Exciton-phonon interaction in semiconductor nanocrystals

Anti‐Stokes cooling in semiconductor nanocrystal quantum dots: A feasibility study

“…Therefore, the theory can underestimate the value of the Huang–Rhys factor, however, the upper theoretical limit can be obtained by considering a lone electron (i.e., an electron–hole pair completely separated in space). This gives a value of S ≈ 0.3 for a 2 nm CdSe QD, about 4 times more than for the “ideal” 1S(e)‐1S 3/2 (h) exciton 47. Both the theory 47 and experiment 44, 56 agree that the strength of the electron–phonon coupling increases as the diameter of the QDs is decreased.…”

“…However, the calculated values of the Huang–Rhys factor are at least one order of magnitude smaller 47, 53. The experimentally observed strong Stokes shift is probably characteristic of the QD size distribution and not of a single dot and it can be even unrelated to optical phonons (in fact, the Stokes shift can alternatively be explained by the exciton fine structure discussed in the previous section 43).…”

“…The interaction with acoustic phonons broadens the discrete energy level structure determined by Eq. (7) and leads to smooth absorption and emission bands that are quite similar with Lorentzian lineshapes unless the temperature is very low 47.…”

“…The importance of phonon effects on the optical properties of semiconductor QD systems has been demonstrated in many works (see reviews 46, 47). Exciton–phonon coupling in an ideal nanocrystal can be considered in terms of two contributions resulting from interactions with confined optical and acoustic phonons 2…”

“…The S factor is a measure of how strong (large value) or weak (small value) the exciton–phonon coupling is. It can be rigorously defined for a non‐degenerate QD exciton state so as to include all the interactions with confined optical phonons 47 and is the only parameter that determines the temperature‐dependent exciton spectral function 42 where $\bar n(T)$ is the mean number of the optical phonons at temperature T (given by the Bose–Einstein function), I n denotes the modified Bessel function, E 0 is the bare exciton energy, Δ ≈ S ħω 0 and ħω 0 is the phonon energy taken the same for all confined modes ( ħω 0 ≈ ħω LO ), which is an approximation of the model. The spectral function (7) (often called the Franck–Condon progression) determines both the absorption and emission spectra of the dot (with the replacement E → − E for the former) and, for large S , peaks at the spectral energy E = E 0 − Δ + Sħω 0 .…”