Localization-Dependent Photoluminescence Spectrum of Biexcitons in Semiconductor Quantum Wires

We study exciton and biexciton spectra in disordered semiconductor quantum wires by means of nanophotoluminescence spectroscopy. We demonstrate a close link between the exciton localization length along the wire and the occurrence of a biexciton spectral line. The biexciton signature appears only if the corresponding exciton state extends over more than a few tens of nanometers. We also measure a nonmonotonous variation of the biexciton binding energy with decreasing exciton localization length. This behavior is quantitatively well reproduced by the solution of the single-band Schrödinger equation of the four-particle problem in a one-dimensional confining potential.

Figure 1

(a) Near-field spectra taken at low-excitation intensity ($I_0=10\mathrm{mW}{\mathrm{cm}}^{-2}$) and at regular spatial intervals of 120 nm along the QWR in a spatial domain of type A, indicating an extension of about 300 nm for the exciton line. (b) Two near-field spectra taken at the center of this domain for different excitation intensities, showing the presence of an additional line at high excitation. (c) Log-log plot of the integrated intensity dependence on the laser power of the exciton and biexciton emission lines. Fits to a power law $I_{\mathrm{PL}}\propto I_{\mathrm{exc}}^n$ are also plotted.

Figure 2

Near-field spectra taken in three different QWR domains of type B and for two different excitation intensities ($I_0=10\mathrm{mW}{\mathrm{cm}}^{-2}$), where, respectively, (a) five, (b) seven, and (c) nine exciton lines are present at low-excitation intensity, but (a) five, (b) one, or (c) no additional line appear upon increasing the excitation intensity. Spectrum (d) shows more clearly the additional peak emerging on the high energy side of one exciton peak in spectrum (a).

Figure 3

Measured biexciton binding energies as a function of the estimated exciton localization lengths (solid dots). The horizontal error bar applies to all experimental points and are determined by the spatial step of 120 nm between two successive spectra. We also plot the calculated biexciton binding energies (triangles) for a one monolayer deep single particle square localization potential (see inset). The vertical error bars are due to the tolerance of the numerical results. The parameters used were $\delta V_e=4.9\mathrm{meV}$, $\delta V_h=1.1\mathrm{meV}$, $m_e=0.067m_0$, and $m_h=0.26m_0$. $m_0$ is the free electron mass.