晶格弛豫方法研究PbSe量子点的带内弛豫过程
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摘要
在晶格弛豫理论框架内,电子-体纵光学声子耦合的Fr?hlich模型基础上,系统研究了PbSe量子点的3个最低激发态之间及其与基态之间的带内弛豫过程.具体讨论了各个弛豫过程中的黄-里斯因子、弛豫率与量子点半径的变化关系,进一步讨论了弛豫率的温度依赖性.得出的理论结果很好地解释了相应的实验.
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 Frohlich 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.
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 Frohlich 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.
引文
[1] Andrew F F, Gao J B, Victor I K 2017 Nat. Phys. 13 604
[2] Frank C M S, Stanko T, Arjan J. H, Laurens D A S 2017ACS Nano 11 6286
[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
[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. 133078
[5] Avila L M, Tritsch J R, Wolcott A, Chan W L, Nelson C A,Zhu X Y 2012 Nano Lett. 12 1588
[6] Svetlana V K, Dmitri S K, Victor V P, Oleg V P 2011 J.Phys. Chem. C 115 21641
[7] Schaller R D, Klimov V I 2004 Phys. Rev. Lett. 92 186601
[8] Moonsub S, Philippe G S 2001 Phys. Rev. B 64 245342
[9] Wang L W, Califano M, Zunger A, Alberto F 2003 Phys.Rev. Lett. 91 056404
[10] Victor I K 2000 J. Phys. Chem. B 104 6112
[11] Brian L W, Wang C J, Philippe G S 2002 J. Phys. Chem. B106 10634
[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
[13] Bonati C, Cannizzo A, Tonti D, Tortschanoff A, Mourik F,Chergui M 2007 Phys. Rev. B 76 033304
[14] Jeffrey M H, Du H, Krauss T D, Cho K S, Murray C B, Wise F W 2005 Phys. Rev. B 72 195312
[15] Li X Q, Arakawa Y 1997 Phys. Rev. B 56 10423
[16] Schroeter D F, Griffiths D J, Sercel P C 1996 Phys. Rev. B 541486
[17] Philippe G S, Brian W, Dong Y 2005 J. Chem. Phys. 123074709
[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
[22] Soma C M A 1999 J. Phys.:Condens. Matter 11 2071
[23] Bulaev D V, Loss D 2007 Phys. Rev. Lett. 98 097202
[24] Vitaly N G, Alexander K, Loss D 2008 Phys. Rev. B 77045328
[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
[27] Goupalov S V 2005 Phys. Rev. B 72 073301
[28] Norris D J, Efros A L, Rosen M, Bawendi M G 1996 Phys.Rev. B 53 16347
[29] Poddubny A N, Goupalov S V 2008 Phys. Rev. B 77 075315
[2] Frank C M S, Stanko T, Arjan J. H, Laurens D A S 2017ACS Nano 11 6286
[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
[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. 133078
[5] Avila L M, Tritsch J R, Wolcott A, Chan W L, Nelson C A,Zhu X Y 2012 Nano Lett. 12 1588
[6] Svetlana V K, Dmitri S K, Victor V P, Oleg V P 2011 J.Phys. Chem. C 115 21641
[7] Schaller R D, Klimov V I 2004 Phys. Rev. Lett. 92 186601
[8] Moonsub S, Philippe G S 2001 Phys. Rev. B 64 245342
[9] Wang L W, Califano M, Zunger A, Alberto F 2003 Phys.Rev. Lett. 91 056404
[10] Victor I K 2000 J. Phys. Chem. B 104 6112
[11] Brian L W, Wang C J, Philippe G S 2002 J. Phys. Chem. B106 10634
[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
[13] Bonati C, Cannizzo A, Tonti D, Tortschanoff A, Mourik F,Chergui M 2007 Phys. Rev. B 76 033304
[14] Jeffrey M H, Du H, Krauss T D, Cho K S, Murray C B, Wise F W 2005 Phys. Rev. B 72 195312
[15] Li X Q, Arakawa Y 1997 Phys. Rev. B 56 10423
[16] Schroeter D F, Griffiths D J, Sercel P C 1996 Phys. Rev. B 541486
[17] Philippe G S, Brian W, Dong Y 2005 J. Chem. Phys. 123074709
[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
[22] Soma C M A 1999 J. Phys.:Condens. Matter 11 2071
[23] Bulaev D V, Loss D 2007 Phys. Rev. Lett. 98 097202
[24] Vitaly N G, Alexander K, Loss D 2008 Phys. Rev. B 77045328
[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
[27] Goupalov S V 2005 Phys. Rev. B 72 073301
[28] Norris D J, Efros A L, Rosen M, Bawendi M G 1996 Phys.Rev. B 53 16347
[29] Poddubny A N, Goupalov S V 2008 Phys. Rev. B 77 075315