Nonradiative Capture of Electrons in Quantum Wells and Wires by Shallow Donor Impurities

The capture of electrons in a quantum well or wire by shallow donor impurities due to the interaction with an acoustic phonon is considered. Wave functions of several lowest bound states are found by the variational method. The rates of transitions between the free and bound states as well as between different bound states are calculated. In the case of well or wire width L less than or of the order of the effective Bohr radius and greater than the phonon wavelength, the transition rates are proportional to ϵ⁻⁵ (nϵ + 1/2 ± 1/2) L⁻⁶, where ϵ is the transferred energy, and nϵ a phonon occupation number.