Coherent Tunneling Through Quantum Wire Tailored by Gaussian Profile

Author(s)
Hassan S. Ashour

ABSTRACT

In this paper, we propose a novel structure of quantum waveguide. In this structure we tailored the quantum wire by Gaussian Profile. Thus, the Dirac-Delta function potentials are weighted according to Gaussian distribution function. We studied the electronic transmission properties through this tailored quantum waveguide structure. We have assumed that single free-electron channel is incident on the structure and the scattering of electrons is solely from the geometric nature of the problem. We have used the transfer matrix method to study the electron transmission. Coherent Tunneling is achieved through this structure, which is well-defined allowed conduction bands. The electronic conductance spectrum depends on the number of the Dirac delta function potential in the quantum wire. When the number of Dirac delta function potentials in the structure and their strengths are increased, both well defined conductance bands and sharper and narrower forbidden bands are formed. This novel structure has a good defect tolerance. The structure tolerates strength defect and tolerates position defect for the central Dirac delta function in the Gaussian distribution.

In this paper, we propose a novel structure of quantum waveguide. In this structure we tailored the quantum wire by Gaussian Profile. Thus, the Dirac-Delta function potentials are weighted according to Gaussian distribution function. We studied the electronic transmission properties through this tailored quantum waveguide structure. We have assumed that single free-electron channel is incident on the structure and the scattering of electrons is solely from the geometric nature of the problem. We have used the transfer matrix method to study the electron transmission. Coherent Tunneling is achieved through this structure, which is well-defined allowed conduction bands. The electronic conductance spectrum depends on the number of the Dirac delta function potential in the quantum wire. When the number of Dirac delta function potentials in the structure and their strengths are increased, both well defined conductance bands and sharper and narrower forbidden bands are formed. This novel structure has a good defect tolerance. The structure tolerates strength defect and tolerates position defect for the central Dirac delta function in the Gaussian distribution.

Cite this paper

nullH. Ashour, "Coherent Tunneling Through Quantum Wire Tailored by Gaussian Profile,"*Journal of Modern Physics*, Vol. 2 No. 3, 2011, pp. 124-130. doi: 10.4236/jmp.2011.23019.

nullH. Ashour, "Coherent Tunneling Through Quantum Wire Tailored by Gaussian Profile,"

References

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[2] M. Wimmer, M. Scheid and K. Richter, “Spin-Polarized Quantum Transport in Mesoscopic Conductors: Computational Concepts and Physical Phenomena,” arXiv:0803.3705v1, 2008.

[3] L. M. Jong, A. D. Greentree, V. I. Conrad, L. C. L. Hollenberg and D. N. Jamieson, “Coherent Tunneling Adiabatic Passage with the Alternating Coupling Scheme,” Nanotechnology, Vol. 20, No. 40, 2009, p. 405402. doi:10.1088/0957-4484/20/40/405402

[4] G. Ariyawansa, S. G. Matsik, A. G. U. Perera and X. H. Su and P. Bhattacharya, “Tunneling Quantum Dot Sensors for Multi-Band Infrared and Terahertz Radiation Detection,” Sensors, IEEE, 2007.

[5] Y. J. Doh, J. A. van Dam, A. L. Roest, P. A. M. Bakkers, L. P. Kouwenhoven and S. de Franceschi, “Tunable Supercurrent through Semiconductor Nanowires,” Science, Vol. 309, No. 5732, 8 July 2005, pp. 272-275. doi:10.1126/science.1113523

[6] N. P. Oxtoby, H. B. Sun and H. M. Wiseman, “Non-Ideal Monitoring of a Qubit State Using a Quantum Tunnelling Device,” Journal of Physics Condensed Matter, Vol. 15, No. 46, November 2003, pp. 8055-8064. doi:10.1088/0953-8984/15/46/020

[7] H. Kajiura, H. Huang and A. Bezryadin, “Quasi-Ballistic Electron Transport in Double-Wall Carbon Nanotubes,” Chemical Physics Letters, Vol. 398, No. 4-6, 11 November 2004, pp. 476-479.

[8] T. Nagahama, H. Saito and S. Yuasa, “Hot Electron Transport in Magnetic Tunnel Transistors with an Epitaxial Mgo Tunnel Barrier,” Applied Physics Letters, Vol. 96, No. 11, 2010, p. 112509. doi:10.1063/1.3360222

[9] G. F. Ross and R. M. Mara, “Coherent Processing Tunnel Diode Ultra Wideband Receiver,” United States Patent 5337054, 1992.

[10] D. W. L. Sprung and H. Wu, “Scattering by a Finite Periodic Potential,” American Journal of Physics, Vol. 61, No. 12, December 1993, p. 1118. doi:10.1119/1.17306

[11] D. Kiang, “Multiple Scattering by a Dirac Comb,” American Journal of Physics, Vol. 42, No. 9, 1974, pp. 785-787. doi:10.1119/1.1987841

[12] P. S. Deo and A. M. Jayannavar, “Quantum Waveguide Transport in Serial Stub and Loop Structures on,” Physical Review B, Vol. 50, No. 16, 1994, pp. 11629-11639. doi:10.1103/PhysRevB.50.11629

[13] M. Sharma, S. X. Wang and J. H. Nickel, “Inversion of Spin Polarization and Tunneling Magnetoresistance in Spin-Dependent Tunneling Junctions,” Physical Review Letters, Vol. 82, No. 3, 1999, pp. 616-619. doi:10.1103/PhysRevLett.82.616

[14] W. G. Wang, C. Ni, G. X. Miao, C. Weiland, L. R. Shah, X. Fan, P. Parson, J. Jordan-Sweet, X. M. Kou, Y. P. Zhang, R. Stearrett, E. R. Nowak, R. Opila, J. S. Moodera and J. Q. Xiao, “Understanding Tunneling Magnetoresistance during Thermal Annealing in Mgo-Based Junctions with CoFeB Electrodes,” Physical Review B, Vol. 81, No. 14, 2010, pp. 144406. doi:10.1103/PhysRevB.81.144406

[15] H. S. Ashour, A. I. Ass’ad, M. M. Shabat and M. S. Hamada, “Electronic Conductance in Binomially Tailored Quantum Wire,” Microelectronic Journal, Vol. 37, No. 1, 2006, pp. 79-83. doi:10.1016/j.mejo.2005.06.018

[16] H. Wu, D. W. L. Sprung, J .Martorell and S. Klarsfeld, “Quantum Wire with Periodic Serial Structure,” Physical Review B, Vol. 44, No. 12, 1991, pp. 6351-6360. doi:10.1103/PhysRevB.44.6351

[17] W. D. Sheng and J. B. Xia, “A Transfer Matrix Approach to Conductance in Quantum Waveguides,” Journal of Physics Condensed Matter, Vol. 8, No. 20, 1996, pp. 3635-3645. doi:10.1088/0953-8984/8/20/009

[18] T. Kostyrko, “Transfer-Matrix Approach for Modulated Structures with Defects,” Physical Review B, Vol. 62, No. 44, 1999, pp. 2458-2465.

[19] E. Merzbacher, “Quantum Mechanics,” Wiley, New York, 1970.

[20] H. Fayad and M. M. Shabat, “Electronic Transmission through Qunatum Wire Containing Hetero-Junction,” Islamic Journal of Gaza (Natural Sciences Series), Vol. 13, No. 2, 2005, pp. 203-211.

[21] H. Fayad, M. M. Shabat, H. Khalil and D. J?ger, Proceeding of the IEEE Electron Devices Society, IEEE, Vol.11, 2001, p. 91.

[22] H. Fayad and M. M. Shabat, “Electronic Conductance through Some Quantum Wire Structure,” Romanian Academy, Eds., Micro and Nano-Engineering Series, Nano science and Nano engineering, Dan Dascalu and Irina Kleps, Bucharest, 2002.

[23] D. W. L. Sprung, H. Wu and J. Martorell, “Periodic Quantum Wires and Their Quasi-One-Dimensional Nature,” American Journal of Physics, Vol. 61, 1993, p. 1118. doi:10.1119/1.17306

[24] L. D. Landau and E. M. Lifshitz, “Quantum Mechanics,” Pergamon Press, Oxford, 1976.

[25] G. Baym, “Lectures on Quantum Mechanics,” W. A. Benjamin Incorporated, Massachusetts, 1973.

[26] Y. Takagaki and D. K. Ferry, “Electronic Conductance of a Two-Dimensional Electron Gas in the Presence of Periodic Potentials,” Physical Review B, Vol. 45, No. 15, 1992, p. 8506-8515. doi:10.1103/PhysRevB.45.8506

[27] S. J. Blundell, “The Dirac Comb and the Kronig-Penney Model: Comment on ‘Scattering from a Locally Periodic Potential,’ by D. J. Griffiths and N. F. Taussig, American Journal of Physics, Vol. 60, 1992, pp. 883-888,” American Journal of Physics, Vol. 61, No. 12, 1993, pp. 1147-1148. doi:10.1119/1.17312

[1] D. Bolmatov and C. Y. Mou, “Tunneling Conductance of the Graphene SNS Junction with a Single Localized Defect,” Journal of Experimental and Theoretical Physics, Vol. 110, No. 4, 2010, pp. 612-616. doi:10.1134/S1063776110040084

[2] M. Wimmer, M. Scheid and K. Richter, “Spin-Polarized Quantum Transport in Mesoscopic Conductors: Computational Concepts and Physical Phenomena,” arXiv:0803.3705v1, 2008.

[3] L. M. Jong, A. D. Greentree, V. I. Conrad, L. C. L. Hollenberg and D. N. Jamieson, “Coherent Tunneling Adiabatic Passage with the Alternating Coupling Scheme,” Nanotechnology, Vol. 20, No. 40, 2009, p. 405402. doi:10.1088/0957-4484/20/40/405402

[4] G. Ariyawansa, S. G. Matsik, A. G. U. Perera and X. H. Su and P. Bhattacharya, “Tunneling Quantum Dot Sensors for Multi-Band Infrared and Terahertz Radiation Detection,” Sensors, IEEE, 2007.

[5] Y. J. Doh, J. A. van Dam, A. L. Roest, P. A. M. Bakkers, L. P. Kouwenhoven and S. de Franceschi, “Tunable Supercurrent through Semiconductor Nanowires,” Science, Vol. 309, No. 5732, 8 July 2005, pp. 272-275. doi:10.1126/science.1113523

[6] N. P. Oxtoby, H. B. Sun and H. M. Wiseman, “Non-Ideal Monitoring of a Qubit State Using a Quantum Tunnelling Device,” Journal of Physics Condensed Matter, Vol. 15, No. 46, November 2003, pp. 8055-8064. doi:10.1088/0953-8984/15/46/020

[7] H. Kajiura, H. Huang and A. Bezryadin, “Quasi-Ballistic Electron Transport in Double-Wall Carbon Nanotubes,” Chemical Physics Letters, Vol. 398, No. 4-6, 11 November 2004, pp. 476-479.

[8] T. Nagahama, H. Saito and S. Yuasa, “Hot Electron Transport in Magnetic Tunnel Transistors with an Epitaxial Mgo Tunnel Barrier,” Applied Physics Letters, Vol. 96, No. 11, 2010, p. 112509. doi:10.1063/1.3360222

[9] G. F. Ross and R. M. Mara, “Coherent Processing Tunnel Diode Ultra Wideband Receiver,” United States Patent 5337054, 1992.

[10] D. W. L. Sprung and H. Wu, “Scattering by a Finite Periodic Potential,” American Journal of Physics, Vol. 61, No. 12, December 1993, p. 1118. doi:10.1119/1.17306

[11] D. Kiang, “Multiple Scattering by a Dirac Comb,” American Journal of Physics, Vol. 42, No. 9, 1974, pp. 785-787. doi:10.1119/1.1987841

[12] P. S. Deo and A. M. Jayannavar, “Quantum Waveguide Transport in Serial Stub and Loop Structures on,” Physical Review B, Vol. 50, No. 16, 1994, pp. 11629-11639. doi:10.1103/PhysRevB.50.11629

[13] M. Sharma, S. X. Wang and J. H. Nickel, “Inversion of Spin Polarization and Tunneling Magnetoresistance in Spin-Dependent Tunneling Junctions,” Physical Review Letters, Vol. 82, No. 3, 1999, pp. 616-619. doi:10.1103/PhysRevLett.82.616

[14] W. G. Wang, C. Ni, G. X. Miao, C. Weiland, L. R. Shah, X. Fan, P. Parson, J. Jordan-Sweet, X. M. Kou, Y. P. Zhang, R. Stearrett, E. R. Nowak, R. Opila, J. S. Moodera and J. Q. Xiao, “Understanding Tunneling Magnetoresistance during Thermal Annealing in Mgo-Based Junctions with CoFeB Electrodes,” Physical Review B, Vol. 81, No. 14, 2010, pp. 144406. doi:10.1103/PhysRevB.81.144406

[15] H. S. Ashour, A. I. Ass’ad, M. M. Shabat and M. S. Hamada, “Electronic Conductance in Binomially Tailored Quantum Wire,” Microelectronic Journal, Vol. 37, No. 1, 2006, pp. 79-83. doi:10.1016/j.mejo.2005.06.018

[16] H. Wu, D. W. L. Sprung, J .Martorell and S. Klarsfeld, “Quantum Wire with Periodic Serial Structure,” Physical Review B, Vol. 44, No. 12, 1991, pp. 6351-6360. doi:10.1103/PhysRevB.44.6351

[17] W. D. Sheng and J. B. Xia, “A Transfer Matrix Approach to Conductance in Quantum Waveguides,” Journal of Physics Condensed Matter, Vol. 8, No. 20, 1996, pp. 3635-3645. doi:10.1088/0953-8984/8/20/009

[18] T. Kostyrko, “Transfer-Matrix Approach for Modulated Structures with Defects,” Physical Review B, Vol. 62, No. 44, 1999, pp. 2458-2465.

[19] E. Merzbacher, “Quantum Mechanics,” Wiley, New York, 1970.

[20] H. Fayad and M. M. Shabat, “Electronic Transmission through Qunatum Wire Containing Hetero-Junction,” Islamic Journal of Gaza (Natural Sciences Series), Vol. 13, No. 2, 2005, pp. 203-211.

[21] H. Fayad, M. M. Shabat, H. Khalil and D. J?ger, Proceeding of the IEEE Electron Devices Society, IEEE, Vol.11, 2001, p. 91.

[22] H. Fayad and M. M. Shabat, “Electronic Conductance through Some Quantum Wire Structure,” Romanian Academy, Eds., Micro and Nano-Engineering Series, Nano science and Nano engineering, Dan Dascalu and Irina Kleps, Bucharest, 2002.

[23] D. W. L. Sprung, H. Wu and J. Martorell, “Periodic Quantum Wires and Their Quasi-One-Dimensional Nature,” American Journal of Physics, Vol. 61, 1993, p. 1118. doi:10.1119/1.17306

[24] L. D. Landau and E. M. Lifshitz, “Quantum Mechanics,” Pergamon Press, Oxford, 1976.

[25] G. Baym, “Lectures on Quantum Mechanics,” W. A. Benjamin Incorporated, Massachusetts, 1973.

[26] Y. Takagaki and D. K. Ferry, “Electronic Conductance of a Two-Dimensional Electron Gas in the Presence of Periodic Potentials,” Physical Review B, Vol. 45, No. 15, 1992, p. 8506-8515. doi:10.1103/PhysRevB.45.8506

[27] S. J. Blundell, “The Dirac Comb and the Kronig-Penney Model: Comment on ‘Scattering from a Locally Periodic Potential,’ by D. J. Griffiths and N. F. Taussig, American Journal of Physics, Vol. 60, 1992, pp. 883-888,” American Journal of Physics, Vol. 61, No. 12, 1993, pp. 1147-1148. doi:10.1119/1.17312