Scattering Processes in Semiconductors and Their Nanostructures

Whenever a semiconductor in thermodynamic equilibrium is excited by an ultrashort laser pulse, it undergoes several stages of energy and momentum relaxation before it returns once again to the thermodynamic equilibrium. The dynamics of photoexcited carriers (electrons and holes) are influenced by the interaction among them, as well as with the phonons, impurities, defects, and interfaces of the system. In the temporal region, one can classify those processes into four regimes: (1) coherent regime (<200 fsec); (2) non-thermal regime (<2 psec); (3) hot carrier regime (~1—100 psec); and (4) isothermal regime (>100 psec). Figure 7 illustrates some of the involved ultrafast scattering processes in the dynamics of photoexcited carriers in semiconductors and their nanostructures.

Carrier-carrier scattering determines the exchange of energy and momentum between carriers. This scattering process is primarily responsible for the mail thermaliza-tion channel of photoexcited nonthermal carriers in the early stage. This process is mainly due to the Coulomb interaction between the electron-electron, hole-hole, and electron-hole. The difference in the masses between electrons and holes reduces the energy exchange between these two species. It was found that photoexcited

[Coherent Regime | |

Hot Carrier Regime |

• Carrier-Carrier Scattering

• Hot Carrier-Phonon Interactions

«Intervalley Scattering

• Decay of Optical Phonons

• Hole-Optical Phonon Scattering

• Carrier-Acoustic Phonon Scattering

• Electron-Hole Scattering

• Electron-Optical Phonon Scattering

• Coherent Phonon Dephasing

• Carrier Trapping in Quantum Wells

* Electron-Hole Recombination

| Non-thermal Regime | i i

| Isothermal Regime | ■ '

100 fsec

1 psec 10 psec

Time

100 psec

FIGURE 7 Typical scattering and energy relaxation processes occurred in photoexcited semiconductors and their nanostructures. Four main relaxation regimes are indicated in the time axis.

100 fsec

1 psec 10 psec

Time

100 psec

FIGURE 7 Typical scattering and energy relaxation processes occurred in photoexcited semiconductors and their nanostructures. Four main relaxation regimes are indicated in the time axis.

holes reach thermal equilibrium faster than the electrons. The long-range Coulomb interaction diverges in the absence of screening. Screening is generally treated as the plasmon-phonon coupling and occurs in the nonthermal regime.

Interaction of carriers with phonons plays a major role in the exchange of energy and momentum between carriers and the lattice, and hence determines the relaxation of photoexcited carriers and their transport properties in semiconductors. Polar optical phonons, particularly, play an important role in carrier-phonon scattering processes in group III-V semiconductors. The interaction between polar optical phonons and low energy carriers is described by the Fröhlich interaction, in which the polar coupling strength varies inversely with the wavevector q of the phonon being emitted or absorbed. Since the Fröhlich interaction rate is expected to vary ml/2, the holes might be expected to interact more strongly with the LO phonons than the electrons, as indicated in Fig. 7. Note that the high-energy electrons and holes in subsidiary valleys can also interact with optical phonons through nonpolar optical deformation potential scattering. This interaction is also responsible for the intervalley scattering of electrons in the nonthermal regime. Interaction with both LA and TA

phonons can also be important in the thermalization process of hot carriers. However, if the carrier has sufficient energy to emit an optical phonon, then the optical phonon scattering rate is generally considerably higher than for the acoustic phonons. In brief summary, carrier-carrier scattering is primarily responsible for redistributing the energy and leads to a thermalized distribution function of the carrier system. The characterized temperature of the carrier system can be higher than the lattice temperature, and may be different for electron and hole systems. Typically, the electrons and holes thermalize among themselves in hundreds of femtoseconds, while the electrons and holes achieve a common temperature in a couple of picoseconds. The carrier system finally reaches lattice temperatures in hundreds of picoseconds through the interaction with various phonons in the semiconductor.

In the isothermal regime, all the carriers and phonons are in thermal equilibrium with each other, i.e., they can be described by the same lattice temperature. However, there is still an excess of electrons and holes compared to the thermodynamic equilibrium. These excess electrons and holes must return to the thermodynamic equilibrium through either radiative recombination or nonradiative recombination.

FIGURE 8 (a) Time-resolved second-harmonic generation spectroscopy reveals the generation of coherent phonon modes in native oxide covered GaAs (100) crystal. (b) Left inset shows the oscillatory part of the time domain data. (c) Right inset shows the Fourier power spectrum of the oscillatory part.

0 500 1000 1500 2000 2500 3000

Time Delay (femtosecond)

FIGURE 8 (a) Time-resolved second-harmonic generation spectroscopy reveals the generation of coherent phonon modes in native oxide covered GaAs (100) crystal. (b) Left inset shows the oscillatory part of the time domain data. (c) Right inset shows the Fourier power spectrum of the oscillatory part.

C. Dephasing of Coherent Phonons

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