[PDF]    https://doi.org/10.3952/physics.2025.65.1.5

Open access article / Atviros prieigos straipsnis
Lith. J. Phys. 65, 57–71 (2025)

HIGH-FREQUENCY CONDUCTIVITY-BASED TERAHERTZ GAIN MODELS IN QUANTUM SEMICONDUCTOR SUPERLATTICES: A COMPARATIVE STUDY
Lukas Stakėla, Kirill N. Alekseev, and Gintaras Valušis
Department of Optoelectronics, Center for Physical Sciences and Technology, Saulėtekio 3, 10257 Vilnius, Lithuania
Email: lukas.stakela@ftmc.lt

Received 19 December 2024; accepted 17 January 2025

The development of high-power, stable and portable terahertz (THz) sources that can operate at room temperature remains one of the biggest challenges in THz and solid-state physics. Despite modern semiconductor devices such as resonant tunnelling diodes and quantum cascade lasers demonstrating a significant progress, they still face several limitations related to a low power output, temperature sensitivity and the lack of frequency tunability. In this respect, semiconductor superlattices operating in the miniband transport regime continue to represent promising quantum materials for the realization of the desirable THz gain. In this study, we briefly overview basic semiclassical models describing the high-frequency conductivity of superlattices. We cover the popular model of Ktitorov et al. and the lesser-known and more advanced model of Ignatov and Shashkin, and also make their comparative analysis with reference to the classical quasistatic model of gain in devices with the negative differential conductivity. This work aims to offer a simple introduction to these models and their practical relevance to THz device design and development.
Keywords: semiconductor superlattices, negative differential conductivity, terahertz gain

AUKŠTADAŽNIU LAIDUMU PAGRĮSTŲ TERAHERCINIO STIPRINIMO MODELIŲ KVANTINĖSE PUSLAIDININKINĖSE SUPERGARDELĖSE PALYGINAMASIS TYRIMAS
Lukas Stakėla, Kirill N. Alekseev, Gintaras Valušis

Fizinių ir technologijos mokslų centro Optoelektronikos skyrius, Vilnius, Lietuva

Didelės galios, stabilių ir mažų matmenų terahercų (THz) šaltinių, galinčių veikti kambario temperatūroje, kūrimas tebėra vienas didžiausių THz ir kietojo kūno fizikos iššūkių. Nors šiuolaikinių puslaidininkinių prietaisų, tokių kaip rezonansiniai tuneliniai diodai ir kvantiniai kaskadiniai lazeriai, technologija padarė milžinišką pažangą, vis dar susiduriama su tam tikrais iššūkiais, susijusiais su maža spinduliuotės galia, jautrumu temperatūrai ir ribotu dažnio derinimu. Šiuo požiūriu puslaidininkinės supergardelės yra perspektyvios puslaidininkinės kvantinės struktūros kompaktiškiems THz osciliatoriams ir stiprintuvams kurti. Šiame tyrime trumpai apžvelgiami pagrindiniai kvaziklasikiniai modeliai, aprašantys supergardelės aukštadažnį laidumą bei jo dispersines savybes. Pagrindinis dėmesys skirtas populiariam ir plačiai naudojamam Ktitorovo ir kt. aukštadažnio laidumo dispersiniam modeliui bei mažiau žinomam, bet sudėtingesniam Ignatovo ir Šaškino modeliui, kuris papildomai įskaito ir erdvinę dispersiją bei plazminių bangų susiformavimą. Remdamiesi klasikiniu kvazistatiniu stiprinimo modeliu supergardelėse su neigiamu diferencialiniu laidumu, mes atlikome jų lyginamąją analizę. Šio darbo tikslas – pateikti paprastą įvadą į šiuos modelius ir jų praktinę reikšmę THz prietaisų kūrimui.


References / Nuorodos

[1] G. Valušis, A. Lisauskas, H. Yuan, W. Knap, and H.G. Roskos, Roadmap of terahertz imaging 2021, Sensors 21, 4092 (2021),
https://doi.org/10.3390/s21124092
[2] Y. Huang, Y. Shen, and J. Wang, From terahertz imaging to terahertz wireless communications, Engineering 22, 106 (2023),
https://doi.org/10.1016/j.eng.2022.06.023
[3] Z. Zhou, A. Kassem, J. Seddon, E. Sillekens, I. Darwazeh, P. Bayvel, and Z. Liu, 938 Gb/s, 5-150 GHz ultra-wideband transmission over the air using combined electronic and photonic-assisted signal generation, J. Lightwave Technol. 42, 7247 (2024),
https://doi.org/10.1109/JLT.2024.3446827
[4] M. Asada and S. Suzuki, Terahertz emitter using resonant-tunneling diode and applications, Sensors 21, 1384 (2021),
https://doi.org/10.3390/s21041384
[5] M.S. Vitiello and P. De Natale, Terahertz quantum cascade lasers as enabling quantum technology, Adv. Quantum Tech. 5, 2100082 (2022),
https://doi.org/10.1002/qute.202100082
[6] L. Esaki and R. Tsu, Superlattice and negative differential conductivity in semiconductors, IBM J. Res. Dev. 14, 61 (1970),
https://doi.org/10.1147/rd.141.0061
[7] E.L. Ivchenko and G.E. Pikus, Superlattices and Other Heterostructures: Symmetry and Optical Phenomena, Springer Series in Solid-State Sciences Vol. 110 (Springer Berlin Heidelberg, Berlin, Heidelberg, 1997),
https://doi.org/10.1007/978-3-642-60650-2
[8] J. Feldmann, K. Leo, J. Shah, D.A.B. Miller, J.E. Cunningham, T. Meier, G. Von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, Optical investigation of Bloch oscillations in a semiconductor superlattice, Phys. Rev. B 46, 7252 (1992),
https://doi.org/10.1103/PhysRevB.46.7252
[9] C. Waschke, H.G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Köhler, Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice, Phys. Rev. Lett. 70, 3319 (1993),
https://doi.org/10.1103/PhysRevLett.70.3319
[10] V.G. Lyssenko, G. Valušis, F. Löser, T. Hasche, K. Leo, M.M. Dignam, and K. Köhler, Direct measurement of the spatial displacement of Bloch-oscillating electrons in semiconductor superlattices, Phys. Rev. Lett. 79, 301 (1997),
https://doi.org/10.1103/PhysRevLett.79.301
[11] K.F. Renk, B.I. Stahl, A. Rogl, T. Janzen, D.G. Pavel'ev, Yu.I. Koshurinov, V. Ustinov, and A. Zhukov, Subterahertz superlattice parametric oscillator, Phys. Rev. Lett. 95, 126801 (2005),
https://doi.org/10.1103/PhysRevLett.95.126801
[12] P.G. Savvidis, B. Kolasa, G. Lee, and S.J. Allen, Resonant crossover of terahertz loss to the gain of a Bloch oscillating InAs/AlSb superlattice, Phys. Rev. Lett. 92, 196802 (2004),
https://doi.org/10.1103/PhysRevLett.92.196802
[13] A. Lisauskas, C. Blöser, R. Sachs, H.G. Roskos, A. Juozapavičius, G. Valušis, and K. Köhler, Time-resolved photocurrent spectroscopy of the evolution of the electric field in optically excited superlattices and the prospects for Bloch gain, Appl. Phys. Lett. 86, 102103 (2005),
https://doi.org/10.1063/1.1867552
[14] T. Hyart, N.V. Alexeeva, J. Mattas, and K.N. Alekseev, Terahertz Bloch oscillator with a modulated bias, Phys. Rev. Lett. 102, 140405 (2009),
https://doi.org/10.1103/PhysRevLett.102.140405
[15] A. Wacker, Coexistence of gain and absorption, Nature Phys. 3, 298 (2007),
https://doi.org/10.1038/nphys603
[16] S.A. Ktitorov, G.S. Simin, and V.Y. Sindalovskii, Bragg reflections and high-frequency conductivity of an electronic solid-state plasma, Sov. Phys. Solid State 13, 1872 (1972)
[17] A.A. Ignatov and V.I. Shashkin, Bloch oscillations of electrons and instability of space-charge waves in superconductor superlattices, Sov. Phys. JETP 66, 526 (1987)
[PDF]
[18] F.G. Bass and A.P. Tetervov, High-frequency phenomena in semiconductor superlattices, Phys. Rep. 140, 237 (1986),
https://doi.org/10.1016/0370-1573(86)90083-9
[19] E.E. Mendez, F. Agulló-Rueda, and J.M. Hong, Stark localization in GaAs-GaAlAs superlattices under an electric field, Phys. Rev. Lett. 60, 2426 (1988),
https://doi.org/10.1103/PhysRevLett.60.2426
[20] M. Dignam, J.E. Sipe, and J. Shah, Coherent excitations in the Stark ladder: excitonic Bloch oscillations, Phys. Rev. B 49, 10502 (1994),
https://doi.org/10.1103/PhysRevB.49.10502
[21] V. Karpus, Dvimačiai elektronai (Ciklonas, 2004), [in Lithuanian]
[22] J. Pozhela, Plasma and Current Instabilities in Semiconductors: International Series on the Science of the Solid State (Elsevier Science, Burlington, 1981),
https://shop.elsevier.com/books/plasma-and-current-instabilities-in-semiconductors/pozhela/978-0-08-025048-9
[23] P.L. Bhatnagar, E.P. Gross, and M. Krook, A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems, Phys. Rev. 94, 511 (1954),
https://doi.org/10.1103/PhysRev.94.511
[24] X.L. Lei, N.J.M. Horing, H.L. Cui, and K.K. Thornber, One-dimensional confinement effects on miniband transport in a semiconductor superlattice, Phys. Rev. B 48, 5366 (1993),
https://doi.org/10.1103/PhysRevB.48.5366
[25] A. Khalatpour, A.K. Paulsen, C. Deimert, Z.R. Wasilewski, and Q. Hu, High-power portable terahertz laser systems, Nat. Photonics 15, 16 (2021),
https://doi.org/10.1038/s41566-020-00707-5
[26] A.E. Seaver, An equation for charge decay valid in both conductors and insulators,
https://arxiv.org/abs/0801.4182
https://doi.org/10.48550/arXiv.0801.4182
[27] H. Willenberg, G.H. Döhler, and J. Faist, Intersubband gain in a Bloch oscillator and quantum cascade laser, Phys. Rev. B 67, 085315 (2003),
https://doi.org/10.1103/PhysRevB.67.085315
[28] H. Kroemer, Large-amplitude oscillation dynamics and domain suppression in a superlattice Bloch oscillator,
https://arxiv.org/abs/cond-mat/0009311
https://doi.org/10.48550/arXiv.cond-mat/0009311
[29] T. Hyart, K.N. Alekseev, and E.V. Thuneberg, Bloch gain in dc-ac-driven semiconductor superlattices in the absence of electric domains, Phys. Rev. B 77, 165330 (2008),
https://doi.org/10.1103/PhysRevB.77.165330
[30] A.A. Ignatov, K.F. Renk, and E.P. Dodin, Esaki-Tsu superlattice oscillator: Josephson-like dynamics of carriers, Phys. Rev. Lett. 70, 1996 (1993),
https://doi.org/10.1103/PhysRevLett.70.1996
[31] N. Sekine and K. Hirakawa, Dispersive terahertz gain of a nonclassical oscillator: Bloch oscillation in semiconductor superlattices, Phys. Rev. Lett. 94, 057408 (2005),
https://doi.org/10.1103/PhysRevLett.94.057408
[32] R. Terazzi, T. Gresch, M. Giovannini, N. Hoyler, N. Sekine, and J. Faist, Bloch gain in quantum cascade lasers, Nat. Phys. 3, 329 (2007),
https://doi.org/10.1038/nphys577
[33] V. Čižas, L. Subačius, N.V. Alexeeva, D. Seliuta, T. Hyart, K. Köhler, K.N. Alekseev, and G. Valušis, Observation of the dissipative parametric gain in a GaAs/AlGaAs superlattice, Phys. Rev. Lett. 128, 236802 (2022),
https://doi.org/10.1103/PhysRevLett.128.236802
[34] T. Hyart, A.V. Shorokhov, and K.N. Alekseev, Theory of parametric amplification in superlattices, Phys. Rev. Lett. 98, 220404 (2007),
https://doi.org/10.1103/PhysRevLett.98.220404
[35] V. Čižas, N. Alexeeva, K.N. Alekseev, and G. Valušis, Coexistence of Bloch and parametric mechanisms of high-frequency gain in doped superlattices, Nanomaterials 13, 1993 (2023),
https://doi.org/10.3390/nano13131993
[36] V. Čižas, N. Alexeeva, K. Alekseev, and G. Valušis, Sum-frequency generation and amplification processes in semiconductor superlattices, Lith. J. Phys. 63, 148 (2023),
https://doi.org/10.3952/physics.2023.63.3.5