universidade Católica de Goiás, 74605-010 Goiânia, Goiás, Brazil 3 Departamento de Física, Universidade Federal do Ceará, Centro de Ciências, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil 4 Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Caixa Postal 1641, 59072-970 Natal, Rio Grande do Norte, Brazil
ABSTRACT We consider the behavior of the absorption coefficient and luminescence spectrum in the steady state when III-nitrides semiconductors (compounds GaN, AlN, and InN) are in far-fromequilibrium conditions created by an electric field. We analyze the high frequency part of the spectra obtaining a generalization of the Roosbroeck-Schockley relation, ΛRS(ω, EF), the ratio between the frequency dependent luminescence I(ω) and the absorption coefficient α(ω), for nonequilibrium conditions which are dependent on the electric field intensity EF. We show that the carrier´s temperature within a small error is proportional to d ln[ΛRS(ω, EF)]/dω. INTRODUCTION Large gap semiconductors of the III-Nitrides family are presently receiving particular attention due to their technological applications in blue/UV light emitting diodes and diodes lasers. The properties of far-from-equilibrium carriers in these systems are a matter of interest since the knowledge of their evolution to the steady state is very important for the design improvement of both devices. For example, heating of photogenerated electrons and holes in highly excited GaN epilayers was probed recently, indicating different patterns of energy dissipation [1]. Hot electron relaxation in n-type doped GaN was show to be dominated by longitudinal optical (LO)-phonon emission with relaxation time as small as 0.1 ps [2], which highlights the role of nonequilibrium statistical physics for the description of the carriers dynamics in GaN. The purpose of this work is to show that the absorption coefficient and luminescence spectrum in far-from-equilibrium III-Nitrides subjected to an electric field EF satisfy a generalized electric-field dependent Roosbroeck-Schockley-like relation. THE GENERALIZED ROOSBROECK-SCHOCKLEY RELATION We consider the absorption coefficient and the luminescence spectrum of III-nitrides in the steady-state in far-from-equilibrium conditions created by an electric field. Resorting to a nonequilibrium formalism in the form of the Nonequilibrium Statistical Operator Method [3,4], the nonequilibrium thermodynamic state of the system is characterized by the mean energy density, and linear momentum of electrons and holes. Alternatively, intensive nonequilibrium G6.44.1
thermodynamic variables can be introduced, which are the so called carrier´s quasitemperature (T*c), quasichemi
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