SEMICONDUCTOR PHYSICS

Multisubband electron mobility in a parabolic quantum well structure under the influence of an applied electric field

N. Sahoo1 and T. Sahu2

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 Corresponding author: N. Sahoo, Email: tsahu_bu@rediffmail.com

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Abstract: We study the multisubband electron mobility in a barrier delta doped AlxGa1-xAs parabolic quantum well structure under the influence of an applied electric field perpendicular to the interface plane. We consider the alloy fraction x=0.3 for barriers and vary x from 0.0 to 0.1 for the parabolic well. Electrons diffuse into the well and confine within the triangular like potentials near the interfaces due to Coulomb interaction with ionized donors. The parabolic structure potential, being opposite in nature, partly compensates the Coulomb potential. The external electric field further amends the potential structure leading to an asymmetric potential profile. Accordingly the energy levels, wave functions and occupation of subbands change. We calculate low temperature electron mobility as a function of the electric field and show that when two subbands are occupied, the mobility is mostly dominated by ionised impurity scattering mediated by intersubband effects. As the field increases transition from double subband to single subband occupancy occurs. A sudden enhancement in mobility is obtained due to curtailment of intersubband effects. Thereafter the mobility is governed by both impurity and alloy disorder scatterings. Our analysis of mobility as a function of the electric field for different structural parameters shows interesting results.

Key words: parabolic quantum wellmultisubband electron mobilityAlGaAs



[1]
Chuang S L, Ahn D. Optical transitions in a parabolic quantum well with an applied electric field-analytical solutions. J Appl Phys, 1989, 65(7):2822 doi: 10.1063/1.342719
[2]
Sergio C S, Gusev G M, Leite J R, et al. Coexistence of a two-and three-dimensional Landau states in a wide parabolic quantum well. Phys Rev B, 2001, 64(11):115314 doi: 10.1103/PhysRevB.64.115314
[3]
Salis G, Kato Y, Ensslin K D, et al. Electrical control of spin coherence in semiconductor nanostructures. Nature, 2001, 414:619 doi: 10.1038/414619a
[4]
Gusev G M, Quivy A A, Lamas T E, et al. Magnetotransport of a quasi-three-dimensional electron gas in the lowest Landau level. Phys Rev B, 2002, 65(20):205316 doi: 10.1103/PhysRevB.65.205316
[5]
Ellenberger C, Simovic B, Leturcq R, et al. Two-subband quantum Hall effect in parabolic quantum wells. Phys Rev B, 2006, 74(19):195313 doi: 10.1103/PhysRevB.74.195313
[6]
Li B, Guo K X, Liu Z L, et al. Nonlinear optical rectification in parabolic quantum dots in the presence of electric and magnetic fields. Phys Lett A, 2008, 372(8):1337 doi: 10.1016/j.physleta.2007.09.075
[7]
Shayegan M, Sajoto T, Santos M, et al. Realization of a quasi-three-dimensional modulation-doped semiconductor structure. Appl Phys Lett, 1988, 53(9):791 doi: 10.1063/1.99834
[8]
Salis G, Wirth P, Heinzel T, et al. Variation of classic scattering across a quantum well. Phys Rev B, 1999, 59(8):R5304
[9]
Seraide R M, Hai G Q. Low-temperature electron mobility in parabolic quantum wells. Braz J Phys, 2002, 32(2A):344 doi: 10.1590/S0103-97332002000200026
[10]
Yu G, Studenikin S A, Spring T A J, et al. Quantum and transport mobilities in an AlGaAs/GaAs parabolic quantum-well structure. J Appl Phys, 2005, 97(10):103703 doi: 10.1063/1.1891277
[11]
Lemas T E, Quivy A A, Sergio C S, et al. High mobility of a three-dimensional hole gas in parabolic quantum wells grown on GaAs(311) A substrates. J Appl Phys, 2005, 97(107):076107
[12]
Gao K H, Yu G, Zhou Y M, et al. Transport properties of AlGaAs/GaAs parabolic quantum wells. J Appl Phys, 2009, 105(1):013712 doi: 10.1063/1.3063690
[13]
Sahu T, Palo S, Panda A K. Enhancement of multisubband electron mobility in parabolic AlxGa1-xAs-GaAs double quantum well structures. J Appl Phys, 2013, 113(8):083704 doi: 10.1063/1.4793317
[14]
Capasso F, Sen S, Beltram F, et al. Quantum functional devices:resonant-tunneling transistors, circuits with reduced complexity, and multiple valued logic. IEEE Trans Electron Devices, 1989, 36(10):2065 doi: 10.1109/16.40888
[15]
Sahu T, Shore K A. Effect of electric field on low temperature multisubband mobility in a coupled GaInP/GaAs quantum well structure. J Appl Phys, 2010, 107(11):113708 doi: 10.1063/1.3391351
[16]
Romeira B, Seunarine K, Ironside C N, et al. A self-synchronized optoelectronic oscillator based on an RTD photo-detector and a laser diode. IEEE Photonics Technol Lett, 2011, 23(16):1148 doi: 10.1109/LPT.2011.2154320
[17]
Lyo S K. Real space and energy representation for the interface-roughness scattering in quantum-well structures. J Phys:Condens Matter, 2001, 13(6):1259 doi: 10.1088/0953-8984/13/6/306
[18]
Subudhi P K, Palo S, Sahu T. Effect of strain on multisubband electron transport in GaAs/InGaAs coupled quantum well structures. Superlattices and Microstructures, 2012, 51(3):430 doi: 10.1016/j.spmi.2012.01.007
[19]
Ando T, Fowler A B, Stern F. Electronic properties of two-dimensional systems. Rev Modern Phys, 1982, 54:437 doi: 10.1103/RevModPhys.54.437
[20]
Adachi S. Material parameters for use in research and device applications. J Appl Phys, 1985, 58(3):R1
[21]
Ando Y, Itoh T. Calculation of transmission tunneling current across arbitrary potential barriers. J Appl Phys, 1987, 61(4):1497 doi: 10.1063/1.338082
[22]
Saxena A K, Adams A D. Determination of alloy scattering potential in Ga1-xAlxAs alloys. J Appl Phys, 1985, 58(7):2640 doi: 10.1063/1.335895
[23]
Pan W N, Masuhara N, Sullivan N S, et al. Impact of disorder on the 5/2 fractional quantum Hall state. Phys Rev Lett, 2011, 106(20):206806 doi: 10.1103/PhysRevLett.106.206806
[24]
Gougam A B, Sicart J, Robert J L. Electron localization and anisotropic magnetoconductivity in GaAs-AlAs superlattices. Phys Rev B, 1999, 59(23):15308 doi: 10.1103/PhysRevB.59.15308
Fig. 1.  Electron mobility as a function of electric field applied along the $z$-axis for a single parabolic quantum well of width 500 Å.

Fig. 2.  Scattering rate matrix elements $B_{nn}^{\rm imp/AL}$, $C_{nm}^{\rm imp/AL}$ and $D_{nm}^{\rm imp/AL}$ as a function of applied electric field $F$ along the $z$-axis for a single parabolic quantum well of width 500 Å.

Fig. 3.  Electron mobility as a function of electric field applied along the $z$-axis for a single parabolic quantum well taking well width $=$ 400 Å, 500 Å and 600 Å.

Fig. 4.  Schematic subband wave functions in a delta doped parabolic single quantum well for $w$ $=$ 500 Å, $d$ $=$ 20 Å, $s$ $=$ 60 Å and $N_{0}$ $=$ 1 $\times$ 10$^{24}$ m$^{-3}$ in the presence of the external electric field $F$ $=$ 15 $\times$ 10$^{2}$ kV/m.

Fig. 5.  Electron mobility in a delta doped square ($x_{\rm p}$ $=$ 0.0) single quantum well structure as a function of the external electric field $F $for $w=$ 400, 500 and 600 Å.

Fig. 6.  Impurity and alloy disorder scattering rate matrix (in 10$^{10}$ s$^{-1}$) for a single square quantum well for $w$ $=$ 500 Å.

Fig. 7.  Electron mobility of a single parabolic quantum well for different ($N_{\rm s}$ $=$ 2, 4 and 5 $\times$ 10$^{15}$ m$^{-2}$) taking $d$ $=$ 20 Å, $s$ $=$ 60 Å and $w$ $=$ 500 Å.

Fig. 8.  Potential profile in a parabolic square potential structure ($x_{\rm p}$ $=$ 0.1) for $N_{\rm s}$ $=$ 2, 4 and 5 $\times$ 10$^{15}$ m$^{-2}$ taking $d$ $=$ 20 Å, $s$ $=$ 60 Å, $w$ $=$ 500 Å.

Fig. 9.  Electron mobility of a single square quantum well for different $N_{\rm s}$ ($N_{\rm s}$ $=$ 2, 4 and 5 $\times$ 10$^{15}$ m$^{-2}$) for $d$ $=$ 20 Å, $s$ $=$ 60 Å and $w$ $=$ 500 Å.

[1]
Chuang S L, Ahn D. Optical transitions in a parabolic quantum well with an applied electric field-analytical solutions. J Appl Phys, 1989, 65(7):2822 doi: 10.1063/1.342719
[2]
Sergio C S, Gusev G M, Leite J R, et al. Coexistence of a two-and three-dimensional Landau states in a wide parabolic quantum well. Phys Rev B, 2001, 64(11):115314 doi: 10.1103/PhysRevB.64.115314
[3]
Salis G, Kato Y, Ensslin K D, et al. Electrical control of spin coherence in semiconductor nanostructures. Nature, 2001, 414:619 doi: 10.1038/414619a
[4]
Gusev G M, Quivy A A, Lamas T E, et al. Magnetotransport of a quasi-three-dimensional electron gas in the lowest Landau level. Phys Rev B, 2002, 65(20):205316 doi: 10.1103/PhysRevB.65.205316
[5]
Ellenberger C, Simovic B, Leturcq R, et al. Two-subband quantum Hall effect in parabolic quantum wells. Phys Rev B, 2006, 74(19):195313 doi: 10.1103/PhysRevB.74.195313
[6]
Li B, Guo K X, Liu Z L, et al. Nonlinear optical rectification in parabolic quantum dots in the presence of electric and magnetic fields. Phys Lett A, 2008, 372(8):1337 doi: 10.1016/j.physleta.2007.09.075
[7]
Shayegan M, Sajoto T, Santos M, et al. Realization of a quasi-three-dimensional modulation-doped semiconductor structure. Appl Phys Lett, 1988, 53(9):791 doi: 10.1063/1.99834
[8]
Salis G, Wirth P, Heinzel T, et al. Variation of classic scattering across a quantum well. Phys Rev B, 1999, 59(8):R5304
[9]
Seraide R M, Hai G Q. Low-temperature electron mobility in parabolic quantum wells. Braz J Phys, 2002, 32(2A):344 doi: 10.1590/S0103-97332002000200026
[10]
Yu G, Studenikin S A, Spring T A J, et al. Quantum and transport mobilities in an AlGaAs/GaAs parabolic quantum-well structure. J Appl Phys, 2005, 97(10):103703 doi: 10.1063/1.1891277
[11]
Lemas T E, Quivy A A, Sergio C S, et al. High mobility of a three-dimensional hole gas in parabolic quantum wells grown on GaAs(311) A substrates. J Appl Phys, 2005, 97(107):076107
[12]
Gao K H, Yu G, Zhou Y M, et al. Transport properties of AlGaAs/GaAs parabolic quantum wells. J Appl Phys, 2009, 105(1):013712 doi: 10.1063/1.3063690
[13]
Sahu T, Palo S, Panda A K. Enhancement of multisubband electron mobility in parabolic AlxGa1-xAs-GaAs double quantum well structures. J Appl Phys, 2013, 113(8):083704 doi: 10.1063/1.4793317
[14]
Capasso F, Sen S, Beltram F, et al. Quantum functional devices:resonant-tunneling transistors, circuits with reduced complexity, and multiple valued logic. IEEE Trans Electron Devices, 1989, 36(10):2065 doi: 10.1109/16.40888
[15]
Sahu T, Shore K A. Effect of electric field on low temperature multisubband mobility in a coupled GaInP/GaAs quantum well structure. J Appl Phys, 2010, 107(11):113708 doi: 10.1063/1.3391351
[16]
Romeira B, Seunarine K, Ironside C N, et al. A self-synchronized optoelectronic oscillator based on an RTD photo-detector and a laser diode. IEEE Photonics Technol Lett, 2011, 23(16):1148 doi: 10.1109/LPT.2011.2154320
[17]
Lyo S K. Real space and energy representation for the interface-roughness scattering in quantum-well structures. J Phys:Condens Matter, 2001, 13(6):1259 doi: 10.1088/0953-8984/13/6/306
[18]
Subudhi P K, Palo S, Sahu T. Effect of strain on multisubband electron transport in GaAs/InGaAs coupled quantum well structures. Superlattices and Microstructures, 2012, 51(3):430 doi: 10.1016/j.spmi.2012.01.007
[19]
Ando T, Fowler A B, Stern F. Electronic properties of two-dimensional systems. Rev Modern Phys, 1982, 54:437 doi: 10.1103/RevModPhys.54.437
[20]
Adachi S. Material parameters for use in research and device applications. J Appl Phys, 1985, 58(3):R1
[21]
Ando Y, Itoh T. Calculation of transmission tunneling current across arbitrary potential barriers. J Appl Phys, 1987, 61(4):1497 doi: 10.1063/1.338082
[22]
Saxena A K, Adams A D. Determination of alloy scattering potential in Ga1-xAlxAs alloys. J Appl Phys, 1985, 58(7):2640 doi: 10.1063/1.335895
[23]
Pan W N, Masuhara N, Sullivan N S, et al. Impact of disorder on the 5/2 fractional quantum Hall state. Phys Rev Lett, 2011, 106(20):206806 doi: 10.1103/PhysRevLett.106.206806
[24]
Gougam A B, Sicart J, Robert J L. Electron localization and anisotropic magnetoconductivity in GaAs-AlAs superlattices. Phys Rev B, 1999, 59(23):15308 doi: 10.1103/PhysRevB.59.15308
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    Received: 27 June 2013 Revised: 22 August 2013 Online: Published: 01 January 2014

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      N. Sahoo, T. Sahu. Multisubband electron mobility in a parabolic quantum well structure under the influence of an applied electric field[J]. Journal of Semiconductors, 2014, 35(1): 012001. doi: 10.1088/1674-4926/35/1/012001 N. Sahoo, T. Sahu. Multisubband electron mobility in a parabolic quantum well structure under the influence of an applied electric field[J]. J. Semicond., 2014, 35(1): 012001. doi: 10.1088/1674-4926/35/1/012001.Export: BibTex EndNote
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      N. Sahoo, T. Sahu. Multisubband electron mobility in a parabolic quantum well structure under the influence of an applied electric field[J]. Journal of Semiconductors, 2014, 35(1): 012001. doi: 10.1088/1674-4926/35/1/012001

      N. Sahoo, T. Sahu. Multisubband electron mobility in a parabolic quantum well structure under the influence of an applied electric field[J]. J. Semicond., 2014, 35(1): 012001. doi: 10.1088/1674-4926/35/1/012001.
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      Multisubband electron mobility in a parabolic quantum well structure under the influence of an applied electric field

      doi: 10.1088/1674-4926/35/1/012001
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      • Corresponding author: N. Sahoo, Email: tsahu_bu@rediffmail.com
      • Received Date: 2013-06-27
      • Revised Date: 2013-08-22
      • Published Date: 2014-01-01

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