On Decreasing Mismatch-Induced Stresses in a Heterostructure by Preliminary Radiation Processing of the Substrate

Authors

https://doi.org/10.48313/maa.v1i3.93

Abstract

The continuous miniaturisation of solid-state devices and the proliferation of multilayer heterostructures in modern microelectronics, optoelectronics, and power electronics have placed epitaxial-layer quality at the centre of device-engineering research. A persistent obstacle in these systems is the lattice- and thermo-elastic mismatch between the substrate and the epitaxial layer, which gives rise to mismatch-induced stresses that degrade crystalline quality, generate threading dislocations, and ultimately limit device yield [1–3]. This article introduces and elaborates an approach aimed at decreasing mismatch-induced stresses in a heterostructure by subjecting the substrate to preliminary radiation processing before the gas-phase epitaxial growth of the active layer. The damaged near-surface region created by ionising radiation acts as a sacrificial defect reservoir whose recombination and accelerated diffusion during high-temperature Vapour-Phase Epitaxy (VPE) modify the local chemical potential and, in turn, the elastic state of the growing interface. To describe this coupled mass-and-heat-transfer problem, the present work develops an analytical framework based on the Method of Averaging of Function Corrections (MAFC), originally introduced by People and Bean [4]. The framework simultaneously accommodates spatial and temporal variations of the transport coefficients, the nonlinearity of the recombination kinetics of point defects and their complexes, and the coupling between the elastic, diffusive, and hydrodynamic fields. Approximate closed-form solutions are obtained to the second order of the MAFC iteration. The analysis indicates that preliminary radiation processing of the substrate may reduce the magnitude of the mismatch-induced stress by approximately 10–30 % for typical VPE conditions and simultaneously smooth the interface between the substrate and the epitaxial layer. The assumptions, the order of accuracy of the iteration, and the principal limitations of the framework are discussed in detail.

Keywords:

Heterostructure, Mismatch-induced stress, Radiation processing of substrate, Vapour-phase epitaxy, Method of averaging of function corrections, Mass and heat transfer

References

  1. [1] Pankratov, E. L. (2025). On increasing of density of field-effect heterotransistors in the framework of a level shifter influence of mismatch-induced stress and porosity of materials on technological process. Computational algorithms and numerical dimensions, 4(2), 196–223. https://doi.org/10.22105/cand.2025.507338.1189
  2. [2] Mahdavi, N., Sadeghi, R., Daliri, A., et al. (2026). Cardiac arrhythmia detection via PQRST analyzed data using an optimized hierarchical fused fuzzy deep reinforcement learning. BMC medical informatics and decision making, 26, 280. https://doi.org/10.1186/s12911-026-03564-4
  3. [3] Jain, S. C., Harker, A. H., & Cowley, R. A. (1997). Misfit strain and misfit dislocations in lattice mismatched epitaxial layers and other systems. Philosophical magazine a, 75(6), 1461–1515. https://doi.org/10.1080/01418619708223740
  4. [4] People, R., & Bean, J. C. (1985). Calculation of critical layer thickness versus lattice mismatch for GexSi1- x/Si strained-layer heterostructures. Applied physics letters, 47(3), 322–324. https://doi.org/10.1063/1.96206
  5. [5] Stepanenko, I. P. (1980). Basis of microelectronics. Moscow: Soviet Radio. (In Russian). https://library.ztu.edu.ua/doccard.php/11691
  6. [6] Zanoni, E., Rampazzo, F., De Santi, C., Gao, Z., Sharma, C., Modolo, N., ... & Meneghini, M. (2022). Failure physics and reliability of GaN‐based HEMTs for microwave and millimeter‐wave applications: A review of consolidated data and recent results. Physica status solidi (a), 219(24), 2100722. https://doi.org/10.1002/pssa.202100722
  7. [7] Ghosh, S., Hinz, A. M., Frentrup, M., Alam, S., Wallis, D. J., & Oliver, R. A. (2023). Design of step-graded AlGaN buffers for GaN-on-Si heterostructures grown by MOCVD. Semiconductor science and technology, 38(4), 44001. https://doi.org/10.1088/1361-6641/acbe1e
  8. [8] Islam, N., Mohamed, M. F. P., Khan, M. F. A. J., Falina, S., Kawarada, H., & Syamsul, M. (2022). Reliability, applications and challenges of GaN HEMT technology for modern power devices: A review. Crystals, 12(11), 1581. https://doi.org/10.3390/cryst12111581
  9. [9] O’loughlin, M. J., Nordby Jr, H. D., & Burk Jr, A. A. (1999). Multi-wafer VPE growth of highly uniform SiC epitaxial layers. MRS online proceedings library (OPL), 572, 161. https://doi.org/10.1557/PROC-572-161
  10. [10] Yang, J. K., Kang, M. G., & Park, H. H. (2004). Chemical and electrical characterization of Gd2O3/ GaAs interface improved by sulfur passivation. Journal of applied physics, 96(9), 4811–4816. https://doi.org/10.1063/1.1785851
  11. [11] Liu, D., Xiong, Y., Li, J., Xiao, W., & Wang, G. (2023). Design of large horizontal gallium nitride hydride vapor-phase epitaxy equipment and optimization of process parameters. Journal of crystal growth, 613, 127231. https://doi.org/10.1016/j.jcrysgro.2023.127231
  12. [12] Mihopoulos, T. G., Hummel, S. G., & Jensen, K. F. (1998). Simulation of flow and growth phenomena in a close-spaced reactor. Journal of crystal growth, 195(1–4), 725–732. https://doi.org/10.1016/S0022-0248(98)00648-4
  13. [13] Schulte, K. L., Simon, J., Roy, A., Reedy, R. C., Young, D. L., Kuech, T. F., & Ptak, A. J. (2016). Computational fluid dynamics-aided analysis of a hydride vapor phase epitaxy reactor. Journal of crystal growth, 434, 138–147. https://doi.org/10.1016/j.jcrysgro.2015.10.033
  14. [14] Matthews, J. W., & Blakeslee, A. E. (1974). Defects in epitaxial multilayers: I. Misfit dislocations. Journal of crystal growth, 27, 118–125. https://doi.org/10.1016/S0022-0248(74)80055-2
  15. [15] Alimoradi, M., Sadeghi, R., Daliri, A., & Zabihimayvan, M. (2025). Statistic deviation mode balancer (SDMB): A novel sampling algorithm for imbalanced data. Neurocomputing, 624, 129484. https://doi.org/10.1016/j.neucom.2024.129484
  16. [16] Zhang, Y. W., & Bower, A. F. (1999). Numerical simulations of island formation in a coherent strained epitaxial thin film system. Journal of the mechanics and physics of solids, 47(11), 2273–2297. https://doi.org/10.1016/S0022-5096(99)00026-5
  17. [17] Sokolov, Y. D. (1967). The method of averaging of functional corrections. Naukova Dumka. (In Russian). https://opac.sciencelib.ge/cgi-bin/koha/opac-detail.pl?biblionumber=67997
  18. [18] Sokolov, J. D. (1967). Metod osrednenija funkcionalʹnych popravok: Method of averaging functional corrections. Naukova Dumka. (In Russian). https://opac.sciencelib.ge/cgi-bin/koha/opac-detail.pl?biblionumber=67997
  19. [19] Asghari, A., Zeinalabedinmalekmian, M., Azgomi, H., Alimoradi, M., & Ghaziantafrishi, S. (2025). Farmer ants optimization algorithm: A novel metaheuristic for solving discrete optimization problems. Information, 16(3), 207. https://doi.org/10.3390/info16030207
  20. [20] Pankratov, E. L. (2011). Optimization of annealing to decrease quantity of radiation defects in a bipolar transistor. Applied nanoscience, 1(3), 123–129. https://doi.org/10.1007/s13204-011-0017-0
  21. [21] Pankratov, E. L., & Bulaeva, E. A. (2012). Decreasing of quantity of radiation defects in an implanted-junction rectifiers by using overlayers. International journal of Micro-Nano scale transport, 3(3), 119-130. https://scispace.com/pdf/decreasing-of-quantity-of-radiation-defects-in-an-implanted-5aax74xf9j.pdf
  22. [22] Fakheri, S., Alimoradi, M., & Yamaghani, M. R. (2024). Colour image multilevel thresholding segmentation using trees social relationship algorithm. International journal of computer information systems and industrial management applications, 18, 34. https://doi.org/10.21203/rs.3.rs-4479475/v1
  23. [23] Pankratov, E. L., & Bulaeva, E. A. (2015). Analytical approach for analysis of mass and heat transport. Journal of radio electronics, 9. http://jre.cplire.ru/koi/sep15/14/abstract_e.html
  24. [24] Carslaw, H. S., & Jaeger, J. C. (1986). Conduction of heat in solids. Clarendon Press. https://www.amazon.com/Conduction-Solids-Oxford-Science-Publications/dp/0198533683
  25. [25] Daliri, A., Roudposhti, K. K., Alimoradi, M., Sheikhha, M., Saraei, M. R. S., & Mohammadzadeh, J. (2025). Optimized categorical boosting for gastric cancer classification using heptagonal reinforcement learning and the water optimization algorithm. 2025 7th international conference on pattern recognition and image analysis (IPRIA) (pp. 1-6). IEEE. https://doi.org/10.1109/IPRIA68579.2025.11263556
  26. [26] Vinetskiy, V. L., & Kholodar’, G. A. (1979). Radiation physics of semiconductors. Naukova Dumka. (In Russian). https://ouci.dntb.gov.ua/works/lx8XpbEl/
  27. [27] Singh, N., Edalatpanah, S. A., & Alimoradi, M. (2025). IoT-driven intelligent traffic systems for congestion management. Supply chain and operations decision making, 2(3), 115–126. https://doi.org/10.48313/scodm.v2i3.37
  28. [28] Fahey, P. M. (1985). Point defects and dopant diffusion in silicon. Stanford University.
  29. [29] Landau, L. D., & Lifshitz, E. M. (1986). Theory of elasticity. Pergamon Press, Oxford. https://books.google.com/books/about/Theory_of_Elasticity.html?id=tpY-VkwCkAIC
  30. [30] Vorob’ev, A. A., Korablev, V. V, & Karpov, S. Y. (2003). The use of magnesium to dope gallium nitride obtained by molecular-beam epitaxy from activated nitrogen. Semiconductors, 37(7), 838–842. https://doi.org/10.1134/1.1592861
  31. [31] Lamtar Gholipoor, M., Alimoradi, M., & Fakheri, S. (2024). A novel metaheuristic approach inspired by trees social relationships and models for fermentation medium. Metaheuristic algorithms with applications, 1(1), 1–11. https://doi.org/10.22105/maa.v1i1.17
  32. [32] Vavilov, V. S., & Ukhin, N. (1977). Radiation effects in semiconductors and semiconductor devices. Springer New York, NY. https://www.amazon.com/Radiation-Effects-Semiconductors-Semiconductor-Devices/dp/1468490710
  33. [33] Korn, G. A., & Korn, T. M. (1968). Mathematical handbook for scientists and engineers: Definitions, theorems, and formulas for reference and review. McGraw-Hill. https://www.amazon.com/Mathematical-Scientists-Engineers-Definitions-Reference/dp/B0000CO5GE
  34. [34] Pankratov, E. L. (2022). On changing the properties of a multilayer structure by preliminary processing of a substrate. Computer methods in materials science, 22(2), 89–100. https://doi.org/10.7494/cmms.2022.2.0790
  35. [35] Pankratov, E. L. (2022). Influence of missmatch-induced stress and porosity of materials on technological process. International journal of research in industrial engineering, 11(2), 92–118. https://doi.org/10.22105/riej.2022.323547.1279
  36. [36] An, X., Xu, S., Tao, H., Su, H., Yang, H., Xu, K., ... & Hao, Y. (2025). High quality GaN epitaxy induced nucleation by Ar Ion implantation into sapphire substrate. Journal of inorganic materials, 40(1), 91-96. https://doi.org/10.15541/jim20240286
  37. [37] Luu, T. A., Trung, N. V. M., Van, T. N., Turek, M., Drozdziel, A., Pyszniak, K., ... & Hung, N. Q. (2026). Ion implantation-driven defect engineering in BiVO4 thin films for catalytic applications. Ceramics international, 52(9), 12572-12588. https://doi.org/10.1016/j.ceramint.2026.01.403
  38. [38] Chalifoux, B. D., Yao, Y., Woller, K. B., Heilmann, R. K., & Schattenburg, M. L. (2019). Compensating film stress in thin silicon substrates using ion implantation. Optics express, 27(8), 11182–11195. https://doi.org/10.1364/OE.27.011182
  39. [39] Pankratov, E. L., & Bulaeva, E. A. (2013). Doping of materials during manufacture p–n-junctions and bipolar transistors. Analytical approaches to model technological approaches and ways of optimization of distributions of dopants. Reviews in theoretical science, 1(1), 58-82. https://doi.org/10.1166/rits.2013.1004
  40. [40] Galib, M., Orhan, O. K., Liu, J., & Ponga, M. (2024). Residual stress development in lattice mismatched epitaxial thin films via atomic and molecular layer depositions. Journal of the mechanics and physics of solids, 193, 105897. https://doi.org/10.1016/j.jmps.2024.105897
  41. [41] Tsai, D. S., Liang, P. Y., Wu, C. Y., Wu, J. R., Chen, C. Y., Chuang, C. M., ... & Kuo, T. C. (2026). Raman mapping analysis of stress and dislocation defect correlation in GaN-on-Si epitaxial layers with and without superlattice structures. Semiconductor science and technology, 41(2), 02LT01. https://doi.org/10.1088/1361-6641/ae4138
  42. [42] Mai, T. T., Dai, J. J., Chiang, C. Y., & Chou, W. C. (2025). Layer-wise dislocation distribution and stress evolution in a GaN-based high electron mobility transistor studied by X ray nanodiffraction. ACS applied nano materials, 8(30), 15187-15195. https://doi.org/10.1021/acsanm.5c02355
  43. [43] Pankratov, E. L., & Bulaeva, E. A. (2016). On optimization of regimes of epitaxy from gas phase in a horizontal reactor. Materials science: An Indian journal, 14(6), 191-201. https://www.tsijournals.com/articles/on-optimization-of-regimes-of-epitaxy-fromgas-phase-in-a-horizontal-reactor.pdf
  44. [44] Wang, Z., Wang, S., Liu, L., Yu, J., Wang, G., Li, Q., ... & Zhang, L. (2024). Growth of freestanding GaN crystals on three-dimensional mesh porous substrates by HVPE. CrystEngComm, 26(38), 5415-5420. https://doi.org/10.1039/d4ce00726c

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Published

2024-09-16

Issue

Vol. 1 No. 3 (1): Metaheuristic Algorithms with Applications (MAA)

Section

Articles

How to Cite

Pankratov, E. L. . (2024). On Decreasing Mismatch-Induced Stresses in a Heterostructure by Preliminary Radiation Processing of the Substrate. Metaheuristic Algorithms With Applications, 1(3), 208-226. https://doi.org/10.48313/maa.v1i3.93

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