Excitonic Photoluminescence in Semiconductor Quantum Wells: Plasma versus Excitons

Time-resolved photoluminescence spectra after nonresonant excitation show a distinct $1s$ resonance, independent of the existence of bound excitons. A microscopic analysis identifies exciton and electron-hole plasma contributions. For low temperatures and low densities, the excitonic emission is extremely sensitive to details of the electron-hole-pair population making it possible to identify even minute fractions of optically active excitons.

Figure 1

Experimental PL spectra (solid lines) for a lattice temperature of 4 K are compared to the KMS result $I_{\mathrm{P}\mathrm{L}}^{\mathrm{e}\mathrm{q}}(\hslash \omega )$ (dashed lines), i.e., the measured nonlinear $\alpha$L multiplied by the Boltzmann factor $\exp (-\Delta E/kT)$. PL is integrated from 0.95 to 1.05 ns after nonresonant excitation, and the densities are for $t=1\mathrm{n}\mathrm{s}$. The corresponding curve pairs are vertically offset by two decades. The bottom graph shows the nonlinear absorption spectra for the highest (dashed line) and lowest densities on a linear scale.

Figure 2

$\beta$ versus carrier density. Full squares refer to experimental values taken at 1 ns after nonresonant excitation at a lattice temperature of 4 K. The densities refer to densities at 1 ns. The theoretical values (dotted line) are calculated using the PL formula (1) for a pure electron-hole plasma with a carrier temperature of $16\pm 2\mathrm{K}$. The solid line shows a theoretical fit including a $q=0$ exciton contribution. Top: same for 50 K lattice temperature and extracted electron-hole plasma temperature of $50\pm 3\mathrm{K}$; the theoretical curves are computed for a carrier temperature of 48 K.

Figure 3

Theoretical PL spectra for various densities for a carrier temperature of 16 K: pure plasma (dotted line) and including excitons (solid line). The exciton contributions used are chosen to give agreement with the experimental $\beta$ as shown in Fig. 2. The KMS result (dashed line) is obtained by multiplying the computed nonlinear $\alpha$L by the Boltzmann factor.

Figure 4

Optically active $q=0$ exciton contributions as a function of the carrier density.