2.1 Ultrafast solid-state lasers - ETH - the Keller Group

84 2.1.4 Loss modulation [Ref. p. 134
Energy E
e
III
phonon
e
II
e
IV
I
Wave vector
k
Fig. 2.1.10. Schematic dispersion diagram of a 2-band bulk semiconductor
showing the time regimes I–IV after optical excitation,
see text for more details. e–e: electron–electron scattering.
e–phonon: electron–phonon scattering.
After the loss of coherence, ultrafast spectroscopy of semiconductors is solely concerned with
the dynamics of the population, i.e., electron and hole distributions. In this incoherent regime,
the time regimes II–IV in Fig. 2.1.10 can be distinguished, as described as follows. The initial
electron and hole distributions are non-thermal in most cases, i.e., they cannot be described by
Fermi–Dirac statistics with a well-defined temperature [85Oud, 86Kno, 87Sch]. Scattering among
charge carriers is mainly responsible for the redistribution of energy within the carrier distributions
and for the formation of thermal distributions. This thermalization is shown as time regime II in
Fig. 2.1.10, for the example of a thermalizing electron distribution where thermalization occurs
through scattering among the electrons. For excitation of the continuum, thermalization usually
occurs on a time scale of 100 fs under most experimental conditions. The exact thermalization time
strongly depends on the carrier density, the excess photon energy with respect to the band edge
and the type of carrier [99Sha].
In general, the carriers have a temperature different from the lattice temperature after thermalization
has been completed. In Fig. 2.1.10 it is assumed that the carriers have a higher temperature
than the lattice. For this case, Fig. 2.1.10 schematically shows the cooling of carriers by the emission
of phonons, i.e., energy transfer to the lattice. Cooling defines the time regime III. Typical
time constants are in the picosecond and tens of picosecond range.
Finally, the optically excited semiconductor returns to thermodynamic equilibrium by the recombination
of electron–hole pairs. Recombination is shown as time regime IV in Fig. 2.1.10. In a
perfect semiconductor crystal, recombination proceeds via the emission of photons or Auger processes
at high carrier densities. These recombination processes in a good quality semiconductor
(i.e. with a low level of defect states) take place on time scales of hundreds of picoseconds and
longer.
Another ultrafast process is encountered if large densities of deep-level traps are incorporated
in a semiconductor. Trapping of carriers into deep levels can proceed on sub-picosecond time
scales (not shown in Fig. 2.1.10). Since carrier trapping is important in many saturable absorber
applications, it is discussed in more details in Sect. 2.1.4.3.2.
We note that the different time regimes temporally overlap. For example, a scattering process
may destroy the coherence and contribute to thermalization. Nevertheless, it is very useful to
distinguish between the different time regimes because they are a convenient means for the description
of the complex semiconductor dynamics. The schematic picture of the different time regimes
also demonstrates that two or more time constants are usually required to describe the temporal
response of a semiconductor absorber. For example, we recall that thermalization typically takes
place on the 100-fs time scale while carrier trapping proceeds on time scales from a few hundreds
Landolt-Börnstein
New Series VIII/1B1