Impact of piezoelectric fields on coherent zone-folded phonons in GaAs/AlAs superlattices

The amplitude decay of folded longitudinal acoustic phonon oscillations in GaAs/AlAs superlattices grown in the [100] and [111] directions is studied as a function of carrier excitation density. Time-resolved pump-probe measurements in reflection reveal decay times on the order of several tens of picoseconds, which are independent of the excitation density for all phonons in the [100] sample and for phonons at wave vectors $q\ne 0$ in the [111] sample. In contrast, the decay time increases with carrier density for the phonon at $q=0$ in the [111] sample. This phonon couples to the photoexcited electron-hole plasma via the piezoelectric interaction. Friction in the carrier plasma induces a damping of the phonon oscillations. The impact of the piezoelectric phonon-electron coupling on the amplitude decay is reduced by screening at high carrier density, resulting in longer phonon decay times.

Figure 1

(a) Transients of the reflectivity change of the [100] sample (blue) and the [111] sample (red). The reflectivity change $\mathrm{\Delta }R/R_0=(R-R_0)/R_0$ is plotted as a function of pump-probe delay ($R,R_0$: reflectivity with and without excitation). The energy of the pump pulse was 9.5 nJ. (b), (c) Oscillatory components of the transients in (a) after subtraction of a ratelike background kinetics. (d) Kinetics of spectrally integrated superlattice photoluminescence (25 ps time resolution) from the [100] sample. The recombination time of 0.9 ns is much longer than the decay times of the coherent phonon amplitudes shown in Fig. 3.

Figure 2

(a) Calculated dispersion curves of folded longitudinal acoustic phonons for the two growth directions. (b), (c) Spectra of the oscillatory signals from Figs. 1 and 1. (d) Same as in (c), but for a lower carrier density. The dashed arrows connect the observed peaks to the dispersion curves.

Figure 3

(a) Envelopes of the $P_0$ oscillation at 510 GHz in the [111] sample at two different carrier densities. A much faster decrease is observed at lower carrier densities. (b), (c) Corresponding linewidths (FWHM) as a function of carrier density.

Figure 4

(a) Displacement of the modes $P_{-1}$ (dashed green line) and $P_0$ (solid black line). (b) Corresponding strain. While both the displacement and the stress are continuous at the layer boundaries [Eqs. (2) and (3)], the strain exhibits jumps because of the different elastic constants. The displacement and the strain look identical for longitudinal folded phonons in both directions, [100] and [111], but the strain generates a piezoelectric polarization only in the [111] direction.