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Within the frame of lattice relaxation model, several intraband relaxation processes between the three lowest excited states and ground state in a PbSe quantum dot are studied based on the electron-longitudinal optical phonon coupling via Fröhlich mechanism. We find that Huang-Rhys factors decrease with the radius of quantum dot increasing in different relaxation processes. More important is the fact that the obtained values of Huang-Rhys factors satisfy the experimental measurements in the strong coupling limit. These intraband relaxation processes follow the asymmetrical Gaussian distribution with respect to the radius, in which the probabilities with which these intraband relaxation transitions occur are different. Among these relaxation processes, two intraband transitions from the third excited state to ground state and to second excited states dominate the relaxation processes on a several nanometer scale of radius. Moreover, the temperature dependence for each of these relaxation processes can be modulated by the radius of quantum dot. These theoretical results are consistent with the experimental measurements and provide an important insight into the intraband relaxation in quantum dots in experiments.
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Keywords:
- quantum dot /
- Huang-Rhys factor /
- intraband relaxation
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Google Scholar
[3] Jeffrey M P, Young S P, Jaehoon L, Andrew F F, Wan K B, Sergio B, Victor I K 2016 Chem. Rev. 116 10513
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[4] Aaron G M, Joseph M L, John T S, Danielle K S, Lazaro A P, Victor I K, Arthur J N, Matthew C B 2013 Nano Lett. 13 3078
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[7] Schaller R D, Klimov V I 2004 Phys. Rev. Lett. 92 186601
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[8] Moonsub S, Philippe G S 2001 Phys. Rev. B 64 245342
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[9] Wang L W, Califano M, Zunger A, Alberto F 2003 Phys. Rev. Lett. 91 056404
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[12] Schaller R D, Pietryga J M, Goupalov S V, Melissa A P, Sergei A I,Victor I K 2005 Phys. Rev. Lett. 95 196401
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[13] Bonati C, Cannizzo A, Tonti D, Tortschanoff A, Mourik F, Chergui M 2007 Phys. Rev. B 76 033304
Google Scholar
[14] Jeffrey M H, Du H, Krauss T D, Cho K S, Murray C B, Wise F W 2005 Phys. Rev. B 72 195312
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[16] Schroeter D F, Griffiths D J, Sercel P C 1996 Phys. Rev. B 54 1486
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[18] Huang K, Rhys A 1950 Pro. Roy. Soc. A 204 406
[19] Huang K 1981 Prog. Phys. 1 31
[20] Huang K 1985 Sci. Chin. 1 1
[21] Li X Q, Arakawa Y 1999 Phys. Rev. B 60 1915
Google Scholar
[22] Soma C M A 1999 J. Phys.: Condens. Matter 11 2071
Google Scholar
[23] Bulaev D V, Loss D 2007 Phys. Rev. Lett. 98 097202
Google Scholar
[24] Vitaly N G, Alexander K, Loss D 2008 Phys. Rev. B 77 045328
Google Scholar
[25] Ridley B K 1982 Quantum Processes in Semiconductors (Oxford: Oxford University Press) p233
[26] Jdira L, Overgaag K, Stiufiuc R, Grandidier B, Delerue C, Speller S, Vanmaekelbergh D 2008 Phys. Rev. B 77 205308
Google Scholar
[27] Goupalov S V 2005 Phys. Rev. B 72 073301
Google Scholar
[28] Norris D J, Efros A L, Rosen M, Bawendi M G 1996 Phys. Rev. B 53 16347
Google Scholar
[29] Poddubny A N, Goupalov S V 2008 Phys. Rev. B 77 075315
Google Scholar
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图 1 (a) PbSe量子点中电子的基态(G)与3个最低的激发态(I, II, III)位型坐标关系; (b) 6种带内弛豫过程的黄-里斯因子与量子点半径的关系
Figure 1. (a) Configuration coordinates for the ground state (G) and three lowest excited states (I, II, III) of electron in PbSe quantum dot; (b) Huang-Rhys factors as a function of the radius of quantum dot for six types of intraband relaxation processes.
图 2 不同温度下, PbSe量子点中带内弛豫率与半径的依赖关系 (a) 5 K; (b) 300 K
Figure 2. Intraband relaxation rates as a function of the radius of PbSe quantum dot at different temperature: (a) 5 K; (b) 300 K.
图 3 在不同的量子点半径下, 弛豫率与温度的变化关系 (a)
${W_{{\rm{II}} \text{-} {\rm{G}}}}$ ; (b)${W_{{\rm{II}} \text{-} {\rm{I}}}}$ ; (c)${W_{{\rm{III}} \text{-} {\rm{I}}}}$ ; (d)${W_{{\rm{III}} \text{-} {\rm{G}}}}$ ; (e)${W_{{\rm{III}} \text{-} {\rm{II}}}}$ Figure 3. Relaxation rates as a function of the temperature at different radii of quantum dot: (a)
${W_{{\rm{II}} \text{-} {\rm{G}}}}$ ; (b)${W_{{\rm{II}} \text{-} {\rm{I}}}}$ ; (c)${W_{{\rm{III}} \text{-} {\rm{I}}}}$ ; (d)${W_{{\rm{III}} \text{-} {\rm{G}}}}$ ; (e)${W_{{\rm{III}} \text{-} {\rm{II}}}}$ . -
[1] Andrew F F, Gao J B, Victor I K 2017 Nat. Phys. 13 604
Google Scholar
[2] Frank C M S, Stanko T, Arjan J. H, Laurens D A S 2017 ACS Nano 11 6286
Google Scholar
[3] Jeffrey M P, Young S P, Jaehoon L, Andrew F F, Wan K B, Sergio B, Victor I K 2016 Chem. Rev. 116 10513
Google Scholar
[4] Aaron G M, Joseph M L, John T S, Danielle K S, Lazaro A P, Victor I K, Arthur J N, Matthew C B 2013 Nano Lett. 13 3078
Google Scholar
[5] Avila L M, Tritsch J R, Wolcott A, Chan W L, Nelson C A, Zhu X Y 2012 Nano Lett. 12 1588
Google Scholar
[6] Svetlana V K, Dmitri S K, Victor V P, Oleg V P 2011 J. Phys. Chem. C 115 21641
Google Scholar
[7] Schaller R D, Klimov V I 2004 Phys. Rev. Lett. 92 186601
Google Scholar
[8] Moonsub S, Philippe G S 2001 Phys. Rev. B 64 245342
Google Scholar
[9] Wang L W, Califano M, Zunger A, Alberto F 2003 Phys. Rev. Lett. 91 056404
Google Scholar
[10] Victor I K 2000 J. Phys. Chem. B 104 6112
Google Scholar
[11] Brian L W, Wang C J, Philippe G S 2002 J. Phys. Chem. B 106 10634
Google Scholar
[12] Schaller R D, Pietryga J M, Goupalov S V, Melissa A P, Sergei A I,Victor I K 2005 Phys. Rev. Lett. 95 196401
Google Scholar
[13] Bonati C, Cannizzo A, Tonti D, Tortschanoff A, Mourik F, Chergui M 2007 Phys. Rev. B 76 033304
Google Scholar
[14] Jeffrey M H, Du H, Krauss T D, Cho K S, Murray C B, Wise F W 2005 Phys. Rev. B 72 195312
Google Scholar
[15] Li X Q, Arakawa Y 1997 Phys. Rev. B 56 10423
Google Scholar
[16] Schroeter D F, Griffiths D J, Sercel P C 1996 Phys. Rev. B 54 1486
Google Scholar
[17] Philippe G S, Brian W, Dong Y 2005 J. Chem. Phys. 123 074709
Google Scholar
[18] Huang K, Rhys A 1950 Pro. Roy. Soc. A 204 406
[19] Huang K 1981 Prog. Phys. 1 31
[20] Huang K 1985 Sci. Chin. 1 1
[21] Li X Q, Arakawa Y 1999 Phys. Rev. B 60 1915
Google Scholar
[22] Soma C M A 1999 J. Phys.: Condens. Matter 11 2071
Google Scholar
[23] Bulaev D V, Loss D 2007 Phys. Rev. Lett. 98 097202
Google Scholar
[24] Vitaly N G, Alexander K, Loss D 2008 Phys. Rev. B 77 045328
Google Scholar
[25] Ridley B K 1982 Quantum Processes in Semiconductors (Oxford: Oxford University Press) p233
[26] Jdira L, Overgaag K, Stiufiuc R, Grandidier B, Delerue C, Speller S, Vanmaekelbergh D 2008 Phys. Rev. B 77 205308
Google Scholar
[27] Goupalov S V 2005 Phys. Rev. B 72 073301
Google Scholar
[28] Norris D J, Efros A L, Rosen M, Bawendi M G 1996 Phys. Rev. B 53 16347
Google Scholar
[29] Poddubny A N, Goupalov S V 2008 Phys. Rev. B 77 075315
Google Scholar
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