Features of recombination radiation temperature reduction in semiconductor quantum dots with extrinsic complexes 

Vladimir D. Krevchik, Doctor of physical and mathematical sciences, professor, dean of the faculty of information technology and electronics, Penza State University (40 Krasnaya street, Penza, Russia), physics@pnzgu.ru
Aleksey V. Razumov, Candidate of physical and mathematical sciences, associate professor, associate professor of the sub-department of general physics and physics teaching methods, Penza State University (40 Krasnaya street, Penza, Russia), physics@pnzgu.ru
Mikhail B. Semenov, Doctor of physical and mathematical sciences, professor, head of the sub-department of physics, Penza State University (40 Krasnaya street, Penza, Russia), physics@pnzgu.ru,
Ekaterina A. Pecherskaya, Doctor of engineering sciences, associate professor, head of the sub-department of information and measuring technology and metrology, Penza State University (40 Krasnaya street, Penza, Russia), pea1@list.ru
Irina M. Moyko, Assistant of the sub-department of higher and applied mathematics, Penza State University (40 Krasnaya street, Penza, Russia), physics@pnzgu.ru
Pavel E. Golubkov, Engineer of the sub-department of information and measuring technology and metrology, Penza State University (40 Krasnaya street, Penza, Russia), golpavpnz@yandex.ru

535.8; 537.9; 539.33 

10.21685/2072-3040-2021-4-12 

Background. Semiconductor quantum dots, due to their unique optical properties, are a promising material for creating optoelectronic devices. At the same time, the devices’ parameters change significantly over a wide temperature range, which requires knowledge of the temperature dependence of both the band structure and the energy of impurity levels in quantum dots. In this case, the electron-phonon interaction acts as the most important mechanism for the temperature shift of energy levels. The purpose of this work is to theoretically study the effect of electron-phonon interaction on the temperature dependence of radiative recombination in an extrinsic complex ( A+ + e ) in a semiconductor quasi-zerodimensional structure. Materials and methods. The theoretical consideration of the temperature effect on the energy levels in a semiconductor quantum dot was carried out by a statistical method under the assumption that the main contribution to the temperature dependence comes from the electron-phonon interaction. The dispersion equation, which determines the binding energy of a hole in an extrinsic complex ( A+ + e ) in a spherically symmetric quantum dot, was obtained in the framework of the adiabatic approximation in the model of a zero-radius potential. The calculation of the spectral intensity of recombination radiation in a quasi-zero-dimensional structure with extrinsic complex ( A+ + e ) was performed in the dipole approximation taking into account the dispersion of the radius of quantum dots. The temperature dependence curves are plotted for the case of InSb-based quantum dots. Results. The temperature dependence of the binding energy in the complex ( A+ + e ) is calculated for various values of the quantum dot radius. It is shown that, with increasing temperature, the hole binding energy decreases, which is associated with the temperature “spreading” of the wave function of the quasistationary A+ -state under conditions of electron-phonon and hole-phonon interactions. It was found that with a decrease in the radius of a quantum dot, the binding energy of the A+ -state increases due to an increase in the energy of the ground state of the adiabatic potential of an electron. The dependence of the spectral intensity of the recombination radiation on the transition energy is calculated for various values of temperature. It was found that with increasing temperature, the threshold transition energy shifts to the short-wavelength region of the spectrum, and temperature quenching of the recombination radiation takes placeThis is due to a decrease in the overlap integral of the wave functions of the initial and final states of an electron due to an increase in the transition energy. Conclusions. The effect of electron-phonon interaction on recombination processes in extrinsic complexes ( A+ + e ) in a spherically symmetric quantum dot manifests itself in temperature reduction of the spectral intensity of the recombination radiation. The effect of reaching a “plateau” appears to be common to different photoluminescence mechanisms. 

quantum dot, extrinsic complex, zero-radius potential method, adiabatic approximation, electron-phonon interaction, intensity of recombination radiation.

1. Shamirzaev T.S., Seksenbaev M.S., Zhuravlev K.S., Nikiforov A.I. [et al.]. Photoluminescence of germanium quantum dots grown in silicon on a monolayer SiO2. Fizika
tverdogo tela = Solid state physics. 2005;47(1):80–82. (In Russ.)
2. Reznitskiy A.N., Klochikhin A.A., Permogorov S.A. Temperature dependence of the photoluminescence intensity of self-organized CdTe quantum dots in the Zn Tepri matrix under different excitation conditions. Fizika tverdogo tela = Solid state physics. 2012;54(1):115–124. (In Russ.)
3. Biryukov D.Yu., Zatsepin A.F. Equation of temperature dependence of photoluminescence of semiconductor quantum dots. Fizika tverdogo tela = Solid state physics.
2014;56(3):611–614. (In Russ.)
4. Zatsepin A.F., Biryukov D.Yu. Temperature dependence of photoluminescence of semiconductor quantum dots under indirect excitation in a dielectric matrix SiO2. Fizika tverdogo tela = Solid state physics. 2015;57(8):1570–1575. (In Russ.)
5. Vaynshteyn I.A., Zatsepin A.F., Kortov V.S. On the applicability of the empirical Varshni relation for the temperature dependence of the band gap. Fizika tverdogo tela = Solid state physics. 1999;41(6):994–998. (In Russ.)
6. Sedrakyan D.M., Petrosyan P.G., Grigoryan L.N., Badalyan V.D. Researching the temperature coefficient of energy of the forbidden zone of semiconductor nanostructures CdSe1-xSx. Izvestiya NAN Armenii, Fizika = Proceedings of the National Academy of Sciences of Armenia, Physics. 2007;42(1):9–16. (In Russ.)
7. Gulyamov G., Sharibaev N.Yu. Effect of temperature on the semiconductor band gap. FІP FIP PSE. 2011;9(1):40–43. (In Russ.)
8. Ridli B. Kvantovye protsessy v poluprovodnikakh = Quantum processes in semiconductors. Moscow: Mir. 1986:304. (In Russ.)
9. Lipatova Zh.O., Kolobkova E.B., Babkina A.H., Nikonorov H.B. Dimensional and temperature dependences of the band gap of cadmium selenide quantum dots in fluorophosphate glasses. Fizika i tekhnika poluprovodnikov = Semiconductor physics and technology. 2017;51(3):339–341. (In Russ.)
10. Piter Yu., Kardona M. Osnovy fiziki poluprovodnikov = Fundamentals of semiconductor physics. Moscow: Fizmatlit, 2002:560. (In Russ.)
11. Ekimov A.I., Onushchenko A.A., Efros Al.L. Quantization of the energy spectrum of holes in the adiabatic potential of an electron. Pis'ma v zhurnal eksperimental'noy i teoreticheskoy fiziki = Letters to the journal of experimental and theoretical physics. 1986;43(6):292–294. (In Russ.)
12. Efros Al.L., Efros A.L. Interband light absorption in a semiconductor ball. Fizika i tekhnika poluprovodnikov = Semiconductor physics and technology. 1982;16(7):1209– 1214. (In Russ.)
13. Krevchik V.D., Grunin A.B., Zaytsev R.V. Anisotropy of magneto-optical absorption of complexes “quantum dot - extrinsic center”. Fizika i tekhnika poluprovodnikov = Semiconductor physics and technology. 2002;36(10):1225–1232. (In Russ.)
14. Zhou Hai-Yang, Gu Shi-Wei, Shi Yao-Ming. Electronic and Shallow Impurity States in Semiconductor Heterostructures Under an Applied Electric Field. Commun. Theor.
Phys. 2005;44:375.
15. Lifshits I.M., Slezov V.V. On the kinetics of diffusional decomposition of supersaturated solid solutions. Zhurnal eksperimental'noy i teoreticheskoy fiziki = Journal of experimental and theoretical physics. 1958;35(2):479–492. (In Russ.)