{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T23:57:48Z","timestamp":1770335868452,"version":"3.49.0"},"reference-count":31,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T00:00:00Z","timestamp":1705968000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"publisher","award":["FSMR-2023-0014"],"award-info":[{"award-number":["FSMR-2023-0014"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, the experimental methodology for the single-crystal circular plate deformation measurement and subsequent procedure for the quantitation of its mechanical properties are developed. The procedure is based on a new numerical-analytical solution of non-linear boundary-value problem for finite deformations of a circular anisotropic plate. Using the developed method, a study of the deformation of single-crystal circular plates formed on the basis of a silicon-on-insulator structure was carried out. The values of residual stresses are determined and it is shown that the presence of these stresses increases the flexural rigidity of the plate by several times.<\/jats:p>","DOI":"10.3390\/sym16020137","type":"journal-article","created":{"date-parts":[[2024,1,24]],"date-time":"2024-01-24T04:54:01Z","timestamp":1706072041000},"page":"137","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Deformations of Single-Crystal Silicon Circular Plate: Theory and Experiment"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7590-1389","authenticated-orcid":false,"given":"Sergey","family":"Lychev","sequence":"first","affiliation":[{"name":"Ishlinsky Institute for Problems in Mechanics RAS, 119526 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6892-7740","authenticated-orcid":false,"given":"Alexander","family":"Digilov","sequence":"additional","affiliation":[{"name":"Ishlinsky Institute for Problems in Mechanics RAS, 119526 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6642-1359","authenticated-orcid":false,"given":"Gleb","family":"Demin","sequence":"additional","affiliation":[{"name":"MEMSEC R&D Center, National Research University of Electronic Technology (MIET),124498 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2819-2599","authenticated-orcid":false,"given":"Evgeney","family":"Gusev","sequence":"additional","affiliation":[{"name":"MEMSEC R&D Center, National Research University of Electronic Technology (MIET),124498 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-8241-0553","authenticated-orcid":false,"given":"Ivan","family":"Kushnarev","sequence":"additional","affiliation":[{"name":"MEMSEC R&D Center, National Research University of Electronic Technology (MIET),124498 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5205-0304","authenticated-orcid":false,"given":"Nikolay","family":"Djuzhev","sequence":"additional","affiliation":[{"name":"MEMSEC R&D Center, National Research University of Electronic Technology (MIET),124498 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vladimir","family":"Bespalov","sequence":"additional","affiliation":[{"name":"MEMSEC R&D Center, National Research University of Electronic Technology (MIET),124498 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"20246","DOI":"10.1109\/JSEN.2022.3195340","article-title":"Design and implementation of a novel membrane-island structured MEMS accelerometer with an ultra-high range","volume":"22","author":"Zhang","year":"2022","journal-title":"IEEE Sensors J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"110065","DOI":"10.1016\/j.vacuum.2021.110065","article-title":"Design and fabrication of an absolute pressure MEMS capacitance vacuum sensor based on silicon bonding technology","volume":"186","author":"Xu","year":"2021","journal-title":"Vacuum"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"112832","DOI":"10.1016\/j.sna.2021.112832","article-title":"Measurement System for Wide-Range Flow Evaluation and Thermal Characterization of MEMS-Based Thermoresistive Flow-Rate Sensors","volume":"330","author":"Djuzhev","year":"2021","journal-title":"Sens. Actuators A Phys."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Yu, L., Guo, Y., Zhu, H., Luo, M., Han, P., and Ji, X. (2020). Low-cost microbolometer type infrared detectors. Micromachines, 11.","DOI":"10.3390\/mi11090800"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"228","DOI":"10.31114\/2078-7707-2022-4-228-233","article-title":"TCAD simulation of the etching of the sacrificial layer in the sensitive element of the IR microbolometer array based on the SOI structure","volume":"4","author":"Evsikov","year":"2022","journal-title":"MES"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"081301","DOI":"10.1088\/1674-4926\/43\/8\/081301","article-title":"Technologies and applications of silicon-based Micro-Optical Electromechanical Systems: A brief review","volume":"43","author":"Chen","year":"2022","journal-title":"J. Semicond."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"105210","DOI":"10.1016\/j.mejo.2021.105210","article-title":"Si-based MEMS resonant sensor: A review from microfabrication perspective","volume":"118","author":"Verma","year":"2021","journal-title":"Microelectron. J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"820","DOI":"10.1109\/JMEMS.2022.3190829","article-title":"A SOI out-of-plane electrostatic MEMS actuator based on in-plane motion","volume":"31","author":"Nabavi","year":"2022","journal-title":"J. Microelectromechanical Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.sna.2019.05.008","article-title":"Stress compensated MEMS magnetic actuator based on magnetostrictive Fe65Co35 thin films","volume":"294","author":"Singh","year":"2019","journal-title":"Sens. Actuators A Phys."},{"key":"ref_10","unstructured":"Glagolev, P.Y., Ovodov, A.I., Demin, G.D., Djuzhev, N.A., and Nezhentsev, A.V. (February, January 29). Peculiarities of the Influence of Nanostructuring of [SiO2\/Si3N4]n Multilayer Membranes on Its Thermal and Mechanical Properties. Proceedings of the 2018 IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering (EIConRus), Moscow and St. Petersburg, Russia."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5233","DOI":"10.1364\/AO.58.005233","article-title":"Mid-infrared optical characterization of thin SiNx membranes","volume":"58","author":"Stocchi","year":"2019","journal-title":"Appl. Opt. AO"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3049","DOI":"10.1515\/nanoph-2020-0045","article-title":"Metamaterials \u2013 from fundamentals and MEMS tuning mechanisms to applications","volume":"9","author":"Chang","year":"2020","journal-title":"Nanophotonics"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Wi, S.J., Jang, Y.J., Kim, H., Cho, K., and Ahn, J. (2022). Investigation of the resistivity and emissivity of a pellicle membrane for EUV lithography. Membranes, 12.","DOI":"10.3390\/membranes12040367"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Uzoma, P.C., Shabbir, S., Hu, H., Okonkwo, P.C., and Penkov, O.V. (2021). Multilayer reflective coatings for BEUV lithography: A review. Nanomaterials, 11.","DOI":"10.3390\/nano11112782"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Fan, L., Zhao, B., Chen, B., Ma, Y., Bi, J., and Zhao, F. (2023). Radiation immune-planar two-terminal nanoscale air channel devices toward space applications. ACS Appl. Nano Mater., 6.","DOI":"10.1021\/acsanm.3c04292"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"012106","DOI":"10.1063\/1.3282783","article-title":"Influence of heavy doping on Seebeck coefficient in Silicon-on-Insulator","volume":"96","author":"Ikeda","year":"2010","journal-title":"Appl. Phys. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2033","DOI":"10.21883\/TP.2022.13.52218.121-21","article-title":"Peculiarities of Deformation of Round Thin-Film Membranes and Experimental Determination of Their Effective Characteristics","volume":"92","author":"Dedkova","year":"2022","journal-title":"Tech. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Lychev, S.A., Koifman, K.G., and Djuzhev, N.A. (2021). Incompatible Deformations in Additively Fabricated Solids: Discrete and Continuous Approaches. Symmetry, 13.","DOI":"10.3390\/sym13122331"},{"key":"ref_19","first-page":"77","article-title":"Bending of a circular disk: From cylinder to ultrathin membrane","volume":"29","author":"Lychev","year":"2023","journal-title":"Vestn. Samara Univ. Nat. Sci. Ser."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"678","DOI":"10.1049\/mnl.2015.0334","article-title":"Effect of crystallographic orientation on tensile fractures of (100) and (110) silicon microstructures fabricated from silicon-on-insulator wafers","volume":"10","author":"Uesugi","year":"2015","journal-title":"Micro Nano Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"045319","DOI":"10.1103\/PhysRevB.82.045319","article-title":"Anisotropy and boundary scattering in the lattice thermal conductivity of silicon nanomembranes","volume":"82","author":"Aksamija","year":"2010","journal-title":"Phys. Rev. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"051001","DOI":"10.1115\/1.4064207","article-title":"A theoretical analysis for arbitrary residual stress of thin film\/substrate system with nonnegligible film thickness","volume":"91","author":"Sun","year":"2024","journal-title":"J. Appl. Mech."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"104004","DOI":"10.1016\/j.ijengsci.2023.104004","article-title":"A phase field fracture model for ultra-thin micro-\/nano-films with surface effects","volume":"195","author":"Li","year":"2024","journal-title":"Int. J. Eng. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"043401","DOI":"10.1116\/6.0002590","article-title":"Determination of stress in thin films using micro-machined buckled membranes","volume":"41","author":"Malhaire","year":"2023","journal-title":"J. Vac. Sci. Technol. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"013003","DOI":"10.1088\/1361-6439\/ac3cd6","article-title":"Mechanical reliability of silicon microstructures","volume":"32","author":"Tsuchiya","year":"2022","journal-title":"J. Micromech. Microeng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"035026","DOI":"10.1088\/1361-6641\/acb2e9","article-title":"Strain relaxation of semiconductor membranes: Insights from finite element modeling","volume":"38","author":"Mooney","year":"2023","journal-title":"Semicond. Sci. Technol."},{"key":"ref_27","unstructured":"(2010). Compressed Air\u2013Part 1: Contaminants and Purity Classes (Standard No. ISO 8573-1:2010)."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1088\/0370-1298\/65\/5\/307","article-title":"The elastic behaviour of a crystalline aggregate","volume":"65","author":"Hill","year":"1952","journal-title":"Proc. Phys. Soc. Sect. A"},{"key":"ref_29","unstructured":"Morse, P.M., and Feshbach, H. (1953). Methods of Theoretical Physics Volume 1\u20132, McGraw-Hill."},{"key":"ref_30","unstructured":"Whittaker, E.T., and Watson, G.N. (1962). A Course of Modern Analysis, Cambridge University Press."},{"key":"ref_31","unstructured":"Watson, G.N. (1922). A Treatise on the Theory of Bessel Functions, The University Press."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/2\/137\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:48:04Z","timestamp":1760104084000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/2\/137"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,23]]},"references-count":31,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,2]]}},"alternative-id":["sym16020137"],"URL":"https:\/\/doi.org\/10.3390\/sym16020137","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,1,23]]}}}