Ukrainian Journal of Physical Optics


2022 Volume 23, Issue 3


ISSN 1816-2002 (Online), ISSN 1609-1833 (Print)

Excitons in resonant tunnelling structures based on AlN/GaN/AlN/AlGaN/AlN nitride: spectral dependences and intensities of interband optical transitions

1Boyko I., 2Petryk M. and 1,2Mykhailyshyn R.

1Ternopil Ivan Puluj National Technical University, 56 Ruska Street, 46001 Ternopil, Ukraine boyko.i.v.theory@gmail.com
2Department of Robotics Engineering, Worcester Polytechnic Institute, 85 Prescott Street, Worcester, Massachusetts, USA

ABSTRACT

We offer a new iterative method for exciton theory and develop a theory of exciton states arising in a plane resonant-tunnelling nanostructure based on semiconducting nitrides. Our approach takes into account the contributions of internal electric fields arising in its layers and employs both iterative and variational methods. We compare our method with the other techniques known in the exciton theory on example of a nanosystem representing a separate cascade of quantum cascade detector, which has been earlier implemented experimentally. The electron and hole spectra, the spectra of excitons and their binding energies, as well as the intensities of electron–hole transitions are calculated as functions of geometric parameters of the nanostructure. Particular cases of light-hole and heavy-hole excitons are analyzed.

Keywords: excitons, nitride semiconductors, quantum cascade detectors, resonant tunnelling structures, variational methods, iterative methods

UDC: 538.958; 538.971

    1. Wang K, Grange T, Lin T, Wang L, Jehn Z, Birner S, Yun J, Terashima W and Hirayama H, 2018. Broadening mechanisms and self-consistent gain calculations for GaN quantum cascade laser structures. Appl. Phys. Lett. 113: 061109. doi:10.1063/1.5029520
    2. Sakr S, Giraud E, Tchernycheva M, Isac N, Quach P, Warde E, Grandjean N and Julien F H, 2012. A simplified GaN/AlGaN quantum cascade detector with an alloy extractor. Appl. Phys. Lett. 101: 251101. doi:10.1063/1.4772501
    3. Pesach A, Sakr S, Giraud E, Sorias O, Gal L, Tchernycheva M, Orenstein M, Grandjean N, Julien F H and Bahir G, 2014. First demonstration of plasmonic GaN quantum cascade detectors with enhanced efficiency at normal incidence. Opt. Express. 22: 21069-21078. doi:10.1364/OE.22.021069
    4. Westmeyer A N, Mahajan S, Bajaj K K, Lin J Y and Jiang H X, 2006. Determination of energy-band offsets between GaN and AlN using excitonic luminescence transition in AlGaN alloys. J. Appl. Phys. 99: 013705. doi:10.1063/1.2158492
    5. Ajia I A, Edwards P R, Liu Z, Yan J C, Martin R W and Roqan I S, 2014. Excitonic localization in AlN-rich AlxGa1-xN/AlyGa1-yN multi-quantum-well grain boundaries. Appl. Phys. Lett. 105: 122111. doi:10.1063/1.4896681
    6. Smith M, Lin J Y, Jiang H X, Khan A and Chen Q, 1997. Exciton-phonon interaction in InGaN/GaN and GaN/AlGaN multiple quantum wells. Appl. Phys. Lett. 70: 2882-2884. doi:10.1063/1.119030
    7. Bayerl D and Kioupakis E, 2019. Room-temperature stability of excitons and transverse-electric polarized deep-ultraviolet luminescence in atomically thin GaN quantum wells. Appl. Phys. Lett. 115: 131101. doi:10.1063/1.5111546
    8. Staszczak G, Trzeciakowski W, Monroy E, Bercha A, Muzioł G, Skierbiszewski C, Perlin P and Suski T, 2020. Room-temperature stability of excitons and transverse-electric polarized deep-ultraviolet luminescence in atomically thin GaN quantum wells. Phys. Rev. B. 101: 085306. doi:10.1103/PhysRevB.101.085306
    9. Fonoberov V A and Balandin A A., 2003. Excitonic properties of strained wurtzite and zinc-blende GaN/AlxGa1-xN quantum dots. J. Appl. Phys. 94: 7178-7186. doi:10.1063/1.1623330
    10. Williams D P, Andreev A D and O'Reilly P, 2006. Dependence of exciton energy on dot size in GaN/AlN quantum dots. Phys. Rev. B. 73: R241301(R). doi:10.1063/1.2730199
    11. Chafai A, Essaoudi I, Ainane A, Dujardin F and Ahuja R, 2019. Binding energy of an exciton in a GaN/AlN nanodot: Role of size and external electric field. Physica B. 559: 23-28. doi:10.1016/j.physb.2019.01.047
    12. Bernardini F and Fiorentini V, 2008. Macroscopic polarization and band offsets at nitride heterojunctions. Phys. Rev. B. 57: R9427-R9430. doi:10.1103/PhysRevB.57.R9427
    13. Boyko I V, 2018. Analytical method for calculation of the potential profiles of nitride-based resonance tunneling structures. Condens. Matter Phys. 21: 43701. doi:10.5488/CMP.21.43701
    14. Duque C M, Mora-Ramos M E and Duque C A, 2012. Exciton properties in zincblende InGaN-GaN quantum wells under the effects of intense laser fields. Nanoscale Res. Lett. 7: 492. doi:10.1186/1556-276X-7-492
    15. Pokatilov E P, Nika D, Fomin V M and Devreese J T, 2008. Excitons in wurtzite AlGaN/GaN quantum-well heterostructures. Phys. Rev. B. 77: 125328. doi:10.1103/PhysRevB.77.125328
    16. Wang H, Farias G A and Freire V N, 1999 Electric field effects on the confinement properties of GaN/AlxGa1-xN zincblende and wurtzite nonabrupt quantum wells. Braz. J. Phys. 29: 670-674. doi:10.1590/S0103-97331999000400010
    17. Rojas-Briseno J G, Rodriguez-Vargas I, Mora-Ramos M E and Martinez-Orozco J C, 2020. Heavy and light exciton states in c-AlGaN/GaN asymmetric double quantum wells. Physica E. 124: 114248. doi:10.1016/j.physe.2020.114248
    18. Ha S H and Ban S L, 2008. Binding energies of excitons in a strained wurtzite GaN/AlGaN quantum well influenced by screening and hydrostatic pressure. Phys. Stat. Solidi B. 248: 384-388. doi:10.1002/pssb.201000615
    19. Zhu J, BanS L and Ha S H, 2010. Binding energies of excitons in strained [0001]-oriented wurtzite AlGaN/GaN double quantum wells. J. Phys.: Condens. Matter. 20: 085218. doi:10.1002/pssb.201000615
    20. Boyko I, 2018. Anisotropic wurtzite resonance tunneling structures: stationary spectrum of electron and oscillator strengths of quantum transitions. J. Phys. Stud. 22: 1701. doi:10.30970/jps.22.1701
    21. Stepnicki P, Pietka B, Morier-Genoud F, Deveaud B and Matuszewski M, 2015. Analytical method for determining quantum well exciton properties in a magnetic field. Phys. Rev. B. 91: 195302. doi:10.1103/PhysRevB.91.195302
    22. Vurgaftman I, Meyer J R and Ram-Mohan L R, 2001. Band parameters for III-V compound semiconductors and their alloys. J. Appl. Phys. 89: 5815-5875. doi:10.1063/1.1368156

    Запропоновано новий ітераційний метод для теорії екситонів і розвинуто теорію екситонних станів, які з’являються в плоскій резонансно-тунельній наноструктурі на основі напівпровідникових нітридів. Наш підхід враховує внески внутрішніх електричних полів, що виникають у шарах наноструктури. Він використовує і ітераційні, і варіаційні методи. Ми порівнюємо наш метод з іншими методами, відомими в теорії екситонів, на прикладі наносистеми, що представляє собою окремий каскад квантового каскадного детектора, який раніше був реалізований експериментально. Розраховано електронні та діркові спектри, спектри екситонів та енергії їхнього зв’язку, а також інтенсивності електронно-діркових переходів як функції геометричних параметрів наноструктури. Проаналізовано окремі випадки екситонів легких і важких дірок.

    Ключові слова: excitons, nitride semiconductors, quantum cascade detectors, resonant tunnelling structures, variational methods, iterative methods

Free download this article 

© Ukrainian Journal of Physical Optics ©