Optical Phonon Sidebands of Electronic Intersubband Absorption in Strongly Polar Semiconductor Heterostructures

We present the first evidence for a distinct optical phonon progression in the linear and nonlinear intersubband absorption spectra of electrons in a $\mathrm{G}\mathrm{a}\mathrm{N}/{\mathrm{A}\mathrm{l}}_{0.8}{\mathrm{G}\mathrm{a}}_{0.2}\mathrm{N}$ heterostructure. Femtosecond two-color pump-probe experiments in the midinfrared reveal spectral holes on different vibronic transitions separated by the LO-phonon frequency. These features wash out with a decay time of 80 fs due to spectral diffusion. The remaining nonlinear transmission changes decay with a time constant of 380 fs. All results observed are described by the independent boson model.

Figure 1

(a) Cross section through the prism-shaped sample. (b) Self-consistent calculation of the triangular potential well and the probability densities of the two lowest electron subbands $n=1$ and $n=2$ near the $\mathrm{G}\mathrm{a}\mathrm{N}/{\mathrm{A}\mathrm{l}}_{0.8}{\mathrm{G}\mathrm{a}}_{0.2}\mathrm{N}$ interface. (c) Measured (symbols) and calculated (solid line) absorption spectrum. The broad absorption band is due to transitions of electrons from the $n=1$ to the $n=2$ subband in the triangular potential well shown in (b).

Figure 2

Time transients from two-color midinfrared pump-probe experiments for detection energies of $E_{\det }=258\mathrm{m}\mathrm{e}\mathrm{V}$ (circles: resonant to $\Delta \nu =0$ transitions) and $E_{\det }=337\mathrm{m}\mathrm{e}\mathrm{V}$ (diamonds: $\Delta \nu =+1$). The transmission change of the $\mathrm{G}\mathrm{a}\mathrm{N}/\mathrm{A}\mathrm{l}\mathrm{G}\mathrm{a}\mathrm{N}$ sample is plotted as a function of the delay between pump and probe. The pump pulse at 355 meV is resonant to the vibronic transition between $|n=1,\nu =0⟩$ and $|n=2,\nu =1⟩$ in the harmonic potential surfaces of the coupled electron–LO-phonon system shown in the upper right corner.

Figure 3

Measured (symbols) [22] and calculated (solid line) transient spectra from two-color pump-probe experiments for different delays between pump and probe. (a) The spectrum of the 100 fs pump pulse (dashed line) is shown for comparison. (c) After spectral diffusion the nonlinear transmission spectrum has the shape of the sum of the linear absorption spectrum (dashed line) and the Stokes-shifted gain spectrum (dotted line).