Elementary processes in a SESAM

3.3 Elementary processes in a SESAM

The intensity dependent reflectivity of a SESAM results from the saturation of the electronic transitions within the quantum well absorber. If an electron from the valence band absorbs incoming light with a photon energy exceeding the band gap energy the electron is excited into the conduction band. Due to the fact that the density of states in the conduction band of semiconductors is smaller than the density of states in the valence band, for high fluence values all states are occupied [Yu03]. Hence, due to band filling and Pauli’s exclusion principle the absorber bleaches and the photons are reflected by the Bragg mirror. This leads to an increase of the reflectivity with increasing light intensity. One distinguishes between single-photon absorption and induced absorption, two effects which will be discussed separately in the next sections.

3.3.1 Single photon absorption

If a SESAM is excited by a laser pulse with photon energy exceeding the band gap energy of the quantum well the absorption process is followed by different regimes of carrier distribution and carrier dynamics. The following regimes are taken from [Sha99]

and are explained in the following paragraph. Fig. 3.4 shows a schematic representa-tion of the carrier distriburepresenta-tion and carrier dynamics.

The excitation energy of the photon exceeds the band gap energy so that the electron is excited in states above the band minimum, as it is shown in transition (1) in Fig. 3.4.

In SESAMs resonant excitation is avoided to prevent excitonic absorption close to the band gap energy. The carrier distribution directly after excitation is called coherent regime, since there is a fixed phase relation between the excited states and the ex-citing electromagnetic wave. Due to electron-phonon scattering and electron-electron scattering this regime is destroyed and the so called nonthermal regime follows. This regime is specified by the temperatures of the carrier distributions which exceed the lat-tice temperature. The excited electron-hole pairs thermalize mainly via carrier-carrier scattering, corresponding to transition (3) in Fig. 3.4, which leads to the hot carrier regime. The hot carriers lose their energy mainly via phonon interaction and relax in the band minimum, as it is shown in process (3) in Fig. 3.4. All carriers and phonons within the semiconductor are now thermally balanced.

The relaxation process is followed by the recombination process, where defect states function as recombination centers, as it is shown in transition Fig. 3.4 (4). The electron-hole pairs recombine nonradiative. The final regime after the relaxation is called isothermal regime.

These carrier dynamics determine the transient reflectivity in pump-probe measure-ments of SESAMs. For low fluence values and an exciting fs-pulse the transients exhibits a biexponential decay: The first decay with a fast time constant in the fs-regime correspond to the thermalization and relaxation process of the excited electrons, whereas the slow time constant correspond to the recombination process [Kel99]. As it is described in Section 3.4, the slow time constant is determined by the amount of defect states and can vary from a few ps up to ns depending on growth parameters.

VB CB

(1) (2)

(3)

(4)

E_gap D

(III) (I)

(II)

k E

Figure 3.4: Carrier dynamics in a semiconductor after optical excitation with photon energy exceeding the band gap energy: E_photon > E_gap. (1) Excitation of the electron from the valence band (VB) into the conduction band (CB) by photon absorption.

The carrier distribution is given by the energy spectrum of the exciting field (I). (2) Thermalization of the nonthermal regime into the hot electron regime by means of electron scattering. (3) Relaxation of the hot electrons into the conduction band mini-mum via phonon scattering. The carrier distribution is given in (II). (4) Electron-hole recombination via defect states (D). (III) shows the carrier distribution of the holes.

The figure is adopted from [Sei03], the carrier dynamics are taken from [Sha99].

3.3 Elementary processes in a SESAM

3.3.2 Induced absorption

In Section 3.2.2 it was already mentioned that due to nonlinear effects at high fluence values the reflectivity curve decreases again exhibiting a roll-over. This roll-over is mainly due to two-photon absorption and free-carrier absorption [Gra05]. Both effects will shortly be explained within this paragraph.

The simultaneous absorption of two photons within a semiconductor is called two-photon absorption (TPA). With the help of a virtual state an electron is raised from the valence band into the conduction band [She84]. The energy difference of the initial and final state of the electron is that of two absorbed photons. Since the absorbed en-ergy of a TPA process is higher than that of single-photon absorption, the electron is excited in high states within the conduction band [Jos00]. TPA generates hot carriers not only in the quantum wells but also in the spacer layers and in the Bragg mirror.

The probability for TPA is proportional to the square of the light intensity [Mil88].

Thus, in a SESAM two-photon absorption increases with increasing fluence and de-creasing pulse duration [Gra05]. Consequently, in a SESAM TPA leads to a stronger roll-over in the fs-regime than in the ps-regime

Free electrons do also absorb photons. This effect is known as free-carrier absorption (FCA). Electrons are already occupying states within the conduction band, so that due to a further photon absorption they are excited into even higher states. In this case photon absorption leads to an intraband transition within the conduction band instead of an interband transition [Fan56]. High-fluence effects such as FCA and TPA are also known as induced absorption [Jos00].

A detailed analysis about induced absorption and its effects on SESAMs is published in [Tho99, Jos00, Gra05, Sar12b]. It is found out that FCA is more important at higher fluences when carriers generated by TPA can contribute to FCA [Jos00].

In general, TPA and FCA reduce the nonlinear reflectivity at high fluence values: Due to induced absorption the electrons occupy higher states within the conduction band which results in free states at lower energy levels. Hence, the absorber is not fully bleached and the reflectivity of the SESAM is decreased. This results in a reduction of the modulation depth leading to the effective modulation depth ∆R_eff, as it is illus-trated in Fig. 3.3. Hence, induced absorption has an important impact on the stability regime of a SESAM mode-locked laser, as it is discussed in detail in [Gra05]. Since it reduces the effective modulation depth, it can suppress Q-switching instabilities but favor double pulsing, too [Gra05].

Methods to influence the roll-over of a SESAM and other important parameters are summarized in the following section.

Lattice constant (Å)

Energyga at 42 K (V)p.e

4.0

3.0

2.0

1.0

0.0

4.4 4.6 4.8 5.4 5.6 5.8 6.0 6.2 6.4 6.6

Figure 3.5: Band gap energy versus lattice constant for different compound semicon-ductors. The figure is taken from [Yu03].