On the energy bandgap in mesoporous semiconductors
A.V. Shishulin, A.V. Shishulina
R.E. Alekseev Nizhny Novgorod State Technical University
DOI: 10.26456/pcascnn/2025.17.317
Original article
Abstract: In this paper, the dependence of the energy bandgap of a mesoporous semiconductor on geometric characteristics (volume and shape) of pores distributed in the material has been analyzed. The obtained estimates demonstrate that the well-known effect (being characteristic of nanoscale particles), which consists in a significant dependence of the bandgap on the size and shape of a particle, can also be realized in mesoporous materials (the pore size being from 5 up to 50 nm) while the mesoporous materials themselves can be of macroscopic dimensions. Using mesoporous CdSe as an example, it has been shown the reducing the pore size and «complicating» the pore shape result in a notable increase in the energy bandgap. The results have been obtained using the cohesive energy-based model, being verified experimentally for CdSe nanoparticles. Geometric characteristics of pores have been determined in the framework of the fractal-geometry approach by the values of their effective diameter and fractal dimension.
Keywords: semiconductors, energy bandgap, mesoporous materials, fractal dimension, cohesion
- Alexander V. Shishulin – Ph. D., Associate Professor, R.E. Alekseev Nizhny Novgorod State Technical University
- Anna V. Shishulina – Ph. D., Associate Professor, R.E. Alekseev Nizhny Novgorod State Technical University
For citation:
Shishulin A.V., Shishulina A.V. O shirine zapreshchennoj zony v mezoporistykh poluprovodnikakh [On the energy bandgap in mesoporous semiconductors], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2025, issue 17, pp. 317-327. DOI: 10.26456/pcascnn/2025.17.317. ⎘
Full article (in Russian): download PDF file
References:
1. Lu K. Nanoparticulate materials: synthesis, characterization, and processing, Hoboken, Wiley, 2012, 464 p.
2. New Frontiers in nanoparticles and nanocomposite materials, ed by. A. Öchsner, A. Shokuhfar. Berlin, Heidelberg, Springer-Verlag, 2013, 371 p. DOI: 10.1007/978-3-642-14697-8.
3. Sdobnyakov N.Yu. Modelirovanie strukturnykh prevrascheniy v odnokomponentnykh i mnogokomponentnykh metallicheskikh nanosistemakh [Simulation of structural transformations in monokomponent and multicomponent metal nanosystems]. Tver, Tver State University Publ., 2025, 408 p. DOI: 10.26456/sny.2025.408. (In Russian).
4. Essajai R., Benhouria Y., Rachadi A. et al. Shape-dependent structural and magnetic properties of Fe nanoparticles studied through simulation methods, RSC Advances, 2019, vol. 9, issue 38, pp. 22057-22063. DOI: 10.1039/C9RA03047F.
5. Guisbiers G. αshape, birth of one universal parameter? Key Engineering Materials, 2010, vol. 444, pp. 69-80. DOI: 10.4028/www.scientific.net/KEM.444.69.
6. Shishulin A.V., Potapov A.A., Shishulina A.V. Several notes on the lattice thermal conductivity of fractal-shaped nanoparticles, Eurasian Physical Technical Journal, 2022, vol. 19, issue 3(41), pp. 10-17. DOI: 10.31489/2022No3/10-17.
7. Guisbiers G. Size-dependent material properties towards a universal equation, Nanoscale Research Letters, 2010, vol. 5, issue 7, art. no. 1132, 5 p. DOI: 10.1007/s11671-010-9614-1.
8. Bogdanov S.S., Sdobnyakov N.Yu. Zakonomernosti strukturoobrazovaniya v binarnykh nanochastitsakh GTsK-metallov pri termicheskom vozdejstvii: atomisticheskoe modelirovanie [Patterns of structure formation in binary nanoparticles of FCC metals under thermal exposure: atomistic simulation]. Tver, Tver State University Publ., 2023, 144 p. DOI: 10.26456/bs.2023.144. (In Russian).
9. Sdobnyakov N.Yu, Kolosov A.Yu, Sokolov D.N. et al. Kompleksnyj podkhod k modelirovaniyu plavleniya i kristallizatsii v pyatikomponentnykh metallicheskikh nanochastitsakh: molekulyarnaya dinamika i metod Monte-Karlo [Complex approach to the simulation of melting and crystallization in five-component metallic nanoparticles: molecular dynamics and the Monte Carlo method], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2023, issue 15, pp. 589-601. DOI: 10.26456/pcascnn/2023.15.589 (in Russian).
10. Shishulin A.V., Shishulina A.V. Nekotorye osobennosti vysokotemperaturnykh fazovykh ravnovesij v nanochastitsakh sistemy Six-Ge1-x [Several peculiarities of high-temperature phase equilibria in nanoparticles of the Six-Ge1-x system], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostructur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2019, issue 11, pp. 268-276. DOI: 10.26456/pcascnn/2019.11.268 (In Russian).
11. Shishulin A.V., Shishulina A.V. Ravnovensnyj fazovyj sostav i vzaimnaya rastvorimost’ komponentov v nanochastitsakh fraktal’noj formy tyazhelogo psevdosplava W-Cr [Equilibrium phase composition and mutual solubility in fractal nanoparticles of the W-Cr heavy pseudo-alloy], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostructur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2019, issue 11, pp. 380-388. DOI: 10.26456/pcascnn/2019.11.380 (in Russian).
12. Shishulin A.V., Shishulina A.V. Vliyanie iskhodnogo sostava na fazovye ravnovesiya pri tverdofaznom rasslaivanii v nanochastitsakh binarnykh splavov (na primere sistemy W-Cr) [Influence of the initial composition on the phase equilibria in the case of the solid phase separation in binary alloy nanoparticles (exemplifying on the W-Cr system)], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2023, issue 15, pp. 299-307. DOI: 10.26456/pcascnn/2023.15.299 (In Russian).
13. Shishulin A.V., Shishulina A.V., Kuptsov A.V. Osobennosti fazovykh ravnovesij «zhidkost’ – tverdoe telo» v nanochastitsakh sistemy Six-Ge1-x pri razlichnom vzaimnom raspolozhenii faz [Peculiarities of «liquid – solid» phase equilibria in Six-Ge1-x nanoparticles for various mutual arrangement of phases], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostructur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2024, issue 16, pp. 437-447. DOI: 10.26456/pcascnn/2024.16.437 (In Russian).
14. Shishulin A.V., Fedoseev V.B. Thermal stability and phase composition of stratifying polymer solutions in small-volume droplets, Journal of Engineering Physics and Thermophysics, 2020, vol. 93, issue 4, pp. 802-809. DOI: 10.1007/s10891-020-02182-9.
15. Shishulin A.V., Shishulina A.V. One more parameter determining the stratification of solutions in small-volume droplets, Journal of Engineering Physics and Thermophysics, 2022, vol. 95, issue 6, pp. 1374-1382. DOI: 10.1007/s10891-022-02606-8.
16. Shishulin A.V., Potapov A.A., Shishulina A.V. On the transition between ferromagnetic and paramagnetic states in mesoporous materials with fractal morphology, Eurasian Physical Technical Journal, 2021, vol. 18, issue 2(36), pp. 6-11. DOI: 10.31489/2021NO2/6-11.
17. Shishulin A.V., Shishulina A.V. K voprosu ob uprugikh kharakteristikakh mezoporistykh materialov [Several notes on the elastic properties of mesoporous materials], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostructur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2023, issue 15, pp. 308-316. DOI: 10.26456/pcascnn/2023.15.308 (in Russian).
18. Shishulin A.V., Shishulina A.V., Kuptsov A.V. K voprosu o plavlenii mezoporistykh materialov [Several notes on the melting behavior of mesoporous materials], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostructur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2024, issue 16, pp. 427-436. DOI: 10.26456/pcascnn/2024.16.427 (in Russian).
19. Goyal M., Singh M. Size and shape dependence of optical properties of nanostructures, Applied Physics A, 2020, vol. 126, issue 3, art. no. 176, 8 p. DOI: 10.1007/s00339-020-3327-9.
20. Singh M., Goyal M., Devlal K. Size and shape effects on the bandgap of semiconductor compound nanomaterials, Journal of Taibah University for Science, 2018, vol. 12, issue. 4, pp. 470-475. DOI: 10.1080/16583655.2018.1473946.
21. Gorer S., Hodes G. Quantum size effects in the study of chemical solution deposition mechanisms of semiconductor films, Journal of Physical Chemistry, 1994, vol. 98, issue 20, pp. 5338-5346. DOI: 10.1021/j100071a026.
22. Vossmeyer T., Katsikas L., Giersig M. et al. CdSe nanoclusters: synthesis, characterization, size-dependent oscillator strength, temperature shift of the excitonic transition energy, and reversible absorbance shift, Journal of Physical Chemistry, 1994, vol. 98, issue 31, pp. 7665-7673. DOI: 10.1021/j100082a044.
23. Guisbiers G., van Overschelde O., Wautelet M. Theoretical investigation of size and shape effects on the melting temperature and energy bandgap of TiO2 nanostructures, Applied Physics Letters, 2008, vol. 92, issue 10, art. no. 103121, 3 p. DOI: 10.1063/1.2897297.
24. Guisbiers G., Abudukelimu G., Wautelet M., Buchaillot L. Size, shape, composition and segregation tuning of InGaAs thermo-optical properties, Journal of Physical Chemistry C, 2008, vol. 112, issue 46, pp. 17889-17892. DOI: 10.1021/jp805760h.
25. Guisbiers G., Wautelet M., Buchaillot L. Phase diagrams and optical properties of phosphide, arsenide, and antimonide binary and ternary III-V nanoalloys, Physical Review B, 2009, vol. 79, issue 15, pp. 155426-1-155426-8. DOI: 10.1103/PhysRevB.79.155426.
26. Aqra F., Ayyad A. Surface free energy of alkali and transition metal nanoparticles, Applied Surface Science, 2014, vol. 324, pp. 308-313. DOI: 10.1016/j.apsusc.2014.07.004.
27. Anofriev V.A., Nizenko A.V., Ivanov D.V., Antonov A.S., Sdobnyakov N.Yu. K problem avtomatizatsii protsessa opredeleniya fraktal'noj razmernosti [To the problem of automation of the process of determination of the fractal dimension], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2022, issue 14, pp. 264-276. DOI: 10.26456/pcascnn/2022.14.264. (In Russian).
28. Shishulin A.V., Potapov A.A., Shishulina A.V. Fractal nanoparticles of phase-separating solid solutions: nanoscale effects on phase equilibria, thermal conductivity, thermoelectric performance, Springer Proceedings in Complexity, ed. by C.H. Skiadas, Y. Dimotikalis. Cham, Springer, 2022, pp. 421-432. DOI: 10.1007/978-3-030-96964-6_30.
29. Gaev D.S., Rekhviashvili S.S. Kinetics of crack formation in porous silicon, Semiconductors, 2012, vol. 46, issue 2, pp. 137-140. DOI: 10.1134/S1063782612020108.
30. Błaszczyński T., Ślosarczyk A., Morawski M. Synthesis of silica aerogel by supercritical drying method, Procedia Engineering, 2013, vol. 57, pp. 200-206. DOI: 10.1016/j.proeng.2013.04.028.
31. Chae H.K., Siberio-Pérez D.Y., Kim J. et al. A route to high surface area, porosity and inclusion of large molecules in crystals, Nature, 2004, vol. 427, pp. 523-527. DOI: 10.1038/nature02311.
32. Chuvil’deev V.N., Nokhrin A.V., Kopylov V.I., et al. Spark plasma sintering for high-speed diffusion bonding of the ultrafine-grained near-α Ti-5Al-2V alloy with high strength and corrosion resistance for nuclear engineering, Journal of Materials Science, 2019, vol. 54, issue 24, pp. 14926-14949. DOI: 10.1007/s10853-019-03926-6.
33. Len’shina N.A., Arenyev M.V., Shurygina M.P. et al. Photoreduction of o-benzoquinone moiety in mono and poly(quinone methcrylate) and on the surface of polymer matrix pores, High Energy Chemistry, 2017, vol. 51, issue 3, pp. 209-214. DOI: 10.1134/S0018143917030080.
34. Fedoseeva E.N., Fedoseev V.B. Interaction of chitosan with benzoic acid in solution and films, Polymer Science. Series A, 2011, vol. 53, issue 11, pp. 1040-1046. DOI: 10.1134/S0965545X1110004X.
35. Li J., Du Q., Sun C. An improved box-counting method for image fractal dimension estimation, Pattern Recognition, 2009, vol. 42, issue 11, pp. 4260-4269. DOI: 10.1016/j.patcog.2009.03.001.