Dynamic processes

Abstract

The purpose of this chapter is to present the results of the dynamics of exciton (polariton)s or more generally of electron–hole pairs. For a recent review of this topic concentrating on quantum wells, see Davies and Jagadish (Laser Photon. Rev. 3(1), 1(2008)). We neither consider the dynamics of carriers, for example, their relaxation time entering in Hall mobility or electrical conductivity, nor the dynamics of phonons or spins, respectively. We give here only a very small selection of references to these topics (Baxter and Schmuttenmaer, J. Phys. Chem. B, 110:25229, 2006; Queiroz et al. Superlattice Microstruct. 42:270, 2007; Niehaus and Schwarz, Superlattice Microstruct. 42:299, 2007; Lee et al., J. Appl. Phys. 93:4939, 2003; A. K Azad, J. Han, W. Zhang, Appl. Phys. Lett. 88:021103, 2006; Janssen et al., QELS 2008 IEEE 2; D. Lagarde et al., Phys. Stat. Sol. C 4:472, 2007; S. Gosh et al., Appl. Phys. Lett. 86:232507, 2005; W. K. Liu et al. Phys. Rev. Lett. 98:186804, 2007). The main characteristic time constants relevant to optical properties close to the fundamental absorption edge are the dephasing time T 2, (i.e. the time after which the polarization amplitude of the optically excited electron–hole pair loses the coherence with the driving light field), the intra band or inter sub band relaxation times T 3 (i.e. the time it takes for the electron–hole pairs to relax from their initial state of excitation to a certain other state e.g. to a thermal distribution with a temperature equal to or possibly still above lattice temperature) and finally the lifetime T 1 (i.e. the time until the electron–hole pairs recombine). The characteristic time constants T 2 and T 1 are also known as transverse and longitudinal relaxation times, respectively. Their inverses are the corresponding rate constants. T 2 is inversely proportional to the homogeneous width Γ, and T 1 includes both the radiative and the generally dominating non-radiative recombination (Hauser et al., Appl. Phys. Lett. 92:211105, 2008). For this point, recall Figs. 6.16 and 6.33. Since the polarisation amplitude is gone in any case after the recombination process, there is an upper limit for T 2 given by T 2 ≤ 2 T1. The factor of two comes from the fact that T 2 describes the decay of an amplitude and T 1 the decay of a population, which is proportional to the amplitude squared. Sometimes T 2 is subdivided in a term due to recombination described by T 1 and another called ‘pure dephasing’ called T 2∗ with the relation 1 ∕ T 2 = 1 ∕ 2 T 1 + 1 ∕ T2∗. The quantity T 2∗ can considerably exceed 2 T 1. In the part on relaxation processes that is on processes contributing to T 3, we give also examples for the capture of excitons into bound, localized, or deep states. For more details on dynamics in semiconductors in general see for example, the (text-) books [Klingshirn, Semiconductor Optics, 3rd edn. (Springer, Berlin, 2006); Haug and Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th edn. (World Scientific, Singapore, 2004); Haug and Jauho, Quantum Kinetics in Transport and Optics of Semiconductors, Springer Series in Solid State Sciences vol. 123 (Springer, Berlin, 1996); J. Shah, Ultrafast Spectroscopy of Semiconductors and of Semiconductor Nanostructures, Springer Series in Solid State Sciences vol. 115 (Springer, Berlin, 1996); Schafer and Wegener, Semiconductor Optics and Transport Phenomena (Springer, Berlin, 2002)]. We present selected data for free, bound and localized excitons, biexcitons and electron–hole pairs in an EHP and examples for bulk materials, epilayers, quantum wells, nano rods and nano crystals with the restriction that – to the knowledge of the author – data are not available for all these systems, density ranges and temperatures. Therefore, we subdivide the topic below only according to the three time constants T 2, T 3 and T 1.