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The surface polarization energy that arises from the difference in dielectric coefficient between the quantum dot (QD) and the background medium is investigated by the equivalent image charge method. A general expression for the bandgap of QD depending on the dielectric coefficient of background medium is presented by solving the exciton Schrödinger equation with the perturbation method. As examples, the sizedependent bandgaps, bandgap shifts, absorption-peak wavelengths and absorption-peakwavelength shifts of PbSe, PbS and CdSe QDs doped in different background media are determined in detail. There is evidence to show that the effects of surface polarization on the bandgap and the first absorption-peak wavelength of QD are considerable. The bandgap decreases with the increase of dielectric coefficient of background medium, which causes the absorption-peak wavelength to be red shifted. The effect of surface polarization on the bandgap depends substantially on the sign and value of image charge. When the dielectric coefficient of QD is greater than that of background medium, the absorption-peak wavelength comes to blue shift due to surface polarization of QD. On the contrary, the absorption-peak wavelength comes to redshift. The absorption-peak wavelength shifts of QDs doped in different background media will reach a maximum in a certain diameter depending on the kind of QD.
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Keywords:
- quantum dots /
- surface polarization /
- bandgap /
- absorption-peak wavelength
[1] Cheng C, Cheng X Y 2017 Nanophotonics and Applications of Quantum Dots (Beijing:Science Press) pp3-69 (in Chinese)[程成, 程潇羽 2017 量子点纳米光子学及应用(北京:科学出版社)第3–69页]
[2] Narayanaswamy A, Feiner L F, Meijerink A, van der Zaag P J 2009 ACS Nano 3 2539
[3] Zhou Y J, Rabe K M, Vanderbilt D 2015 Phys. Rev. B 92 041102
[4] Brus L E 1984 J. Chem. Phys. 80 4403
[5] Tyrrell E J, Smith J M 2011 Phys. Rev. B 84 165328
[6] Takagahara T 1993 Phys. Rev. B 47 4569
[7] Pereira T A S, de Sousa J S, Freire J A K, Farias G A 2010 J. Appl. Phys. 108 054311
[8] Slachmuylders A F, Partoens B, Magnus W, Peeters F M 2006 Phys. Rev. B 74 235321
[9] El-Kork N, Huisken F, von Borczyskowski C 2011 J. Appl. Phys. 110 074312
[10] Lyu Y R, Hsieh T E 2013 J. Appl. Phys. 113 184303
[11] Rodina A V, Efros Al L 2016 J. Exp. Theor. Phys. 122 554
[12] Murphy C J 2002 Anal. Chem. 74 520A
[13] Pejova B, Grozdanov I 2005 Mater. Chem. Phys. 90 35
[14] Cheng C, Yan H Z 2009 Phys. E:Low Dimension. Syst. and Nanostruc. 41 828
[15] Hyun B R, Chen H, Rey D A, Wise F W, Batt C A 2007 J. Phys. Chem. B 111 5726
[16] Wang L W, Zunger A 1996 Phys. Rev. B 53 9579
[17] Chang K, Xia J B 1997 Solid State Commum. 104 351
[18] Miao M S, Yan Q, van de Walle C G, Lou W K, Li L L, Chang K 2012 Phys. Rev. Lett. 109 186803
[19] Zhang D, Lou W K, Miao M S, Zhang S C, Chang K 2013 Phys. Rev. Lett. 111 156402
[20] Cheng C, Li J J 2017 Acta Opt. Sin. 37 01300011 (in Chinese)[程成, 李婕婕 2017 光学学报 37 01300011]
[21] Ushakova E V, Litvin A P, Parfenov P S, Fedorov A V, Artemyev M, Prudnikau A V, Rukhlenko I D, Baranov A V 2012 ACS Nano 6 8913
[22] Cheng C, Li Z W 2016 Acta Opt. Sin. 36 02160011 (in Chinese)[程成, 李志伟 2016 光学学报 36 02160011]
[23] Kumar S, Biswas D 2007 J. Appl. Phys. 102 084305
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[1] Cheng C, Cheng X Y 2017 Nanophotonics and Applications of Quantum Dots (Beijing:Science Press) pp3-69 (in Chinese)[程成, 程潇羽 2017 量子点纳米光子学及应用(北京:科学出版社)第3–69页]
[2] Narayanaswamy A, Feiner L F, Meijerink A, van der Zaag P J 2009 ACS Nano 3 2539
[3] Zhou Y J, Rabe K M, Vanderbilt D 2015 Phys. Rev. B 92 041102
[4] Brus L E 1984 J. Chem. Phys. 80 4403
[5] Tyrrell E J, Smith J M 2011 Phys. Rev. B 84 165328
[6] Takagahara T 1993 Phys. Rev. B 47 4569
[7] Pereira T A S, de Sousa J S, Freire J A K, Farias G A 2010 J. Appl. Phys. 108 054311
[8] Slachmuylders A F, Partoens B, Magnus W, Peeters F M 2006 Phys. Rev. B 74 235321
[9] El-Kork N, Huisken F, von Borczyskowski C 2011 J. Appl. Phys. 110 074312
[10] Lyu Y R, Hsieh T E 2013 J. Appl. Phys. 113 184303
[11] Rodina A V, Efros Al L 2016 J. Exp. Theor. Phys. 122 554
[12] Murphy C J 2002 Anal. Chem. 74 520A
[13] Pejova B, Grozdanov I 2005 Mater. Chem. Phys. 90 35
[14] Cheng C, Yan H Z 2009 Phys. E:Low Dimension. Syst. and Nanostruc. 41 828
[15] Hyun B R, Chen H, Rey D A, Wise F W, Batt C A 2007 J. Phys. Chem. B 111 5726
[16] Wang L W, Zunger A 1996 Phys. Rev. B 53 9579
[17] Chang K, Xia J B 1997 Solid State Commum. 104 351
[18] Miao M S, Yan Q, van de Walle C G, Lou W K, Li L L, Chang K 2012 Phys. Rev. Lett. 109 186803
[19] Zhang D, Lou W K, Miao M S, Zhang S C, Chang K 2013 Phys. Rev. Lett. 111 156402
[20] Cheng C, Li J J 2017 Acta Opt. Sin. 37 01300011 (in Chinese)[程成, 李婕婕 2017 光学学报 37 01300011]
[21] Ushakova E V, Litvin A P, Parfenov P S, Fedorov A V, Artemyev M, Prudnikau A V, Rukhlenko I D, Baranov A V 2012 ACS Nano 6 8913
[22] Cheng C, Li Z W 2016 Acta Opt. Sin. 36 02160011 (in Chinese)[程成, 李志伟 2016 光学学报 36 02160011]
[23] Kumar S, Biswas D 2007 J. Appl. Phys. 102 084305
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