J. Semicond. > 2023, Volume 44 > Issue 3 > 032702, doi: 10.1088/1674-4926/44/3/032702
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ARTICLES

Exciton radiative lifetime in CdSe quantum dots

Zhimin Ji1, 2 and Zhigang Song1,

+ Author Affiliations

 Corresponding author: Zhigang Song, songzhigang@semi.ac.cn

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Abstract: Colloidal CdSe quantum dots (QDs) are promising materials for solar cells because of their simple preparation process and compatibility with flexible substrates. The QD radiative recombination lifetime has attracted enormous attention as it affects the probability of photogenerated charges leaving the QDs and being collected at the battery electrodes. However, the scaling law for the exciton radiative lifetime in CdSe QDs is still a puzzle. This article presents a novel explanation that reconciles this controversy. Our calculations agree with the experimental measurements of all three divergent trends in a broadened energy window. Further, we proved that the exciton radiative lifetime is a consequence of the thermal average of decays for all thermally accessible exciton states. Each of the contradictory size-dependent patterns reflects this trend in a specific size range. As the optical band gap increases, the radiative lifetime decreases in larger QDs, increases in smaller QDs, and is weakly dependent on size in the intermediate energy region. This study addresses the inconsistencies in the scaling law of the exciton lifetime and gives a unified interpretation over a widened framework. Moreover, it provides valuable guidance for carrier separation in the thin film solar cell of CdSe QDs.

Key words: solar cells, CdSe quantum dot, radiative lifetime, scaling law, optical band gap, exciton fine structure, room temperature



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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 Califano et 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.

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Fig. 2.  (Color online) (a) Schematic of the near-edge single-particle levels of ZB-CdSe QD. The P hole states are indicated by short-dashed lines. (b) Scheme of band-edge exciton levels. (c) Diagram showing the exciton fine structures of $1S_{3/2}1S_{\rm{e}}$ and $1P_{3/2}1S_{\rm{e}}$ 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 ($J_{\rm{h}}$) and electron ($S_{\rm{e}}$). From left to right are the exciton states that exclude the exchange interaction ($K = 0$), include the exchange interaction ($K \ne 0$), and consider the anisotropic effect ($\varDelta > 0$ and $\varDelta < 0$).

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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 by $\check{\mathrm{C}}$apek et al.[63], (purple solid curve) and WZ-CdSe sizing curves according to Jasieniak et al.[71] (black dotted curve), Yu et al.[35] (black dashed curve), and de Mello Donega et al.[17] (black solid curve) are displayed. Dash–dot curve: prediction of EMA by Brus et al.[42]; purple dashed line: band gap of bulk CdSe at room temperature[50].

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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 Califano et 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 with $n = 1.496$, except for Kasier's measurement in water[28].

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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, see Fig. 4. $\tau_1$ (blue points): only the bright states in the $1S_{3/2}1S_{\rm{e}}$ exciton manifold; $\tau_2$ (green points): thermal average of the $1S_{3/2}1S_{\rm{e}}$ exciton manifold; $\tau_3$ (orange points): thermal average of exciton states derived from $1S_{3/2}1S_{\rm{e}}$ and $1P_{3/2}1S_{\rm{e}}$; $\tau_4$ (purple points): thermal average of all thermally accessible states (same data as denoted by the purple data points in Fig. 4). On the upper x-axis, three representative QD effective sizes are shown. Inset: dependence of the radiative rate of the $1S_{3/2}1S_{\rm{e}}$-derived bright exciton on the excitonic gap.

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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 in $1S_{3/2}1S_{\rm{e}}$; green solid line: oscillator strength line of `bright' states in $1P_{3/2}1S_{\rm{e}}$; 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).

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    Received: 18 September 2022 Revised: 21 October 2022 Online: Accepted Manuscript: 08 November 2022Uncorrected proof: 09 November 2022Published: 10 March 2023

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      Article Navigation >  Journal of Semiconductors  > 2023  >  44(3): 032702
      Zhimin Ji, Zhigang Song. Exciton radiative lifetime in CdSe quantum dots[J]. Journal of Semiconductors, 2023, 44(3): 032702. doi: 10.1088/1674-4926/44/3/032702 Z M Ji, Z G Song. Exciton radiative lifetime in CdSe quantum dots[J]. J. Semicond, 2023, 44(3): 032702. doi: 10.1088/1674-4926/44/3/032702Export: BibTex EndNote
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      Zhimin Ji, Zhigang Song. Exciton radiative lifetime in CdSe quantum dots[J]. Journal of Semiconductors, 2023, 44(3): 032702. doi: 10.1088/1674-4926/44/3/032702

      Z M Ji, Z G Song. Exciton radiative lifetime in CdSe quantum dots[J]. J. Semicond, 2023, 44(3): 032702. doi: 10.1088/1674-4926/44/3/032702
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      Exciton radiative lifetime in CdSe quantum dots

      doi: 10.1088/1674-4926/44/3/032702
      • 1.

        State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China

      • 2.

        Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

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      • Author Bio:

        Zhimin Ji is a Ph.D. candidate in State Key Laboratory of Superlattices and Microstructures at Institute of Semiconductors CAS. His research focuses on the theoretical study of luminescence properties of semiconductor nanostructures, and the fabrication process of semiconductor lasers and optical amplifiers

        Zhigang Song Associate Researcher, graduated from the Institute of Semiconductors, Chinese Academy of Sciences (CAS) with a Ph.D. in 2017 and worked at the Max Planck Institute of Solid State Physics and Chemistry, Germany and Nanyang Technological University, Singapore, before returning to China to join the State Key Laboratory of Semiconductor Superlattices, Institute of Semiconductors, CAS in October 2020. He has been engaged in the simulation and design of semiconductor materials and devices

      • Corresponding author: songzhigang@semi.ac.cn
      • Received Date: 2022-09-18
      • Revised Date: 2022-10-21
        • Available Online: 2022-11-08

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