Direct determination of ultrafast intersubband hole relaxation times in voltage biased SiGe quantum wells by a density matrix interpretation of femtosecond resolved photocurrent experiments

• We report the quantitative and direct determination of hole intersubband relaxation times in a voltage biased SiGe heterostructure using density matrix calculations applied to a four-level system in order to interpret photocurrent (PC) pump-pump experiments. One consistent set of parameters allows the simulation of two kinds of experiments, namely pump-pump photocurrent experiments at a free electron laser (wavelength 7.9 mu m) and the laser-power dependence of the PC signal. This strongly confirms the high reliability of these parameter values, of which the most interesting in respect to Si based quantum cascade laser development is the extracted heavy-hole relaxation time. The simulations show that this relaxation time directly determines the experimentally observed decay of the pump-pump photocurrent signal as a function of the delay time. For a heavy hole intersubband spacing of 160 meV, a value of 550 fs was obtained. The experimental method was further applied to determine the LH1-HH1 relaxation time of a second sample with a transition energy below the optical phonon energy. The observed relaxation time of 16 ps is consistent with the value found for the same structure by transmission pump-probe experiments.

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