Population decay time and distribution of exciton states analyzed by rate equations based on theoretical phononic and electron-collisional rate coefficients

• Published in: Physical review. B 2017-11, Vol.96 (20), Article 205204
• Main Authors: Oki, Kensuke, Ma, Bei, Ishitani, Yoshihiro
• Format: Article
• Language: English
• Subjects: Boltzmann distribution; Decay rate; Dependence; Electrons; Excitation; Excitons; Fluxes; Hydrogen plasma; Kinetic energy; Mathematical models; Population; Population distribution
• ISSN: 2469-9950; 2469-9969
• DOI: 10.1103/PhysRevB.96.205204

Population distributions and transition fluxes of the A exciton in bulk GaN are theoretically analyzed using rate equations of states of the principal quantum number n up to 5 and the continuum. These rate equations consist of the terms of radiative, electron-collisional, and phononic processes. The dependence of the rate coefficients on temperature is revealed on the basis of the collisional-radiative model of hydrogen plasma for the electron-collisional processes and theoretical formulation using Fermi's “golden rule” for the phononic processes. The respective effects of the variations in electron, exciton, and lattice temperatures are exhibited. This analysis is a base of the discussion on nonthermal equilibrium states of carrier-exciton-phonon dynamics. It is found that the exciton dissociation is enhanced even below 150 K mainly by the increase in the lattice temperature. When the thermal-equilibrium temperature increases, the population fluxes between the states of n>1 and the continuum become more dominant. Below 20 K, the severe deviation from the Saha-Boltzmann distribution occurs owing to the interband excitation flux being higher than the excitation flux from the 1S state. The population decay time of the 1S state at 300 K is more than ten times longer than the recombination lifetime of excitons with kinetic energy but without the upper levels (n>1 and the continuum). This phenomenon is caused by a shift of population distribution to the upper levels. This phonon-exciton-radiation model gives insights into the limitations of conventional analyses such as the ABC model, the Arrhenius plot, the two-level model (n=1 and the continuum), and the neglect of the upper levels.