Fig. 1. (Color online) (a)–(c) Three trends in the relationship between the radiative lifetime and excitonic gap of CdSe QDs at room temperature. (d) Overall trend in a wider energy range. The small energy difference (millielectronvolt order) between the optical band gap and PL peak energy (electronvolt order) is ignored. Solid dots: calculated results obtained by Califanoet al.^[21]; circles: experimental values for CdSe QDs^{[16,17,20,24]}; hollow diamonds: experimental values for CdSe/ZnS core/shell QDs^[23,25,26]; dashed curves: polynomial fitting curves; shaded region: permitted deviation.

Fig. 2. (Color online) (a) Schematic of the near-edge single-particle levels of ZB-CdSe QD. TheP hole states are indicated by short-dashed lines. (b) Scheme of band-edge exciton levels. (c) Diagram showing the exciton fine structures of1S3/21Se and1P3/21Se states. The dotted lines represent the 'dark' states, whereas the solid lines represent the 'bright' states. The numbers in brackets represent the degeneracy of energy levels. The total angular momentum of an exciton (F) is the sum of the total angular momentum of the hole (Jh) and electron (Se). From left to right are the exciton states that exclude the exchange interaction (K=0), include the exchange interaction (K≠0), and consider the anisotropic effect (Δ>0 andΔ<0).

Fig. 3. (Color online) Excitonic gap of ZB-CdSe QDs as a function of the effective diameter. The current calculation results are represented by purple points, where the regular triangles, dots, and inverted triangles denote the data for prolate, spherical, and oblate QDs, respectively. Experimental data: ■ from Ref. [67]; ●, □, and ○ from Ref. [63]; ◆ from Ref. [65]; ◇ from Ref. [62]; ● from Ref. [68]; ◆ from Ref. [66]; ■ from Ref. [64]. An empirical fitting curve for ZB-CdSe QDs byC⌣apeket al.^[63], (purple solid curve) and WZ-CdSe sizing curves according to Jasieniaket al.^[71] (black dotted curve), Yuet al.^[35] (black dashed curve), and de Mello Donegaet al.^[17] (black solid curve) are displayed. Dash–dot curve: prediction of EMA by Bruset al.^[42]; purple dashed line: band gap of bulk CdSe at room temperature^[50].

Fig. 4. (Color online) Comparison of our simulated QD radiative lifetimes with experimental data over a wide energy window. Purple solid points: present calculated values, where the regular triangles, dots, and inverted triangles represent the data for prolate, spherical, and oblate QDs, respectively. Green solid dots: calculated results by Califanoet al.^[21]; circles: experimental values for CdSe QDs^{[16,17,20,24,27]}; diamonds: experimental values for CdSe/ZnS core/shell QDs^{[23,25,26,28,29]}; purple curve: polynomial fitting curve; shaded region: permitted deviation. Note: * All experiments were conducted in a medium withn=1.496, except for Kasier's measurement in water^[28].

Fig. 5. (Color online) Dependence of the room-temperature radiative lifetime on the optical gap for different levels of complexity in the many-particle treatment. For the meanings of the regular triangles, dots, and inverted triangles, seeFig. 4.τ1 (blue points): only the bright states in the1S3/21Se exciton manifold;τ2 (green points): thermal average of the1S3/21Se exciton manifold;τ3 (orange points): thermal average of exciton states derived from1S3/21Se and1P3/21Se;τ4 (purple points): thermal average of all thermally accessible states (same data as denoted by the purple data points inFig. 4). On the upperx-axis, three representative QD effective sizes are shown. Inset: dependence of the radiative rate of the1S3/21Se-derived bright exciton on the excitonic gap.

Fig. 6. (Color online) Single-exciton absorption spectra of (a–c) the spherical ZB-CdSe QDs with diameters of 2 (left), 4 (middle), and 8 nm (right) as well as those of (d–f) the oblate ZB-CdSe QDs and (g–i) prolate ZB-CdSe QDs with excitonic gaps similar to these spherical QDs. Blue dashed line: position of the first exciton transition energy; blue solid line: oscillator strength line of bright states in1S3/21Se; green solid line: oscillator strength line of `bright' states in1P3/21Se; black solid line: oscillator strength line of higher-energy states; orange curve: Boltzmann population at 300 K. The transition intensity is logarithmic (left), whereas the distribution probability is linear (right). The QD radiative lifetime at 300 K is also shown. Inset: 3D model of the QDs (to scale).