Hole system heating by ultrafast interband energy transfer in optically excited Ge/SiGe quantum wells

An efficient scattering process between the electron system in the $L$ valley and the hole system in the $\Gamma$ valley in Ge/SiGe quantum wells is identified. Its dependencies on excitation energy and carrier density are analyzed using spectrally and time-resolved pump-probe experiments. This carrier scattering causes an ultrafast heating of the hole system leading to an additional bleaching signature appearing a few tens of picoseconds after the excitation. Our findings are supported by microscopic calculations of the absorption spectra for various carrier densities and temperatures based on the semiconductor Bloch equations. Additionally, this scattering mechanism explains the enhanced free carrier absorption observed in previously reported pump-probe experiments.

Figure 1

Typical time evolution of the Ge quantum well absorption around the direct band gap after optical excitation with 0.965 eV laser pulses. A clear ultrafast bleaching “recovers” after 1 ps and then starts to increase again on a picosecond timescale. The curves are shifted for clarity.

Figure 2

(a) Time evolution of the decreasing absorption for an excitation energy of 0.965 eV. (b) Calculated absorption for different hole temperatures showing very good agreement with the experiment shown in (a) and verifying the observation of a cooling hole system. (c) and (d) are similar to (a) and (b) and present results for a higher excitation energy (1.016 eV) showing no significant difference from the dynamics of (a), thus proving the minor contribution of the excess energy of the optical pulse to the heating of the holes in the monitored excess energy window. The curves are shifted for clarity.

Figure 3

Theoretically extracted hole temperatures during the first 50 ps after the optical excitation are shown for two excitation energies, 0.965 eV and 1.016 eV, respectively. Near-resonant and far-above-resonant optical excitations with different carrier densities show similar hole temperatures and cooling characteristics. Hence, the source of the hole temperature has to be attributed to intrinsic scattering mechanisms. The dashed line is a guide to the eye.

Figure 4

Influence of the carrier density on the heating and cooling of the hole system by an excitation energy of 0.965 eV. $p$ is the scaling factor for the different photon fluencies and $n$ is the scaling factor for the different carrier densities. (a) Experimental and (b) calculated absorption spectra for different excitation intensities and a time delay of 5 ps showing no change in the hole system temperature. (c) and (d) are the same as (a) and (b) but for a time delay of 500 ps demonstrating that the cooled hole systems have reached equal temperatures but the pump probe signals show different strengths of bleaching due to different carrier densities. The curves are shifted for clarity.