(The converse effect - spontaneous phonon emission
by the current-carrying electrons - is at the root of Joule heating and is one of the most difficult effects to capture theoretically.) Another velocity-dependent force, proposed by our collaborators in Denmark, originates strictly from the current.
Nevertheless, all of the studies in the area agree on two key factors: the enhancement of the Coulombic coupling between exciton and biexciton states and the suppression of excitons' radiative relaxation pathways (predominantly phonon emission) are critical for increasing QY [5, 6, 31, 32].
Other relaxation pathways other than phonon emission were also taken into account in this study, such as charge transfer and radiative recombination .
Capture and relaxation in self-assembled In(Ga)As/GaAs QDs happen through complicated dynamics involving emission of longitudinal optical (LO) phonon emission
, polaron (electron-phonon coupling) decay, defect-mediated relaxation, carrier-carrier scattering, and so forth (see, e.g., [22-24] and the references therein).
Few capturing mechanisms can bring the carrier onto those levels, for example, phonon emission by a WL carrier .
Leon, "Rapid carrier relaxation by phonon emission in [In.sub.0.6][Ga.sub.0.4]As/GaAs quantum dots," Physical Review B, vol.
However, the probability of the transition via phonon emission
is small because the simultaneous emission of about 10 phonons is required at room temperature (thermal energy 25meV).
At higher electric field, inter-valley optical phonon emission
dominates causing the drift velocity to saturate at around 0.
The implicit transition forms a loop because the phonon absorption process maintains a balance with the phonon emission process and there are reverse processes because phonon (photon) absorption and emission processes occur independently.
In a loop, the red (upper) and blue (lower) half circles correspond to phonon emission ([N.sub.q] + 1) and phonon absorption ([N.sub.q]), respectively.
[P.sub.+] ([lambda], [beta]) means that the reverse implicit transition from the final state p to the implicit state [lambda] with phonon absorption should be subtracted from the forward implicit transition from the implicit state to the final state with phonon emission. This means that when an electron-phonon interaction is involved in an electron transition, a transition occurs via implicit states induced by local fluctuations.
On the other hand, although a dynamical conductivity formula for superconducting materials could be obtained from Eliashberg theory  where the electron-phonon interaction is described by the spectral function, the result did not contain the distribution function for phonons, so the phonon emissions and absorptions as well as photon absorptions and emissions in all electron transition processes could not be presented in an organized manner.