半导体量子点系统的拉曼散射研究
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摘要
科学技术的迅速发展,使得各种低维半导体材料,如量子阱、量子线、量子点等都已经在实验室制备出来。由于在低维结构中载流子的运动在空间受到封闭性限制,从而使其有着与三维体材料不同的物理内涵和丰富的光学现象及效应。这些低维结构在未来的各种半导体光电和微电子量子器件的设计和制造中具有十分重要的价值,因此,人们迫切地需要了解这类体系的电子、声子等各方面的物理特性。拉曼散射,由于其具测量方便、快捷、对样品无损伤等优点,已经成为研究低维半导体结构的最有效手段之一。通过对散射带频移、线宽、散射强度和偏振等的研究,拉曼散射已成为精确地获取低维半导体结构中电子和声子等微观信息的强有力工具。本文从理论上研究了低维半导体量子点的拉曼散射,全文由以下四章组成。
第一章,绪论。介绍了拉曼散射的基本理论:讨论了半导体量子点结构的特性及发展;简述拉曼散射在低维材料的研究进展。
第二章,主要研究了无限深球型量子点中的电子拉曼散射。采用有效质量近似和量子力学二阶微扰理论,推导了电子拉曼散射微分散射截面的表达式,给出了散射过程的选择定则,选用GaAs和CdS材料进行数值计算,获得了一系列相关拉曼散射光谱,结果显示散射截面随着量子点尺寸的变化而改变,给出电子和空穴对拉曼散射微分散射截面的不同贡献。
第三章,研究了在半抛物量子点中激子参与的拉曼散射。采用有效质量近似,运用量子力学二阶微扰理论推导出了拉曼散射微分散射截面,进一步计算了GaAs/AlGaAs量子点的拉曼散射微分散射截面。最后通过数值计算结果发现激子对拉曼散射具有较大影响。
第四章,总结全文主要计算结果及研究结论,作出展望。
With the rapid development of science and technology,kinds of the low dimensional semiconductor structures,such as quantum wells,quantum wires and quantum dots have been prepared in the laboratory. Due to the beneficial effects of strong confinement to current carriers in these low dimensional structures,many new optical phenomenon and effects have been investigated. For the using value that the design and manufacture of many semiconductor photo-electric devices,microelectronic quantum devices, these low dimensional structures will have an important position in the future,so people are desirous of getting the physical feature of the electron and phonon in these low dimensional structures. Raman scattering, for its convenience and no damage to the materials being measured, has become one of the most effective methods to provide direct information in the low dimensional semiconductor systems, and by means of investigating frequency shift ,line width,intensity and polarization of Raman scattering,it has become a strong instrument to obtain the accurate information about electron and phonon in these quantum systems. In this dissertation, we have presented a theoretical study of the electron Raman scattering process in semiconductor quantum dot structures. The dissertation includes four chapters:
In the first chapter, The basic theory of the Raman scattering is provided .The character and the development of low dimensional semiconductor quantum dots structures have been summarized briefly . A introduction to the current research of Raman scattering in low dimensional structures has been given.
In the second chapter, electron Raman scattering is investigated in infinite potential spherical quantum dot systems. Use the effective mass approximation and second-order infinitesimal disturbance in quantum dots ,the expression of the differential cross-section are derived and the selection rules for the process are given.The numerical calculation is in the GaAs and CdS materials,and a series of Raman scattering optical spectrum are given.The result shows that the differential cross-section are changed with the size of the quantum dot and the different contribution between the electron and the hole.
In the third chapter,Raman scattering is investigated in semi-parabolic quantum dot systems. The intermediate state of the Raman scattering process are exciton states. Also use the effective mass approximation and second-order infinitesimal disturbance in quantum mechanics ,the expression of the differential cross-section are derived and the selection rules for the process are given.The numerical calculation is in the GaAs/AlGaAs materials,and a series of Raman scattering optical spectrum are given.The result shows that the differential cross-section are changed with the confinement potential frequency of the exciton.
In the last chapter, summary of the paper and the main results are given; the shortage and further research are also mentioned.
第一章,绪论。介绍了拉曼散射的基本理论:讨论了半导体量子点结构的特性及发展;简述拉曼散射在低维材料的研究进展。
第二章,主要研究了无限深球型量子点中的电子拉曼散射。采用有效质量近似和量子力学二阶微扰理论,推导了电子拉曼散射微分散射截面的表达式,给出了散射过程的选择定则,选用GaAs和CdS材料进行数值计算,获得了一系列相关拉曼散射光谱,结果显示散射截面随着量子点尺寸的变化而改变,给出电子和空穴对拉曼散射微分散射截面的不同贡献。
第三章,研究了在半抛物量子点中激子参与的拉曼散射。采用有效质量近似,运用量子力学二阶微扰理论推导出了拉曼散射微分散射截面,进一步计算了GaAs/AlGaAs量子点的拉曼散射微分散射截面。最后通过数值计算结果发现激子对拉曼散射具有较大影响。
第四章,总结全文主要计算结果及研究结论,作出展望。
With the rapid development of science and technology,kinds of the low dimensional semiconductor structures,such as quantum wells,quantum wires and quantum dots have been prepared in the laboratory. Due to the beneficial effects of strong confinement to current carriers in these low dimensional structures,many new optical phenomenon and effects have been investigated. For the using value that the design and manufacture of many semiconductor photo-electric devices,microelectronic quantum devices, these low dimensional structures will have an important position in the future,so people are desirous of getting the physical feature of the electron and phonon in these low dimensional structures. Raman scattering, for its convenience and no damage to the materials being measured, has become one of the most effective methods to provide direct information in the low dimensional semiconductor systems, and by means of investigating frequency shift ,line width,intensity and polarization of Raman scattering,it has become a strong instrument to obtain the accurate information about electron and phonon in these quantum systems. In this dissertation, we have presented a theoretical study of the electron Raman scattering process in semiconductor quantum dot structures. The dissertation includes four chapters:
In the first chapter, The basic theory of the Raman scattering is provided .The character and the development of low dimensional semiconductor quantum dots structures have been summarized briefly . A introduction to the current research of Raman scattering in low dimensional structures has been given.
In the second chapter, electron Raman scattering is investigated in infinite potential spherical quantum dot systems. Use the effective mass approximation and second-order infinitesimal disturbance in quantum dots ,the expression of the differential cross-section are derived and the selection rules for the process are given.The numerical calculation is in the GaAs and CdS materials,and a series of Raman scattering optical spectrum are given.The result shows that the differential cross-section are changed with the size of the quantum dot and the different contribution between the electron and the hole.
In the third chapter,Raman scattering is investigated in semi-parabolic quantum dot systems. The intermediate state of the Raman scattering process are exciton states. Also use the effective mass approximation and second-order infinitesimal disturbance in quantum mechanics ,the expression of the differential cross-section are derived and the selection rules for the process are given.The numerical calculation is in the GaAs/AlGaAs materials,and a series of Raman scattering optical spectrum are given.The result shows that the differential cross-section are changed with the confinement potential frequency of the exciton.
In the last chapter, summary of the paper and the main results are given; the shortage and further research are also mentioned.
引文
[1]Esaki.L,Tsu.R.IBM.J.Res.Dev.,14(1970)467
[2]T.Brunhes,P.Boucaud,S.Sauvage,Phys.Rev.B 61(2000) 5562.
[3]J.Khurgin,Phys.Rev.B 38(1988) 4056.
[4]G.Bastard,E.E.Mendez,L.L.Chang,L.Esaki,Phys.Rev.B 28(1983) 3214.
[5]K.X.Guo,C.Y.Chen,J.Phys.:Condens.Matter 7(1995) 6583.
[6]C.Liu,Chin.Phys.11(2002) 0730.
[7]G.Wang,Phys.Rev.B 72(2005) 155329.
[8]Tyndall.J,Proc.Roy.Soc,19(1868-1869)233
[9]Lord.Rayleigh,Phil.Mag,47(1899)375
[10]Raman C.V.,Ind.J.Phys,2(1928)387.
[11]沈学础,《半导体光谱和光学性质》,科学出版社,(2002)
[12]Rocksby.H.P,J.Soc.Glass.Techn,16(1932) 171
[13]Ekimov.A.I,Onushenko.A.A,JETP.Lett,40(1984) 1137
[14]J.R.Arther,J.Appl.Physics 39(1968)4032.
[15]A.Y.Chao,J.R.Authur,Progr.Solid State.Chem.10(1975) 157.
[16]W.T.Tswang,'Semiconductors and Semimetals',New York:Academic Press,1985.
[17]T.Kerr.,Ⅲ- Vs Review(4) 3(1991) 20.
[18]H.M.Manasevil,Appl.Phys.Lett.12(1990) 20.
[19]Mukai.k,Ohtsuka.N,Sugawara.M,Yamzaki.S,Jpn.J.Appl.Phys.33(1994)L1710
[20]Grundman.M,Ledentsov.N.N,et al,Appl phys Lett 68(1996)979[10]
[21]Heiz.R,Grundman.M,Ledentsov.N.N,et al,Appl phys Lett 68(1996)361.
[22]Mukai.k,Shoji.H,Sugawara.M,YOhtsuka.N,Phys.B.54(1996)R5243.
[23]Wei-ming Que,George Kirczenow,Phys.Rev.B 38(1988)3614
[24]K.Kash,A.Scherer,J.M.Worlock,H.G.Craighead,and M.C.Tamargo,Appl.Phys.Lett 49(1986) 1043
[25]H.Temkin,G.J.Dolan,M.B.Panish,and S.N.G.Chu,Appl.Phys.Lett 50(1987)413
[26]Y.Z.Hu,M.Lindberg,and S.W.Koch,Phys.Rev.B 42(1990)1713
[27]Garnett W.Bryant,Phys.Rev.B 37(1988)8763 - 8772
[28]Sotirios Baskoutas,Emmanuel Paspalakis,Andreas F.Terzis,Phys.Rev.B 74(2006) 153306
[29]WeimingQue,Phys.Rev.B 45(1992)11036
[30]Scoee.J.F.,Fleury.P.A.,Worlock.J.M.Phys.Rev 117(1963) 1288.
[31]Henry.C.H,Hop?eld.J.M,Phys.Rev Lett 15(1965)964.[17]
[32]Fleury.P.A,Worlock.J.M,Phys.Rev Lett 18(1967)665.[18]
[33]F.Comas,C.Trallero-Giner,R.J.Perez-Alvarez,J.Phys.C 16(1986)6479.
[34]M.Cardona,Superlattices Microstruct.7(1990) 183.
[35]A.Mooradian,Phys.Rev.Lett 20(1968)1102
[36]A.Mooradian and G.B.Wright,Phys.Rev.Lett 16(1966)999
[37]A.Mooradian and A.L.McWhorter,Phys.Rev.Lett 19(1967)849
[38]阿雷克F T,舒尔茨-杜波依斯E O,激光的物理应用,北京:科学出版社,1979,9
[39]C.H.Henry,J.J.Hopfield,Phys.Rev.Lett 15(1965)964
[40]Livescu,Brafman O,Solid State Commun,35(1980) 73
[41]James E.Gunn and Jeremiah P.Ostriker,Phys.Rev.Lett.22(1969)728
[42]Washington,M.A.;Genack,A.Z.;Cummins,H.Z.;Bruce.R.H.;Compaan;A.:Forman,R.A,Physical Review B(Solid State),15(1977) 2145
[43]B.F.Zhu,K.Huang,T.Tang,Phys.Rev.B 40(1989-Ⅱ) 6299.
[44]K.Huang,B.F.Zhu,T.Tang,Phys.Rev.B 41(1989-Ⅱ) 5825.
[45]E.Men(e|¨)ndez,C.Trallero-Giner,M.Cardona,Phys.Stat.Sol.(b)199(1997) 81.
[46]J.M.Bergues,R.Betancourt-Riera,R.Riera,J.L.Matin,J.Phys.:Condens.Matter 12(2000) 7983.
[47]C.H.Liu,B.K.Ma,C.Y.Chen,Chinese Physics 11(2002) 7.
[48]Xiang-Fu Zhao,Cui-Hong Liu,Phyaics Letters A.70(2007) 364.
[49]Xiang-Fu Zhao,Cui-Hong Liu,Physica E.36(2007) 34.
[50]A.Garcia-Cristobal,A.Cantarero,C.Trallero-Giner,M.Cardona,Phys.Rev.B.49(1994-Ⅰ)13430.
[51]C.Trallero-Giner,A.Cantarero,M.Cardona,Phys.Rev.B 40(1989-Ⅱ) 4030.
[52]M.P.Chamberlain,C.Trallero-Giner,M.Cardona,Phys.Rev.B 51(1995) 1680.
[53]A.J.Shields,C.Trallero-Giner,M.Cardona,et.al.,Phys.Rev.B 46(1992-Ⅰ) 4990.
[54]A.Cros,A.Cantarero,C.Trallero-Giner,M.Cardona,Phys.Rev.B46(1992) 12627.
[55]W.Kauschke,A.K.Sood,M.Cardona,K.Ploog,Phys.Rev.B 36(1987-Ⅰ) 1612.
[56]J.E.Zucker,A.Pinczuk,D.S.Chemla,Phys.Rev.B 15(1988) 4278.
[57]Y.Arakawa and H.Sakaki,Appl.Phys.Lett.40(1982) 939.
[58]M.Cardona,G.G(u|¨)ntherodt(Eds.),'Light Scattering in Solids V',Topics in Applied Physics,Springer,Heidelberg,1989.
[59]M.Cardona,Superlattices Microstruct.7(1990)183.
[60]M.V.Klein,IEEE J.Quantum Electron.QE-22(1986) 1760.
[61]F.Comas,C.Trallero-Giner,and R.J.Perez-Alvarez,J.Phys.C 19(1986) 6479.
[62]X.-F.Zhao,C.-H.Liu,Eur.Phys.J.B 53(2006) 209.
[63]Qing-Hu Zhong,and Cui-Hong Liu,Thin Solid Films.516(2008)3405.
[64]J.M.Bergues,R.Riera,F.Comas,C.Trallero-Giner,J.Phys.:Condens.Matter 7(1995) 7273.
[65]X.F.Zhao,C.H.Liu,Phys.B 392(2007)11-15
[66]Y.L.Xie,Z.H.Chen,D.F.Cui,et al.,Phys.Rev.B 43(1991) 12477.
[67]J.Khurgin,Appl.Phys.Lett.51(1987) 2100.
[68]C.-J.Zhang,K.X.Guo,Physica B 383(2006) 183.
[69]C.Sirtori,F.Capasso,et al.,Phys.Rev.Lett.68(1992) 1010.
[70]S.Sauvage,P.Boucaud,Phys.Rev.B 59(1999) 9830.
[71]K.X.Guo,C.Y.Chen,T.P.Das,Opt.Quantum Electron.33(2001) 231.
[72]L.Tsang,D.Ahn,S.L.Chuang,Appl.Phys.Lett.52(1988) 697.
[73]D.Ahn,S.L.Chuang,Phys.Rev.B 35(1987) 4149.
[74]A.Harwit,J.S.Harris Jr.,Appl.Phys.Lett.50(1987)685.
[75]M.M.Fejer,S.J.B.Yoo,R.C.Byer,et al.,Phys.Rev.Lett.62(1989) 1041.
[76]D.Bimberg,M.Grundmann,F.Heinrichsdorff,et al.,Thin SolidFilms 367(2000)235.
[77]D.Bimberg,M.Grundmann,and N.N.Ledentsov,'Quantum Dot Heterostructures',Wiley,Chichester,1999.
[78]曾谨言,《量子力学》(第三版),科学出版社,北京(2000)
[79]Ekimov.A.L,Efros.Al.L,Ivanov.M.G,Onushenko.A.A,Shumilov.S.K,Solid State commun,69(1989)565
[80]Schmidt.H.M,Weller.H,Chem Phys Lett,129(1986)615
[81]Kayanuma.Y,Momiji.H,Phys Rev,B41(1990)1713
[82]S.L.Zhang,et.al,Phys.Lett.A186(1994) 433.
[83]Fleury.P.A,Worlock.J.M,Phys.Rev Lett 18(1967)665.
[84]Henry.C.H,Hopfield.J.J,Phys.Rev Lett 15(1965)964.
[85]F.Comas,C.Trallero-Giner,R.J.Perez-Alvarez,J.Phys.C 19(1986)6479.
[86]J.H.Burnett,H.M.Cheong,R.M.Westervelt,W.Paul,P.F.Hopkins,M.Sundaram,A.C.R.Cossard,Phys.Rev.B.48(1993)4524.
[87]B.F.Zhu,K.Huang,H.Tang Phys.Rev.B40(1989) 9.
[88]Z.P.Wang,H.X.Han,et.al.,J.Phys.:Condens.Matter 4(1992)367.
[89]M.P.Chamberlain,C.Trallero-Giner and M.Cardona,Phys.Rev.B 51(1995) 3.
[90]E.Zucker,A.pinczuk,D.S.Chenmla,A.C.Gossard,W.Wiegmann,Phys.Rev.Lett51(1983)1293.
[91]J.E.Zucker,A.Pinczuk,D.S.Chemla,Phys.Rev.B 15(1988)4278.
[2]T.Brunhes,P.Boucaud,S.Sauvage,Phys.Rev.B 61(2000) 5562.
[3]J.Khurgin,Phys.Rev.B 38(1988) 4056.
[4]G.Bastard,E.E.Mendez,L.L.Chang,L.Esaki,Phys.Rev.B 28(1983) 3214.
[5]K.X.Guo,C.Y.Chen,J.Phys.:Condens.Matter 7(1995) 6583.
[6]C.Liu,Chin.Phys.11(2002) 0730.
[7]G.Wang,Phys.Rev.B 72(2005) 155329.
[8]Tyndall.J,Proc.Roy.Soc,19(1868-1869)233
[9]Lord.Rayleigh,Phil.Mag,47(1899)375
[10]Raman C.V.,Ind.J.Phys,2(1928)387.
[11]沈学础,《半导体光谱和光学性质》,科学出版社,(2002)
[12]Rocksby.H.P,J.Soc.Glass.Techn,16(1932) 171
[13]Ekimov.A.I,Onushenko.A.A,JETP.Lett,40(1984) 1137
[14]J.R.Arther,J.Appl.Physics 39(1968)4032.
[15]A.Y.Chao,J.R.Authur,Progr.Solid State.Chem.10(1975) 157.
[16]W.T.Tswang,'Semiconductors and Semimetals',New York:Academic Press,1985.
[17]T.Kerr.,Ⅲ- Vs Review(4) 3(1991) 20.
[18]H.M.Manasevil,Appl.Phys.Lett.12(1990) 20.
[19]Mukai.k,Ohtsuka.N,Sugawara.M,Yamzaki.S,Jpn.J.Appl.Phys.33(1994)L1710
[20]Grundman.M,Ledentsov.N.N,et al,Appl phys Lett 68(1996)979[10]
[21]Heiz.R,Grundman.M,Ledentsov.N.N,et al,Appl phys Lett 68(1996)361.
[22]Mukai.k,Shoji.H,Sugawara.M,YOhtsuka.N,Phys.B.54(1996)R5243.
[23]Wei-ming Que,George Kirczenow,Phys.Rev.B 38(1988)3614
[24]K.Kash,A.Scherer,J.M.Worlock,H.G.Craighead,and M.C.Tamargo,Appl.Phys.Lett 49(1986) 1043
[25]H.Temkin,G.J.Dolan,M.B.Panish,and S.N.G.Chu,Appl.Phys.Lett 50(1987)413
[26]Y.Z.Hu,M.Lindberg,and S.W.Koch,Phys.Rev.B 42(1990)1713
[27]Garnett W.Bryant,Phys.Rev.B 37(1988)8763 - 8772
[28]Sotirios Baskoutas,Emmanuel Paspalakis,Andreas F.Terzis,Phys.Rev.B 74(2006) 153306
[29]WeimingQue,Phys.Rev.B 45(1992)11036
[30]Scoee.J.F.,Fleury.P.A.,Worlock.J.M.Phys.Rev 117(1963) 1288.
[31]Henry.C.H,Hop?eld.J.M,Phys.Rev Lett 15(1965)964.[17]
[32]Fleury.P.A,Worlock.J.M,Phys.Rev Lett 18(1967)665.[18]
[33]F.Comas,C.Trallero-Giner,R.J.Perez-Alvarez,J.Phys.C 16(1986)6479.
[34]M.Cardona,Superlattices Microstruct.7(1990) 183.
[35]A.Mooradian,Phys.Rev.Lett 20(1968)1102
[36]A.Mooradian and G.B.Wright,Phys.Rev.Lett 16(1966)999
[37]A.Mooradian and A.L.McWhorter,Phys.Rev.Lett 19(1967)849
[38]阿雷克F T,舒尔茨-杜波依斯E O,激光的物理应用,北京:科学出版社,1979,9
[39]C.H.Henry,J.J.Hopfield,Phys.Rev.Lett 15(1965)964
[40]Livescu,Brafman O,Solid State Commun,35(1980) 73
[41]James E.Gunn and Jeremiah P.Ostriker,Phys.Rev.Lett.22(1969)728
[42]Washington,M.A.;Genack,A.Z.;Cummins,H.Z.;Bruce.R.H.;Compaan;A.:Forman,R.A,Physical Review B(Solid State),15(1977) 2145
[43]B.F.Zhu,K.Huang,T.Tang,Phys.Rev.B 40(1989-Ⅱ) 6299.
[44]K.Huang,B.F.Zhu,T.Tang,Phys.Rev.B 41(1989-Ⅱ) 5825.
[45]E.Men(e|¨)ndez,C.Trallero-Giner,M.Cardona,Phys.Stat.Sol.(b)199(1997) 81.
[46]J.M.Bergues,R.Betancourt-Riera,R.Riera,J.L.Matin,J.Phys.:Condens.Matter 12(2000) 7983.
[47]C.H.Liu,B.K.Ma,C.Y.Chen,Chinese Physics 11(2002) 7.
[48]Xiang-Fu Zhao,Cui-Hong Liu,Phyaics Letters A.70(2007) 364.
[49]Xiang-Fu Zhao,Cui-Hong Liu,Physica E.36(2007) 34.
[50]A.Garcia-Cristobal,A.Cantarero,C.Trallero-Giner,M.Cardona,Phys.Rev.B.49(1994-Ⅰ)13430.
[51]C.Trallero-Giner,A.Cantarero,M.Cardona,Phys.Rev.B 40(1989-Ⅱ) 4030.
[52]M.P.Chamberlain,C.Trallero-Giner,M.Cardona,Phys.Rev.B 51(1995) 1680.
[53]A.J.Shields,C.Trallero-Giner,M.Cardona,et.al.,Phys.Rev.B 46(1992-Ⅰ) 4990.
[54]A.Cros,A.Cantarero,C.Trallero-Giner,M.Cardona,Phys.Rev.B46(1992) 12627.
[55]W.Kauschke,A.K.Sood,M.Cardona,K.Ploog,Phys.Rev.B 36(1987-Ⅰ) 1612.
[56]J.E.Zucker,A.Pinczuk,D.S.Chemla,Phys.Rev.B 15(1988) 4278.
[57]Y.Arakawa and H.Sakaki,Appl.Phys.Lett.40(1982) 939.
[58]M.Cardona,G.G(u|¨)ntherodt(Eds.),'Light Scattering in Solids V',Topics in Applied Physics,Springer,Heidelberg,1989.
[59]M.Cardona,Superlattices Microstruct.7(1990)183.
[60]M.V.Klein,IEEE J.Quantum Electron.QE-22(1986) 1760.
[61]F.Comas,C.Trallero-Giner,and R.J.Perez-Alvarez,J.Phys.C 19(1986) 6479.
[62]X.-F.Zhao,C.-H.Liu,Eur.Phys.J.B 53(2006) 209.
[63]Qing-Hu Zhong,and Cui-Hong Liu,Thin Solid Films.516(2008)3405.
[64]J.M.Bergues,R.Riera,F.Comas,C.Trallero-Giner,J.Phys.:Condens.Matter 7(1995) 7273.
[65]X.F.Zhao,C.H.Liu,Phys.B 392(2007)11-15
[66]Y.L.Xie,Z.H.Chen,D.F.Cui,et al.,Phys.Rev.B 43(1991) 12477.
[67]J.Khurgin,Appl.Phys.Lett.51(1987) 2100.
[68]C.-J.Zhang,K.X.Guo,Physica B 383(2006) 183.
[69]C.Sirtori,F.Capasso,et al.,Phys.Rev.Lett.68(1992) 1010.
[70]S.Sauvage,P.Boucaud,Phys.Rev.B 59(1999) 9830.
[71]K.X.Guo,C.Y.Chen,T.P.Das,Opt.Quantum Electron.33(2001) 231.
[72]L.Tsang,D.Ahn,S.L.Chuang,Appl.Phys.Lett.52(1988) 697.
[73]D.Ahn,S.L.Chuang,Phys.Rev.B 35(1987) 4149.
[74]A.Harwit,J.S.Harris Jr.,Appl.Phys.Lett.50(1987)685.
[75]M.M.Fejer,S.J.B.Yoo,R.C.Byer,et al.,Phys.Rev.Lett.62(1989) 1041.
[76]D.Bimberg,M.Grundmann,F.Heinrichsdorff,et al.,Thin SolidFilms 367(2000)235.
[77]D.Bimberg,M.Grundmann,and N.N.Ledentsov,'Quantum Dot Heterostructures',Wiley,Chichester,1999.
[78]曾谨言,《量子力学》(第三版),科学出版社,北京(2000)
[79]Ekimov.A.L,Efros.Al.L,Ivanov.M.G,Onushenko.A.A,Shumilov.S.K,Solid State commun,69(1989)565
[80]Schmidt.H.M,Weller.H,Chem Phys Lett,129(1986)615
[81]Kayanuma.Y,Momiji.H,Phys Rev,B41(1990)1713
[82]S.L.Zhang,et.al,Phys.Lett.A186(1994) 433.
[83]Fleury.P.A,Worlock.J.M,Phys.Rev Lett 18(1967)665.
[84]Henry.C.H,Hopfield.J.J,Phys.Rev Lett 15(1965)964.
[85]F.Comas,C.Trallero-Giner,R.J.Perez-Alvarez,J.Phys.C 19(1986)6479.
[86]J.H.Burnett,H.M.Cheong,R.M.Westervelt,W.Paul,P.F.Hopkins,M.Sundaram,A.C.R.Cossard,Phys.Rev.B.48(1993)4524.
[87]B.F.Zhu,K.Huang,H.Tang Phys.Rev.B40(1989) 9.
[88]Z.P.Wang,H.X.Han,et.al.,J.Phys.:Condens.Matter 4(1992)367.
[89]M.P.Chamberlain,C.Trallero-Giner and M.Cardona,Phys.Rev.B 51(1995) 3.
[90]E.Zucker,A.pinczuk,D.S.Chenmla,A.C.Gossard,W.Wiegmann,Phys.Rev.Lett51(1983)1293.
[91]J.E.Zucker,A.Pinczuk,D.S.Chemla,Phys.Rev.B 15(1988)4278.