Comparison of ultrafast carrier thermalization in ${\text{Ga}}_x{\text{In}}_{1-x}\text{As}$ and Ge quantum wells

The thermalization of photoexcited carriers is investigated using femtosecond pump-probe spectroscopy in both (GaIn)As and Ge quantum wells. In both materials a nonthermal electron distribution is observed. The continuous relaxation from the point of injection toward the ground state and the thermalization of the carrier distribution are monitored on a time scale of up to 500 fs at room temperature. Carriers in (GaIn)As thermalize within 300 fs when injected with an excess energy of 250 meV. Separate carrier distributions for the heavy-hole and light-hole systems are found since the angular momentum transfer required for a transition is slow. Thermalization in Ge is found to be slightly slower in comparison due to the lack of Fröhlich interaction.

Figure 1

(Color online). Differential absorption spectrum of the (GaIn)As quantum well sample shown in false color for (a) 293 and (b) 10 K. The sample was in both cases excited by 80 fs pulses centered in the continuum of the hh2-c2 transition. In (a), the linear absorption spectrum is shown for reference as solid black line. The three fundamental transitions can be best seen in the low-temperature differential absorption spectrum (see text).

Figure 2

(Color online). Shift and bleaching signals of the hh1-c1 transition at 293 K for varying carrier injection excess energy. Ultrafast charge screening and the ac Stark effect lead to a quasi-instantaneous shift of the resonance as the sample is excited. The population transfer from the point of injection downwards to the hh1 and c1 states at the respective band edges is delayed by 310, 430, and 520 fs for an excess energy of 90, 120, and 210 meV, respectively.

Figure 3

(Color online). Shift and bleaching signals of the hh1-c1 transition at 10 K for varying carrier injection excess energy. The population transfer is significantly slower than at 293 K and takes 470, 500, and 1000 fs for an excess energy of 80, 130 and 280 meV, respectively.

Figure 4

(Color online). Bleaching signal at the three fundamental transitions of the GaInAs QW excited in the continuum of the hh2-c2 resonance. Rabi flops of the polarization at the hh2-c2 transition are observed. The carriers relax in energy toward the band edges and subsequently populate the states in between. This leads to bleaching at the hh1-c1 transition after 200 fs and, with a delay of 300 fs, the lh1-c1 transition.

Figure 5

(Color online) (a) Linear absorption spectrum of the Ge quantum well sample. Differential absorption spectra on a false-color scale for excitation at the (b) $\text{hh}3\text{-c}\Gamma 3$ and at the (c) $\text{hh}1\text{-c}\Gamma 1$ transition. The black arrows follow the relaxation.

Figure 6

(Color online) False-color-coded differential absorption spectra for (a) 293 and (b) 100 K lattice temperature. The sample is excited at the $\text{hh}2\text{-c}\Gamma 2$ transition in both cases, as indicated by the gray pulse shape. The colored arrowheads at the top indicate the spectral positions of the time traces shown in Fig. 7.

Figure 7

(Color online) Temporal evolution of the differential absorption (a) at the transition energies as shown in the center part (b). The time traces reveal the scattering dynamics in the carrier system as schematically depicted in (c). Here, both scattering to states higher in energy is observed as well as depopulation of the $\text{c}\Gamma$ states to the L valley.