Influence of carrier-carrier interaction on time-dependent intersubband absorption in a semiconductor quantum well

Using ultrafast terahertz spectroscopy, we measure the temporal evolution of the intersubband absorption spectrum of a $\mathrm{GaAs}∕{\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ double-quantum-well structure with an energy spacing between the first two subbands smaller than the longitudinal optical phonon energy. We show that the interaction between the photoexcited carriers has a considerable influence on the time-dependent absorption. When varying the photoexcited sheet carrier density between $1\times {10}^{10}{\mathrm{cm}}^{-2}$ and more than $1\times {10}^{12}{\mathrm{cm}}^{-2}$, we find (i) a strong dependence of the intersubband scattering rate on the density of optically generated carriers, and (ii) a temporal shift of the intersubband resonance as the population in the second subband decays, i.e., as the photoexcited carriers relax into the quantum-well ground state.

Figure 1

(a) Energy-band diagram of the double-QW structure and (b) corresponding ISB absorption spectrum. (c) Schematic drawing of the sample geometry and pump-probe configuration.

Figure 2

(a) ISB absorption spectra at different time delays after the interband pump pulse for an excitation density of $n_{\mathrm{S}}=1\times {10}^{10}{\mathrm{cm}}^{-2}$. (b) Electron populations in subbands 1 and 2 as a function of time delay after the excitation (symbols, experiment; lines, results from a phenomenological rate-equation model).

Figure 3

(a) ISB absorption spectra at different time delays after the interband pump pulse for an excitation density of $n_{\mathrm{S}}=3\times {10}^{11}{\mathrm{cm}}^{-2}$. (b) Energetic position of the (1-3) ISB resonance as a function of the electron population in the second subband.

Figure 4

Calculated energies of the (1-3) and (2-3) ISB resonances for total sheet carrier densities of $n_{\mathrm{S}}=3\times {10}^{11}{\mathrm{cm}}^{-2}$ (circles), $6\times {10}^{11}{\mathrm{cm}}^{-2}$ (squares), $8\times {10}^{11}{\mathrm{cm}}^{-2}$ (diamonds), and $1\times {10}^{12}{\mathrm{cm}}^{-2}$ (triangles).

Figure 5

(a) Experimental ISB relaxation times (symbols). The calculation (dashed line) confirms the experimental results. (b) Maximum energy shift of the (1-3) ISB resonance.