Ultrashort Laser Pulse Phenomena, 2nd Edition

Ultrafast Processes in Solid-State Materials 545

electronic system can exceed the lattice temperature by far. Depending on the

band structure and photon energy, intervalley scattering can occur.

Energy is transferred to the lattice (heating) by inelastic electron–phonon col-

lisions, and the carriers relax into states at the bottom of the band. The Fermi

distribution which is finally reached, can be characterized by a temperature which

is equivalent to the lattice temperature. If the excitation density is sufficiently

high, a local change in the lattice temperature can readily be observed. Extremely

high excitation can even result in melting. While the initial carrier scattering pro-

ceeds on a time scale of tens of fs or less, the intraband energy relaxation times

can amount to a few ps.

11.4.2. Excitons

Another interesting feature of the excitation spectrum of solids is the exci-

ton resonance. Excitons can be viewed as an electron–hole pair bound together

through the Coulomb attraction, with properties similar to a hydrogen atom.

Because of the positive Coulomb interaction, the corresponding energy levels

are below the band gap (cf. Fig. 11.7). If the energy of the exciton is raised by

an amount larger than the binding energy (E

b

), the bound systems decay into a

free electron and hole (exciton ionization). Such a process can be induced, for

example, by longitudinal optical (LO) phonon scattering and typically proceeds

on a time scale of about 100 fs in bulk materials at room temperature.

Owing to the strong excitonic oscillator strength and nonlinear susceptibili-

ties, transient properties of excitons have attracted much attention. In particular

in MQW structures, the exciton resonances can be clearly distinguished from the

bulk absorption at room temperature. Figure 11.8 displays the absorption spec-

trum of a CdZnTe–ZnTe MQW and the results of a pump–probe experiment [31].

The pump spectrum was chosen to excite predominantly excitons. The differential

transmission at the exciton resonance shows a fast increase and a partial recovery.

Its dynamics can be explained by exciton excitation, exciton ionization because

of LO-phonon scattering, and the presence of a coherent artifact. The increase of

the transmission at photon energies, which probe the occupation of states at the

bottom of the bands (λ = 610 nm), is a direct indication of the exciton ionization

into free carriers. The characteristic ionization time was determined to be about

110 fs [31].

11.4.3. Intraband Relaxation

Intraband relaxation processes can conveniently be observed using pump–

probe absorption techniques. A pump pulse of certain energy creates carriers at

546 Examples of Ultrafast Processes in Matter

Exciton absorption

Pump spectrum

Probe spectrum

580 600 620

Wavelength (nm)

640 660 680

500

1.0

0.5

0.0

0 1000

610 nm

620 nm

500

Relative delay (fs)

500 0 1000500

Relative delay (fs)

Differential transmission (a.u.)

1.0

0.5

0.0

Differential transmission (a.u.)

(a)

(b)

(c)

Figure 11.8 (a) Room temperature absorption spectrum of a CdZnTe–ZnTe MQW and the spectra

of the 80-fs pump pulse and 14-fs probe pulse. The latter is a self-phase modulated and compressed

part of the pump pulse. (b) Differential transmission at 620 nm and (c) 610 nm for a pump excitation

level of 2 × 10

11

carriers/cm

2

. The wavelength filtering was done after the sample with a filter with

a bandwidth of ≈8 nm (from Becker et al. [31]).

corresponding states above the band gap. Temporally delayed probe pulses of var-

ious frequencies test the occupation of states at different energies above the gap.

The results of such an experiment for Al

0.2

Ga

0.3

As are shown in Figure 11.9 [32].

A quantitative evaluation of the data is rather complicated, in view of the com-

plexity of the processes involved in highly excited semiconductors. The interested

reader is referred to the book by Haug and Koch [33]. Qualitatively, however,

the time resolved transmission data follow a pattern consistent with the basic

properties of the band model.

A rapid transmission change occurs not only at the excitation energy, but

over a broader spectral range, indicating a thermalization within a time range

significantly shorter than 100 fs. At 1.88 eV and 1.94 eV, a reduced change

in transmission can be attributed to the cooling of the electronic system through

energy transfer to the phonon system (lattice). This cooling results in a relaxation

of carriers toward the bottom of the band, thus emptying higher energy states.