Tunneling transport in semiconductor nanostructures considering the presence of a weak time-dependent electromagnetic field: Lewis–Riesenfeld approach
DOI (Low Temperature Physics):
https://doi.org/10.1063/10.0042294Ключові слова:
quasistationary states, electron tunnel transport, quantum mechanical invariant, resonance energy, resonance widthАнотація
Запропоновано квантово-механічну теорію електронного транспорту в напівпровідникових резонансно-тунельних структурах за умови впливу на процес тунелювання слабкого нетаціонарного електромагнітного поля та зовнішнього постійного електричного поля. Теорія розвинута шляхом побудови точних розв’язків повного рівняння Шредінгера з використанням методу Льюїса–Різенфельда, адаптованого до квазістаціонарних станів. Досліджено резонансні енергії та ширини квазістаціонарних електронних станів, а також їх еволюцію у часі з використанням параметрів активної зони квантового каскадного лазера. Шляхом розрахунків коефіцієнта прозорості наносистеми у різні моменти часу, які зумовлені релаксаційними процесами, проаналізовано процеси розпаду електронних квазістаціонарних станів у досліджуваній наносистемі та встановлені механізми цього процесу.
Посилання
1. C. Song, M. Salih, L. H. Li, J. Mangeney, J. Tignon, A. G. Davies, E. H. Linfield, and S. Dhillon, “High–power density, single plasmon, terahertz quantum cascade lasers via transverse mode control,” Appl. Phys. Lett. 122, 121108 (2023). https://doi.org/10.1063/5.0142359
2. A. Cargioli, D. Piciocchi, M. Bertrand, J. Faist, and G. Scalari, “Fast Fourier transform spectroscopy with broadband frequency combs,” Appl. Phys. Lett. 125, 131103 (2024). https://doi.org/10.1063/5.0226044
3. F. Jia, S. J. Addamane, J. L. Reno, and S. Kumar, “High–power 2.2 THz quantum–cascade laser with sixth–order distributed–feedback,” Appl. Phys. Lett. 126, 261101 (2025). https://doi.org/10.1063/5.0273563
4. H. Machhadani, M. Tchernycheva, S. Sakr, L. Rigutti, R. Colombelli, E. Warde, C. Mietze, D. J. As, and F. H. Julien, “Intersubband absorption of cubic GaN/Al(Ga)N quantum wells in the near-infrared to terahertz spectral range,” Phys. Rev. B 83, 075313 (2011). https://doi.org/10.1103/PhysRevB.83.075313
5. N. C. Giebink, G. P. Wiederrecht, M. R. Wasielewski, and S. R. Forrest, “Thermodynamic efficiency limit of excitonic solar cells,” Phys. Rev. B 83, 195326 (2011). https://doi.org/10.1103/PhysRevB.83.195326
6. Y. Cho, J. Encomendero, S.-T. Ho, H. G. Xing, and D. Jena, “N-polar GaN/AlN resonant tunneling diodes,” Appl. Phys. Lett. 117, 143501 (2020). https://doi.org/10.1063/5.0022143
7. Y. Zhou, R. Ahsan, H. U. Chae, R. Kapadia, and P. Zhang, “Theoretical analysis of resonant tunneling enhanced field emission,” Phys. Rev. Appl. 20, 014043 (2023). https://doi.org/10.1103/PhysRevApplied.20.014043
8. A. Demić, A. Valavanis, P. Dean, L. Li, A. G. Davies, E. H. Linfield, J. Cunningham, J. Bailey, A. Akimov, A. Kent, and P. Harrison, “Acoustic band engineering in terahertz quantum-cascade lasers and arbitrary superlattices,” Phys. Rev. B 107, 235411 (2023). https://doi.org/10.1103/PhysRevB.107.235411
9. S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97, 053106 (2005). https://doi.org/10.1063/1.1855394
10. D. O. Winge, E. Dupont, and A. Wacker, “Ignition of quantum cascade lasers in a state of oscillating electric field domains,” Phys. Rev. A 98, 023834 (2018). https://doi.org/10.1103/PhysRevA.98.023834
11. M. Mohammed, A. S. Verhulst, D. Verreck, M. L. Van de Put, W. Magnus, B. Sorée, and G. Groeseneken, “Phonon-assisted tunneling in direct-bandgap semiconductors,” J. Appl. Phys. 125, 015701 (2019). https://doi.org/10.1063/1.5044256
12. U. Aeberhard, “Theoretical investigation of direct and phonon-assisted tunneling currents in InAlGaAs/InGaAs bulk and quantum-well interband tunnel junctions for multijunction solar cells,” Phys. Rev. B 87, 081302(R) (2013). https://doi.org/10.1103/PhysRevB.87.081302
13. S. Fathololoumi, E. Dupont, Z. R. Wasilewski, C. W. I. Chan, S. G. Razavipour, S. R. Laframboise, S. Huang, Q. Hu, D. Ban, and H. C. Liu, “Effect of oscillator strength and intermediate resonance on the performance of resonant phonon-based terahertz quantum cascade lasers,” J. Appl. Phys. 113, 113109 (2013). https://doi.org/10.1063/1.4795614
14. C. Jirauschek and T. Kubis, “Modeling techniques for quantum cascade lasers,” Appl, Phys. Rev. 1, 011307 (2014). https://doi.org/10.1063/1.4863665
15. R. Benchamekh, J.-M. Jancu, and P. Voisin, “Potential-inserted quantum well design for quantum cascade terahertz lasers,” Phys. Status Solidi RRL 11, 1600334 (2017). https://doi.org/10.1002/pssr.201600334
16. H. R. Lewis, Jr. and W. B. Riesenfeld, “An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field,” J. Math. Phys. 10, 1458 (1969). https://doi.org/10.1063/1.1664991
17. A. L. de Lima, A. Rosas, and I. A. Pedrosa, “On the quantum motion of a generalized time-dependent forced harmonic oscillator,” Ann. Phys. 323, 2253 (2008). https://doi.org/10.1016/j.aop.2007.12.006
18. I. A. Pedrosa and D. A. P. de Lima, “Coherent states and geometric phases of a generalized damped harmonic oscillator with time-dependent mass and frequency,” Int. J. Mod. Phys. B 28, 1450177 (2014). https://doi.org/10.1142/S021797921450177X
19. I. A. Pedrosa, “Adiabatic and nonadiabatic evolution of a generalized damped harmonic oscillator,” Mod. Phys. Lett. A 36, 2150201 (2021). https://doi.org/10.1142/S0217732321502011
20. B. F. Ramos, I. A. Pedrosa, and A. L. de Lima, “Lewis and riesenfeld approach to time-dependent non-hermitian hamiltonians having PT symmetry,” Eur. Phys. J. Plus 133, 449 (2018). https://doi.org/10.1140/epjp/i2018-12251-3
21. A. Fring and R. Tenney, “Lewis–riesenfeld invariants for PT-symmetrically coupled oscillators from two-dimensional point transformations and Lie algebraic expansions,” J. Math. Phys. 63, 123509 (2022). https://doi.org/10.1063/5.0110312
22. I. Boyko, M. Petryk, and N. Lebovka, “Application of the lewis–riesenfeld quantum mechanical invariant method for description of electron tunneling transport in nitride multilayer quantum well nanostructures,” Phys. Lett. A 489, 129152 (2023). https://doi.org/10.1016/j.physleta.2023.129152
23. I. Boyko, M. Petryk, and N. Lebovka, “Tunnel transport problem for open multilayer nitride nanostructures with an applied constant magnetic field and time-dependent potential: An exact solution,” Phys. Rev. B 110, 045438 (2024). https://doi.org/10.1103/PhysRevB.110.045438
24. O. Spitz, J. Wu, M. Carras, C.-W. Wong, and F. Grillot, “Low-frequency fluctuations of a mid-infrared quantum cascade laser operating at cryogenic temperatures,” Laser Phys. Lett. 15, 116201 (2018). https://doi.org/10.1088/1612-202X/aadc5a
25. Y. Ren, D. Zhang, Z. Wang, K. Zhou, J. Zhong, D. Liu, W. Miao, W. Zhang, and S. Shi, “Quantum cascade laser based, fiber coupled demultiplexed mid-infrared local oscillator for cryogenic applications,” Appl. Phys. Lett. 116, 131108 (2020). https://doi.org/10.1063/1.5145131
26. H. Bekkar, F. Benamira, and M. Maamache, “Comment on “solution of the schrödinger equation for the time-dependent linear potential,” Phys. Rev. A 68, 016101 (2003). https://doi.org/10.1103/PhysRevA.68.016101
27. C. W. I. Chan, Q. Hu, and J. L. Reno, “Tall-barrier terahertz quantum cascade lasers,” Appl. Phys. Lett. 103, 151117 (2013). https://doi.org/10.1063/1.4824878
28. I. Boyko and M. Petryk, “Tunneling transport in open nitride resonant tunneling structures taking into account the acoustic phonons: A variational approach,” Phys. B: Condens. Matter 636, 413862 (2022). https://doi.org/10.1016/j.physb.2022.413862
29. J. Zou and A. Balandin, “Phonon heat conduction in a semiconductor nanowire,” J. Appl. Phys. 89, 2932 (2001). https://doi.org/10.1063/1.1345515
30. J. Z. Kamiński and E. Saczuk, “Resonant tunneling in laser and constant electric fields,” Acta Phys. Pol. A 122, 53 (2012). https://doi.org/10.12693/APhysPolA.122.53
