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Yıl 2023, Cilt: 41 Sayı: 6, 1292 - 1297, 29.12.2023

Öz

Kaynakça

  • REFERENCES
  • [1] Maiman TH. Stimulated optical radiation in ruby. Nature 1960;187:493–494. [CrossRef]
  • [2] Holonyak Jr N, Bevacqua SF. Coherent (visible) light emission from Ga(As1−xPx) junctions. Appl Phys Lett 1962;1:82–83. [CrossRef]
  • [3] Kroemer H. Theory of hall effect isolators for tunnel diode amplifiers. In Electron Devices Meeting, International IEEE 1963;9:84. [CrossRef]
  • [4] Alferov ZI, Kazarinov R. Semiconductor laser with electric pumping. Inventor’s certificate 1963;181737.
  • [5] Alferov ZI, Andreev VM, Portnoi EL, Trukan MK. AlAs − GaAs heterojunction injection lasers with a low room-temperature threshold. Sov Phys Semiconductors 1970; 3:1107–1110.
  • [6] Hayashi I, Panish MB, Reinhart FK, GaAs−AlxGa1−xAs double heterostructure injection lasers. Journal of Applied Physics 1971;42:1929–1941. [CrossRef]
  • [7] Dupuis R, Dapkus PD, Holonyak Jr N, Rezek EA, Chin R. Room-temperature laser operation of quantum-well Ga1−xAlxAs − GaAs laser diodes grown by metalorganic chemical vapor deposition. Applied Physics Letters 1978;32:295–297. [CrossRef]
  • [8] Kazarinov R. Possibility of amplification of electromagnetic waves in a semiconductor with superlattice. Sov Phys-Semicond 1971;5:707709.
  • [9] Jerome F, Capasso F, Deborah LS, Sirtori C, Hutchinson A, Alfred YC. Quantum cascade laser. Science 1994;264:553–556. [CrossRef]
  • [10] Ban SL, Hasbun JE, Liang XX. A novel method for quantum transmission across arbitrary potential barriers. J Lumin 2000;87:369–371. [CrossRef]
  • [11] Anemogiannis E, Glytsis EN, Gaylord TK. Bound and quasibound state calculations for biased/unbiased semiconductor quantum heterostructures. IEEE J Quantum Electron 1993;29:2731–2740. [CrossRef]
  • [12] Singh J. A new method for solving the ground-state problem in arbitrary quantum wells: Application to electron-hole quasi-bound levels in quantum wells under high electric field. Appl Phys Lett 1986;48:434–436. [CrossRef]
  • [13] Harrison P. Quantum wells, wires and dots: Theoretical and computational physics of semiconductor nanostructures. New York: John Wiley & Sons; 2005. [CrossRef]
  • [14] Ando Y, Itoh T. Calculation of transmission tunneling current across arbitrary potential barriers. Journal of Applied Physics 1987; 61:1497–1502. [CrossRef]
  • [15] Ram-Mohan LR, Yoo KH, Moussa J. The schrodinger–poisson self-consistency in layered quantum semiconductor structures. Journal of Applied Physics 2004;95:3081–3092. [CrossRef]
  • [16] Bellotti E, Doshi BK, Brennan KF, Albrecht JD, Ruden PP. Ensemble monte carlo study of electron transport in wurtzite inn. J Appl Phys 1999;85:916–923. [CrossRef]
  • [17] Lebwohl PA, Price PJ. Direct microscopic simulation of gunn-domain phenomena. Appl Phys Lett 1971; 19:530–532. [CrossRef]
  • [18] Stupovski BM, Crnjanski JV, Gvozdić DM. Application of coordinate transformation and finite differences method in numerical modeling of quantum dash band structure. Comput Phys Commun 2011; 182:289–298. [CrossRef]
  • [19] Paul SF-P, Fouckhardt H. An improved shooting approach for solving the time-independent schrodinger equation for iii/v qw structures. Physics Letters A 2001;286:199–204. [CrossRef]
  • [20] Gavryushin V. Asymmetric double quantum wells with smoothed interfaces. Central Eur J Phys 2012;10:459–469. [CrossRef]
  • [21] Thierry F, Le Rouzo J, Flory F, Berginc G, Escoubas L. Fast and reliable approach to calculate energy levels in semiconductor nanostructures. Journal of Nanophotonics 2015;9:093080. [CrossRef]
  • [22] Cheng C, Liu QH, Lee JH, Massoud HZ. Spectral element method for the schrodinger-poisson system. J Comput Electron 2004;3:417–421. [CrossRef]
  • [23] Leveque RJ, Li Z. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J Numer Anal 1994;31:1019–1044. [CrossRef]
  • [24] Momox E, Zakhleniuk N, Balkan N. Solution of the 1d schrodinger equation in semiconductor heterostructures using the immersed interface method. J Comput Phys 2012;231:6173–6180. [CrossRef]
  • [25] Rostampour E. Effect of position-dependent effective mass on electron tunneling of inas/gasb type-ii superlattice having triangular and parabolic geometries. Optics Laser Technol 2021;138:106840. [CrossRef]
  • [26] Althib H. Effect of quantum barrier width and quantum resonant tunneling through ingan/gan parabolic quantum well-led structure on led efficiency. Results Phys 2021;22:103943. [CrossRef]
  • [27] Alaydin BÖ. Optical Properties of Gaas/Alxga1-xas Superlattice Under E-Field for Quantum Cascade Laser Application. Gazi Univ J Sci 2021;34:1179–1191. [CrossRef]
  • [28] Almansour S, Dakhlaoui H. Electromodulation of the Negative Differential Resistance in an AlGaAs/GaAs Resonant Tunneling Diode. J Korean Phys Soc 2019;74:36–40. [CrossRef]
  • [29] Gain J, Das Sarkar M, Kundu S. Energy effective mass dependence of electron tunneling through cds/cdse, alxga1-xas/gaas and alsb/inas multiple quantum barriers. Continuity 2021; 2:2. [CrossRef]
  • [30] Almansour S. Theoretical study of electronic properties of resonant tunneling diodes based on double and triple algaas barriers. Results Physics 2020;17:103089. [CrossRef]
  • [31] Khabibullin RA, Shchavruk NV, Ponomarev DS, Ushakov DV, Afonenko AA, Volkov OY, Pavlovskiy VV, Maremyanin KV, Dubinov AA. Limiting factors to the performance and operation frequency range of thz quantum cascade laser based on gaas/algaas heterostructures. In AIP Conference Proceedings 2021; 2359:020014. [CrossRef]
  • [32] Yadav SL, Najeeb-ud-din H. A simple analytical model for the resonant tunneling diode based on the transmission peak and scattering effect. J Comput Electron 2020;1061–1067. [CrossRef]
  • [33] Adams RW, Vijayraghavan K, Wang QJ, Fan J, Capasso F, Khanna SP, Davies AG, Linfield EH, Belkin MA. Gaas/al0.15ga0.85as terahertz quantum cascade lasers with double-phonon resonant depopulation operating up to 172 k. Appl Phys Lett 2010;97:131111. [CrossRef]
  • [34] Sebbar D, Boudjema B, Boukaoud A, Chiba Y, Houhou O. Investigation the Optical Intersubband Absorption in Double Barriers of Resonant Tunneling Superlattice. In: Chiba Y, Tlemçani A, Smaili A. (eds) Advances in Green Energies and Materials Technology. Springer Proceedings in Energy. Springer, Singapore 2021. [CrossRef]
  • [35] Algün G. The determination of barrier height during vertical transport in GaAs/AlXGa1-XAs quantum well structures. Sigma J Eng Nat Sci 2008;26:1–10.
  • [36] Bozkurt K. Electrolumınescence study of InP/InGaAsP/InAs/InP P-I-N LASER heterostructure. Sigma J Eng Nat Sci 2016;34:255–259.
  • [37] Gürel HH, Akinci Ö, Ünlü H. Modeling of heterostructures for nanoelectronic devices: Tight binding view. Sigma J Eng Nat Sci 2004;1:1.
  • [38] Vatannia S, Gildenblat G. Airy’s functions implementation of the transfer-matrix method for resonant tunneling in variably spaced finite superlattices. IEEE J Quantum Electron 1996;32:1093–1105. [CrossRef]
  • [39] Airy GB. On the intensity of light in the neighbourhood of a caustic. Trans Cambridge Philosophical Soc 1838;6:379.
  • [40] Ghatak AK, Goyal IC, Gallawa RL. Mean lifetime calculations of quantum well structures: a rigorous analysis. IEEE J Quantum Electron 1990;26:305–310. [CrossRef]
  • [41] Sirtori C, Capasso F, Faist J, Hutchinson AL, Sivco DL, Cho AY. Resonant tunneling in quantum cascade lasers. IEEE Journal of Quantum Electronics 1998;34:1722–1729. [CrossRef]
  • [42] Djelti R, Bentata S, Aziz Z, Besbes A. Mixed disorder in gaas/al x ga 1- x as superlattices and its effect on the range of wavelength infrared lasers. Optik-Int JLight Electron Optics 2013;124:3812–3815. [CrossRef]
  • [43] Bendahma F, Bentata S, Djelti R, Aziz Z. Effect of the aluminium concentration on the resonant tunnelling time and the laser wavelength of random trimer barrier al x ga 1- x as superlattices. Physica B: Condensed Matter 2014;449:150–154. [CrossRef]
  • [44] Terkhi S, Bentata S, Djelti R, Bouadjemi B. Electronic transmission in random trimer inas/in x ga 1- x as superlattices. Results Phys 2012;2:198–202. [CrossRef]
  • [45] BenDaniel DJ, Duke CB. Space-charge effects on electron tunneling. Phys Rev 1966;152:683–692. [CrossRef]
  • [46] Bastard G. Superlattice band structure in the envelope-function approximation. Phys Rev B 1981;24:5693. [CrossRef]
  • [47] Wayne WL, Fukuma M. Exact solution of the schrodinger equation across an arbitrary one-dimensional piecewise-linear potential barrier. J Appl Phys 1986;60:1555–1559. [CrossRef]
  • [48] Brennan KF, Summers CJ. Theory of resonant tunneling in a variably spaced multiquantum well structure: An airy function approach. J Appl Phys 1987;61:614–623. [CrossRef]
  • [49] Raphael T, Esaki L. Tunneling in a finite superlattice. Appl Phys Lett 1973; 22:562–564. [CrossRef]
  • [50] Vassell M, Johnson L, Lockwood HF. Multibarrier tunneling in ga1- xalxas/gaas heterostructures. J Appl Phys 1983;54:5206–5213. [CrossRef]
  • [51] Rüdeger K, Alessandro T, Fabio B, Harvey EB, Edmund HL, Davies AG, et al. Terahertz semiconductor-heterostructure laser. Nature 2002;417:156–159. [CrossRef]
  • [52] Mikhail AB, Qijie W, Pflügl C, Belyanin A, Khanna SP, Davies AG, et al. High-temperature operation of terahertz quantum cascade laser sources. IEEE J Selected Topics Quantum Electronics 2009;15:952–967. [CrossRef]

Modeling of the effects of non-uniform electric field on resonant tunneling in superlattices

Yıl 2023, Cilt: 41 Sayı: 6, 1292 - 1297, 29.12.2023

Öz

We study superlattices in non-uniform electric field to obtain mid infrared laser. We exploit the transfer matrix method and the transmission coefficient to find the suitable parameters that lead to resonant energy levels that are appropriate for generating three and four-level
laser. In particular, we consider superlattice of GaAs/Al0.45Ga0.55 As consisting of four barriers, and we apply a graduated electric field. Our calculations predict that under the effect of the electric field equal to 10KV/cm and its graduation step equals to 1.26 KV/cm with the condi-tion of the transition resonant with LO phonon, the obtained electronic transitions are shown to have wavelengths of 23.49 µm and 32.15 µm. We found that the variation of the electric field has an influence on the energy profile of the electron in the superlattice.

Kaynakça

  • REFERENCES
  • [1] Maiman TH. Stimulated optical radiation in ruby. Nature 1960;187:493–494. [CrossRef]
  • [2] Holonyak Jr N, Bevacqua SF. Coherent (visible) light emission from Ga(As1−xPx) junctions. Appl Phys Lett 1962;1:82–83. [CrossRef]
  • [3] Kroemer H. Theory of hall effect isolators for tunnel diode amplifiers. In Electron Devices Meeting, International IEEE 1963;9:84. [CrossRef]
  • [4] Alferov ZI, Kazarinov R. Semiconductor laser with electric pumping. Inventor’s certificate 1963;181737.
  • [5] Alferov ZI, Andreev VM, Portnoi EL, Trukan MK. AlAs − GaAs heterojunction injection lasers with a low room-temperature threshold. Sov Phys Semiconductors 1970; 3:1107–1110.
  • [6] Hayashi I, Panish MB, Reinhart FK, GaAs−AlxGa1−xAs double heterostructure injection lasers. Journal of Applied Physics 1971;42:1929–1941. [CrossRef]
  • [7] Dupuis R, Dapkus PD, Holonyak Jr N, Rezek EA, Chin R. Room-temperature laser operation of quantum-well Ga1−xAlxAs − GaAs laser diodes grown by metalorganic chemical vapor deposition. Applied Physics Letters 1978;32:295–297. [CrossRef]
  • [8] Kazarinov R. Possibility of amplification of electromagnetic waves in a semiconductor with superlattice. Sov Phys-Semicond 1971;5:707709.
  • [9] Jerome F, Capasso F, Deborah LS, Sirtori C, Hutchinson A, Alfred YC. Quantum cascade laser. Science 1994;264:553–556. [CrossRef]
  • [10] Ban SL, Hasbun JE, Liang XX. A novel method for quantum transmission across arbitrary potential barriers. J Lumin 2000;87:369–371. [CrossRef]
  • [11] Anemogiannis E, Glytsis EN, Gaylord TK. Bound and quasibound state calculations for biased/unbiased semiconductor quantum heterostructures. IEEE J Quantum Electron 1993;29:2731–2740. [CrossRef]
  • [12] Singh J. A new method for solving the ground-state problem in arbitrary quantum wells: Application to electron-hole quasi-bound levels in quantum wells under high electric field. Appl Phys Lett 1986;48:434–436. [CrossRef]
  • [13] Harrison P. Quantum wells, wires and dots: Theoretical and computational physics of semiconductor nanostructures. New York: John Wiley & Sons; 2005. [CrossRef]
  • [14] Ando Y, Itoh T. Calculation of transmission tunneling current across arbitrary potential barriers. Journal of Applied Physics 1987; 61:1497–1502. [CrossRef]
  • [15] Ram-Mohan LR, Yoo KH, Moussa J. The schrodinger–poisson self-consistency in layered quantum semiconductor structures. Journal of Applied Physics 2004;95:3081–3092. [CrossRef]
  • [16] Bellotti E, Doshi BK, Brennan KF, Albrecht JD, Ruden PP. Ensemble monte carlo study of electron transport in wurtzite inn. J Appl Phys 1999;85:916–923. [CrossRef]
  • [17] Lebwohl PA, Price PJ. Direct microscopic simulation of gunn-domain phenomena. Appl Phys Lett 1971; 19:530–532. [CrossRef]
  • [18] Stupovski BM, Crnjanski JV, Gvozdić DM. Application of coordinate transformation and finite differences method in numerical modeling of quantum dash band structure. Comput Phys Commun 2011; 182:289–298. [CrossRef]
  • [19] Paul SF-P, Fouckhardt H. An improved shooting approach for solving the time-independent schrodinger equation for iii/v qw structures. Physics Letters A 2001;286:199–204. [CrossRef]
  • [20] Gavryushin V. Asymmetric double quantum wells with smoothed interfaces. Central Eur J Phys 2012;10:459–469. [CrossRef]
  • [21] Thierry F, Le Rouzo J, Flory F, Berginc G, Escoubas L. Fast and reliable approach to calculate energy levels in semiconductor nanostructures. Journal of Nanophotonics 2015;9:093080. [CrossRef]
  • [22] Cheng C, Liu QH, Lee JH, Massoud HZ. Spectral element method for the schrodinger-poisson system. J Comput Electron 2004;3:417–421. [CrossRef]
  • [23] Leveque RJ, Li Z. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J Numer Anal 1994;31:1019–1044. [CrossRef]
  • [24] Momox E, Zakhleniuk N, Balkan N. Solution of the 1d schrodinger equation in semiconductor heterostructures using the immersed interface method. J Comput Phys 2012;231:6173–6180. [CrossRef]
  • [25] Rostampour E. Effect of position-dependent effective mass on electron tunneling of inas/gasb type-ii superlattice having triangular and parabolic geometries. Optics Laser Technol 2021;138:106840. [CrossRef]
  • [26] Althib H. Effect of quantum barrier width and quantum resonant tunneling through ingan/gan parabolic quantum well-led structure on led efficiency. Results Phys 2021;22:103943. [CrossRef]
  • [27] Alaydin BÖ. Optical Properties of Gaas/Alxga1-xas Superlattice Under E-Field for Quantum Cascade Laser Application. Gazi Univ J Sci 2021;34:1179–1191. [CrossRef]
  • [28] Almansour S, Dakhlaoui H. Electromodulation of the Negative Differential Resistance in an AlGaAs/GaAs Resonant Tunneling Diode. J Korean Phys Soc 2019;74:36–40. [CrossRef]
  • [29] Gain J, Das Sarkar M, Kundu S. Energy effective mass dependence of electron tunneling through cds/cdse, alxga1-xas/gaas and alsb/inas multiple quantum barriers. Continuity 2021; 2:2. [CrossRef]
  • [30] Almansour S. Theoretical study of electronic properties of resonant tunneling diodes based on double and triple algaas barriers. Results Physics 2020;17:103089. [CrossRef]
  • [31] Khabibullin RA, Shchavruk NV, Ponomarev DS, Ushakov DV, Afonenko AA, Volkov OY, Pavlovskiy VV, Maremyanin KV, Dubinov AA. Limiting factors to the performance and operation frequency range of thz quantum cascade laser based on gaas/algaas heterostructures. In AIP Conference Proceedings 2021; 2359:020014. [CrossRef]
  • [32] Yadav SL, Najeeb-ud-din H. A simple analytical model for the resonant tunneling diode based on the transmission peak and scattering effect. J Comput Electron 2020;1061–1067. [CrossRef]
  • [33] Adams RW, Vijayraghavan K, Wang QJ, Fan J, Capasso F, Khanna SP, Davies AG, Linfield EH, Belkin MA. Gaas/al0.15ga0.85as terahertz quantum cascade lasers with double-phonon resonant depopulation operating up to 172 k. Appl Phys Lett 2010;97:131111. [CrossRef]
  • [34] Sebbar D, Boudjema B, Boukaoud A, Chiba Y, Houhou O. Investigation the Optical Intersubband Absorption in Double Barriers of Resonant Tunneling Superlattice. In: Chiba Y, Tlemçani A, Smaili A. (eds) Advances in Green Energies and Materials Technology. Springer Proceedings in Energy. Springer, Singapore 2021. [CrossRef]
  • [35] Algün G. The determination of barrier height during vertical transport in GaAs/AlXGa1-XAs quantum well structures. Sigma J Eng Nat Sci 2008;26:1–10.
  • [36] Bozkurt K. Electrolumınescence study of InP/InGaAsP/InAs/InP P-I-N LASER heterostructure. Sigma J Eng Nat Sci 2016;34:255–259.
  • [37] Gürel HH, Akinci Ö, Ünlü H. Modeling of heterostructures for nanoelectronic devices: Tight binding view. Sigma J Eng Nat Sci 2004;1:1.
  • [38] Vatannia S, Gildenblat G. Airy’s functions implementation of the transfer-matrix method for resonant tunneling in variably spaced finite superlattices. IEEE J Quantum Electron 1996;32:1093–1105. [CrossRef]
  • [39] Airy GB. On the intensity of light in the neighbourhood of a caustic. Trans Cambridge Philosophical Soc 1838;6:379.
  • [40] Ghatak AK, Goyal IC, Gallawa RL. Mean lifetime calculations of quantum well structures: a rigorous analysis. IEEE J Quantum Electron 1990;26:305–310. [CrossRef]
  • [41] Sirtori C, Capasso F, Faist J, Hutchinson AL, Sivco DL, Cho AY. Resonant tunneling in quantum cascade lasers. IEEE Journal of Quantum Electronics 1998;34:1722–1729. [CrossRef]
  • [42] Djelti R, Bentata S, Aziz Z, Besbes A. Mixed disorder in gaas/al x ga 1- x as superlattices and its effect on the range of wavelength infrared lasers. Optik-Int JLight Electron Optics 2013;124:3812–3815. [CrossRef]
  • [43] Bendahma F, Bentata S, Djelti R, Aziz Z. Effect of the aluminium concentration on the resonant tunnelling time and the laser wavelength of random trimer barrier al x ga 1- x as superlattices. Physica B: Condensed Matter 2014;449:150–154. [CrossRef]
  • [44] Terkhi S, Bentata S, Djelti R, Bouadjemi B. Electronic transmission in random trimer inas/in x ga 1- x as superlattices. Results Phys 2012;2:198–202. [CrossRef]
  • [45] BenDaniel DJ, Duke CB. Space-charge effects on electron tunneling. Phys Rev 1966;152:683–692. [CrossRef]
  • [46] Bastard G. Superlattice band structure in the envelope-function approximation. Phys Rev B 1981;24:5693. [CrossRef]
  • [47] Wayne WL, Fukuma M. Exact solution of the schrodinger equation across an arbitrary one-dimensional piecewise-linear potential barrier. J Appl Phys 1986;60:1555–1559. [CrossRef]
  • [48] Brennan KF, Summers CJ. Theory of resonant tunneling in a variably spaced multiquantum well structure: An airy function approach. J Appl Phys 1987;61:614–623. [CrossRef]
  • [49] Raphael T, Esaki L. Tunneling in a finite superlattice. Appl Phys Lett 1973; 22:562–564. [CrossRef]
  • [50] Vassell M, Johnson L, Lockwood HF. Multibarrier tunneling in ga1- xalxas/gaas heterostructures. J Appl Phys 1983;54:5206–5213. [CrossRef]
  • [51] Rüdeger K, Alessandro T, Fabio B, Harvey EB, Edmund HL, Davies AG, et al. Terahertz semiconductor-heterostructure laser. Nature 2002;417:156–159. [CrossRef]
  • [52] Mikhail AB, Qijie W, Pflügl C, Belyanin A, Khanna SP, Davies AG, et al. High-temperature operation of terahertz quantum cascade laser sources. IEEE J Selected Topics Quantum Electronics 2009;15:952–967. [CrossRef]
Toplam 53 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Yapısal Biyoloji
Bölüm Technical Note
Yazarlar

Djamel Sebbar 0000-0003-4463-1982

Bouzid Boudjema Bu kişi benim 0000-0002-3072-9543

Yayımlanma Tarihi 29 Aralık 2023
Gönderilme Tarihi 18 Ekim 2021
Yayımlandığı Sayı Yıl 2023 Cilt: 41 Sayı: 6

Kaynak Göster

Vancouver Sebbar D, Boudjema B. Modeling of the effects of non-uniform electric field on resonant tunneling in superlattices. SIGMA. 2023;41(6):1292-7.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK https://eds.yildiz.edu.tr/sigma/