Continuous Voltage Tunability of Intersubband Relaxation Times in Coupled SiGe Quantum Well Structures Using Ultrafast Spectroscopy

We demonstrate continuous voltage control of the nonradiative transition lifetime in semiconductor heterostructures. The results were obtained by picosecond time-resolved experiments on biased SiGe valence band quantum well structures using a free electron laser. By varying the applied voltage, the intersubband hole relaxation times for quantum well structures were varied by a factor of 2 as the wave functions and their overlaps were tuned. The range of magnitudes for the lifetime indicates a possible route to silicon-based quantum cascade lasers.

Figure 1

Two-photon PC experiments and simulation results. In (a), two-photon PC spectra obtained by varying the FEL wavelength in different polarizations are presented. The spectra for $S1$ and $S2$ are offset vertically for clarity. (b),(c) show the calculated HH, LH, and split-off (red, green, black) band edges at 1 V ($S1$) and 1.5 V ($S2$) bias and a contour plot of the absolute squared wave functions at their eigenenergy values for samples $S1$ and $S2$, respectively. The calculated LH1-HH1 energy differences are consistent with the spectral peak positions. The photoconducting final states of the two-photon absorption are highlighted by ellipses. The vertical lines in (a) indicate the energy at which the time-resolved measurements were performed.

Figure 2

Logarithmic plot of the PC through sample $S1$ as a function of the delay between pulse 1 ($\mathrm{TM}+\mathrm{TE}$) and pulse 2 (TE) for different bias voltages at a temperature of 4 K (positive delay means pulse 1 arrives second). A constant background equivalent to the current integral over the two noninteracting pulses (i.e., delays $>100\mathrm{ps}$) is subtracted separately for positive and negative delays and the traces are offset vertically for clarity. The additional, nonlinear PC signal clearly decays slower for increasing bias. The dotted lines indicate the measurements’ noise levels. The FEL micropulse energy density was $5\mu \mathrm{J}/{\mathrm{cm}}^2$ for both pulses. Also shown are results of the fitting procedure described in the text (blue lines).

Figure 3

Voltage dependence of the LH1-HH1 relaxation time. The dots show a clear, bias induced monotonic rise by a factor of 2 of both samples’ intersubband relaxation times extracted from the pump-pump data gained at 4 K. The red error bars and the green error bars indicate the 68% confidence limits of the fitted relaxation times. The solid lines serve as a guide for the eye.

Figure 4

Change in the band structure of $S1$ for applied voltages of 0.75 and 1.7 V. The plots show the calculated heavy and light (red lines and green lines) hole band edges and the absolute squared wave functions at their eigenenergy values. In (a) the LH1 state of the central well is confined, while it couples to the LH state of the side well in (b). Therefore, for a bias of 1.6 V the center of mass for holes excited from HH1 into LH states is shifted from the central well, the relaxing transition to the HH ground state is a diagonal one with a reduced hole density overlap. Consequently, the relaxation time increases from (a) to (b).