This Demonstrations shows a threelevel scheme useful for describing the luminescence decays of lowdimensional quantum systems, such as singlewalled carbon nanotubes and quantum dots. The excitedstate photophysics of these systems can be modeled with an optically active exciton state, namely bright exciton , with an optically forbidden level below, known as dark exciton , separated by a splitting energy (of the order of a few meV). Recombination from both levels to the electronic ground state is recovered by the related rates (mainly nonradiative) and (purely nonradiative), respectively. The inverse quantities give the lifetimes of these excitons. Thermalization between dark and bright states can occur through coupling to acoustic phonon modes, involving one phonon absorption and emission process, with upward and downward scattering rates, where is the phonon occupation number given by the Bose–Einstein distribution function and is the temperatureindependent scattering rate (set to a typical value of 0.05 for simplicity). The kinetic equations for the bright and dark state populations and as a function of time are given by the following system of coupled differential equations: This Demonstration implements the numerical solution of this system of equations and lets you explore dynamically the solutions at a given temperature as a function of scattering rates, brightdark energy splitting, and the initial population of bright state . The initial population of the dark state is set to .
For more information, see [1], [2], and [3]. In [3] is a treatment of spinflip processes using the FermiDirac distribution function, but with similar rate equations as in [1] and [2]. [1] T. Gokus, L. Cognet, J. G. Duque, M. Pasquali, A. Hartschuh, and B. Lounis, "Mono and Biexponential Luminescence Decays of Individual SingleWalled Carbon Nanotubes," Journal of Physical Chemistry C 114(33), 2010 pp. 14025–14028. [2] R. Matsunaga, Y. Miyauchi, K. Matsuda, and Y. Kanemitsu, "SymmetryInduced Nonequilibrium Distributions of Bright and Dark Exciton States in Single Carbon Nanotubes," Physical Review B, 80, 2009 p. 115436. [3] P. A. Dalgarno, J. M. Smith, B. D. Gerardot, A. O. Govorov, K. Karrai, P. M. Petroff, and R. J. Warburton, "Dark Exciton Decay Dynamics of a Semiconductor Quantum Dot," Physica Status Solidi A 202(14), 2005 pp. 2591–2597.
(University of Padova, Italy)
