Electron capture in quantum wells via scattering by electrons, holes, and optical phonons

Electron-capture times due to the electron-electron ($e-e$), electron-hole ($e-h$), and electron-polar optical phonon ($e$-pop) interactions are calculated in the GaAs quantum well (QW) with electron and hole densities ${10}^{11}$ ${\mathrm{cm}}^{-2\mathrm{}}$. The calculated capture times oscillate as a function of the QW width with the same period but with different amplitudes. The $e-h$ capture time is two to four orders larger and the $e-e$ capture time one to three orders larger than the $e$-pop capture time. The exceptions are the QW widths near resonance minima, where the $e-e$ capture time is only 2-3 times larger and the $e-h$ capture time 10-100 times larger. A different physical origin of the oscillatory behavior is demonstrated for the $e-e$ and $e$-pop capture times. Effects of exchange and degeneracy on the $e-e$ capture are analyzed. The exchange effect increases the $e-e$ capture time approximately two times while the degeneracy does not change the capture time except for the QW depths and widths near the resonance.