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Excitonic lasing in semiconductor quantum wires

Direct experimental evidences for excitonic lasing is obtained in optically pumped V-groove quantum wire structures. We demonstrate that laser emission at a temperature of 10 K arises from a population inversion of localized excitons within the inhomogenously-broadened luminescence line. At the lasing threshold, we estimate a maximum exciton density of about 1.8 105cm-1.

Semiconductor lasers incorporating low-dimensional heterostructures, quantum wires and quantum boxes, are attracting considerable interest because of their potential for improved performance over quantum well lasers 1 . This prediction is based, in the single-particle picture, on the sharper density of states resulting from the confinement of the charge carriers in two or three directions. The inclusion of electron-hole Coulomb correlations in the theoretical description of the optical spectra of semiconductor quantum wires has, however, dampened these early expectations. The primary effect of Coulomb correlations is to remove the singularity of the one-dimensional (1D) joint density of states and to greatly reduce the absorption above the band edge 2 . In the regime of high carrier densities screening of the Coulomb interaction, band gap renormalization and phase space filling might become important 3 . The evolution of the optical response as the density of electron-hole pairs is increased has been intensively studied in 1D systems in recent years. However, contrasting theoretical predictions were made: in several studies [4][5] , gain was found to appear only at densities above the Mott density (about mid 10 5 cm -1 ) while, in another one, substantial gain was calculated at densities largely below this value when a self-consistent treatment of the electronhole correlations was included 6 . The occurrence of excitonic gain that is predicted by the latter study is an interesting feature of 1D quantum structures. Laser emission from excitons confined in quantum wells has so far not been observed in III-V semiconductor heterostructures, but has been observed in their II-VI counterparts for which the exciton binding energy is much larger 7 .
Evidence for lasing attributed to excitons has been previously reported in T-shaped quantum wire structures (QWR's), for which only one electron 1D-subband was present 8 .
In the present study, we report on the observation of lasing from excitons in optically excited V-groove GaAs/AlGaAs QWR laser structures. The emission is attributed to the recombination of excitons associated with the lowest energy electron-and hole-subbands of the QWR. Moreover, we find that the emission energy remains nearly constant within the inhomogenously broadened photoluminescence line of the QWRs for both continuous wave (cw) and pulsed optical excitation over a wide range of power densities. These results corroborate the important role played by electron-hole Coulomb correlations in the optical emission from quasi-1D quantum wires in the density regime of the Mott transition.
The sample used for our study was grown by low-pressure organometallic chemical vapor deposition on a GaAs substrate patterned with a 3 µm-pitch grating. It is a semiconductor laser structure that incorporates five vertically stacked GaAs quantum wires separated by 47 nm thick Al 0.25 Ga 0.75 As barriers placed in the core region of an optical wave guide. The core region has a total thickness of 370 nm and is cladded with 1 µm thick Al 0.62 Ga 0.38 As layers on both sides. The center of the QWRs-stack was displaced by 72 nm from the center of the core region in order to obtain an optimal mode confinement factor 9 . The position of the QWRs-stack can be seen in the cross-sectional transmission electron micrograph of the core region of our QWR laser structure depicted in Fig.1. The V-shape of the dielectric waveguide yields an optical mode in the shape of a heart that is well confined in the core region of the waveguide according to our calculation of the electromagnetic field distribution of the optical modes 9 .
Cleaved optical cavities were mounted in a helium-flow cryostat and kept at 10 K. The laser cavities were optically pumped using 3 ps pulses from a mode-locked Ti-Sapphire laser operating at a wavelength of 720 nm (1.72eV) with a repetition rate of 80 MHz. The excitation light was incident on the growth surface and focused through two cylindrical lenses onto a stripe 46 µm wide and 1.5 mm long oriented in the direction parallel to the optical wave guide. The QWRs were perpendicular to the cleaved facets forming the mirrors of the optical cavity. The emitted light was collected from one of the cleaved facets, dispersed by a double-grating spectrometer and detected with a cooled GaAs photomultiplier tube.
Optical emission spectra of the QWR laser structure are displayed in Fig. 2 for different values of the optical power density below, at and above the threshold for lasing in the QWR.
Upon increasing the pump power, we observe a nearly constant energy of the peak at 1.581 eV that corresponds to the optical transition e 1 -h 1 associated with the ground electron-and holesubband of the QWRs. A significant spectral narrowing is also found as the power density is increased and crosses the lasing threshold. This evidences the existence of amplified spontaneous emission within this inhomogenously broadened PL line in this density regime. A typical light output versus input power characteristic is shown in Fig. 2 b for a cavity length of about 0.9 mm. The emission intensity varies linearly at low excitation power over three orders of magnitude (from 0.1 to 100 mW). Above the lasing threshold (at 350 mW) the intensity variation is again linear, indicating that the modal gain has saturated. In Fig. 2  spectrum a high contrast ratio, the value of which being mainly limited, however, by the nonuniform pumping profile of the focussed laser beam.
In order to identify the regime in which lasing takes place, we now estimate the electronhole pair density that was directly generated in each QWR by the 3 ps optical pulse. The electron-hole pair density is given by where α is the excitonic absorption coefficient, t and w are respectively the effective wire thickness and width, R (0.3) is the normal incidence reflectivity at the laser energy hω, P is the power density, T is the pulse repetition period ( The relevance of excitonic recombination at low temperature in the PL and PLE spectra has already been established in previous studies of similar QWR structures 12 . From the absence of any significant shift (less than 2 meV) we infer that the lasing emission originates from the recombination of excitons as it is the case for the QWR-peak of the cw-PL spectrum.
We will now address the origin of the energy blueshift that is observed as the power density is increased up to about 100 W/cm 2 (below lasing threshold). It could originate from an imperfect compensation between the renormalization of the band-gap energy introducing a redshift (BGR) and a lowering of the exciton binding energy yielding a blue-shift as the carrier density is increased. In the density range of the present experiment, these many-body effects were evaluated resulting in an absorption peak that exhibits a weak blueshift as the carrier density approaches the Mott density 3 . Alternatively, the energy blueshift may be attributed to effects related to disorder. We note that, under cw excitation condition, similar shifts were indeed observed along with the appearance of a high energy tail in the PL spectrum that is indicative of a heating of the hot carrier distribution 14 . These latter findings can also be related to disorder effects that broaden the peaked optical density, thereby yielding a blueshift of the emission for a heated Maxwell-Boltzmann distribution of electron-hole pairs 15 . Beyond the lasing threshold an energy redshift is finally observed, which is caused by a local heating of the sample.
The PL and PLE spectra, which are depicted in Fig. 4, were obtained from the same sample in a standard pseudo-backscattering configuration at a temperature of 10 K 16  localized states within the inhomogenous luminescence line. However, the relaxation into these localized sites must occur on a time scale that is shorter than the average radiative lifetime of the excitonic population. Further experimental work and theoretical development are deemed necessary to address the dynamical aspect of the gain generation.
In conclusion, we have demonstrated laser emission that is sustained by excitonic gain at a temperature of 10 K in a semiconductor quantum wire structure. Laser emission is shown to arise from the population inversion of localized excitons. Whether disorder and hence localization of the excitons is necessary to obtain excitonic gain remains to be explored as our understanding of the gain generation in a weakly-disorded semiconductor gain medium is not yet complete. This study should stimulate further a theoretical description of the effects of electron-hole Coulomb correlations in the gain regime of quasi one-dimensional semiconductor systems.
We wish to acknowledge helpful discussions on the excitonic gain in 1D systems with C.
Piermarocchi. We are also grateful to K. Leifer for providing the TEM micrographs. This work was supported in part by the Swiss National Foundation for Sciences. Al0.25Ga0.75As