Long-Distance Diffusion of Excitons in Double Quantum Well Structures

In this Letter we report on lateral diffusion measurements of excitons at low temperature in double quantum wells of various widths. The structure is designed so that excitons live up to $30\mu \mathrm{s}$ and diffuse up to $500\mu \mathrm{m}$. Particular attention is given to establishing that the transport occurs by exciton motion. The deduced exciton diffusion coefficients have a very strong well width dependence, and obey the same power law as the diffusion coefficient for electrons.

Figure 1

Composite of the time-integrated luminescence from the 100 Å well structure, recorded with an imaging spectrometer, for various applied voltages and with an excitation power of 2.7 mW. The narrow vertical line in the center of each image is impurity luminescence from the GaAs substrate, which is also excited by the laser. The chevronlike cloud spreading out from the central line shows the motion of the excitons away from the laser spot.

Figure 2

Indirect exciton luminescence intensity as a function of time for various points on the sample with 100 Å well width. The curves are labeled by the distance $x$ in the plane from the central laser spot. The average excitation power was $30\mu \mathrm{W}$ and the repetition period $4\mu \mathrm{s}$.

Figure 3

Expansion of the exciton cloud at different times after the excitation. In this particular case the well width was 100 Å. The measured luminescence intensities are normalized. Also shown are the Gaussian fits with the value of the variance. The conditions are the same as in Fig. 2.

Figure 4

Measured variance squared vs time for the four samples, for average laser power $30\mu \mathrm{W}$ and pulse period $4\mu \mathrm{s}$. The straight lines represent linear fits to the measured values in the range of 1000–4000 ns, i.e., when the expansions are purely diffusive.

Figure 5

Measured diffusion coefficient as a function of well width. For comparison, also shown is the theoretical dependence, $D\propto L^6$.