Carrier relaxation

The optical excitation of electron-hole pairs represents a non-equilibrium state. The subsequent relaxation processes from the initial state includes both carrier-carrier interactions and coupling to the bath phonons. In some treatments, there is a distinction made between carrier-carrier and carrier-phonon interactions in which the latter is referred to as thermalisation. A two-temperature model is invoked in that the carrier-carrier scattering leads to a statistical distribution that can be described by an elevated electronic temperature, relative to the temperature characterising the lattice phonons (Schoenlein et al, 1987 Schmuttenmaer et al, 1996). This two-temperature model is valid only if the carrier-carrier energy redistribution occurs on time scales much faster ( 10 times) than relaxation into phonons. This distinction has limited value when there is not a sufficient separation in time scale to make a two-temperature model applicable. The main emphasis in this section is on the dynamics of the energy distribution of the carriers as this is most relevant to energy storage applications. 

In the event that the optical excitation involves above-band-gap light or field-accelerated carriers, the kinetic energy of the electrons is above that of the k = 0 extremes of the valence band and conduction band and the carrier distribution includes hot carriers. The following discussion will chronicle the series of events that lead to the relaxation from this excess energy condition. 

In the case of photon absorption, the incident light field drives a polarisation in the material that promotes an electron from the valence band to the conduction band. At the instant of creation of the electron-hole pair, the spatial envelope functions of the electron and hole wavefunctions overlap and have a well-defined phase relationship. This initial state preparation is different from an exciton in that the electron-hole pairs are formed within an electronic continuum of states and are therefore unbounded. In such circumstances, the use of dynamics to describe the state evolution is more appropriate than an eigenstate description with perturbative couplings between states. 

The first process that occurs is the dephasing of the electron and hole wavefunctions. During the time interval that the electron and hole wavefunction have a degree of spatial overlap, there is an extremely rapid electron-hole scattering 

To provide some substantive details, carrier-carrier scattering is generally treated within a first-order time-dependent perturbation approach in which the transition rate from an initial k state to a final k is given by (Reggiani, 1985 Zhou, 1989) 

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Harb M, Emstorfer R, Dartigalongue T, Hebeisen CT, Jordan RE, Dwayne Miller RJ (2006) Carrier relaxation and lattice heating dynamics in silicon revealed by femtosecond electron diffraction. J Phys Chem B 110 25308-25313... 

Tb3+ The effect of the doping concentration on the optical spectra of Tb3+ in ZnO nanocrystals (5 nm) was investigated in details (Liu et al., 2001b). The PL intensity of Tb3+ centers increases with increasing Tb content at the expense of emission from defect states in the ZnO nanocrystals. The characteristic emission of Tb3+ at 544 nm is the strongest upon excitation of the ZnO host at 345 nm, which implies an efficient carrier relaxation from ZnO hosts to Tb3+ centers. For a 3-nm ZnO sample, the band-gap excitation is blue-shifted to 315 nm due to quantum size confinement. This significant ET from the ZnO nanociystal host to Tb3+ centers confirmed that Tb3+ ions can to some extent be effectively incorporated into ZnO nanocrystals. 

Carrier relaxation due to both optical and nonradiative intraband transitions in silicon quantum dots (QDs) in SiOa matrix is considered. Interaction of confined holes with optical phonons is studied. The Huang-Rhys factor governing intraband multiphonon transitions induced by this interaction is calculated. The new mechanism of nonradiative relaxation based on the interaction with local vibrations in polar glass is studied for electrons confined in Si QDs. 

Peak photocurrents excited In a polymer of bis ( -toluene-sulfonate) of 2,4-hexadlyne-l,6-dlol (PTS) by N2-laser pulses vary superquadratically with electric field. The ratio ip(E)/((i(E), where ()i denotes the carrier generation efficiency, increases linearly with field. This indicates that on a 10 ns scale the carrier drift velocity is a linear function of E. Information on carrier transport kinetics in the time domain of barrier controlled motion is inferred from the rise time of photocurrents excited by rectangular pulses of A88 nm light. The intensity dependence of the rate constant for carrier relaxation indicates efficient interaction between barrier-localized carriers and chain excitons promoting barrier crossing. 

In the spirit of providing an updated account of the various photophysical and photochemical process to help drive paradigm shifts in solar energy conversion, we will emphasise the specific details of the carrier-relaxation dynamics with respect to... 

Space-charge field and surface effects on carrier relaxation... 

The most significant relaxation process in terms of understanding the reaction branching ratios is the relaxation of the field accelerated minority carrier. The field further acts to localise the minority carrier in the surface region. For 1 eV of band bending and a space-charge width of 300 A (Ad lO cm ), the 1/e point in the minority-carrier distribution is localised to within 10 A of the surface. Thus the surface is expected to play a significant role in the minority-carrier relaxation. 

In terms of predictive capabilities, this distinction creates problems as most of the studies of hot-carrier relaxation have been confined to bulk processes by the virtue of the experimental limitations associated with all optical methods. The majority of the carriers are generated and probed in the bulk of the crystal. Fortunately, in the last few years significant progress has been made in the development of femtosecond photoemission spectroscopy (Bokor et al, 1986 Goldman and Prybyla, 1994 Haight, 1996 Schmuttenmaer et al, 1996) which is sensitive to the near-surface carrier relaxation processes. 

The main message from this class of experiments is that the details of the surface do affect the carrier relaxation. In the presence of surface defects associated with conventional surface preparation, the carrier relaxation in the surface region is exceptionally fast relative to bulk processes (10-100 fs dynamics). As can be seen by comparing the dynamics shown in Fig. 2.9, the effect of the surface is to increase the rate of relaxation and thermalisation. The asymmetry, more anharmonic character to the surface modes and increased mixing of states at defect sites all conspire to speed up the relaxation processes. With proper attention to surface structure, it is possible to intervene in the relaxation process and achieve carrier and phonon scattering rates that approach bulk processes. In this limit, 200 fs to picosecond dynamics define the operative time scales. 

Figure 2.11 Electron relaxation dynamics in 2-D-layered materials, (a) The electron relaxation dynamics for SnSi are shown for two different excess energy conditions within 0.1 eV of the CBM (the bandgap is 2.1 eV) and approximately 1 eV above the CBM. In both cases, the relaxation is extremely fast and occurs on 10 fs time scales. The Unes running through the data are best fits to single relaxation times of 40 fs and 60 fs for the 1 eV and 0.1 eV case, (b) The excess energy dependence corresponds to predictions where coupling to the broad plasmon band of these layered systems opens a new channel that significantly increases carrier relaxation above 3-D materials (compare Fig. 2.9).

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Zhou X. and Hsiang T. Y. (1990), Monte-Carlo determination of femtosecond dynamics of hot-carrier relaxation and scattering processes in bulk GaAs , J. Appl. Phys. 67,7399-7403. 

Figure 3.1 Hot-carrier relaxation/cooling in semiconductors. Source Nozik (2001b).

Mukai K. and Sngawara M. (1998), Slow carrier relaxation among snblevels in annealed self-formed InGaAs/GaAs quantum dots , Jpn. J. Appl. Phys. 37, 5451-5456. 

Rosker M. J., Wise F. W. and Tang C. L. (1986), Eemtosecond optical measurement of hot-carrier relaxation in GaAs, AlGaAs, and GaAs/AlGaAs multiple quantum well structures , App/. Phys. Lett. 49, 1726-1728. 

Sosnowski T. S., Norris T. B., Jiang H., Singh J., Kamath K. and Bhattacharya P. (1998), Rapid carrier relaxation in Ino.4Gao.6As/GaAs qnantum dots characterized... 

Vurgaftman 1. and Singh J. (1994), Effect of spectral broadening and electron-hole scattering on carrier relaxation in GaAs quantum dots , Appl. Phys. Lett. 64, 232-234. 

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