Interacting Drift-Diffusion Theory for Photoexcited Electron-Hole Gratings in Semiconductor Quantum Wells

Phase-resolved transient grating spectroscopy in semiconductor quantum wells has been shown to be a powerful technique for measuring the electron-hole drag resistivity ${\rho }_{eh}$, which depends on the Coulomb interaction between the carriers. In this Letter we develop the interacting drift-diffusion theory, from which ${\rho }_{eh}$ can be determined, given the measured mobility of an electron-hole grating. From this theory we predict a crossover from a high-excitation-density regime, in which the mobility has the “normal” positive value, to a low-density regime, in which Coulomb drag dominates and the mobility becomes negative. At the crossover point, the mobility of the grating vanishes.

Figure 1

(a) ${\rho }_e$ (red solid curve) and ${\rho }_{eh}$ (blue dashed curve) as functions of temperature with $n_i=0.005n_0$. The green dotted curve represents ${\rho }_e$ with $n_i=0.2n_0$. Inset: zoom in on the low temperature region $T<3.5\mathrm{K}$. (b) Grating mobility as a function of temperature. The blue squares are experimental data from Ref. 27. The apparent breaks in the curves as they cross zero are artifacts of the logarithmic scale.

Figure 2

Grating mobility as a function of pumping intensity (the latter quantified by the ratio $p/n_0$) at 20 and 200 K.

Figure 3

Grating mobility as a function of equilibrium electron density.

Figure 4

Ambipolar diffusion constant (blue dashed curve) and hole diffusion constant (red solid curve) as a function of temperature for $n_b=n_0$ in the weak pumping case. Notice that the two curves are essentially identical. The filled squares represent the experimental data for the ambipolar diffusion constant reported by Yang et al. [27]. The green dotted curve shows the ratio between the ambipolar diffusion constants with and without Coulomb drag, while the pink chain curve shows the corresponding ratio for the $e\mathrm{\text{−}}h$ grating mobility.