J. Semicond. > Volume 37 > Issue 11 > Article Number: 112001

Donor impurity-related optical absorption coefficients and refractive index changes in a rectangular GaAs quantum dot in the presence of electric field

Sheng Wang 1, 2, , , Yun Kang 1, and Xianli Li 1,

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Abstract: Within the quasi-one-dimensional effective potential model and effective mass approximation, we obtain the wavefunctions and energy eigenvalues of the ground (j=1) and first 2 excited states (j=2 and 3) of a donor impurity in a rectangular GaAs quantum dot in the presence of electric field. The donor impurity-related linear and nonlinear optical absorption as well as refractive index changes for the transitions j=1-2 and j=2-3 are investigated. The results show that the impurity position, incident optical intensity and electric field play important roles in the optical absorption coefficients and refractive index changes. We find that the impurity effect induces the blueshift for j=1-2 and redshift for j=3-2 in the absence of the electric field, but it leads to redshift for j=1-2 and blueshift for j=3-2 in the existence of the field. Also, the optical coefficient for the higher energy transitions j=2-3 is insensitive to variation of impurity positions, while that for the low energy transition j=1-2 depends significantly on the positions of impurity. In addition, the saturation and splitting phenomenon of the optical absorption are observed as the incident optical intensity increases.

Key words: quasi-one-dimensional effective potentialrectangular GaAs quantum dotoptical absorptionrefractive index changes

Abstract: Within the quasi-one-dimensional effective potential model and effective mass approximation, we obtain the wavefunctions and energy eigenvalues of the ground (j=1) and first 2 excited states (j=2 and 3) of a donor impurity in a rectangular GaAs quantum dot in the presence of electric field. The donor impurity-related linear and nonlinear optical absorption as well as refractive index changes for the transitions j=1-2 and j=2-3 are investigated. The results show that the impurity position, incident optical intensity and electric field play important roles in the optical absorption coefficients and refractive index changes. We find that the impurity effect induces the blueshift for j=1-2 and redshift for j=3-2 in the absence of the electric field, but it leads to redshift for j=1-2 and blueshift for j=3-2 in the existence of the field. Also, the optical coefficient for the higher energy transitions j=2-3 is insensitive to variation of impurity positions, while that for the low energy transition j=1-2 depends significantly on the positions of impurity. In addition, the saturation and splitting phenomenon of the optical absorption are observed as the incident optical intensity increases.

Key words: quasi-one-dimensional effective potentialrectangular GaAs quantum dotoptical absorptionrefractive index changes



References:

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Milanović V, Ikonić Z. Intraband absorption of infrared radiation in a semiconductor quantum dot[J]. Phys Rev B, 1989, 39(11): 7982. doi: 10.1103/PhysRevB.39.7982

[2]

Garduno-Nolasco E, Missous M, Donoval D. Temperature dependence of InAs/GaAs quantum dots solar photovoltaic devices[J]. Journal of Semiconductors, 2014, 35(5): 054001. doi: 10.1088/1674-4926/35/5/054001

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Peter A J. Hydrogenic impurities in cylindrical quantum wires in the presence of a magnetic field[J]. Physica E, 2007, 39(1): 115. doi: 10.1016/j.physe.2007.01.008

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Li S S, Xia J B. Electronic structure and binding energy of a hydrogenic impurity in a hierarchically self-assembled GaAs=AlxGa1-xAsGaAs=AlxGa1-xAs quantum dot[J]. J Appl Phys, 2006, 100(8): 083714. doi: 10.1063/1.2358406

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Zounoubi A, Zorkani I, Messaoudi K E. Magnetic field effect on the polarizability of shallow donor in cylindrical quantum dot[J]. Phys Lett A, 2003, 312(3): 220.

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Manaselyan A K, Kirakosyan A A. Effect of the dielectricconstant mismatch and magnetic field on the binding energy of hydrogenic impurities in a spherical quantum dot[J]. Physica E, 2004, 22(4): 825. doi: 10.1016/j.physe.2003.09.045

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Manaselyan A K, Kirakosyan A A. Barrier penetration in Kane type semiconductor nanostructures[J]. Physica E, 2005, 28(4): 452.

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Mazur Y I, Dorogan V G, Marega E. Excited state coherent resonant electronic tunneling in quantum well-quantum dot hybrid structures[J]. Appl Phys Lett, 2011, 98(8): 083118. doi: 10.1063/1.3560063

[9]

Kang Yun, Wang Sheng, Li Xianli. Electron energy states in a two-dimensional GaAs quantum ring with hydrogenic donor impurity in the presence of magnetic field[J]. Journal of Semiconductors, 2015, 36(3): 032003. doi: 10.1088/1674-4926/36/3/032003

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Kazarinov R F, Suris R A. Possibility of the amplification electromagnetic waves in a semiconductor with superlattice[J]. Sov Phys Semicond, 1971, 5(3): 707.

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Capasso F, Mohammed K, Cho A Y. Resonant tunneling through double barriers, perpendicular quantum transport phenomena in superlattices, and their device applications[J]. IEEE J Quantum Electron, 1986, 22(9): 1853. doi: 10.1109/JQE.1986.1073171

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Miller A B. Quantum well optoelectronic switching devices[J]. Int J High Speed Electron Syst, 1991, 1(1): 19.

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Lee S W, Hirakava K, Shimada Y. Bound-to-continuum intersubband photoconductivity of self-assembled InAs quantum dots in modulation-doped heterostructures[J]. Appl Phys Lett, 1999, 75(10): 1428. doi: 10.1063/1.124715

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Klimov V I, McBrauch D W, Leatherdale C A. Electron and hole relaxation pathways in semiconductor quantum dots[J]. Phys Rev B, 1999, 60(19): 13740. doi: 10.1103/PhysRevB.60.13740

[15]

Mackowski S, Kyrychenko F, Karczewski G. Thermal carrier escape and capture in CdTe quantum dots[J]. Phys Status Solidi B, 2001, 224(2): 465. doi: 10.1002/(ISSN)1521-3951

[16]

Sauvage S, Boucaud P, Brunhes T. Midinfrared absorption and photocurrent spectroscopy of InAs/GaAs self-assembled quantum dots[J]. Appl Phys Lett, 2001, 78(16): 2327. doi: 10.1063/1.1365411

[17]

Xie W. Absorption spectra of a donor impurity in a quantum ring[J]. Physica Status Solidi B, 2009, 246(6): 1313. doi: 10.1002/pssb.v246:6

[18]

Xie W. Nonlinear optical rectification of a hydrogenic impurity in a disc-like quantum dot[J]. Physica B, 2009, 404(21): 4142. doi: 10.1016/j.physb.2009.07.177

[19]

Xie W. Impurity effects on optical property of a spherical quantum dot in the presence of an electric field[J]. Physica B, 2010, 405(16): 3436. doi: 10.1016/j.physb.2010.05.019

[20]

Liang S, Xie W. Effects of the hydrostatic pressure and temperature on optical properties of a hydrogenic impurity in the discshaped quantum dot[J]. Physica B, 2011, 406(11): 2224. doi: 10.1016/j.physb.2011.03.035

[21]

Chen T, Xie W, Liang S. The nonlinear optical rectification of an ellipsoidal quantum dot with impurity in the presence of an electric field[J]. Physica E, 2012, 44(4): 786. doi: 10.1016/j.physe.2011.11.027

[22]

Özmen A, Yakar Y, Cakir B. Computation of the oscillator strength and absorption coefficients for the intersubband transitions of the spherical quantum dot[J]. Opt Commun, 2009, 282(19): 3999. doi: 10.1016/j.optcom.2009.06.043

[23]

Yakar Y, Cakir B, Özmen A. Calculation of linear and nonlinear optical absorption coefficients of a spherical quantum dot with parabolic potential[J]. Opt Commun, 2010, 283(9): 1795. doi: 10.1016/j.optcom.2009.12.027

[24]

Cakir B, Yakar Y, Özmen A. Linear and nonlinear optical absorption coefficients and binding energy of a spherical quantum dot[J]. Superlattices Microstruct, 2010, 47(4): 556. doi: 10.1016/j.spmi.2009.12.002

[25]

Yakar Y, Cakir B, Özmen A. Linear and nonlinear optical properties in spherical quantum dots[J]. Commun Theory Phys, 2010, 53(6): 1185. doi: 10.1088/0253-6102/53/6/39

[26]

Zhang L, Yu Z, Yao W. Linear and nonlinear optical properties of strained GaN/AlN quantum dots:effects of impurities, radii of QDs, and the incident optical intensity[J]. Superlattices Microstruct, 2010, 48(4): 434. doi: 10.1016/j.spmi.2010.08.001

[27]

Chen B, Guo K X, Wang R Z. Linear and nonlinear intersubband optical absorption in double triangular quantum wells[J]. Solid State Commun, 2009, 149(7): 310.

[28]

Yuan J H, Huang J S, Yin M. The correlation energies and nonlinear optical absorptions of an exciton in a disc-like quantum dot[J]. Opt Commun, 2010, 283(18): 3529. doi: 10.1016/j.optcom.2010.05.011

[29]

Sahin M. Third-order nonlinear optical properties of a one-and two-electron spherical quantum dot with and without a hydrogenic impurity[J]. J Appl Phys, 2009, 106(6): 063710. doi: 10.1063/1.3225100

[30]

Karimi M J, Rezaei G. Effects of external electric and magnetic fields on the linear and nonlinear intersubband optical properties of finite semi-parabolic quantum dots[J]. Physica B, 2011, 406(23): 4423. doi: 10.1016/j.physb.2011.08.105

[31]

Zhang Z H, Guo K X, Chen B. Theoretical studies on the optical absorption coefficients and refractive index changes in parabolic quantum dots in the presence of electric and magnetic fields[J]. Superlattices Microstruct, 2010, 47(2): 325. doi: 10.1016/j.spmi.2009.12.004

[32]

Niculescu E C. Dielectric mismatch effect on the photoionization cross section and intersublevel transitions in GaAs nanodots[J]. Opt Commun, 2011, 284(13): 3298. doi: 10.1016/j.optcom.2011.02.071

[33]

Burileanu L M, Radu A. THz laser field effect on the optical properties of cylindrical quantum well wires[J]. Opt Commun, 2011, 284(7): 2050. doi: 10.1016/j.optcom.2010.12.033

[34]

Tas H, Sahin M. The inter-sublevel optical properties of a spherical quantum dot-quantum well with and without a donor impurity[J]. J Appl Phys, 2012, 112(5): 053717. doi: 10.1063/1.4751483

[35]

Barseghyan M G, Restrepo R L, Mora-Ramos M E. Donor impurity-related linear and nonlinear intraband optical absorption coefficients in quantum ring:effects of applied electric field and hydrostatic pressure[J]. Nanoscale Research Letters, 2012, 7(1): 538. doi: 10.1186/1556-276X-7-538

[36]

Cakir B, Yakar Y, Özmen A. Refractive index changes and absorption coefficients in a spherical quantum dot with parabolic potential[J]. J Lumin, 2012, 132(10): 2659. doi: 10.1016/j.jlumin.2012.03.065

[37]

Duque C M, Mora-Ramos M E, Duque C A. On-center donor impurity-related nonlinear corrections to optical absorption and refractive index in a two-dimensional quantum ring[J]. Opt Commun, 2012, 285(24): 5456. doi: 10.1016/j.optcom.2012.07.119

[38]

Yuan J, Xie W, He L. An off-center donor and nonlinear absorption spectra of spherical quantum dots[J]. Physica E, 2009, 41(5): 779. doi: 10.1016/j.physe.2008.12.012

[39]

Mora-Ramos M E, Duque C A, Kasapoglu E. Linear and nonlinear optical properties in a semiconductor quantum well under intense laser radiation:effects of applied electromagnetic fields[J]. J Lumin, 2012, 132(4): 901. doi: 10.1016/j.jlumin.2011.11.008

[40]

Kirak M, Yilmaz S, Sahin M. The electric field effects on the binding energies and the nonlinear optical properties of a donor impurity in a spherical quantum dot[J]. J Appl Phys, 2011, 109(9): 094309. doi: 10.1063/1.3582137

[41]

Bednarek S, Szafran B, Chwiej T. Effective interaction for charge carriers confined in quasi-one-dimensional nanostructures[J]. Phys Rev B, 2003, 68(4): 045328. doi: 10.1103/PhysRevB.68.045328

[42]

Wang S, Kang Y, Li X L. Binding energy of the ground and first few excited states of hydrogenic donor impurity in a rectangular GaAs quantum dot in the presence of electric field[J]. Superlattices Microstruct, 2014, 76: 221. doi: 10.1016/j.spmi.2014.10.010

[43]

Boyd W. Nonlinear optics. 2nd ed. New York:Academic Press, 2003

[1]

Milanović V, Ikonić Z. Intraband absorption of infrared radiation in a semiconductor quantum dot[J]. Phys Rev B, 1989, 39(11): 7982. doi: 10.1103/PhysRevB.39.7982

[2]

Garduno-Nolasco E, Missous M, Donoval D. Temperature dependence of InAs/GaAs quantum dots solar photovoltaic devices[J]. Journal of Semiconductors, 2014, 35(5): 054001. doi: 10.1088/1674-4926/35/5/054001

[3]

Peter A J. Hydrogenic impurities in cylindrical quantum wires in the presence of a magnetic field[J]. Physica E, 2007, 39(1): 115. doi: 10.1016/j.physe.2007.01.008

[4]

Li S S, Xia J B. Electronic structure and binding energy of a hydrogenic impurity in a hierarchically self-assembled GaAs=AlxGa1-xAsGaAs=AlxGa1-xAs quantum dot[J]. J Appl Phys, 2006, 100(8): 083714. doi: 10.1063/1.2358406

[5]

Zounoubi A, Zorkani I, Messaoudi K E. Magnetic field effect on the polarizability of shallow donor in cylindrical quantum dot[J]. Phys Lett A, 2003, 312(3): 220.

[6]

Manaselyan A K, Kirakosyan A A. Effect of the dielectricconstant mismatch and magnetic field on the binding energy of hydrogenic impurities in a spherical quantum dot[J]. Physica E, 2004, 22(4): 825. doi: 10.1016/j.physe.2003.09.045

[7]

Manaselyan A K, Kirakosyan A A. Barrier penetration in Kane type semiconductor nanostructures[J]. Physica E, 2005, 28(4): 452.

[8]

Mazur Y I, Dorogan V G, Marega E. Excited state coherent resonant electronic tunneling in quantum well-quantum dot hybrid structures[J]. Appl Phys Lett, 2011, 98(8): 083118. doi: 10.1063/1.3560063

[9]

Kang Yun, Wang Sheng, Li Xianli. Electron energy states in a two-dimensional GaAs quantum ring with hydrogenic donor impurity in the presence of magnetic field[J]. Journal of Semiconductors, 2015, 36(3): 032003. doi: 10.1088/1674-4926/36/3/032003

[10]

Kazarinov R F, Suris R A. Possibility of the amplification electromagnetic waves in a semiconductor with superlattice[J]. Sov Phys Semicond, 1971, 5(3): 707.

[11]

Capasso F, Mohammed K, Cho A Y. Resonant tunneling through double barriers, perpendicular quantum transport phenomena in superlattices, and their device applications[J]. IEEE J Quantum Electron, 1986, 22(9): 1853. doi: 10.1109/JQE.1986.1073171

[12]

Miller A B. Quantum well optoelectronic switching devices[J]. Int J High Speed Electron Syst, 1991, 1(1): 19.

[13]

Lee S W, Hirakava K, Shimada Y. Bound-to-continuum intersubband photoconductivity of self-assembled InAs quantum dots in modulation-doped heterostructures[J]. Appl Phys Lett, 1999, 75(10): 1428. doi: 10.1063/1.124715

[14]

Klimov V I, McBrauch D W, Leatherdale C A. Electron and hole relaxation pathways in semiconductor quantum dots[J]. Phys Rev B, 1999, 60(19): 13740. doi: 10.1103/PhysRevB.60.13740

[15]

Mackowski S, Kyrychenko F, Karczewski G. Thermal carrier escape and capture in CdTe quantum dots[J]. Phys Status Solidi B, 2001, 224(2): 465. doi: 10.1002/(ISSN)1521-3951

[16]

Sauvage S, Boucaud P, Brunhes T. Midinfrared absorption and photocurrent spectroscopy of InAs/GaAs self-assembled quantum dots[J]. Appl Phys Lett, 2001, 78(16): 2327. doi: 10.1063/1.1365411

[17]

Xie W. Absorption spectra of a donor impurity in a quantum ring[J]. Physica Status Solidi B, 2009, 246(6): 1313. doi: 10.1002/pssb.v246:6

[18]

Xie W. Nonlinear optical rectification of a hydrogenic impurity in a disc-like quantum dot[J]. Physica B, 2009, 404(21): 4142. doi: 10.1016/j.physb.2009.07.177

[19]

Xie W. Impurity effects on optical property of a spherical quantum dot in the presence of an electric field[J]. Physica B, 2010, 405(16): 3436. doi: 10.1016/j.physb.2010.05.019

[20]

Liang S, Xie W. Effects of the hydrostatic pressure and temperature on optical properties of a hydrogenic impurity in the discshaped quantum dot[J]. Physica B, 2011, 406(11): 2224. doi: 10.1016/j.physb.2011.03.035

[21]

Chen T, Xie W, Liang S. The nonlinear optical rectification of an ellipsoidal quantum dot with impurity in the presence of an electric field[J]. Physica E, 2012, 44(4): 786. doi: 10.1016/j.physe.2011.11.027

[22]

Özmen A, Yakar Y, Cakir B. Computation of the oscillator strength and absorption coefficients for the intersubband transitions of the spherical quantum dot[J]. Opt Commun, 2009, 282(19): 3999. doi: 10.1016/j.optcom.2009.06.043

[23]

Yakar Y, Cakir B, Özmen A. Calculation of linear and nonlinear optical absorption coefficients of a spherical quantum dot with parabolic potential[J]. Opt Commun, 2010, 283(9): 1795. doi: 10.1016/j.optcom.2009.12.027

[24]

Cakir B, Yakar Y, Özmen A. Linear and nonlinear optical absorption coefficients and binding energy of a spherical quantum dot[J]. Superlattices Microstruct, 2010, 47(4): 556. doi: 10.1016/j.spmi.2009.12.002

[25]

Yakar Y, Cakir B, Özmen A. Linear and nonlinear optical properties in spherical quantum dots[J]. Commun Theory Phys, 2010, 53(6): 1185. doi: 10.1088/0253-6102/53/6/39

[26]

Zhang L, Yu Z, Yao W. Linear and nonlinear optical properties of strained GaN/AlN quantum dots:effects of impurities, radii of QDs, and the incident optical intensity[J]. Superlattices Microstruct, 2010, 48(4): 434. doi: 10.1016/j.spmi.2010.08.001

[27]

Chen B, Guo K X, Wang R Z. Linear and nonlinear intersubband optical absorption in double triangular quantum wells[J]. Solid State Commun, 2009, 149(7): 310.

[28]

Yuan J H, Huang J S, Yin M. The correlation energies and nonlinear optical absorptions of an exciton in a disc-like quantum dot[J]. Opt Commun, 2010, 283(18): 3529. doi: 10.1016/j.optcom.2010.05.011

[29]

Sahin M. Third-order nonlinear optical properties of a one-and two-electron spherical quantum dot with and without a hydrogenic impurity[J]. J Appl Phys, 2009, 106(6): 063710. doi: 10.1063/1.3225100

[30]

Karimi M J, Rezaei G. Effects of external electric and magnetic fields on the linear and nonlinear intersubband optical properties of finite semi-parabolic quantum dots[J]. Physica B, 2011, 406(23): 4423. doi: 10.1016/j.physb.2011.08.105

[31]

Zhang Z H, Guo K X, Chen B. Theoretical studies on the optical absorption coefficients and refractive index changes in parabolic quantum dots in the presence of electric and magnetic fields[J]. Superlattices Microstruct, 2010, 47(2): 325. doi: 10.1016/j.spmi.2009.12.004

[32]

Niculescu E C. Dielectric mismatch effect on the photoionization cross section and intersublevel transitions in GaAs nanodots[J]. Opt Commun, 2011, 284(13): 3298. doi: 10.1016/j.optcom.2011.02.071

[33]

Burileanu L M, Radu A. THz laser field effect on the optical properties of cylindrical quantum well wires[J]. Opt Commun, 2011, 284(7): 2050. doi: 10.1016/j.optcom.2010.12.033

[34]

Tas H, Sahin M. The inter-sublevel optical properties of a spherical quantum dot-quantum well with and without a donor impurity[J]. J Appl Phys, 2012, 112(5): 053717. doi: 10.1063/1.4751483

[35]

Barseghyan M G, Restrepo R L, Mora-Ramos M E. Donor impurity-related linear and nonlinear intraband optical absorption coefficients in quantum ring:effects of applied electric field and hydrostatic pressure[J]. Nanoscale Research Letters, 2012, 7(1): 538. doi: 10.1186/1556-276X-7-538

[36]

Cakir B, Yakar Y, Özmen A. Refractive index changes and absorption coefficients in a spherical quantum dot with parabolic potential[J]. J Lumin, 2012, 132(10): 2659. doi: 10.1016/j.jlumin.2012.03.065

[37]

Duque C M, Mora-Ramos M E, Duque C A. On-center donor impurity-related nonlinear corrections to optical absorption and refractive index in a two-dimensional quantum ring[J]. Opt Commun, 2012, 285(24): 5456. doi: 10.1016/j.optcom.2012.07.119

[38]

Yuan J, Xie W, He L. An off-center donor and nonlinear absorption spectra of spherical quantum dots[J]. Physica E, 2009, 41(5): 779. doi: 10.1016/j.physe.2008.12.012

[39]

Mora-Ramos M E, Duque C A, Kasapoglu E. Linear and nonlinear optical properties in a semiconductor quantum well under intense laser radiation:effects of applied electromagnetic fields[J]. J Lumin, 2012, 132(4): 901. doi: 10.1016/j.jlumin.2011.11.008

[40]

Kirak M, Yilmaz S, Sahin M. The electric field effects on the binding energies and the nonlinear optical properties of a donor impurity in a spherical quantum dot[J]. J Appl Phys, 2011, 109(9): 094309. doi: 10.1063/1.3582137

[41]

Bednarek S, Szafran B, Chwiej T. Effective interaction for charge carriers confined in quasi-one-dimensional nanostructures[J]. Phys Rev B, 2003, 68(4): 045328. doi: 10.1103/PhysRevB.68.045328

[42]

Wang S, Kang Y, Li X L. Binding energy of the ground and first few excited states of hydrogenic donor impurity in a rectangular GaAs quantum dot in the presence of electric field[J]. Superlattices Microstruct, 2014, 76: 221. doi: 10.1016/j.spmi.2014.10.010

[43]

Boyd W. Nonlinear optics. 2nd ed. New York:Academic Press, 2003

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S Wang, Y Kang, X L Li. Donor impurity-related optical absorption coefficients and refractive index changes in a rectangular GaAs quantum dot in the presence of electric field[J]. J. Semicond., 2016, 37(11): 112001. doi: 10.1088/1674-4926/37/11/112001.

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Manuscript received: 09 November 2015 Manuscript revised: 22 June 2016 Online: Published: 01 November 2016

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