Cascade Capture of Electrons in Solids

TLDR

Electron capture cross sections in Si and Ge are orders of magnitude larger than predicted by multiphonon transitions because capture into excited states followed by a cascade of one‑phonon transitions, and the polarizability of neutral centers, explain the observed large cross sections. Capture initiates with an optical phonon or intervalley collision at room temperature, with acoustic phonons dominating at low temperatures, and subsequent collisions either eject the electron or increase its binding energy; the sticking probability becomes significant when binding energies are on the order of kT. Measured capture cross sections reach 10⁻¹⁵ to 10⁻¹² cm² for Coulomb centers in Si and Ge, and the cross section rises sharply as temperature and electron energy decrease, particularly for acoustic‑phonon mediated capture.

Abstract

Enormous capture cross sections in the range ${10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$ to ${10}^{\ensuremath{-}12}$ ${\mathrm{cm}}^{2}$ have been observed for a wide variety of Coulomb attractive centers in Si and Ge, some involving binding energies many times the Debye energy. Whereas multiphonon transitions to the ground state yield cross sections five to ten orders of magnitude too small, capture into excited states of large radius followed by a cascade of one-phonon transitions leads to cross sections of the right order of magnitude. The initial capturing event is likely to involve an optical phonon or an intervalley collision in the room temperature range, but the acoustic phonon contribution will predominate at low temperatures.Subsequent collisions may eject the electron or cause it to increase its binding energy. The "sticking probability," or probability of eventual capture into the ground state, becomes significant for binding energies of order $\mathrm{kT}$. As the temperature is reduced capture into orbits of larger radius becomes effective, and, at least for the acoustic phonon case the cross section increases rapidly with decreasing temperature, and with decreasing electron energy. The large cross sections ${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ to ${10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$ found for neutral centers can be explained on a similar basis, the attractive potential in this case being provided by the large polarizability of the neutral center.